User's manual for the software SILDIS (*)

User's manual for the software SILDIS (*)

I s o l a t i o n

Technologie Services

ITS

acoustique

User’s manual for the software SILDIS (*)

* Sound Impact Limitation: Design for Industrialized Solutions

Revised by Philippe Reynaud on April 2015 the 1st ([email protected])

Report

PhR15-008A

Abstract:

The prediction of performances of products and construction systems for noise control engineering often requires an approach whose nature is computationally intensive, making its application difficult for most acoustics practitioners. The software SILDIS has been developed in order to make possible such a prediction without any computational effort from users, by the means of a single

PC-tool appropriate for a wide range of industrial engineering purposes.

Regarding the multi-disciplinary scientific and technical background, suitable approaches of all times, able to be included in the general layout of the program, have been selected and encapsulated in a easy-to-use Excel based software using dropdown menus and providing results in tabular and graphical form (French or English language) with comprehensive input/output data on a unique printable simulation report.

Almost all acoustics calculations are performed at single frequencies and displayed per 1/3 and/or 1/1 octave band: global

values with respect to a chosen reference spectrum are computed whenever it makes sense.

MODULE 1

prediction of acoustic and aerodynamic performance of silencers:

-

either dissipative silencers (for those equipments the considered cross section can be either rectangular or round, with or

without a central pod, with or without an intermediate annular splitter) for a lining including up to 4 porous media, up to

4 series cloths, up to 4 series perforated protections selected among a library including for each kind of layer more than

20 referenced materials.

-

or resonant silencers with so called Pine Tree splitters (for those equipments the considered cross section can be

rectangular) for a lining including up to 4 porous media, up to 4 series cloths, up to 4 series perforated protections

selected among a library including for each kind of layer more than 20 referenced materials

For a rectangular silencer the results of the calculations are comparable with the standardized measurement: see NF EN ISO

7235 Acoustics - Laboratory measurement procedures for ducted silencers and air terminal units- Insertion loss, flow noise and total pressure loss.

MODULE 1A

prediction of acoustic and aerodynamic performance of silencers with discontinued splitters:

-

dissipative silencers (considered cross section being rectangular) for a lining including 1 porous medium, 1 series cloth, 1

series perforated protection (material properties registered in database)

For a rectangular silencer the results of the calculations are comparable with the standardized measurement: see NF EN ISO

7235 Acoustics - Laboratory measurement procedures for ducted silencers and air terminal units- Insertion loss, flow noise and total pressure loss.

MODULE 2

prediction of acoustic performance of plane partitions for an acoustic structure including up to 2 porous media,

up to 2 series cloths, up to 2 series perforated protections, up to 2 sets of identical series thin plates with up to 1 complementary rear set of identical series thin plates selected among a library including for each kind of layer more than 20

referenced materials (with an atmospheric back or with an impervious rigid back).

The results of the calculations are comparable with the standardized measurement: (in case of an atmospheric back) see NF EN ISO

10140-2 Acoustics – Laboratory measurement of sound insulation of building elements. Measurement of airborne sound insulation and (in case of rigid impervious back) see NF EN ISO 354 Acoustics – Measurement of sound absorption in a reverberation room and also ISO 10534-1 Acoustics – Determination of sound absorption coefficient and impedance in impedance tubes – Part 1: Method using standing wave ratio.

MODULE 3

prediction of acoustic performance of duct walls: either with a rectangular cross section, or with a circular cross

section (including folded spiral seam ducts).

The obtained results are not comparable with standardized measurement due to the lack of documents formalizing corresponding measurement procedures.

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MODULE 4

prediction of acoustic performance of straight ducts either with a rectangular cross section, or with a circular

cross section (including folded spiral seam ducts).

The obtained results are not comparable with standardized measurement due to the lack of documents formalizing corresponding measurement procedures.

MODULE 5

prediction of break-out noise: either of straight ducts (with a rectangular cross section, or with a circular cross

section - including folded spiral seam ducts) or of silencers.

The obtained results are not comparable with standardized measurement due to the lack of documents formalizing corresponding measurement procedures.

MODULE 6

prediction of acoustic performance of bends: with a rectangular cross section, or with a circular cross section , or

with mixed cross sections).

The obtained results are not comparable with standardized measurement due to the lack of documents formalizing corresponding measurement procedures.

MODULE 7

prediction of nozzle reflection: with a rectangular cross section or with a circular cross section.

The obtained results are not comparable with standardized measurement due to the lack of documents formalizing corresponding measurement procedures.

MODULE 8

prediction of the sound impact of duct systems including components such as silencers (dissipative or resonant),

straight ducts sections, bends with a rectangular cross section, or with a circular cross section, or with mixed cross sections

(for some components)

MODULE 9

modelling of sound decay in enclosed spaces

The obtained results are comparable with standardized measurement: cf. NF EN ISO 3382-2 Acoustics - Measurement of room acoustics parameters- Part 2: reverberation time in ordinary rooms.

In this user’s manual, a presentation of this calculation program is made, for the people concerned (at ITS or elsewhere) by the design of soundproofing equipment related to applications in the field of industry, environment as well as building.

To be continued (work in progress).

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Contents

page

General considerations

0.1: Introduction

.................................................................................................................................. 17

What does the present user’s manual aims at ............................................................................................. 17

Comments .................................................................................................................................................... 17

Operating conditions / security level / safety .............................................................................................. 17

General layout of the program .................................................................................................................... 17

Worksheets .................................................................................................................................................. 20

Input data..................................................................................................................................................... 20

0.2: Scientific and technical background

.................................................................................. 20

System of units ............................................................................................................................................. 20

Reference conditions .................................................................................................................................... 20

Fluid ............................................................................................................................................................. 20

Electro-acoustic analogies ........................................................................................................................... 20

Remark regarding construction systems ..................................................................................................... 23

Appendix to general considerations: list of symbols and acronyms

.............................. 24

Section 1: computation of silencers (MODULE 1 of the software)

1.1: Introduction

.................................................................................................................................. 28

Terms and definitions................................................................................................................................... 28

Mountings and geometry.............................................................................................................................. 28

1.2: Scientific and technical background

.................................................................................. 32

1.2.1 Thermodynamics and fluid dynamics ................................................................................................. 32

Steps of the computation.............................................................................................................................. 32

1.2.2 Acoustics............................................................................................................................................... 34

Bloc diagram for rectangular dissipative silencers and comments for other dissipative silencers and for

resonators ..................................................................................................................................................... 34

Steps of the computation............................................................................................................................... 35

Step [A]

conditions of the applications

........................................................................................................... 35

Step [B]

porous media used in the acoustic structure

......................................................................................... 35

Step [C]

series cloths used in the acoustic structure

........................................................................................... 38

Step [D]

series perforated protections used in the acoustic structure

...................................................................... 39

Step [E]

surface impedance of the multilayered acoustic structure (with an appropriate back)……….....………….…...….

41

Step [F]

propagation loss with flow of the silencer

............................................................................................ 43

Step [G]

by-pass correction

........................................................................................................................ 46

Step [H]

reflection loss in the silencer

........................................................................................................... 47

Step [I]

self noise of the silencer (noise produced by the airflow)

......................................................................... 47

Step [J]

insertion loss without taking into account the self noise

.......................................................................... 49

Step [K]

insertion loss of the silencer including the self noise

............................................................................. 49

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Step [L]

complementary step for resonant silencers with pine tree splitters

............................................................ 49

1.2.3 Aerodynamics...................................................................................................................................... 50

Steps of the computation.............................................................................................................................. 50

1.3: How to use SILDIS

.................................................................................................................... 51

Operating conditions / security level / safety .............................................................................................. 51

Worksheets................................................................................................................................................... 51

Input data, alerts and results: the key points.............................................................................................. 52

Worksheet [in COALA]

.........................

............................................................................................... 53

Worksheet [in COSIL]

.............................

............................................................................................ 55

Worksheet [in-out CODIS1], [in-out CODIS2], [in-out CORESPTR], [in-out CORESPTL]

............

.. 57

1.4: Examples of computation with SILDIS

............................................................................ 58

Example 1.4.1 dissipative silencer with a rectangular cross section ........................................................... 58

Envisaged application ............................................................................................................................. 58

Input data................................................................................................................................................. 58

Screenshots of the worksheets (for the example of computation)........................................................... 61

Example 1.4.2a dissipative silencer with a square cross section ................................................................. 63

Envisaged application ............................................................................................................................. 63

Input data................................................................................................................................................. 63

Screenshots of the worksheets (for the example of computation)........................................................... 64

Example 1.4.2b dissipative silencer with a circular cross section ............................................................... 66

Envisaged application ............................................................................................................................. 66

Input data................................................................................................................................................. 66

Screenshots of the worksheets (for the example of computation)........................................................... 67

1.5: Illustrations of effects taken into account with SILDIS

............................................. 69

Introduction.................................................................................................................................................. 69

Effects of the properties of a porous medium in a non-laminated lining.................................................... 69

Effects of the properties of porous media in a laminated lining.................................................................. 70

Effects of the conditions of propagation of sound inside the lining............................................................. 71

Effects of the limitation of the propagation loss........................................................................................... 72

Effects of the reflection loss.......................................................................................................................... 73

Effects of temperature.................................................................................................................................. 74

Effects of pressure........................................................................................................................................ 75

Effects of a series cloth................................................................................................................................. 76

Effects of a series perforated protection...................................................................................................... 77

Effects of the velocity of air flow (other than regenerated noise)................................................................ 78

Effects of the velocity of air flow (regenerated noise).................................................................................. 79

Effects of the unsilenced sound power spectrum (and of other uncertainties)............................................ 80

Appendix to Section 1: list of symbols

........................................................................................ 81

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Section 1A: computation of silencers with discontinued splitters (MODULE 1A of the software)

1A.1: Introduction

............................................................................................................................... 85

Terms and definitions................................................................................................................................... 85

Mountings and geometry.............................................................................................................................. 85

1A.2: Scientific and technical background

............................................................................... 86

1A.2.1 Thermodynamics and fluid dynamics .............................................................................................. 86

Steps of the computation.............................................................................................................................. 86

1A.2.2 Acoustics............................................................................................................................................ 89

Bloc diagram for rectangular dissipative silencers ..................................................................................... 89

Steps of the computation............................................................................................................................... 89

Steps [A-1A] to [F-1A]

conditions of the applications & propagation loss with flow of the silencer

........................... 89

Step [G-1A]

by-pass correction

................................................................................................................... 90

Step [H-1A]

reflection loss in the silencer

...................................................................................................... 91

Step [I-1A]

self noise of the silencer (noise produced by the airflow)

..................................................................... 91

Step [J-1A]

insertion loss without taking into account the self noise

......................................................................92

Step [K-1A]

insertion loss of the silencer including the self noise

..........................................................................92

1A.2.3 Aerodynamics.................................................................................................................................... 92

Steps of the computation.............................................................................................................................. 92

1A.3: How to use SILDIS

................................................................................................................ 94

Operating conditions / security level / safety .............................................................................................. 94

Worksheets................................................................................................................................................... 94

Input data, alerts and results: the key points.............................................................................................. 94

Worksheet [in COALA-1A]

......................

............................................................................................... 95

Worksheet [in COSIL-1A]

..........................

............................................................................................ 97

Worksheet [in-out CODIS-1A]

................................................................................................

.. 98

1A.4: Examples of computation with SILDIS

......................................................................... 99

Example 1A.4.1 dissipative silencer with a rectangular cross section ........................................................ 99

Envisaged application ............................................................................................................................. 99

Input data................................................................................................................................................. 99

Screenshots of the worksheets (for the example of computation).......................................................... 100

Appendix to Section 1A: list of symbols

.................................................................................. 104

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Section 2: computation of plane partitions (MODULE 2 of the software)

2.1: Introduction

................................................................................................................................ 108

Terms and definitions................................................................................................................................. 108

Geometry.................................................................................................................................................... 108

2.2: Scientific and technical background

................................................................................ 109

2.2.1 Thermodynamics and fluid dynamics ............................................................................................... 109

Steps of the computation............................................................................................................................ 109

2.2.2 Acoustics............................................................................................................................................. 109

Bloc diagram............................................................................................................................................... 109

Steps of the computation............................................................................................................................. 110

Step [A]

conditions of the applications

.................................................................................................... 110

Step [B]

porous media used in the acoustic structure

.................................................................................. 110

Step [C]

series cloths used in the acoustic structure

................................................................................... 110

Step [D]

series perforated protections used in the acoustic structure

.............................................................. 110

Step [E]

surface impedance of the multilayered acoustic structure (with an appropriate back) ……................….…...

110

Step [M]

series thin plates in the acoustic structure

................................................................................... 113

Step [M’]

series perforated thin plate

.................................................................................................... 114

Step [M’’]

series thin plates with an extensional damping in the acoustic structure

........................................... 115

Step [M’’’]

series thin plates with a constrained damping in the acoustic structure

........................................... 115

Step [M’’’’]

series orthotropic plates in the acoustic structure

.................................................................... 116

Step [N]

absorption coefficient at normal incidence

.................................................................................. 118

Step [O]

absorption coefficient for statistic incidence

................................................................................ 119

Step [O’]

Sabine’s factor

................................................................................................................... 120

Step [P]

sound reduction index for coupling 0 % without sound leaks

........................................................... 121

Step [P’]

sound reduction index (1 leaf) without sound leaks

.......................................................................122

Step [Q]

sound reduction index for coupling 100 % without sound leaks

.........................................................126

Step [R]

sound reduction index with connections without sound leaks

........................................................... 126

Step [S]

sound reduction index of sound leaks

.......................................................................................... 127

Step [S’]

sound reduction index of sound leaks (1 leaf)

............................................................................. 128

Step [T]

sound reduction index for coupling 0 % with sound leaks

............................................................... 128

Step [T’]

sound reduction index with sound leaks for 1 leaf

........................................................................ 128

Step [U]

insertion loss for coupling 0 % with sound leaks

........................................................................... 128

Step [V]

sound reduction index for coupling 100 % with sound leaks

............................................................ 129

Step [W]

sound reduction index with connections and with sound leaks (2 leaves)

..........................................129

2.3: How to use SILDIS

.................................................................................................................. 129

Operating conditions / security level / safety ............................................................................................ 129

Worksheets................................................................................................................................................. 129

Input data, alerts and results: the key points............................................................................................ 130

Worksheet [in-out COPERF]................................................................................................................ 131

Worksheet [in-out CODAP].................................................................................................................. 131

Worksheet [in-out COORT].................................................................................................................. 133

Worksheet [in COALA]......................................................................................................................... 134

Worksheet [in-out COPPA]................................................................................................................... 134

Worksheet [in-out COPPA0]................................................................................................................. 136

Worksheet [in-out COPPA1]................................................................................................................ 136

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Worksheet [in-out COPPA2]................................................................................................................ 136

2.4: Examples of computation with SILDIS

.......................................................................... 137

Example 2.4.0 porous medium with series cloth ....................................................................................... 137

Envisaged application ............................................................................................................................. 137

Input data................................................................................................................................................. 137

Screenshots of the worksheets (for the example of computation)........................................................... 138

Example 2.4.1a single isotropic plate (general method) ............................................................................139

Envisaged application ............................................................................................................................ 139

Input data................................................................................................................................................ 139

Screenshots of the worksheets (for the example of computation).......................................................... 141

Example 2.4.1a single isotropic plate (alternative method) ...................................................................... 143

Envisaged application ........................................................................................................................... 143

Input data............................................................................................................................................... 143

Screenshots of the worksheets (for the example of computation).......................................................... 145

Example 2.4.2b double-leaf partition ....................................................................................................... 146

Envisaged application .......................................................................................................................... 146

Input data.............................................................................................................................................. 146

Screenshots of the worksheets (for the example of computation)........................................................ 149

Example 2.4.3 perforated plate ……………………................................................................................... 150

Envisaged application ........................................................................................................................... 150

Input data............................................................................................................................................... 150

Screenshots of the worksheets (for the example of computation)......................................................... 151

Example 2.4.4 plate with an extensional damping .................................................................................... 151

Envisaged application ........................................................................................................................... 151

Input data............................................................................................................................................... 151

Screenshots of the worksheets (for the example of computation)......................................................... 152

Example 2.4.5 plate with a constrained damping ..................................................................................... 152

Envisaged application .......................................................................................................................... 152

Input data.............................................................................................................................................. 152

Screenshots of the worksheets (for the example of computation)......................................................... 153

Example 2.4.6 orthotropic plate ................................................................................................................ 153

Envisaged application .......................................................................................................................... 153

Input data.............................................................................................................................................. 153

Screenshots of the worksheets (for the example of computation)......................................................... 154

2.5: Illustrations of effects taken into account with SILDIS

........................................... 155

Introduction................................................................................................................................................ 155

Effects of the properties of a porous medium in a non-laminated lining.................................................. 155

Effects of the properties of porous media in a laminated lining................................................................ 156

Effects of temperature................................................................................................................................ 157

Effects of pressure...................................................................................................................................... 158

Effects of a series cloth............................................................................................................................... 159

Effects of a series perforated protection.................................................................................................... 160

Effects of membrane resonator ................................................................................................................ 161

Effects of back............................................................................................................................................ 162

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Appendix to Section 2: list of symbols

...................................................................................... 163

Section 3: computation of duct walls (MODULE 3 of the software)

3.1: Introduction

................................................................................................................................ 165

Terms and definitions................................................................................................................................. 165

Mountings and geometry............................................................................................................................ 165

3.2: Scientific and technical background

................................................................................ 165

3.2.1 Thermodynamics and fluid dynamics ............................................................................................... 165

Steps of the computation........................................................................................................................... 165

3.2.2 Acoustics............................................................................................................................................. 166

3.2.2.1 Acoustics: rectangular ducts .......................................................................................................... 166

3.2.2.1.a Acoustics: rectangular ducts, break out noise............................................................................. 166

Bloc diagram for rectangular duct walls break out noise...................................................................... 166

Steps of the computation for rectangular duct walls break out noise.................................................... 166

Steps [A] to [V] .............................................................................................................................. 166

Preliminary remarks common to step [X] and step [X’] .............................................................. 166

Step [X]

sound reduction index of a single-leaf (rectangular) duct made of 1 plate alone

..................................... 166

Step [X’]

sound reduction index of a single-leaf (rectangular) duct made of 1 steel plate alone

............................. 167

Step [Z] insertion loss of set 1 when compared to set 0.................................................................... 168

Step [AA] transmission loss with sound leaks.................................................................................. 168

Step [AB] break out sound power level............................................................................................ 168

3.2.2.1.b Acoustics: rectangular ducts, break in noise .............................................................................. 169

Bloc diagram for rectangular duct walls break in noise..................................................................... 169

Steps of the computation for rectangular duct walls break in noise.................................................. 169

Steps [A] to [V] .................................................................................................................................... 169

Preliminary remarks common to step [AC] and step [AC’] ............................................................... 170

Step [AC] sound reduction index of a single leaf (rectangular duct)....................................................... 170

Step [AC’] sound reduction index of a single leaf (rectangular duct)...................................................... 170

Step [AE] insertion loss of set 1 when compared to set 0....................................................................... 170

Step [AF] transmission loss with sound leaks........................................................................................ 171

Step [AG] break in sound power level................................................................................................... 171

3.2.2.2 Acoustics: circular ducts ................................................................................................................ 171

3.2.2.2.a Acoustics: circular ducts, break out noise.................................................................................... 171

Bloc diagram for circular duct walls break out noise................................................................... 171

Steps of the computation for circular duct walls break out noise................................................. 172

Steps [A] to [V] .............................................................................................................................. 172

Preliminary remarks common to step [AH] and step [AH’] ........................................................ 172

Step [AH]

sound reduction index of a single-leaf (circularr) duct ………………………

...................................... 172

Step [AH’]

sound reduction index of a single-leaf (circular) duct ………………………………..

.......................... 173

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Step [AJ] insertion loss of set 1 when compared to set 0.................................................................. 173

Step [AK] transmission loss with sound leaks.................................................................................. 174

Step [AL] break out sound power level............................................................................................ 174

3.2.2.2.b Acoustics: circular ducts, break in noise .................................................................................... 175

Bloc diagram for circular duct walls break in noise........................................................................... 175

Steps of the computation for circular duct walls break in noise........................................................ 175

Steps [A] to [V] ................................................................................................................................... 175

Preliminary remarks common to step [AP] and step [AQ] ............................................................... 175

Step [AP] sound reduction index of a single leaf circular duct.............................................................. 175

Step [AQ] sound reduction index of a single leaf circular duct.............................................................. 176

3.3: How to use SILDIS

.................................................................................................................. 176

Operating conditions / security level / safety ............................................................................................ 176

Worksheets................................................................................................................................................. 176

Input data, alerts and results: the key points............................................................................................. 177

Worksheet [in-out CORED IN->OUT].................................................................................................. 178

Worksheet [in-out CORED OUT->IN].................................................................................................. 179

Worksheet [in-out COCID IN->OUT].................................................................................................. 180

Worksheet [in-out COCID OUT->IN].................................................................................................. 181

3.4: Examples of computation with SILDIS

.......................................................................... 182

Example 3.4.1 rectangular duct wall ......................................................................................................... 182

Envisaged application .............................................................................................................................. 182

Input data.................................................................................................................................................. 182

Screenshots of the worksheets (for the example of computation)............................................................ 183

Example 3.4.2 circular duct wall ............................................................................................................... 185

Envisaged application .............................................................................................................................. 185

Input data.................................................................................................................................................. 185

Screenshots of the worksheets (for the example of computation)............................................................ 186

Example 3.4.3 circular duct wall (spiral-seam pipe) ................................................................................ 188

Envisaged application .............................................................................................................................. 188

Input data.................................................................................................................................................. 188

Screenshots of the worksheets (for the example of computation)............................................................ 189

Appendix to Section 3: list of symbols

...................................................................................... 191

Section 4: computation of duct straight runs (MODULE 4 of the software)

4.1: Introduction

................................................................................................................................ 194

Terms and definitions ................................................................................................................................ 194

Mountings and geometry............................................................................................................................ 194

4.2: Scientific and technical background

................................................................................ 194

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4.2.1Thermodynamics and fluid dynamics .............................................................................................. 194

Steps of the computation .................................................................................................................... 194

4.2.2 Acoustics .................................................................................................................................... 194

Bloc diagram …………………………………..……….................................................................... 194

Steps of the computation ………………………..………………….................................................. 195

Step [AR] longitudinal attenuation per unit length................................................................. 195

Step [AS] insertion loss without flow noise............................................................................. 196

Step [AT] flow noise............................................................................................................... 196

Step [AU] insertion loss with flow noise.................................................................................. 196

4.3: How to use SILDIS

.................................................................................................................. 197

Operating conditions / security level / safety ............................................................................................ 197

Worksheets ................................................................................................................................................ 197

Input data, alerts and results: the key points............................................................................................. 197

4.4: Examples of computation with SILDIS

.......................................................................... 199

Example 4.4.1 rectangular straight duct (air conditioning system) ......................................................... 199

Envisaged application ........................................................................................................................... 199

Input data .............................................................................................................................................. 199

Screenshots of the worksheets (for the example of computation) .......................................................... 200

Example 4.4.2 circular straight duct (air conditioning system) ............................................................... 201

Envisaged application ........................................................................................................................... 201

Input data .............................................................................................................................................. 201

Screenshots of the worksheets (for the example of computation) .......................................................... 203

Example 4.4.3 circular straight duct (exhaust stack) ............................................................................... 204

Envisaged application ........................................................................................................................... 204

Input data .............................................................................................................................................. 204

Screenshots of the worksheets (for the example of computation) .......................................................... 205

Appendix to Section 4: list of symbols

..................................................................................... 206

Section 5: computation of break-out noise (MODULE 5 of the

software)

5.1: Introduction

................................................................................................................................ 209

Terms and definitions................................................................................................................................. 209

Mountings and geometry............................................................................................................................ 209

5.2: Scientific and technical background

................................................................................ 209

5.2.1 Thermodynamics and fluid dynamics ............................................................................................... 209

Steps of the computation........................................................................................................................... 209

5.2.2 Acoustics............................................................................................................................................. 209

Bloc diagram …………………………………..……….................................................................... 209

Steps of the computation ………………………..………………….................................................. 211

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Step [AV] breakout noise ............................ ....................................................................... 211

5.3: How to use SILDIS

.................................................................................................................. 211

Operating conditions / security level / safety ............................................................................................ 211

Worksheets................................................................................................................................................. 212

Input data, alerts and results: the key points............................................................................................. 212

5.4: Examples of computation with SILDIS

.......................................................................... 213

Example 5.4.1 circular duct wall (spiral-seam pipe) ................................................................................ 213

Envisaged application .......................................................................................................................... 213

Input data.............................................................................................................................................. 213

Screenshots of the worksheets (for the example of computation)........................................................ 215

Appendix to Section 5: list of symbols

...................................................................................... 218

Section 6: computation of bends (MODULE 6 of the software)

6.1: Introduction

................................................................................................................................ 221

Terms and definitions................................................................................................................................. 221

Mountings and geometry............................................................................................................................ 221

6.2: Scientific and technical background

................................................................................ 221

6.2.1 Thermodynamics and fluid dynamics ............................................................................................... 221

Steps of the computation........................................................................................................................... 221

6.2.2 Acoustics............................................................................................................................................. 221

Bloc diagram …………………………………..……….................................................................... 221

Steps of the computation ………………………..………………….................................................. 222

Step [AW] insertion loss without flow noise.............................................................................. 222

Step [AX] flow noise................................................................................................................. 222

Step [AY] insertion loss with flow noise.................................................................................... 222

6.3: How to use SILDIS

.................................................................................................................. 223

Operating conditions / security level / safety ............................................................................................ 223

Worksheets................................................................................................................................................. 223

Input data, alerts and results: the key points............................................................................................. 223

6.4: Examples of computation with SILDIS

.......................................................................... 225

Example 6.4.1 circular bend ...................................................................................................................... 225

Envisaged application ......................................................................................................................... 225

Input data............................................................................................................................................. 225

Screenshots of the worksheets (for the example of computation)....................................................... 225

Appendix to Section 6: list of symbols

...................................................................................... 228

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Section 7: computation of nozzle reflection (MODULE 7 of

the software)

7.1: Introduction

................................................................................................................................ 230

Terms and definitions................................................................................................................................. 230

Mountings and geometry............................................................................................................................ 230

7.2: Scientific and technical background

................................................................................ 230

7.2.1 Thermodynamics and fluid dynamics ............................................................................................... 230

Steps of the computation........................................................................................................................... 230

7.2.2 Acoustics............................................................................................................................................. 230

Bloc diagram …………………………………..……….................................................................... 230

Steps of the computation ………………………..………………….................................................. 230

Step [AZ] insertion loss without flow noise.............................................................................. 230

Step [AAA] flow noise.............................................................................................................. 231

Step [AAB] insertion loss with flow noise................................................................................. 231

7.3: How to use SILDIS

.................................................................................................................. 231

Operating conditions / security level / safety ............................................................................................ 231

Worksheets................................................................................................................................................. 231

Input data, alerts and results: the key points............................................................................................. 232

7.4: Examples of computation with SILDIS

.......................................................................... 233

Example 7.4.1 circular mouth ................................................................................................................... 233

Envisaged application ......................................................................................................................... 233

Input data............................................................................................................................................. 233

Screenshots of the worksheets (for the example of computation)....................................................... 234

Appendix to Section 7: list of symbols

...................................................................................... 236

Section 8: computation of sound impact of a duct system

(MODULE 8 of the software)

8.1: Introduction

................................................................................................................................ 239

Terms and definitions ................................................................................................................................ 239

Mountings and geometry ........................................................................................................................... 239

8.2: Scientific and technical background

................................................................................ 239

8.2.1Thermodynamics and fluid dynamics: .............................................................................................. 239

Steps of the computation ..................................................................................................................... 239

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8.2.2 Acoustics regarding the longitudinal noise propagation i.e. for the computation of the sound power

level downstream of the duct system: ........................................................................................................ 239

Bloc diagram ....................................................................................................................................... 240

Steps of the computation ..................................................................................................................... 240

Step [BAA] sound power level downstream ............................................................................. 240

Step [BAB] sound pressure level downstream at a specified distance ....................................... 240

8.2.3 Acoustics regarding the transverse noise propagation i.e. for the computation of the sound power

level transmitted by the walls of the duct system: .................................................................................... 240

Bloc diagram ....................................................................................................................................... 240

Steps of the computation ..................................................................................................................... 241

Step [BAC] sound pressure level at a specified distance .......................................................... 241

8.3: How to use SILDIS

.................................................................................................................. 241

Operating conditions / security level / safety ……………………………................................................. 241

Worksheets regarding the longitudinal noise propagation i.e. for the computation of the sound power level

downstream of the duct system ................................................................................................................. 241

Worksheets regarding the transverse noise propagation i.e. for the computation of the sound power level

transmitted by the walls of the duct system ............................................................................................. 243

8.4: Examples of computation with SILDIS

.......................................................................... 244

Example 8.4.1 cylindrical attenuator without core + bend + (straight) duct , the acoustic performance of

each component being predetermined ...................................................................................................... 244

Envisaged application ................................................................................................................................ 244

Input data ................................................................................................................................................... 244

Screenshots of the worksheets (for the example of computation) ............................................................. 246

Appendix to Section 8: list of symbols

...................................................................................... 248

Section 9: computation of sound decay in enclosed spaces

(MODULE 9 of the software)

9.1: Introduction

................................................................................................................................ 251

Terms and definitions ................................................................................................................................ 251

Mountings and geometry ........................................................................................................................... 251

9.2: Scientific and technical background

................................................................................ 251

9.2.1Thermodynamics and fluid dynamics: .............................................................................................. 251

Bloc diagram ....................................................................................................................................... 251

Steps of the computation ..................................................................................................................... 251

9.3: How to use SILDIS

.................................................................................................................. 256

Operating conditions / security level / safety ……………………………................................................. 256

Worksheets ................................................................................................................................................ 257

Input data, alerts and results: the key points............................................................................................. 258

9.4: Examples of computation with SILDIS

.......................................................................... 259

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Example 9.4.1 room with discrepancies in dimensions & with non-homogene distribution of absorbing

areas ........................................................................................................................................................... 259

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General considerations

0.1: Introduction

What does the present user’s manual aims at

The software SILDIS (Sound Impact Limitation Design for Industrialized Solutions) has been developed in order to allow (for users among the team ITS or elsewhere) the prediction of acoustic and aerodynamic performances of dissipative silencers and the

prediction of acoustic performances of plane partitions and ducts.

The present user’s manual aims at: o providing the scientific and technical background of this software o presenting the available features of this software o answering the question: how to use SILDIS ? o giving illustrative examples of the use of this software

Note 1: see also report [PhRxx-013x] (Sound Impact Limitation Design for Industrialized Solutions: a single Excel based software for a wide range of applications) to get answers to the question: why/when use SILDIS ?

Note 2: see also report [PhRxx-015x] Collection of soundproofing constructions systems: a companion to “User’s manual for the software SILDIS”

Comments

SILDIS is a rolling tool, for which work is on progress in relation with existing features (being made available for users as soon as possible) and with features to come/to be modified, involving possibly, during a transient period:

- the evaluation of some indicators of performance to be done thanks to several separate predictions until sufficient feedback allows to reduce the most appropriate separate predictions to the smallest amount necessary for the best use

- some features to not be available because not 100% implemented or not sufficiently verified (some features may also be available although not 100% verified indeed…)

In order to include the calculations in the general layout of the program, some models associated with known bibliographic sources have not been used, despite their level of interest from an academic point of view: SILDIS is sometimes based on simplified (although rarely simple) methods of computation, satisfying the requirements of the conditions of implementation and (hopefully) the requirements of the conditions of use of the program.

All unfavorable cases involved by the non limitation of the input data for different models are not always known with accuracy.

In case of an evaluation of an indicator of performances done thanks to several separate predictions, the preferred models (at the time of the writing) of the author of this manual are written in bold and underlined (like this for the model MOD: MOD)

SILDIS is a tool supposed to be shared by users being more or less experienced in computational noise control engineering, involving possibly for some users the feeling that some elements in this manual are not very familiar for them. Should this happen, those users would consider that such elements are dedicated to other users and would kindly focus on data foreseen to be entered by them in the software and on results - as mentioned above and detailed below - given to them by the software, that are - hopefully - not of that kind (in case of doubt: please ask).

Operating conditions / security level / safety

SILDIS is a PC program requiring the use of Excel 2010 (or a more recent version). The best operating conditions have been obtained with a computer whose technical characteristic are as follows: Intel®Core™i7 3920XM CPU @ 2.9 GHz 3.10 GHz ; 32 Go of RAM.

SILDIS is a program with a restricted access: see report [PhRxx-014x] (Procedure for the use of Excel based programs with a restricted access).

General layout of the program

The general layout of the program SILDIS is as shown on fig. 0.1a & fig. 0.1b below (cf. appendix for abbreviations).

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Fig. 0.1a

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Fig. 0.1b

Fig. 0.1c

As far as MODULES 1 to 9 are concerned

A common routine referred to as COALA (COmputation of Acoustic LAyers) is associated with specific (complementary) routines: o on the one hand: the routine COSIL (COmputation of SILencers), this association basing the features of th e MODULE 1 of the software (described in the Section 1 of the present user’s manual) o on the other hand: the routine COPPA (COmputation of Plane PArtitions), this association basing the features of the

MODULE 2 of the software (described in the Section 2 of the present user’s manual) o furthermore: the routine CODUW (COmputation of DUct Walls), this association basing the features of the MODULE 3 of the software (described in the Section 3 of the present user’s manual)

The routine referred to ass COSTDU (COmputation of STraight DUcts) is basing the features of the MODULE 4 of the software

(described in the Section 4 of the present user’s manual).

The routine referred to as COSTDU (COmputation of STraight DUcts) and the routine COSIL (COmputation of SILencers) are associated with a specific (complementary) routine: o the routine COBON (COmputation of Break Out Noise), this association basing the features of the MODULE 5 of the software (described in the Section 5 of the present user’s manual)

The routine referred to as COBEND (COmputation of BENDs) is basing the features of the MODULE 6 of the software (described in the Section 6 of the present user’s manual).

The routine referred to as CONOZ (COmputation of NOZzle reflection) is basing the features of the MODULE 7 of the software

(described in the Section 7 of the present user’s manual).

The routine referred to as IDS (COmputation of Impact of Duct Work) is basing the features of the MODULE 8 of the software

(described in the Section 8 of the present user’s manual).

All MODULEs 1 to 8 are encapsulated in a single file.

The routine referred to as COSOD (COmputation of SOund Decay) is basing the features of the MODULE 9 of the software

(described in the Section 9 of the present user’s manual).

MODULE 9 is encapsulated in a separate file.

As far as MODULES 1A is concerned

A routine referred to as COALA-1A (COmputation of Acoustic LAyers) is associated with specific (complementary) routine the routine COSIL-1A (COmputation of SILencers), this association basing the features of the MODULE 1A of the software

(described in the Section 1A of the present user’s manual)

MODULE 1A is encapsulated in a separate file.

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Worksheets

The software SILDIS is configurated in order to allow the user to access to several worksheets as shown on fig. 0.1a, 0.1.b and 0.1.c above (in case of “in” in the name of a given worksheet, the user should be prepared to input data, in case of “out” in the name of a given worksheet, the user should be prepared to get results).

Input data

The software SILDIS is configurated in order to allow the user to input data by filling/modifying yellow cells (*), sometimes by the means of drop-down menus (**) allowing the selection of references of materials, engineering constants, models, conditions of the application… (***)

* something like that ** something like that

*** some users may not be allowed to input data by filling/modifying some yellow cells for the sake of simplicity

0.2: Scientific and technical background

System of units

The system of units used with the software SILDIS for input data and displayed results (and consequently the system of units used in the present document) is the International System of units, some conversions factors being given when useful

Reference conditions

Reference conditions are involved in the expression on the one hand of input data and on the other hand of results with the software

SILDIS (different definitions of reference conditions being more or less currently used all over the world).

For the purposes of the present user’s manual, the following terms and definition apply:

Normal conditions: set of conditions including a temperature t

0

N

= 0°C and a pressure P

0

N

= 101325 Pa.

Note: with the software SILDIS, flow rates expressed in Nm3/h are related to normal conditions

(Test) room conditions (i.e. typically encountered in a room): conditions for which measurement of engineering data of materials

(porous media, cloths, perforated protections, plates) are usually (sometimes implicitly) performed, namely with a temperature t

0

5

* generally not too far from 20°C, with a pressure P

0

* generally not too far from 10 Pa, and with an air speed not too far from 0 m/s.

Note 1: in the worksheets of the software (and consequently in the present document), “usual” refers to input data for (test) room conditions

Note 2: a unique (i.e. common) value of temperature and a unique (i.e. common) value of pressure (being input data themselves in order to allow to some users a fine tuning in some circumstances) are assumed for all “usual” input data.

Service conditions: conditions for which the design of the envisaged soundproofing equipment is performed, possibly influenced by various changes when compared to (test) room conditions, notably with a temperature sometimes far away from (test) room temperature or/and with a pressure sometimes far away from (test) room pressure or/and with an air speed sometimes far from zero.

Note: in the worksheets of the software (and consequently in the present document), “special” refers to input data for service conditions

Fluid

The fluid involved on the one hand: in pores of porous media, on the other hand: in perforations of perforated protections an d generally speaking: in atmosphere is assumed to be in all cases (clean) dry air.

Note for dissipative silencers: the fluid of which the carriage is considered through the dissipative silencer is assumed to be (clean) dry air.

Electro-acoustic analogies

The (popular) application of an equivalent network is a convenient representation and a useful method for the solution of many tasks in relation with the computation of acoustic layers (based on electro-acoustic analogies with electrical circuits: sound pressure, particle velocity and acoustic impedance being respectively analogous to voltage, current and electrical impedance).

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Terms and definitions

For the purposes of the present user’s manual, the following terms and definition apply:

Element: 1 porous medium or 1 cloth or 1 perforated protection or 1 thin plate (indeed: 1 or several identical thin plates treated as a whole)

Note: 1 element can consist of 1 or several acoustic layer(s) each (examples: a pair of identical plates with a negligible interspa ce is 1 element consisting of 2 acoustic layers; a plate with an extensional damping is 1 element consisting of 2 acoustic layers, etc…)

Set (of elements): stacking of several elements gathered for a sake of simplicity of implementation/use of the software (sometimes reduced to1 element).The position (rank) of each element is constant within each set.

Note 1 for dissipative silencers: each set (indexed from an impervious rigid back at the rear to the front: 1 to 4) consists (from the rear to the front) of up to 1 porous medium, up to 1 cloth, up to 1 perforated protection.

Note 2 for plane partitions: each set (indexed from the rear to the front: 1 to 4) consists (from the rear to the front) of up to 1 porous medium, up to 1 cloth, up to 1 perforated protection, and up to 1 (or several identical) thin plate(s). A complementary set (set 0) is used (at the rear of set 1) consisting of up to 1 thin plate (indeed up to 1 or several identical thin plates treated as a whole) backed by atmosphere or backed by an impervious rigid wall). Remark: for the set 0, the number of identical plates only can be freely selected

by the user - the material and the thickness being selected by the user among those of the plate(s) of the set 1 or of the set 2 -

Maximum set index imax: index (up to 4) of the set located as far on the front side, taken into account for the computation (among the sets taken into account for the computation). The elements belonging to sets with an index i

imax are taken into account for the computation under the condition of selected quantities of elements different of 0; the elements belonging to sets with an index i>imax are not taken into account for the computation whatever the selected quantities of those elements are (example: if imax=1, a perforated protection belonging to set 1 will be taken into account for the computation unless the considered quantity is 0; a perforated protection belonging to set 2 will not be taken into account for the computation even if the selected quantity is 1).

Acoustic structure: the whole stacking of acoustic layers of interest

Note 1 for dissipative silencers: the acoustic structure consists of elements (for which the selected quantity is not 0) belonging to sets

1 to imax. The acoustic structure is sometimes referred to as “lining”, assuming an impervious rigid back for the considered duct and sometimes referred to as “splitter” (assuming a symmetry plane - opposite to the airway side - equivalent to an impervious rigid back: requiring sometimes for field applications a rigid centre plate implicitly supposed to be added to the real construction despite the lack of explicit corresponding input data with the software SILDIS)

Note 2 for plane partitions: the acoustic structure consists of elements (for which the selected quantity is not 0) belonging to sets 0 to

imax. Remark: for the set 0, the number of identical plates only can be freely selected by the user - the material and the thickness

being selected by the user among those of the plate(s) of the set 1 or of the set 2 -

Equivalent network

The general equivalent circuit considered for the purposes of the routine COALA (COmputation of Acoustic LAyers) common to the

COmputation of DIssipative Silencers (CODIS) and to the COmputation of Plane PArtitions (COPPA) with the software SILDIS is as shown on the figure 0.2 below (with Pi : sound pressure of the incident wave; Zis: internal source impedance; Zr: radiation impedance):

2Pi

Zis

Zr

Fig. 0.2 source acoustic structure load

The source represents the acoustic field (present in the upstream atmosphere) impinging on the acoustic structure.

The unique 4-poles representing the acoustic structure itself can be represented as an equivalent network, including several 4-poles.

Note 1 for dissipative silencers: the equivalent network is including 4 such 4-poles: the above mentioned sets indexed from 1 to 4

(the load being infinite in case of an impervious rigid back) see figure 0.3 below

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Set4 Set3 Set2 Set1 acoustic structure acoustic structure

The 4-poles representing the sets themselves can be represented as equivalent networks, consisting of a combination of 4-poles elements (such as porous media) and, by using an “old school” approach of 2-poles elements (series elements): such as cloths and perforated protections (see figure 0.4 below) perforated protection cloth porous medium set 1 to 4 set 1 to 4

By using a “new wave” approach: cloths, perforated protections are 4-poles elements (the quantities of corresponding series elements being set equal to 0 by the user in this case)

Note 2 for plane partitions: the equivalent network is including 5 such 4-poles: the above mentioned sets indexed from 1 to 4 and a complementary set indexed 0 (the load being either infinite in case of an impervious rigid back or the radiation impedance of air in case of an atmospheric back) (see figure 0.5 below) Remark: for the set 0, the number of identical plates only can be freely selected

by the user - the material and the thickness being selected by the user among those of the plate(s) of the set 1 or of the set 2 –

Set4 Set3 Set2 Set1 Set0 acoustic structure acoustic structure

Fig. 0.5

The 4-poles representing the sets themselves can be represented as equivalent networks, consisting of a combination of 4 -poles elements (such as porous media) and of 2-poles elements (series elements): such as thin plates and, by using an “old school” approach with other 2-poles elements (series elements): such as cloths and perforated protections (see figures 0.6 and 0.7 below) thin plate perforated protection cloth porous medium set 1 to 4 set 1 to 4

Fig. 0.6

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By using a “new wave” approach: cloths, perforated protections are 4-poles elements (the quantities of corresponding series elements being set equal to 0 by the user in this case)

Remark regarding construction systems

Construction systems (for field applications: including sketches and nomenclatures) for which the design is possible with the software

SILDIS are not described in an exhaustive manner in the present document, being the object of a separate document for a sake of simplicity.

One will see the document referenced Collection of soundproofing constructions systems: a companion to “User’s manual for the software SILDIS” illustrating the possibilities of use of the software for practical cases

(report [PhRxx-015x])

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Appendix to general considerations: list of symbols and acronyms

General

Cf. corresponding § in Section 1

Electro-acoustic analogies

Pi : sound pressure of the incident wave

Zis: internal source impedance

Zr: radiation impedance

Reference conditions

Cf. corresponding § in Section 1 for dry air

Miscellaneous

See also corresponding § in Section 1 and in Section 2

Acronyms

COALA: COmputation of Acoustic Layers

CODAP: COmputation of DAmped Plates

COORT: COmputation of ORThotropic plates

COPERF: COmputation of PERForated plates

COPPA: COmputation of Plane PArtitions

COPPA0: with 0 thin plate in the acoustic structure

COPPA1: with 1 thin plate in the acoustic structure

COPPA2: with 2 thin plates in the acoustic structure)

COSIL: COmputation of SILencers

CODIS: COmputation of DIssipative Silencers

CODIS1: attenuation accounted 1 time

CODIS2: attenuation accounted 2 times

CORESPT: COmputation of REsonant Silencers with Pine-Tree splitters

CORESPTL: COmputation of REsonant Silencers with Pine-Tree splitters with a Lateral lining

CORESPTR: COmputation of REsonant Silencers with Pine-Tree splitters with a Rear lining

CODUW: COmputation of DUct Walls

COCID: COmputation of Circular Duct walls

CORED: COmputation of REctangular Duct walls

COEDLA: COmputation of Empty Ducts Longitudinal Attenuation

COSTDU: COmputation of Straight DUcts

COBON: COmputation of Break-Out Noise

COBEND: COmputation of BENDs

COSOD: COmputation of SOund Decay

CONOZ: COmputation of NOZzle reflection

IDS: computation of Sound Impact of Duct Systems

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Section 1: computation of silencers

(MODULE 1 of the software)

1.1: Introduction

Terms and definitions

For the needs of the present user’s manual, the following terms and definition apply (see NF EN ISO 14163 Acoustics - Guidelines for noise control by silencers, 1999):

Silencer: device reducing the acoustic transmission in a duct, a pipe or an aperture, without preventing the carriage of the fluid

Dissipative silencer: silencer attenuating the wideband sounds with a relatively low pressure loss and converting partially the acoustic energy into heat by friction on tubes having a porous or fibrous structure

Resonant silencer: silencer producing an acoustic attenuation from weakly damped resonances of elements. The elements of the splitters can contain or not contain absorbing materials.

Mountings and geometry

Silencers having various cross sections are frequently used for industrial applications.

For dissipative silencers, the various mountings for which predictions can be done with the software SILDIS are shown in fig.1.1 and fig. 1.2

mounting R’’ mounting R mounting R'

mounting C0 ½ mounting C1 mounting C1 ½ mounting C2

fig. 1.1 cf. worksheet CODIS1

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mounting C2 ½ mounting C3 mounting C3 ½

mounting CR

fig. 1.1 (continue) cf. worksheet CODIS1

mounting Q mounting C0

fig. 1.2 cf. worksheet CODIS 2

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Key of the previous figures d=2d/2: thickness of extreme inner lagging (for mountings R, C1, C2 only) = thickness of lining (for mounting Q, C0 only)

2d: thickness of central splitters (for mountings R, R’’) = diameter of central pod (for mountings C1, C2 only) = thickness of intermediate splitter (for mounting C2 only) h=2h/2: width of extreme air way (for mounting R’’only)

2h: width of central airways (for mounting R, R’’ only) = width of the airways (for mountings R, R’’, C1, C2, Q) a=h*2*π -0.5

2a: width of airway (for mounting C0 only)

L: length of the silencer without aerodynamic extremities

N’’: number of central splitters (for mounting R’’ only); N’’ = B / 2 / (d + h)

N: number of central splitters (for mounting R only); N = N’’ – 1

Concerning the area of the duct upstream and downstream (above and below the silencer) A compared to the area of the overall section of the silencer Af, predictions with the software SILDIS can be done:

 for mountings R, R’’, C2 with A = Af

 for mounting C1 with A = Af or with A = Af* < Af *)

 for mountings Q, C0 with A = Af* < Af *)

Section of the duct above and below the silencer A depending on mounting

R, R’’

C1 C2 Q C0 if A=Af if A=Af* < Af *)

B*H

-

π*(D1) 2

/4

π*(D1-2d)

2

/4

π*(D2) 2

/4

π*(D2-2d)

2

/4

(Q)

2

(Q-2d)

2

π*(D0) 2

/4

π*(D0-2d)

2

/4

*2d being subtracted to the overall dimension of the silencer in order to obtain the corresponding dimension of the considered duct)

The direction parallel to the axis of the duct is referred to as x, the direction normal to the axis of the duct (along the thickness of the lining) is referred to as y according to the fig. 1.3 below (example for a mounting R)

In case of a rectangular silencer, the direction perpendicular to x and y is referred to as z according to the fig. 1.3 below (not considered for the computation with SILDIS) fig.1.3

For resonant silencers, the various mountings for which predictions can be done with the software SILDIS are shown in fig.1.4 and fig. 1.5

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mounting RPTR’’

mounting RPTR

mounting RPTL’’

mounting RPTL

Key of the previous figures d*=2d*/2: thickness of extreme inner lagging (for mountings RPTR, RPTL only)

2d*: thickness of central splitters h*=2h*/2: width of extreme air way (for mounting RPTR’’, RPTL’’ only)

2h*: width of central airways

L: length of the silencer without aerodynamic extremities

N’’*: number of central splitters (for mounting RPTR’’, RPTL’’ only); N’’* = B / 2 / (d + h)

N’: number of central splitters (for mounting R only); N* = N’’* – 1 fig. 1.4 cf. worksheet CORESPTR fig. 1.5 cf. worksheet CORESPTL

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Concerning the area of the duct upstream and downstream (above and below the silencer) A compared to the area of the overall section of the silencer Af, predictions with the software SILDIS can be done with A = Af

Section of the duct above and below the silencer A depending on mounting

A=Af

RPTR, RPTR’’

RPTL, RPTL’’

B*H

1.2: Scientific and technical background

The prediction of acoustic and aerodynamic performances of dissipative silencers with SILDIS is founded on a scientific and technical background in relation with: o analytical models for taking into account the properties of materials and various physical phenomena useful on the occasion of the computation o measurement results for feeding some of those models and for allowing the necessary improvement (through correction factors) of the correlation between some calculations and on site observations

For a rectangular silencer, the obtained results are comparable with the standardized measurement with the plane wave excited alone as much as possible: see NF EN ISO 7235 Acoustics - Laboratory measurement procedures for ducted silencers and air terminal units

- Insertion loss, flow noise and total pressure loss (2004).

1.2.1 Thermodynamics and fluid dynamics:

Steps of the computation

Step [a]

All computations have been gathered in this single step for the sake of simplicity. o

Bibliography (references) :

[a1]

[a2]

[a3]

[a4]

-

[a5] o

Comments in relation with partial derivatives:

Partial derivatives (and related quantities), which are usually employed to measure the equation of state of the fluid near the equilibrium state (with various notations according bibliographic sources) are written for the purpose of the present user’s manual with the following notations:

 the isothermal compressibility of dry air is referred to as C

T

C

T

-

 

= =

V

T

1

∂P

 

T

  

T

with K

T

=1/C

T

 the adiabatic compressibility of dry air is referred to as C s

C s

=

-

1

V

∂V

∂P

=

T

1



∂P

T because C s

= C

T

/

 s

with K s

=1/C s

 the coefficient of thermal expansion of dry air is referred to as β

β = =

V

∂V

∂T

P o

Other comments:

-

1

∂T

 

P

 when used the density of dry air

 is computed according various models as shown in the table below:

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MEC

source

[a1] using ideal gas law

(derived from

MARiottes’s law) (*)

[a1] using a regression

* the gas constant of dry air R (J/kg/K) is set to 287 or 287.053 or 287.10 depending on the eponym selected model

 when used the dynamical viscosity of dry air

is computed according various models as shown in the table below: model source limiting temperature

SUT

[a2] using

SUTherland

’s law)

-20 to 800

°C

VER

[a4]

?

MEC

IDE

[a1] using a regression

-173.15 to

926.85 °C

[a2] using a regression

-20 to 800

°C

Conversion factors micropoise centipoise poise

= g/cm/s kg/m/s

= Nsm-2 micropoise

1

10

4

10

10

6

7 centipoise

10

1

10

10

-4

2

3 poise

= g/cm/s

10

-6

10

-2

1

10

 when used the kinematic viscosity of dry air

is computed from [a1]

Note :

=

/

 kg/m/s

= Nsm-2

10

-7

10

-3

10

-1

1

Conversion factors centistokes

= mm2/s stokes = cm2/s m2/s centistokes

= mm2/s

1

10

10

2

6 stokes = cm2/s

10

1

-2

10

4 m2/s

10

10

1

-6

-4

 when used the adiabatic exponent of dry air

is computed according various models as shown in the table below: model source limiting temperature

INV

(*)

-

MEC

[a1] using a regression

-73.15

to

926.85 °C

*

 is set to 1.399 or 1.400 or 1.401 or 1.402 depending on the eponym selected model

 when used the specific heat (capacity) (at constant pressure) of dry air c p is computed according various models as shown in the table below:

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MEC

[a1] using a regression for a (the regression for c p

being in error)

-73.15

to

926.85 °C

MEC2

[a1] using a regression for Pr (the regression for c p being in error)

-173.15 to

926.85 °C

KRA

[a3] using a regression

-20 to 800

°C

Conversion factors

J cal

J

1

4.1868 cal

0.2388

1

 the following relation apply:

- 1

β

2

.T

=

S

.c

p

.

C

 when used the thermal conductivity of dry air

is computed according various models as shown in the table below: model

MEC

KRA source limiting temperature

[a1] using a regression

-173.15 to

926.85 °C

[a3] using a regression

-20 to 800

°C

Conversion factors

J cal

J

1

4.1868 cal

0.2388

1

 when used the diffusivity of dry air a is computed from [a1]

Note : a =

/

/c p

 when used the Prandtl number of dry air Pr is computed according various models as shown in the table below: in case of model for c p

MEC

MEC2 KRA source limiting temperature

[a1] from c p

and

-73.15

to

926.85 °C

,

[a1] using a regression

-173.15 to

926.85 °C

[a3] from

, c p

and

-20 to 800

°C

Note : Pr =

/a =

/

/a =

.c

p

/

 when used the (adiabatic) sound velocity in dry air c is computed from [a5]

Note : c = (K s

/

)

0.5

 when used the characteristic impedance of dry air Z is computed from [a1]

Note : Z =

 c

1.2.2 Acoustics:

Bloc diagram for rectangular dissipative silencers and comments for other dissipative silencers and for resonators:

the computation scheme for rectangular dissipative silencers is as shown on fig 1.6 below

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Fig. 1.6

Note 1: the service conditions dependence has been omitted for the sake of simplicity. See: report [PhRxx-002x] pages 6 to 7, report

[PhRxx-006x] pages 2 to 3, report [PhRxx-015x]

Note 2: the main steps (the steps involving a physical modeling) being referred to as [A] to [K] have been taken into account for the bloc-diagram above (some of the parameters of the above bloc diagram are not independent); the frequency dependence has been omitted for the sake of simplicity; the calculation is carried out with the hypothesis of plane waves, typically regarded as the least attenuated mode (only for step [H] are other modal contributions taken into account)

Note 3: analytical calculations are involved in steps [B] to [F] and [J] to [K]; empirical methods are involved in steps [G] to [I]

Note 4: step [F] is depending on the conditions of axial sound propagation inside the lining

Note 5: the bloc diagram above is suitable for rectangular dissipative silencers, whatever the considered mounting is among R, R’’ .

Note 6 (comments for other dissipative silencers)(under the condition of same speed in the airways): o for the mounting C1 and C2: the performance (from step [F] to step [K]) is extrapolated from the performance of the mounting R to which steps [A] to [E] are referring (not suitable for silencers with too small diameters) o for the mounting Q and C0: the performance (of step [F]) is extrapolated from the performance of the mounting R to which steps [A] to [E] are referring (not suitable for silencers with too small diameters in case of mounting C0)

Note 7 (comments for resonators): a complementary step referred to as [L] is necessary between step [E] and step [F] allowing the computation of the admittance in the plane of the outlet side of (the neck of) the chamber

Steps of the computation

Step [A]

This step aims at taking into account what is on the back (i.e. at the rear of the acoustic structure ) o

Bibliography (references) :

[A1] o

Comments :

No comment

Step [B]

This step aims at taking into account porous media used in the acoustic structure.

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Fig. 1.5 o

Bibliography (references) :

[B1]

[B2]

-

[B3]

-

[B4]

-

[B5]

[B6]

[B7]

[B8]

[B9]

-

[B10]

[B11]

[B12]

- porous medium

[B13] o

Comments :

The following governing equation is considered in the absorber layer (with notations adapted from various sources: will be specified on the occasion of a future revision of this user’s manual)

:

Where

(

 ax



∂x)

2

(

 ay

∂x)



( + - 1 ) p

2

 a

(x,y,t) = 0 p a

: pressure (Pa) t: time (s)

 ax

: propagation constant in the x-direction (rad.m

-1

)

 ay

: propagation constant in the y-direction (rad.m

-1

) model source

 depending on the used model, some of the following parameters are taken into account in relation to the properties of a porous medium (sometimes only in a direction perpendicular to its surface): σ (Nsm

-4

) airflow resistivity, ø porosity,

∞ tortuosity, Λ’ (m) thermal characteristic length, Λ (m) viscous characteristic length, RG (kg/m3) (bulk) density parameters

DB

[B1]

σ

BH

[B2]

σ

AB

[B3]

σ

ORV

[B4]

σ

M76

σ

ø

M76+

[B5]

σ

ø

RG

M76+-

σ

ø

RG

M84R

σ

[B6]

M84V

σ porous medium polyester only made of mineral fiber or of glass fiber only rockwool and basalt wool only glasswool only comment related to frequency range low frequency extension only

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M89

σ

ø

M89+

σ

ø

RG

[B7]

M89+-

σ

ø

RG

M89+*

σ

ø

RG made of mineral fiber or of glass fiber only

JKD

[B8]

σ

ø

Λ’

Λ all kind

AIR

- air only

CUM

[B9] (*)

σ

JK2

[B8] (**)

σ

ø

Λ’

Λ perforated protection with round holes only comment related to frequency range low frequency extension only with smoo thing

Cancelled because was in error

other comments

(valid for a porous medium being not a perforated protection only) model of added impedanc e should be set to

ZER other comments

(valid for a porous medium being a perforated protection only) other comments

(valid for a porous medium being a perforated protection only account interactio ns with rear

porous

layer (*) and front

porous layer (**) like in

[B12],

RDE model for added impedanc e should be selected] interactio ns with rear

porous

layer (*) and front

porous

layer (**) accounted by selecting appropriat e model of added impedanc e (cf. below) in case of a perforated protection

,when one wishes to

* interaction with rear series cloth not accounted

** interaction with front series cloth not accounted

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 the following models of added impedance:

Model of added impedance source interaction

RDE

[B12] without additional resistance effects

ROA

[B13] with additional resistance effects

ZER no interaction (*)

*the model ZER applies notably for modeling a front added length “blown away” by an airflow

* in case of normalized propagation constant characteristic impedance Z an

expressed as Z an

 an

expressed as

 is the density of air (kg/m3) an

= a’/E

+ j * (1 + a”/E c

1

= b’ ; c

2

= -

’ ; c

3

= b” ; c

4

= -

” ; c

5

= a’ ; c

6

= -

’ ; c

7

= a” ; c

8

= -

” with E =

.f / σ where f is the frequency (Hz) and

) and in case of normalized

= (1 + b’/E

 ’

) – j * b”E

 ” the following relations apply:

**see the comments concerning series perforated protections

 no influence of the speed of the airflow is taken into account for the computation

Conversion factors

MKS

Rayl/m =

Nsm

-4

CGS units

MKS

Rayl/m =

Nsm

-4

CGS units

1

10

3

10

-3

1

Step [C]

This step aims at taking into account series cloths used in the acoustic structure.

Fig. 1.6 o

Bibliography (references) :

[C1] series cloth

[C2]

[C3]

-

[C4]

-

[C5] o

Comments :

 depending on the (general) used model, some of the following parameters are taken into account: superficial flow resistance Rs (Nsm-3), surface density M’ (kg/m2), parallel resistance (losses due to mounting) Rp (Nsm-3), E

(N/m2) Young’s modulus, Poisson’s ratio ν, plate dimension a (m), as well as boundary conditions general model parameters

PLATE 1

M’

E

ν a

PLATE 2

M’

E

ν a

PLATE 3

M’

E

ν a

PLATE 4

M’

E

ν a comment boundary conditions as entered for thin plate

1 except for M’

(computed from ρ as entered for thin plate 1 and from d as entered boundary conditions as entered for thin plate

2 except for M’

(computed from ρ as entered for thin plate 2 and from d as entered boundary conditions as entered for thin plate

3 except for M’

(computed from ρ as entered for thin plate 3 and from d as entered boundary conditions as entered for thin plate

4 except for M’

(computed from ρ as entered for thin plate 4 and from d as entered

FRO

Rs

M’

Rp

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 for (general) model PLATE 1, PLATE 2, PLATE 3 and PLATE 4, boundary conditions are taken into account using various models general model comment

CE

Clamped Edges

SSE

Simply

Supported Edges

 for (general) model FRO only, using electro acoustic analogies, complementary impedances can be accounted (for some predictions to be done in relation with the COomputation of Acoustic LAyers), with respect to the base impedance Zbase= Rs’ (with Rs’=superficial flow resistance): see fig.1.7

- a parallel reactance jM’

(Nsm-3)

- a parallel resistance (losses due to mounting conditions) Rp’ (Nsm-3) fig.1.7

Particular cases cloth, fabric according to [C3]

Rs’ (Nsm

-3

) free input

Rp’ (Nsm

-3

) 0

M’ (kg/m2) free input closed foil according to [C3]

0 free input

Note: no influence of the speed of the airflow is taken into account for the computation

Conversion factors

MKS Rayl

= Nsm

-3

CGS units

MKS Rayl

= Nsm

-3

1

10

CGS units

10

-1

1

Step [D]

This step aims at taking into account series perforated protections used in the acoustic structure.

Fig. 1.8 series perforated protection o

Bibliography (references) :

[D1]

[D2]

-

[D3]

[D4]

[D5]

-

[D6]

-

[D7]

[D8]

[D9]

-

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Comments :

 depending on the used (general) model, some of the following parameters are taken into account in relation with the properties of a perforated protection: d (m) diameter of the holes/width of the slits, t (m) thickness,

open area ratio; depending on the used (general) model, various effects are (or are not) taken into account general model parameters source comment (general) comment regarding the calculation of impedances comment regarding the porous layer at the rear and at the front other comment

DYM d t

[D1] in contact with air only, holes circular only, square array only

L+C d t

[D2] in contact with air only, holes circular only, square array only

MOI d t

[D3],[D4] in contact with a porous layer (at the front and/or at the rear), with various geometries total impedance calculated as the sum of the impedance at the rear (using appropriate effective density) + tunnel impedance + impedance at the front rear (using appropriate effective density) even if of set index

<imax, even if of thickness zero, the nature of the porous layer at the rear and at the front is accounted

MOI and ICH seems to provide identical results in case of a perforated sheet with round holes and in case of the use of the simplified model for the tunnel model MOI and in case of input data for the model

MOI with tortuosity 1 and characteristic length appropriate

ICH d t

[D3],[D4],[D5] in contact with a porous layer (at the front and/or at the rear), with various geometries total impedance calculated using appropriate effective density accounting interactions at rear and at front even if of set index

<imax, even if of thickness zero, the nature of the porous layer at the rear and at the front is accounted

 with the general model MOI the effects of the interaction of the perforated protection with a porous layer are taken into account by the means of:

 an added length (increasing the mass of the vibrating air in the neck), depending on the geometry of the perforation:

Model of added length according the perforation geometry source

Geometry of the perforation

Open area ratio

COA

[D3]

<0.16

COB

[D2]

COC

[D6] circular, square array

<0.78

5

COJ

[D9]

COM

[D7]

CHC

[D6] circular, hexagonal array

<0.90

6

CHM

[D7]

CAR

[D7] square

<0.16

FEM

[D7]

FED

[D8] infinite slot

ZER no added length

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 the following models of added impedance:

Model of added impedance source interaction

RDE

[D5] without additional resistance effects

ROA

[D7] with additional resistance effects

ZER no interaction (*)

*the model ZER applies notably for modeling a front added length “blown away” by an airflow

 using electro acoustic analogies, complementary impedances can be accounted (for some predictions to be done in relation with the COmputation of Acoustic LAyers) with respect to the base impedance Zbase: see fig.1.9

- a series resistance R’’ (Nsm-3) for models MOI and ICH

- a parallel reactance jM’’

(Nsm-3)

- a parallel resistance (losses due to mounting conditions) Rp’’ (Nsm-3) fig.1.9

Note: the recourse to a complementary parallel reactance jM’’

and to a complementary parallel resistance (losses due to mounting conditions) Rp’’ can be envisaged in order to try to improve all general models listed above

Particular cases

Special cases

R'’ (Nsm

-3

)

Rp'’ (Nsm -

3

) free input free input

M’ (kg/m2) free input often (in case of pure models of added length among those listed above)

0

 simplified tunnel model is appropriate in case of thickness of the perforated sheet sufficiently low (simplified tunnel model not based on the comprehensive calculation using cascade). Simplified tunnel model is used in [D3], [D4],

[D5], [D7]

 no influence of the speed of the airflow is taken into account for the computation (except * above)

Step [E]

This step aims at predicting the surface impedance of a multilayered acoustic structure (including porous media, series cloths and series perforated protections with a back selected in a way appropriate for the considered simulation). o

Bibliography (references) :

[E1]

[E2]

[E3] o

Comments :

It has been taken into account:

 that the most sophisticated lining of interest for the applications foreseen at ITS (or elsewhere) consists of a 4 layers filling (see report [PhRxx-006x ]):

- 2 layers of porous media

- 1 layer of cloth

- 1 layer of perforated sheet (being presently with diameter of holes 3mm in a hexagonal array with a perforation rate of

32 % thickness 1.5mm)

 the rear boundary condition for the arrangement of materials of interest for the COmputation of DIssipative Silencers:

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- either considered without a symmetry plane opposite to the airway side (case of a lining with an impervious rigid back)

- or considered with a symmetry plane opposite to the airway side (case of a 1/2 splitter, requiring sometimes for field applications a sufficiently thick rigid centre plate implicitly supposed to be added to the real construction when required despite the lack of more explicit corresponding information in the present document), with an equivalence of this configuration to the previously mentioned one

 possible other useful arrangements of materials (for other predictions to be done in relation with the COmputation of

Acoustic LAyers, not only in the context of COmputation of DIssipative Silencers)

Consequently (see figure 1.10 below, taking into account the present status of implementation of the software):

 a variable (from 1 to 4) number of sets of elements is considered for the computation, the sets being indexed from an impervious rigid back to the front (airway side): 1 to 4

set 4 set 3 set 2 set 1

fig. 1.10 symetry plane / impervious rigid back

 each set consists (from the rear to the front) of up to 1 porous medium, up to 1 series cloth and up to 1 series perforated protection (the “series” concept being in relation with electro-acoustic analogies basing equivalent network): see figure 1.11 below.

set 1 to 4: zoom

series perforated protection fig. 1.11 porous medium

. series cloth

 the surface impedance of the acoustic structure with an impervious rigid back is calculated above the set imax: the COmputation of the DIssipative Silencer is performed for an acoustic structure (with an impervious rigid back) including sets from 1 to imax

(with 1

imax

4)

The less complicated models available for taking into account the physical properties of a porous medium are based on the hypothesis of homogeneity in directions parallel to and perpendicular to the surface of the material (i.e. same properties in directions x, y and z). But some porous media (including some stone wools, some glass wools) are known to be non homogeneous in directions parallel to and perpendicular to the surface of the material having (in particular) an airflow resistivity normal to laminae of fibers σ

N

and an airflow resistivity parallel to laminae of fibers σ

P that can notably differ (with σ

P

reaching only 0.5*σ

N sometimes). So, in this case, the airflow resistivity of a material non homogeneous in directions parallel to and

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N

+σ

P

) would be only 0.75*σ

N with a ratio σ

P

N

of 0.5). This (a difference along the direction normal or parallel to the laminae) is also the case for other properties of numerous materials.

In the software SILDIS, a possible inhomogeneity in directions parallel to and perpendicular to its surface (i.e. different properties - depending on the used model - in directions x and y) is considered (for the routine COmputation of DIssipative

Silencers) for the porous medium of set 1 (porous media for sets 2 to 4 being considered homogeneous in directions parallel to and perpendicular to the surface).

Note 1: each layer is assumed to not be glued to another

Note 2: concerning the perforated protection of the set i, the porous medium taken into account with the models of added impedance ROA and RDE is:

 at the rear: the porous medium of set i

 at the front: the porous medium of set i+1 if i<4 (even if i+1>imax: the selection of a reference different of AIR for the porous media of set i such as i>imax is highly discouraged) or the front atmosphere if i=4

Note 3: the use in practical cases (and the corresponding prediction of performance) of a perforated protection in contact with something else than a porous medium (that can be air at the front or a thin wire mesh spacer at the rear in some cases) is highly discouraged

 for the total thickness of the acoustic structure d the following formula apply:



d = imax

∑ d i

+ imax

I’ i

* d’ i

+ imax

I’’ i

* d’’ i i = 1 i = 1 i = 1

d i

(resp. d’ i

I’ i

and d’’

(resp.Id’’ i i

) = thickness of the porous medium (resp. the series cloth and the series perforated protection) of set i

) = 0 or 1 depending on the incorporation (or not) of the considered element of set i in the acoustic structure

(omitted in the worksheets displays of the software for the sake of simplicity)

Note: this formula is compatible with the definition of d given in § 1.1)

Step [F]

This step aims at calculating the propagation loss with flow of the silencer. o

Bibliography (references) :

[F1]

[F2]

-

[F3]

-

[F4]

[F5] o

Comments :

The following governing equation is considered for the free duct (with notations adapted from various sources: will be specified on the occasion of a future revision of this user’s manual)

:



1

 c

0



D



Dt

Where

 c

0

: (adiabatic) velocity of sound (ms

-1

) p: pressure (Pa) t: time (s)





∂x

 

∂y

D

= c

Dt

0

[jk

0

∂x

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0

: wave number (rad/m)

M: Mach number

conditions of the propagation of sound inside the absorbing material (for dissipative silencers)

- a sound propagation exists in the lining of a dissipative silencer, in a direction y (taken into account in the software SILDIS), depending on σy that is the flow resistance of the lining in the direction y : the attenuation of a dissipative silencer is always depending on this phenomenon (not only sometimes)

- without transverse very thick metal sheets (with a very short distance between them: below 1/4 (maybe 1/6 ?) of the wavelength corresponding to the frequency of interest) acting as partitions, a sound propagation exists in the lining, in a direction x, depending on σx that is the flow resistance of the lining in the direction x. Consequently, the following cases are of interest: σx1/σy1=∞ (absorber locally reacting) (*), σx1/σy1=1 (absorber bulk reacting), σx1/σy1=variable being the general case including the previous cases

* the case of an axial wave propagation inhibited by transverse very thick metal sheets (with a very short distance between them) acting as partitions is also referred to as σx1/σy1=∞ whatever the properties of the absorber are

complementary definitions in relation with the cross section of the silencer

- the total number

of cloths and perforated protections accounted as porous media i.e. not accounted as series cloth (resp. series perforated protections) using electro acoustic analogies is considered:

 with an “old school” approach,

=0 (since cloths and perforated protections are accounted exclusively as series cloths and series perforated protections using electro acoustic analogies)

 with a “new wave” approach,

≠0 (possibly): if some cloths or some perforated protections are (in some cases) accounted as porous media

- consequently, the following definitions apply:

ilim: limit set index (indeed: limit between dlocal and hlocal: see below) with 1

ilim

imax

 with an “old school” approach, ilim = imax

 with a “new wave” approach, ilim has to be selected (by the user) such as ilim = imax-

dlocal = ilim

∑ d i

with d i

= thickness of the porous medium of set i

i = 1

dbulk: such as dbulk = d1 (thickness of porous medium of set 1)

Numerical application: for a dissipative silencer with a rectangular cross section having rectangular splitters of thickness 2d such as 2d-2d’1=200mm made of one porous medium with a cloth of thickness d’1=5/100 mm

 with an “old school” approach: imax=1;

=0; ilim=1;dlocal=200mm

 with a “new wave” approach: imax=2;

=1; ilim=1;dlocal=200mm

- the following definitions also apply in case of rectangular dissipative silencers and in case of mounting Q:

hlocal = d + h – dlocal ; hbulk = d + h – dbulk

- the following definitions apply in case of round dissipative silencer without a central pod (mounting C0):

alocal = d + a – dlocal ; abulk = d + a – dbulk

- the following definitions also apply in case of mounting RPTL, RPTL’’

Hslocal = d + Hs – dlocal ; Hsbulk = d + Hs – dbulk

determination of the propagation loss

The propagation loss (Da in dB/m) is basically computed at frequency steps of 1/21 octave (then averaged per 1/3 octave frequency band) for the fundamental mode (being considered as the least attenuated mode), the cut off frequency for the first higher mode fco depending on the speed of sound c, the Mach number in the airways M, and the geometry of the duct (see [F5])

for the mountings R,R’, fco = 0.5 * c

0

/ max [B,H] * (1- M

2

)

0.5

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for the mounting C1 (resp. C2), fco = 0.586 * c

0

/ D’1 * (1- M

2

)

0.5 resp. fco = 0.586 * c

0

/ D’2 * (1- M

2

)

0.5

In case of an area of the duct above and below the silencer A equal to the area of the overall section of the silencer Af, D’1=D1 else D’1=D1-2d (resp. D’2=D2 else D’2=D2-2d)

for the mountings Q, fco = 0.5 * c

0

/ Q’ * (1- M

2

)

0.5

In case of an area of the duct above and below the silencer A equal to the area of the overall section of the silencer Af, Q’=Q else Q’=Q-2d

for the mounting C0, fco = 0.586 * c

0

/ D’0 * (1- M 2

)

0.5

In case of an area of the duct above and below the silencer A equal to the area of the overall section of the silencer Af, D’0=D0 else D’0=D0-2d

The determination of the propagation loss is done (depending on the choice of the user) for one among the following cases,

σx1/σy1=∞ (absorber locally reacting), depending on dlocal and hlocal (resp. alocal for mounting C0)

σx1/σy1=1 (absorber bulk reacting), depending on dbulk and hbulk (resp. abulk for mounting C0)

σx1/σy1=variable (for an inhomogeneous absorber in directions parallel to and perpendicular to its surface including the cases of an absorber locally reacting and the case of an absorber bulk reacting with appropriate values of σx1/σy1), depending on dbulk and hbulk (resp. abulk for mounting C0) o

particular case for imax=1 (i.e. only one porous medium in the lining), σx1 (resp. σy1) being the flow resistivity of the porous medium of set 1 in the x (resp. y) direction:

For the case σx1/σy1=1 and for the case σx1/σy1=variable, a minimum flow resistance r>rmini is required with r = σy1*d1/Z

0

(d1 being the thickness of the porous medium of set 1, Z

0

being the characteristic impedance of air). Otherwise some important discontinuities may appear in the curves showing the propagation loss, and some accuracy of some displayed results may be anticipated: attention has to be paid that no such important discontinuity occurs this will be detailed in a future revision of the user’s manual

(perhaps) o

particular case for imax>1 (i.e. more than one porous medium in the lining)

For the different mountings, the determination of the propagation loss can be done for the following cases,

σxi (resp. σyi) being the flow resistivity of the porous medium of set i in the x (resp. y) direction:

σx1/σy1=∞ (absorber locally reacting) and σxi/σyi=∞ for i>1 (absorbers locally reacting), depending on

dlocal and hlocal (resp. alocal for mounting C0)

σx1/σy1=1 (absorber bulk reacting), and porous media of sets with i>1 accounted as series porous media

(i.e. porous media acting as series impedances: see remark and fig. 1.9 below) depending on dbulk and

hbulk (resp. abulk for mounting C0)

σx1/σy1=variable (inhomogeneous absorber in directions parallel to and perpendicular to its surface including the case of an absorber locally reacting and the case of an absorber bulk reacting with appropriate values of σx1/σy1), and porous media of sets with i>1 accounted as series porous media (i.e. porous media acting as series impedances: see remark and fig. 1.9 below) depending on dbulk and hbulk (resp. abulk for mounting C0)

Remark: the conditions of the propagation of sound inside an absorbing material are considered only with respect to a single (given) porous medium. For σx1/σy1=1 or σx1/σy1=variable, the other layers (whatever they are, if different of the porous of set1) have consequently to be taken into account (using the electro acoustic analogies) as series impedances. Consequently, porous media of sets i>1 are turned into series impedances in the following way: the surface impedance obtained above the porous medium of set 1 is substracted to the surface impedance above set imax in order to get a series impedance that can be added to the 4-pole consisting of the porous medium of set 1 (see fig 1.12 below)

Set4 Set3 Set2 Set1

Series impedance porous medium of set1 acoustic structure acoustic structure

Fig. 1.12

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influence of air flow

The presence of airflow modifies the propagation loss: the computation is done with the hypothesis of a uniform air flow

(supposed to not be rotational). Concerning flow rates and air speeds: a positive value is related to a direction of airflow equal to the direction of propagation of sound, a negative value is related to a direction of airflow opposite to the direction of propagation of sound

Step [G]

This step aims at taking into account a bypass correction (i.e. a limitation of the propagation loss in case of a length of the silencer over 1m: indeed, compared with the estimation obtained with an hypothesis of proportionality of the performance to the length of the silencer, in order to predict an insertion loss). o

Bibliography (references) :

[G1]

-

[G2]

-

[G3] o

Comments :

The bypass correction (Dk in dB) is basically computed at frequency steps of 1/3 octave:

for L≤1m: Dk = 0 and for L>1m: Dk =

D * ( 1 – L ) with

D in dB/m

general case

An extrapolation of the original value of

D mentioned in [G1] is used for SILDIS, allowing calculations in an extended range of values of σy1 for values of Λ=d/h to be précised on the occasion of a future revision of this user’s manual

Note 1: the data pool used for the determination of the original value of

D mentioned in [G1] is related to splitters filled with 1 porous medium with a flow resistivity σx1 =? σy1 from 9 to 15 kNsm

-4

: no influence of the speed of the airflow seems to be taken into account for the computation, no influence of a series cloth seems to be taken into account for the computation, no influence of a series perforated protection seems to be taken into account for the computation

Note 2: in [G3] is mentioned for [G2] basing [G1] complementary information. The data pool used for

D is related to splitters “in 1 piece” with a thickness 2d=0.1 or 2d=0.2 m with Λ=d/h=0.5 to 4

Model

Bypass correction

FRO as above

ZER no limitation

*although at the time of the present user’s manual the conditions of the measurement of the data pool

([G1],[G2]) are not known with accuracy, one can consider that: Dk = Dk1 + Dk2 (the 2 terms being presently not known separately) with:

Dk1 to be accounted for the vibration transmission along the duct wall, for the sound transmission over the duct wall, for the vibration transmission along the splitter frame (as described in [G1] an d for the imperfection of the interface between the lining and the duct

Dk2 to be accounted for the inhomogeneity of the used absorber in directions parallel to and perpendicular to its surface: a unique model is used for taking into account the limitation of propagation whatever σx1/σy1 is (may be that this correction should be used only in the case of an inhomogeneous absorber in directions parallel to and perpendicular to its surface when the hypothesis σx1/σy1=1 is used for the computation).

For those reasons, the value obtained by the means of the unique model FRO has to be considered as a typical general estimation of the limitation of the propagation loss useful when no accurate regression is available for a silencer with a particular filling and particular modalities of construction (this is often the case)

particular cases:

- for the mounting R’’, the bypass correction is supposed (in all cases) to be equal to the bypass correction calculated for the mounting R (all things being also equal)

- for the mounting C1,C2, the bypass correction is supposed to be equal to the bypass correction calculated for the mounting R under the condition of an equal speed in the airways (all things being also equal)

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- for the mounting Q, C0, the bypass correction (normalized to Da) is extrapolated from the bypass correction calculated for mounting R under the condition of an equal ratio d/h

- for the mounting RPTR’’ (resp. RPTL’’), the bypass correction is supposed (in all cases) to be equal to the bypass correction calculated for the mounting RPTR (resp. RPTL) (all things being also equal)

Step [H]

This step aims at taking into account the reflection loss in the silencer, in order to predict an insertion loss. o

Bibliography (references) :

[H1]

-

[H2]

-

[H3] o

Comments :

The reflection loss (Dr in dB) is basically computed at frequency steps of 1/21 octave (then averaged per 1/3 octave frequency band).

general case: no influence of the speed of the airflow is taken into account for the computation

Model

Reflection loss

MUL (*) as above

(higher modes integrated)

ZER no reflection

* No influence of a series cloth is taken into account for the computation, no influence of a series perforated protection is taken into account for the computation. The data pool used for Dr is related to splitters with a thickness 2d=0.1 or

0.2 or 0.3 m, filled with 1 porous medium with a flow resistivity σx1 = σy1 from 9 to 15 kNsm-4 (an extrapolation of

Dr with a different thickness has been used). At the time of the present user’s manual the conditions of the measurement of the data pool ([H2],[H3]) are not known with accuracy, especially the higher modes propagating in the duct in relation with the characteristics of the testing facility mentioned in [H2] (with a front section from

0.5m*0.5m to 1.3m*0.5m). For those reasons, the value obtained by the means of the unique model MUL has to be considered as a typical estimation of the reflection loss for a duct of dimensions comparable to testing facility mentioned in [H2] when no accurate information is available regarding the higher order modes (this is often the case).

particular cases:

- for the mounting R’’, the reflection loss is supposed (in all cases) to be equal to the reflection loss calculated for the mounting R (all things being also equal)

- for the mounting C1,C2, the reflection loss is supposed to be equal to the reflection loss calculated for the mounting R under the condition of an equal speed in the airways (all things being also equal) in case of A=Af (cf.

§ 1.1)

- for the mountings Q and C0, no reflection loss has to be taken into account since A=Af* < Af for the present revision of the software

- for the mounting RPTR’’ (resp. RPTL’’), the reflection loss is supposed (in all cases) to be equal to the reflection loss calculated for the mounting RPTR (resp. RPTL) (all things being also equal)

Step [I]

This step aims at taking into account the self noise of the silencer (noise produced by the airflow).

For dissipative silencers o

Bibliography (references) :

[I1]

[I2]

[I3]

[I4]

[I5]

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[I6]

[I7]

[I8]

[I9]

-

[I10]

[I11]

o

Comments: the self noise (acoustic power of flow noise Lw in dB ref 1E-12W) is basically computed at frequency steps of

1/1 octave.

for the mountings of the worksheet CODIS1 (R, R’’, C1,C2), the determination of the self noise is done according various models as shown in the tables below: model DN1 DN2 NF1 NF2 2081A source [I1] [I1] [I2]

[I2]

(*)

[I3]

(**) (***) model source source

2081B

[I4]

(**)(***)

2081R

[I5]

(**)(***)

2081C1

[I5]

(**)(***)

MUN

[I8]

(***)

(*) B (dB) and

(m) are input data (**) with an additional correction for temperature

(***) with an additional correction for pressure

Note: for the mounting C1,C2, the self noise is supposed to be equal to the self noise calculated for the mounting R,

R’ under the condition of an equal speed in the airways (all things being also equal). Furthermore a complementary model (2081C1) applies (according [I5] for the mounting C1only (not for other mountings indeed), and with A = Af*

<Af (see § 1.1) and see comments above (**)(***)

for the mountings of the worksheet CODIS2 (Q, C0), the determination of the self noise is done according various models as shown in the tables below: model

2081B

3733A1 3733A2 3733B

[I4]

(**)(***)

[I6]

(**)(***)

[I6]

(**)(***)

[I7]

(**)(***)

VER

[I9]

(***)

 for the models 2081 and 3733, a spectral correction is used according various models as shown in the tables below: model source

2081

[I5]

FRO

[I11]

3733

[I7]

Warning: at the time of the writing of this manual, all the consequences of the choice of one or the other model are not known with accuracy. The choice of the model can be done by the user allowing tests and feed-back.

For resonators o

Bibliography (references) :

[I12]

o

Comments: the self noise (acoustic power of flow noise Lw in dB ref 1E-12W) is basically computed at frequency steps of

1/1 octave.

for the mountings RPTR, RPTR’’, RPTL, RPTL’’, the determination of the self noise is done according various models as shown in the tables below: model FRO source [I12]

 for the model FRO, a spectral correction is used according various models as shown in the tables below: model 2081 FRO 3733 source [I5] [I11] [I7]

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Step [J]

This step aims at calculating the insertion loss without taking into account the self noise. o

Bibliography (references) :

[J1]

o

Comments :

The insertion loss without taking into account the self noise (Di’ in dB) is computed at frequency steps of 1/3 octave (then calculated per 1/1 octave frequency band for a reference acoustic power spectrum Lw0 in dB ref 1E-12W).

Di’ = Da * L + Dk + Dr

Step [K]

This step aims at calculating the insertion loss of the silencer including its self noise. o

Bibliography (references) :

[K1]

o

Comments :

The sound power level with silencer including self noise (Lw1 in dB ref 1E-12W) is basically computed at frequency steps of 1/1 octave (in reference to a reference acoustic power spectrum Lw0 ref 1E-12W).

Lw1 = 10 * log [10^ (0.1 * (Lw0 – Di’)) + 10^ (0.1 * Lw)]

Lw being the self noise (acoustic power of flow noise in dB ref 1E-12W)

The insertion loss taking into account the self noise (Di in dB) is basically computed at frequency steps of 1/1 octave (in reference to a reference acoustic power spectrum Lw0 ref 1E-12W).

Di = Lw0 – Lw1

In case of rectangular silencers, the obtained results are comparable with the standardized measurement: see NF EN ISO

7235 Acoustics - Laboratory measurement procedures for ducted silencers and air terminal units- Insertion loss, flow noise and total pressure loss (2004).

Step [L]

For resonators with pine tree splitters (only), this step (complementary, to be added between step [E] and step [F]) aims at the computation of the admittance in the plane of the outlet side of (the neck of) the chamber o

Bibliography (references) :

[L1]

-

[L2] o

Comments :

The software allows the prediction of performance of silencers with chambers containing absorbing material located either at the Rear (mounting RPTR, RPTR’’) or at Lateral (mountings RPTL, RPTL’’).

The determination of the propagation loss is done (depending on the choice of the user) for the following cases,

σx1/σy1=∞ (absorber locally reacting), depending on dlocal and hlocal for mountings RPTR, RPTR’’(resp.

dlocal and Hslocal for mountings RPTL, RPTL’’)

σx1/σy1=1 (absorber bulk reacting), depending on dbulk and hbulk for mountings RPTR, RPTR’’(resp. dbulkl

and Hsbulk for mountings RPTL, RPTL’’)

For high frequency, a correction (HF correction) can be applied depending on the choice of the user (see [L1], [L2])

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Aerodynamics:

Steps of the computation

Step [α]

All computations have been gathered in this single step for the sake of simplicity (this step aims at computing the total pressure

loss due to the silencer). o

Bibliography (references) :

[

α

1]

[

α

2]

-

[

α

3]

[

α

4]

[

α

5]

[

α

6]

[

α

7]

[

α

8] o

Comments :

The total pressure loss due to the silencer is computed with the hypothesis of a uniform air flow (supposed to not be rotational), taking into account the aerodynamics type upstream and downstream (*):

Aerodynamics type downstream R C

mountings R, R’’, C1, C2, RPTR,

RPTR’’, RPTL, RPTL’’ only *)

Rectangular

1/2 Circle

1/2 Circle for central splitters, 1/4 Circle for extreme inner lagging

1/4 Circle for extreme inner lagging

Aerodynamics type downstream

mountings R, R’’, C1, C2, RPTR,

RPTR’’, RPTL, RPTL’’ only *)

R

Rectangular

C

1/2 Circle

1/2 Circle for central splitters, 1/4 Circle for extreme inner lagging

P

Profiled according sketch, the dotted line showing either a symmetry plane or an impervious rigid back

(see fig.1.13)

1/4 Circle for extreme inner lagging

*for mountings Q and C0: A=Af* < Af for the present revision of the software

Fig.1.13

for the mountings of the worksheet CODIS1 (R, R’’, C1,C2), the determination of the total pressure loss is done is done according various models as shown in the tables below:

Model source

FRO

[

α

1]

MEC

[

α

2]

2081C1

[

α

6]

BER

[

α

3]

ISO

[

α

4]

[

α

7]

for the mounting R, the total pressure loss is supposed (in all cases) to be sufficiently close to the total pressure loss calculated for the mounting R’’ (all things being also equal).

for the mounting C1,C2, the total pressure loss is supposed to be equal to the total pressure loss calculated for the mounting

R under the condition of an equal speed in the airways (all things being also equal). Furthermore a complementary model

(2081C1) applies for mounting C1 only (not for other mountings indeed), (according [

α

6] for the mounting C1 with

A=Af*<A: see § 1.1).

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for the mountings of the worksheet CODIS2 (Q, CO), the determination of the total pressure loss is done is done according various models as shown in the tables below:

Model source

IDE

[

α5

]

for the mountings Q, C0, the determination of the total pressure loss is done (A=Af* < Af for the present revision of the software ) .

for the mountings RPTR, RPTR’’, RPTL, RPTL’’, the determination of the total pressure loss is done is done according various models as shown in the tables below:

Model source

IDE

[

α8

]

for the mounting RPTR (resp. RPTL), the total pressure loss is supposed (in all cases) to be sufficiently close to the total pressure loss calculated for the mounting RPTR’’ (resp. RPTL’’) (all things being also equal).

In case of rectangular silencers, the obtained results are comparable with the standardized measurement: see NF EN ISO 7235

Acoustics - Laboratory measurement procedures for ducted silencers and air terminal units- Insertion loss, flow noise and total pressure loss.

*a safety factor has to be used (by the user) for taking into account the inhomogeneity of the inflow (see [

α

2],[

α

5]) leading to predictions lower than on-site values

1. 3: How to use SILDIS

Operating conditions / security level / safety

See corresponding § in the chapter General considerations

For safety reasons, some cells of the original file provided to the user (as mentioned in the table below) for which input data are foreseen to be entered by the user are pre-filled with the value “1/0”, among the yellow cells for which the color orange is used (*).

Worksheet

[in COALA]

Cells

E13, J37

* something like that

[in COSIL]

D25, BD25, D37, D43,

D44, D45

X53, X54 (**)

** attention has to be paid to the fact that the considered

[in-out COPPA]

sheet is not included in the worksheets listed below

Worksheets

Regarding the COmputation of DIssipative Silencers, the software SILDIS is configurated in order to allow the user to access to 4 worksheets being linked as shown in fig.1.14 (the overview of the worksheets being shown in table below).

Fig. 1.14

Note: a partly common background is required for several steps of the computation schemes of different acoustic components

(insertion loss of a silencer, absorption coefficient / sound reduction index of a plane partition, sound reduction index of a duct wall...).

For this reason worksheets [in COALA] and [in COSIL] are distinct due to the existence of other calculations (by the means of

SILDIS) using the routine COALA (COmputation of Acoustic LAyers) but not using the routine COSIL (COmputation of SILencers).

For this reason also, concerning the worksheet [in COALA]:

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 a complementary set (set 0) and a rear atmosphere are displayed: they are none of interest for the COmputation of DIssipative

Silencers, they are none of interest for the COmputation of REsonant Silencers with Pine Tree splitters (only the case of an impervious rigid back at the rear of set1 applies for the COmputation of SILencers)

 data concerning series thin plates are displayed: they are none of interest for the COmputation of DIssipative Silencers, they are none of interest for the COmputation of REsonant Silencers with Pine Tree splitters (not taken into account whatever the input data concerning thin plates are in worksheet in [COALA])

Worksheet Suitable for mountings Input data Results

[in COALA]

all for sets, for reference spectrum particular conditions for the design of

[in COSIL]

all the silencer

[in-out CODIS1]

[in-out CODIS2]

[in-out COREPTR]

[in-out CORESPTL]

R, R’’, C1, C2

Q, C0

RPTR, RPTR’’

RPTL, RPTL’’

Input data, alerts and results: the key points

condition of propagation (of sound)

The best use of the software requires the knowledge of some key points in relation with:

--

-- indicators of performance (acoustics

& Aerodynamics) o the input data

See corresponding § in the chapter General considerations

As far as porous media, series cloths and series perforated protections are concerned, specific data bases (libraries) ( will ) allow the design to be made with in-built engineering data (constants) referred to as “Usual” in the worksheets of the software.

Warning: some properties of the presently referenced materials still not have been checked by reliable sources.

See also report

[PhRXX-015] Collection of soundproofing constructions systems: a companion to “User’s manual for the software SILDIS”

data base (library) for porous media

 contents of the library: 21 possible references of material layers

data base (library) for series cloths

 contents of the library: 21 possible references of material layers

Note: the cloth referenced RESISTAIR can be used (with an appropriate value for the flow resistance) for the simulation of losses of a thin plate (for example at normal incidence: due to the conditions of mounting)

data base (library) for series perforated protections

 contents of the library: 21 possible references of material layers o some alerts in case of input data involving a warning of the user o the place where (and the way) some results are presented

Those key points are reviewed worksheet per worksheet hereafter: the cells will be referred to thanks to their EXCEL’s coordinates

(column / line) in the following part of the present user’s manual.

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Worksheet [in COALA]

o

Input data :

Item

Cell for input

Foreseen action Comment

Language

Date

Project

Title

Temperature

C1

B3

E3

M3

D6 for English input E, for

French input F

Modification of the displayed date

Input a string

Input a string

Input a real number common value applicable to the fluid, to porous media, to series cloths, to perforated protection common value applicable to the fluid, to porous media, to series cloths, to perforated protection

Pressure

Maximum set index imax

D7

E13

Input a real positive number

Input an integer from 0 to

4

Reference

G18 to

K18

Select a material (in the proposed list) for each layer of interest for CODIS only: a possible inhomogeneity in directions parallel to and perpendicular to its surface (i.e. different properties - depending on the used model - in directions x and y) is considered for the porous medium of set 1 ( porous media of sets 2 to 4 being considered homogeneous)

Thickness

Reference

Incorporation of the series perforated protection (0/1)

G37 to J37

G45 to J45

G57 to J57

Input a real positive number

Select a reference of element (material in the proposed list) for each layer of interest

For NO press 0, for YES press 1

imax is the maximum set index taken into account for the computation, despite the status of the selection of the parameters related to sets with an index i> imax

Thickness G58 to J58

Input a real positive number taken into account for the computation as a non zero value only if 1 in cell just above

Reference

Incorporation of the series cloths (0/1)

T18 to

W18

T23 to

W23

Select a reference of element (material in the proposed list) for each layer of interest

For NO input 0, for YES input 1

Thickness

Lw0 only known per 1/1 octave frequency band (0/1)

Lw0

Lw0

T24 to

W24

R62

B65 to

K65

B70 to P70

B73 to P73

Input a real positive number

For NO input 0, for YES input 1

Input a real positive number as requested for a

1/1 octave band sound power level

Input a real positive number as requested for a

1/1 octave band sound power level taken into account for the computation as a non zero value only if 1 in cell just above

In case of input “0”: the input data of the table below are not applicable, the next table only must be filled

In case of Lw0 only known per 1/1 octave frequency band, default values are foreseen such as

Lw0 1/3 oct = Lw0 1/1 oct - 4.8 (dB)

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Comments :

 data of the second table (below) are not taken into account for the design of dissipative silencers (useful for other calculations in relation with the COmputation of Acoustic LAyers)

Item

Cell for input

Foreseen action Comment

Rear atmosphere ? (0/1)

Reference

(1/2)

Model of losses

Model of effective critical frequency

Number of identical plates

Thickness

O8

T31 to

W31

Y31

T36 to

W36

T37 to

W37

T38 to X38

T39 to

W39

For NO input 0, for YES input 1

Select a reference of element (material in the proposed list) for each layer of interest

Select a number (in the proposed list)

Select a model (in the proposed list)

Select a model (in the proposed list)

Input a real positive number

Input a real positive number not taken into account for CODIS select 1 (resp. 2) to get for set 0 the same plate as for set

1 (resp. set 2) taken into account for the computation as a non zero value only if a non zero value in cell just above

Note: temperature (resp. pressure) of cell D6 (resp. D7) also apply to thin plates

 data of the third table (below) are not modifiable by the user despite the displayed color of the cell

Item

Cell for input

Foreseen action Comment

For (test) room conditions below: temperature

For (test) room conditions below: pressure

S48

S49

Input a real number

Input a real positive number common value applicable to the fluid, to porous media, to series cloths, to perforated protection common value applicable to the fluid, to porous media, to series cloths, to perforated protection

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Worksheet [in COSIL]

o

Input data :

Item

d* (m)

Θ (°)

Ss (m)

Sa (m)

HF correction (0/1)

Mounting R’’ to get N’’ =

Mounting C0 ½ to get D0 ½

= (m)

Mounting C1to get D1 = (m)

Mounting C1to get D1-2d =

(m)

Mounting C1 ½ to get D1 ½

= (m)

Mounting C2 to get D2 =

(m)

Mounting C2 to get D2-2d =

(m)

Mounting C2 ½ to get D2 ½

= (m)

Mounting C3 to get D3 =

(m)

Mounting C3 to get D3-2d =

(m)

Mounting C3 ½ to get D3 ½

= (m)

Mounting CR to get D = (m)

For D (m) =

Mounting Q to get Q = (m)

Mounting Q to get Q-2d =

(m)

Mounting C0 to get D0 =

(m)

Mounting C0 to get D0-2d =

(m)

Mounting C0 to get d/a =

(m)

Mounting C0 to get

(d/a)bulk = (m)

Mounting RPT’’ to get N’’*

=

Cell for input

BD8

BD10

BD12

BD13

BD15

AI24

AL24

AM24

AQ24

Foreseen action

Input a positive real

Input a positive real

Input a positive real

Input a positive real

For NO input 0, for YES input 1

Input an integer from 1 to

imax

Comment

For the COmputation of REsonant Silencers with Pine

Tree splitters only

Limit set index ilim

To get h/(d+h) =

To get d/h =

To get (d/h)local =

To get (d/h)bulk =

Half airway h (m)

Half airway h* (m)

D18

G24

H24

J24

K24

O24

Q24

T24

U24

W24

Z24

AA24

AC24

AF24

AG24

AR24

AU24

AV24

AW24

AX24

BH24

D25

BD25

Input a positive real

Input a positive real

Input a positive real <1

Input a positive real <1

Input a positive real

Input a positive real

Input a positive real

Input a positive real

Input a positive real

Input a positive real

Input a positive real

Input a positive real

Input a positive real

Input a positive real

Input a positive real

Input a positive real

Input a positive real

Input a positive real

Input a positive real

Input a positive real

Input a positive real

Input a positive real

Input a positive real

Input a positive real

Input a positive real

imax-

ilim

imax (

being the total number of cloths and perforated protections accounted as porous media)

If a particular value of h/(d+h) is wished

If a particular value of d/h is wished

If a particular value of

(d/h)local is wished

If a particular value of

(d/h)bulk is wished

If a particular value of N’’ is wished (given B)

If a particular value of D0

½ is wished

If a particular value of D1 is wished

If a particular value of D1-

2d is wished

If a particular value of D1

½ is wished

If a particular value of D2 is wished

If a particular value of D2-

2d is wished

If a particular value of D2

½ is wished

If a particular value of D3 is wished

If a particular value of D3-

2d is wished

If a particular value of D3

½ is wished

If a particular value of D is wished

If a particular value of Q is wished

If a particular value of Q-

2d is wished

If a particular value of D0 is wished

If a particular value of D0-

2d is wished

If a particular value of a/h is wished

If a particular value of

(a/h)bulk is wished

If a particular value of

N’’* is wished (given B)

If a particular value of h/(d+h) resp. (d/h),

(d/h)local…is wished then input the value given in

G25 (resp. H25, J25…)

If a particular value of

N’’* is wished then input

For the COmputation of

DIssipative Silencers only

(no compulsory input

)data

No compulsory input data

For the COmputation of

REsonant Silencers with

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Mass flow rate

Mounting R’’ to get N’’ =

Mounting CR to get Ncr =

Mounting RPT’’ to get N’’*

=

D37

O42

AL42

BHQ42

Input a real

Input a positive real

Input a positive real

Input a positive real the value given in AQ25 Pine Tree splitters only

A positive value is related to a direction of airflow equal to the direction of propagation of sound, a negative value is related to a direction of airflow opposite to the direction of propagation of sound

If a particular value of N’’

For the COmputation of is wished (given h)

DIssipative Silencers only

If a particular value of Ncr is wished (given h)

(no compulsory input data)

If a particular value of

N’’* is wished (given h*)

For the COmputation of

REsonant Silencers with

Pine Tree splitters only

No compulsory input data

Width B (m)

Height H (m)

D43

D44

Input a positive real

Input a positive real

If a particular value of N’’

(resp. N’’*) is wished then input the value given in

O43 (resp. AQ43). If the extrapolation from mounting R to a particular mounting is wished then input the value given in

R43 (resp. U43, AA43…)

If the extrapolation to a particular mounting is wished then input the value given in R44 (resp.

U44, AA44…)

Without aerodynamics extremities Length L (m)

Model of reflection loss

Model of by-pass correction

Aerodynamics upstream

Aerodynamics downstream

D45

G47

E51 to G51

D54

D55

Input a positive real

Select a model (in the proposed list)

Select a model (in the proposed list)

Select a model (in the proposed list)

Select a model (in the proposed list)

Not applicable for mountings Q, C0

Not applicable for mountings Q, C0

Not applicable for mountings Q, C0

The direction of flow is the direction of the foot of the pine tree when the branches shape of the splitters is considered (0/1)

BH59

For NO input 0, for YES input 1

For the COmputation of REsonant Silencers with Pine

Tree splitters only

Roughness of lining Δ (m)

Model of total pressure loss

Model of total pressure loss

For model NF2 only B (dB)

For model NF2 only



(m)

AW61

V63

BH63

E64

G64

Input a positive real

Select a model (in the proposed list)

Select a model (in the proposed list)

Input a positive real

Input a positive real

For the COmputation of DIssipative Silencers with mountings Q, C0 only

For the COmputation of DIssipative Silencers with mountings R, R’’, C0 ½, C1, C1 ½, C2, C2 ½, C3, C3

½, CR only

For the COmputation of REsonant Silencers with Pine

Tree splitters only

For the COmputation of DIssipative Silencers with mountings R, R’’, C0 ½, C1, C1 ½, C2, C2 ½, C3, C3

½, CR only

For all models 2081,3733,

FRO only spectral correction model

Model for the flow acoustic power o

Comments :

Item

G65

V65,AW65

Select a model (in the proposed list)

Select a model (in the proposed list)

Used for the interpolation of a ponderation curve

(generally of secondary importance)

For the COmputation of DIssipative Silencers only

STOP ilim>imax not applicable

Cell

D19, E19

G48

Foreseen action

--

--

Comment

In case of such an alert, the input value for ilim has to be changed, such as ilim

imax (*)

In case of such an alert, the input value for the model of reflection loss has to be changed

*the use of results obtained with worksheets including at least 1 alert is highly discouraged

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Worksheets [in-out CODIS1], [in-out CODIS2], in-out CORESPTR], [in-out CORESPTL]

o

Input data :

Item

Cell for input

Foreseen action Comment

Condition of propagation W182

Select a model (in the proposed list) among the possible conditions of propagation in porous medium of set 1 (for the COmputation of DIssipative

Silencers σx1/σy1=∞, σx1/σy1=1, σx1/σy1=var.; for the

COmputation of REsonant Silencers with Pine Tree splitters only

σx1/σy1=∞, σx1/σy1=1

) o

Comments :

Item

STOP r < rmini: σx1/σy1 ≠ ∞ discouraged

reflection loss noise

Cell

E14

R50, V97

Foreseen action

--

--

Comment

In case of such an alert, the input value for ilim has to be changed, such as ilim

imax (*)

In case of such an alert, the flow resistance of the porous medium of set 1 has to be increased if results for non local absorber are wished (*)

*the use of results obtained with worksheets including at least 1 alert is highly discouraged o

Main displays of the results :

total pressure loss: see lines 98 to 100

Note: the following equation is considered for the definition of total pressure loss coefficients

f,

f*,

p:

pt =

p . 0.5 .



(Vp

2

=

f . 0.5 .



(Vf

2

=

f * . 0.5 .



(Vf*

2

pt: total pressure loss (Pa)

 density of fluid (kgm-3)

Vp: speed in the area Ap (ms-1)

Vf: speed in the area Sf (ms-1)

Vf*: speed in the area Sf (ms-1)

insertion loss without flow: see line 105 per 1/1 octave frequency band and in terms of A weighted global value with reference to the reference acoustic power spectrum.

Note: those results are intermediate/complementary results not equal (generally speaking) to the insertion loss with flow and self noise that the user has to use as the only reliable indicator of performance of the performance of the silencer. Those results are only displayed in order to allow the evaluation of the impact of airflow - other than self noise - by the means of a comparison with results displayed line 106.

insertion loss with flow without flow noise (Di’): see line 106 per 1/1 octave frequency band and in terms of A weighted global value with reference to the reference acoustic power spectrum.

Note 1: those results are intermediate/complementary results not equal (generally speaking) to the insertion loss with flow and self noise that the user has to use as the only reliable indicator of performance of the performance of the silencer. Those results are only displayed in order to allow the evaluation of the impact:

- of airflow - other than self noise - by the means of a comparison with results displayed line 105

- of flow noise by the means of a comparison with results displayed line 162

Note 2: since the insertion loss is predicted from the sum of the longitudinal attenuation, a bypass correction and reflection loss, the results corresponding to the different terms of the sum are also displayed in order to allow the evaluation of the impact of each one (see table below).

Term of the sum

longitudinal attenuation by pass correction insertion loss without self

Cells for display

A108 to L127

M108 to X127

A129 to L148

M129 to X148

Notation

Da.L

Dk

Dr

D’i= Da.L+ Dk+ Dr

Comment curve and table of results per 1/3 octave band, per

1/1 octave frequency band and in terms of A weighted global value with reference to the reference acoustic power spectrum

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self noise (acoustic power of flow noise): see line 153 per 1/1 octave frequency band and in terms of A weighted global value

not A-weighted acoustic power with silencer (Lw1): see line 156 per 1/1 octave frequency band and in terms of A weighted global value with reference to the reference acoustic power spectrum.

A-weighted acoustic power with silencer: see line 157 per 1/1 octave frequency band

insertion loss with flow and self noise (Di): see line 162 per 1/1 octave frequency band and in terms of A weighted global value with reference to the reference acoustic power spectrum.

acoustic power without silencer (Lw0) and acoustic power with silencer including self noise (Lw1) versus frequency

see lines 164 to 184 columns A to F per 1/1 octave frequency band and in terms of A weighted global value with reference to the reference acoustic power spectrum.

insertion loss with flow without self noise (Di’) and insertion loss with flow and self noise (Di) versus frequency see

lines 164 to 184 columns G to L per 1/1 octave frequency band and in terms of A weighted global value with reference to the reference acoustic power spectrum.

1.4: Examples of computation with SILDIS

Example 1.4.1 dissipative silencer with a rectangular cross section

Envisaged application

It is wished to compute the acoustic and aerodynamic performances of a dissipative silencer with a rectangular cross section (width

B=1200mm [1], height H=2000mm [2], length L=1500mm [3]), having rectangular edged [4] splitters of thickness 2d such as 2d-

2d’1=200mm [5] with a open area ratio of 50% [6] made of one [7] homogeneous in directions parallel to and perpendicular to its surface bulk absorber [8] having the reference DEMO in the database for porous media of SILDIS [9] with [10] a cloth of thickness d’1=5/100 mm [11] having the reference DEMO in the series cloths database of SILDIS [12] without perforated protection [13]

It is foreseen to use the silencer with an air flow rate of 24.1 kg/s [14] at 20 °C [15] at a pressure of 101325 Pa [16].

It is decided to take into account a limitation of the propagation loss for L>1m [17] and to take into account the reflection loss [18].

The reference spectrum is supposed of the type “pink noise” [19] with a sound power level of 130 dB/oct [20]

It is chosen to predict the self noise of the silencer in the way described with the model referred to as 2081B [21]

It is chosen to predict the back pressure with the model referred to as FRO [22]

Input data

The input data required for the computation are listed hereafter in reference with the above data (see figures in brackets in the previous

§, used as placemarks for explaining the selection below).The input cells will be referred to thanks to their EXCEL’s coordinates

(column / line) in the following part of the present user’s manual.

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Worksheet [in COALA] for example 1.4.1 and for example 1.4.2a and for example 1.4.2b

Item

Cell for input

Foreseen action (see

§1.3)

Input

See placemark / comment

Temperature D6 20 [15]

Pressure

Maximum set index imax

Reference

Thickness

Incorporation of the series perforated protections (0/1)

Reference

Incorporation of the series cloths (0/1)

Thickness

Lw0 only known per 1/1 octave frequency band (0/1)

Lw0

D7

E13

J18 to K18

J37

J57

W18

W23

W24

R62

B65 to

K65

Input a real number

Input a real positive number

Input an integer from 1 to

4

Select a reference

(material in the proposed list) for each layer of interest

Input a real positive number

For NO press 0, for YES press 1

Select a material (in the proposed list) for each layer of interest

For NO input 0, for YES input 1

Input a real positive number

For NO input 0, for YES input 1

Input a real positive number as requested for a

1/1 octave band sound power level

101325

1

DEMO

0.1

0

DEMO

1

0.00005

1

130

[16]

[7]

[8],[9]

[5]

[13]

[12]

[10]

[11]

[20]

[20]

Worksheet [in COSIL] for example 1.4.1 only

Item

Limit set index ilim

Cell for input

D18

Foreseen action (see

§1.3)

Input an integer from 1 to

imax h/(d+h)

Half airway

Mass flow rate

Width B (m)

Height H (m)

Length L (m)

G24

D25

D37

D43

D44

D45

Input a positive real <1

Input a positive real

Input a real

Input a positive real

Input a positive real

Model of reflection loss

Model of by-pass correction for L>1m

Aerodynamics upstream

Aerodynamics downstream

Model of total pressure loss

Model for the flow acoustic power

G47

F51

D54

D55

V63

V65

Input a positive real

Select a model (in the proposed list)

Select a model (in the proposed list)

Select a model (in the proposed list)

Select a model (in the proposed list)

Select a model (in the proposed list)

Select a model (in the proposed list)

Worksheet [in-out CODIS1] for example 1.4.1 only

Item

Cell for input

Foreseen action (see

§1.3)

Condition of propagation W182

Select a model (in the proposed list)

Input

1

0.5

=G25 i.e. 0.10005

24.1

1.2

2

1.5

MUL

FRO

R

R

FRO

2081B

Input

σx1/σy1=1

See placemark

[7]

[6]

[14]

[1]

[2]

[3]

[18]

[17]

[4]

[4]

[22]

[21]

See placemark

[8]

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Worksheet [in-out COPPA] for example 1.4.1 and for example 1.4.2a and for example 1.4.2b

Item

Cell for input

Foreseen action (see

§1.3)

Input See placemark

Size of the partition along the x-direction

Size of the partition along the z-direction

X53

X54

Input a positive real

Input a positive real

1

1

(*)

(*)

*see § 1. 3: How to use SILDIS Operating conditions / security level / safety

Screenshots of the worksheets (for the example of computation)

Screenshot of worksheet [in COALA] for example 1.4.1 and for example 1.4.2a and for example 1.4.2b

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Screenshot of worksheet [in COSIL] for example 1.4.1

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Screenshot of worksheet [in-out CODIS1] for example 1.4.1

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Example 1.4.2a: dissipative silencer with a square cross section

Envisaged application

It is wished to compute the acoustic and aerodynamic performance of a dissipative silencer with a square cross section, the area of the duct upstream and downtream (above and below the silencer) being not equal to the area of the overall section of the silencer

(overall width=overall height Q=1100mm [1’]) but being equal to the inner width, length L=1500mm [3]), having a lining of thickness d such as d-d’1=100mm [5] made of one [7] homogeneous in directions parallel to and perpendicular to its surface bulk absorber [8] having the reference DEMO in the database for porous media of SILDIS [9] with [10] a cloth of thickness d’1=5/100 mm [11] having the reference DEMO in the series cloths database of SILDIS [12] without perforated protection [13]

It is foreseen to use the silencer with an air flow rate of 24.1 kg/s [14] at 20 °C [15] at a pressure of 101325 Pa [16].

It is decided to take into account a limitation of the propagation loss for L>1m [17].

The reference spectrum is supposed of the type “pink noise” [19] with a sound power level of 130 dB/oct [20]

It is chosen to predict the self noise of the silencer in the way described with the model referred to as 2081B [21]

A roughness of 1 mm is assumed for the lining [23])

Input data

The input data required for the computation are listed hereafter in reference with the above data (see figures in brackets in the previous

§, used as placemarks for explaining the selection below).The input cells will be referred to thanks to their EXCEL’s coordinates

(column / line) in the following part of the present user’s manual.

Worksheet [in COALA] for example 1.4.2a

See corresponding § for

example 1.4.1

Worksheet [in COSIL] for example 1.4.2a only

Item

Limit set index ilim

Mounting Q to get Q = (m)

Airway h (m)

Mass flow rate

Width B (m)

Height H (m)

Length L (m)

Model of by-pass correction for L>1m

Roughness of lining

Model for the flow acoustic power

Cell for input

D18

AQ24

D25

D37

D43

D44

D45

F51

AW61

AW65

Foreseen action (see

§1.3)

Input an integer from 1 to

imax

Input a positive real

Input a positive real

Input a real

Input a positive real

Input a positive real

Input a positive real

Select a model (in the proposed list)

Input a real

Select a model (in the proposed list)

Input

1

1.100

=AQ25 i.e. 0.44995

24.1

=AQ43 i.e. 0.99493

=AQ44 i.e. 0.99493

1.5

FRO

0.001

3733B

Worksheet [in-out CODIS2] for example 1.4.2a and for example 1.4.2b only

Item

Condition of propagation

Cell for input

W182

Foreseen action (see

§1.3)

Select a model (in the proposed list)

Input

σx1/σy1=1

See placemark

[7]

[1’]

[14]

[3]

[17]

[23]

[21]

See placemark

[8]

Worksheet [in-out COPPA] for example 1.4.2a

See corresponding § for

example 1.4.1

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Screenshots of the worksheets (for the example of computation)

Screenshot of worksheet [in COALA]

See corresponding § for

example 1.4.1

Screenshot of worksheet [in COSIL] for example 1.4.2a

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Screenshot of worksheet [in-out CODIS2] for example 1.4.2a

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Example 1.4.2b dissipative silencer with a circular cross section

Envisaged application

It is wished to compute the acoustic and aerodynamic performance of a dissipative silencer with a circular cross section, the area of the duct upstream and downtream (above and below the silencer) being not equal to the area of the overall section of the silencer

(overall diameter D0=1400mm [1’’]) but being equal to the inner diameter, length L=1500mm [3]), having a lining of thickness d such as d-d’1=100mm [5] made of one [7] homogeneous in directions parallel to and perpendicular to its surface bulk absorber [8] having the reference DEMO in the database for porous media of SILDIS [9] with [10] a cloth of thickness d’1=5/100 mm [11] having the reference DEMO in the series cloths database of SILDIS [12] without perforated protection [13]

It is foreseen to use the silencer with an air flow rate of 24.1 kg/s [14] at 20 °C [15] at a pressure of 101325 Pa [16].

It is decided to take into account a limitation of the propagation loss for L>1m [17].

The reference spectrum is supposed of the type “pink noise” [19] with a sound power level of 130 dB/oct [20]

It is chosen to predict the self noise of the silencer in the way described in the model referred to as 2081B [21]

A roughness of 1 mm is assumed for the lining [23])

Input data

The input data required for the computation are listed hereafter in reference with the above data (see figures in brackets in the previous

§, used as placemarks for explaining the selection below).The input cells will be referred to thanks to their EXCEL’s coordinates

(column / line) in the following part of the present user’s manual.

Worksheet [in COALA] for example 1.4.2b

See corresponding § for

example 1.4.1

Worksheet [in COSIL] for example 1.4.2b only

Item

Limit set index ilim

Cell for input

D18

Foreseen action (see

§1.3)

Input an integer from 1 to

imax

Input

1

Mounting C0 to get D0 =

(m)

Half airway h (m)

Mass flow rate

Width B (m)

Height H (m)

Length L (m)

Model of by-pass correction for L>1m

Roughness of lining

Model for the flow acoustic power

AU24

D25

D37

D43

D44

D45

F51

AW61

AW65

Input a positive real

Input a positive real <1

Input a real

Input a positive real

Input a positive real

Input a positive real

Select a model (in the proposed list)

Input a real

Select a model (in the proposed list)

1.4

=AD25 i.e. 0.53169

24.1

=AV43 i.e. 1.15912

=AV 44 i.e. 1.15912

1.5

FRO

0.001

3733B

Worksheet [in-out CODIS2] for example 1.4.2a and for example 1.4.2b only

Item

Condition of propagation

Cell for input

W182

Foreseen action (see

§1.3)

Select a model (in the proposed list)

Input

σx1/σy1=1

See placemark

[7]

[1’’]

[14]

[3]

[17]

[23]

[21]

See placemark

[8]

Worksheet [in-out COPPA] for example 1.4.2b

See corresponding § for

example 1.4.1

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Screenshots of the worksheets (for the example of computation)

Screenshot of worksheet [in COALA]

See corresponding § for

example 1.4.1

Screenshot of worksheet [in COSIL] for example 1.4.2b

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Screenshot of worksheet [in-out CODIS2] for example 1.4.2b

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1.5: Illustrations of effects taken into account with SILDIS

Introduction

The prediction of acoustic performances of dissipative silencers with the software SILDIS is founded on a scientific and technical background as presented in § 1.2 of this user’s manual, combining various knowledges in relation with physics. Some (future possible) users may not be perfectly familiar with some aspects of this background: in order to be anyway in a position of making the best use of this calculation tool, attention has to be paid by such users to some particular effects taken into account for the predictions thanks to illustrations (applying for a rectangular cross section) given in this section of the user’s manual. The intention is not to give a comprehensive list of the various effects of each parameter that may (alone or coupled with others) influence the acoustic p erformance of a dissipative silencer, what would be very difficult to do. The goal is (thanks to examples): highlighting major key-points

(considered separately) of the design of a dissipative silencer, given some known laws of the physics, some of the input data being chosen in order to be as demonstrative as possible, given the plausible field of typical engineering applications.

All the numerical results below have been obtained using the software SILDIS with some post treatment for comparisons notably

(some of those results can not be obtained by the user in the presented form for a sake of simplicity of the software).

Effects of the properties of a porous medium in a non-laminated lining (illustration 1.5.1)

Imput data: a silencer is considered at (test) room pressure and temperature, with an open area ratio of 50%, the splitters having transverse solid partitions inhibiting the sound propagation along the duct axis inside the non-laminated lining consisting of a single porous medium having (at room temperature) a flow resistivity in the direction normal to the axis of the duct σy1 varying from 8 to 72 kNsm-4, a porosity ø=0.95 (model M76), with a thickness d=0.1m. No series cloth is considered, no series perforated protection is considered.

Illustration of one of the effects: see below the prediction of the propagation loss depending on the flow resistivity of the porous medium (see key in the graph)

propagation loss Da

45

40

35

30

25

20

15

10

5

8kNsm-4

12kNsm-4

16kNsm-4

24kNsm-4

48kNsm-4

72kNsm-4

0

1 10 100

f(Hz)

1000 10000 100000 f1/3oct (Hz)

8kNsm-4

12kNsm-4

16kNsm-4

24kNsm-4

48kNsm-4

72kNsm-4

25

0,1

0,1

0,1

0,2

0,4

0,5

31,5

0,1

0,2

0,2

0,3

0,6

0,8

40

0,2

0,3

0,4

0,5

0,9

1,1

50

0,3

0,4

0,6

0,8

1,3

1,6

63

0,5

0,7

0,9

1,2

1,9

2,1

80

0,8

1,1

1,4

1,8

2,6

2,6

100

1,3

1,7

2,1

2,8

3,4

3,2

125

2,1

2,7

3,3

4,0

4,3

3,8

160

3,5

4,3

4,9

5,6

5,2

4,3

200

5,9

6,8

7,3

7,6

6,1

4,9

250

9,8

10,7 16,3 23,2 29,6 32,7 32,2 31,6 33,7 32,2 19,9 12,7

10,6 15,0 19,8 24,1 26,9 28,7 30,9 34,5 32,8 21,6 13,6

9,8 12,2 14,8 17,6 20,4 23,7 28,1 33,0 33,7 24,9 15,2

7,0

5,5

315 400 500 630 800 1k 1,25k 1,6k 2k 2,5k 3,15k

16,2 26,0 37,6 42,6 37,0 31,1 30,3 32,0 18,1 11,4 7,6

8,0

6,3

9,2

7,3

10,7 12,9 16,0 20,1 25,0 30,0 31,1 19,9

8,6 10,2 12,4 15,4 19,5 24,7 29,9 25,0

7,8

8,1

8,8

11,0

13,2

4k

4,4

4,7

4,9

5,2

6,1

7,1

5k

2,8

2,9

2,9

3,1

3,5

3,9

6,3k

1,7

1,8

1,8

1,9

2,1

2,3

8k

1,1

1,1

1,1

1,1

1,2

1,3

10k 12,5k 16k

0,7 0,4 0,3

0,7

0,7

0,7

0,8

0,8

0,4

0,4

0,4

0,5

0,5

0,3

0,3

0,3

0,3

0,3

Comment: the choice of the flow resistivity of the porous medium influences sometimes considerably the acoustic performance of the silencer (at least: for some frequencies). In particular, the choice of a flow resistivity of the porous medium too big compared with the optimum required - as far as acoustics is concerned - can lead to a degradation of the performance for frequencies possibly within the range of interest.

For a given porous medium, an increase of the density involves - generally speaking - an increase of the flow resistivity (everything else supposed to be equal): for example, attention has to be paid to the consequences of the use (in some locations…) of high

20k

0,2

0,2

0,2

0,2

0,2

0,2

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density rock wools using bonded short fibers producing possibly linings with a high flow resistance in some cases (especially

when nothing is known regarding the properties of those materials in terms of flow resistivity, porosity…).

Effects of the properties of porous media in a laminated lining (illustration 1.5.2)

Imput data: a silencer is considered at (test) room pressure and temperature, with an open area ratio of 50%, the splitters having transverse solid partitions inhibiting the sound propagation along the duct axis inside the laminated lining consisting of:

- a surface layer being a porous medium having (at room temperature) a flow resistivity in the direction normal to the axis of the duct σy1=72 kNsm-4, a porosity ø=0.95 (model M76), with a thickness ds=0.02m. No series cloth is considered, no series perforated protection is considered.

- a core layer being a porous medium having (at room temperature) a flow resistivity in the direction normal to the axis of the duct

σy1=12 kNsm-4, a porosity ø=0.95 (model M76), with a thickness dc=0.08m. No series cloth is considered, no series perforated protection is considered.

Illustration of one of the effects: see below the prediction of the propagation loss of the mix (laminated lining) and the comparison with a non-laminated lining made (with a thickness d=ds+dc=0.10m) either 100 % of the material of the surface layer or 100 % of the material of the core layer (see key in the graph)

propagation loss Da

40

35

30

25

20

15

12kNsm-4

72kNsm-4 mix

10

5

0

1 10 100

f(Hz)

1000 10000 100000 f1/3oct (Hz)

12kNsm-4

72kNsm-4 mix

25

0,1

0,5

0,3

31,5

0,2

0,8

0,5

40

0,3

1,1

0,8

50

0,4

1,6

1,2

63

0,7

2,1

1,8

80

1,1

2,6

2,6

100

1,7

3,2

3,7

125

2,7

3,8

4,9

160

4,3

4,3

6,1

200

6,8

4,9

7,4

250 315 400 500 630

10,7 16,3 23,2 29,6 32,7

5,5 6,3 7,3 8,6 10,2

8,6 9,5 10,3 10,9 11,5

800 1k 1,25k 1,6k 2k 2,5k 3,15k

32,2 31,6 33,7 32,2 19,9 12,7

12,4 15,4 19,5 24,7 29,9 25,0

12,3 13,9 17,2 22,5 28,4 26,8

7,8

13,2

13,3

4k

4,7

7,1

7,0

5k

2,9

3,9

3,9

6,3k

1,8

2,3

2,3

8k

1,1

1,3

1,3

10k 12,5k 16k

0,7

0,8

0,8

0,4

0,5

0,5

0,3

0,3

0,3

Comment: in case of a laminated lining, the choice of the flow resistivity of the porous media influences sometimes considerably the

20k

0,2

0,2

0,2 acoustic performance of the silencer (at least: for some frequencies). In particular, the choice of a flow resistivity of the porous medium for the surface layer too big compared with the optimum required - as far as acoustics is concerned - can (even with a thickness small compared to the total thickness of the lining) lead to a degradation of the performance for frequencies possibly within the range of interest.

See also the last paragraph of illustration 1.5.1

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Effects of the conditions of propagation of sound inside the lining (illustration 1.5.3)

Imput data: a silencer is considered at (test) room pressure and temperature, with an open area ratio of 50%, the splitters being filled with a single porous medium having (at room temperature) a flow resistivity in the direction normal to the axis of the duct

σy1=22332Nsm-4, a porosity ø=0.95 (model M76), with a thickness d=0.05m. No series cloth is considered, no series perforated protection is considered. The longitudinal attenuation with a length L=1.5m is considered for the following cases, σx1 being the flow resistivity of the porous medium in the direction parallel to the axis of the duct: σx1/σy1=∞ (absorber locally reacting), (*) σx1/σy1=1

(absorber bulk reacting), σx1/σy1=var. with var.=0.5

Illustration of one of the effects: see below the prediction of the propagation loss depending on the conditions of propagation of sound inside the porous medium (see key in the graph)(*)

longitudinal attenuation Da*L

120

σx1/σy1=∞ σx1/σy1=1 σx1/σy1=var.

100

80

60

40

20

0

1 10 100

f(Hz)

1000 10000 100000 f 1/3 oct (Hz)

σx1/σy1=∞

σx1/σy1=1

σx1/σy1=var.

25

0,1

0,1

0,2

31,5

0,1

0,2

0,2

40

0,2

0,3

0,4

50

0,3

0,5

0,6

63

0,5

0,7

1,0

80

0,8

1,1

1,5

100

1,2

1,8

2,3

125

2,0

2,8

3,6

160

3,1

4,4

5,5

200

4,9

6,7

8,2

250

7,7

315

12,2

400

19,4

500

30,6

10,1 15,0 22,1 31,6

11,8 16,5 22,7 30,2

630 800 1000 1250 1600 2000 2500 3150 4000 5000 6300 8000 10000 12500 16000 20000

47,1 68,8 91,2 102,5 99,0 95,0 99,2 92,5 54,6 36,4 22,2 13,7 8,4 5,2 3,2 2,0

43,6 58,0 74,0 88,6 92,8 85,4 76,5 66,5 50,8 34,3 22,6 14,9 9,9 6,5 4,3 2,9

38,9 49,0 60,8 74,3 84,8 80,4 69,4 58,6 47,1 34,4 23,6 15,9 10,7 7,2 4,8 3,3

Comment: the conditions of propagation inside the porous medium of the lining (*) influences sometimes considerably the acoustic performance of the silencer (at least: for some frequencies). In particular, an overestimation of the (not always known) flow resistivity of the porous medium in the direction parallel to the axis of the duct can lead to a degradation of the performance for frequencies possibly within the range of interest.

Attention has to be paid to the question of the possibility (or not, given the consequences in terms of construction modalities and corresponding costs) of an inhibition of the axial wave propagation inside the lining with transverse solid partitions.

* the case of an axial wave propagation inhibited by transverse very thick metal sheets (with a very short distance between them) acting as partitions is also referred to as σx1/σy1=∞ whatever the properties of the absorber are (else: no such partitions is considered)

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Effects of the by-pass correction (illustration 1.5.4)

Imput data: a silencer is considered at (test) room pressure and temperature, with an open area ratio of 50%, the splitters having no transverse solid partitions being filled with a single porous medium homogeneous in directions parallel to and perpendicular to its surface, having (at room temperature) a flow resistivity in the direction normal to the axis of the duct σy1=12000Nsm-4, a porosity

ø=0.95 (model M76), with a thickness d=0.1m and a length L=2m. No series cloth is considered, no series perforated protection is considered. The longitudinal attenuation is considered with or without the by-pass correction.

Illustration of one of the effects: see below the prediction of the longitudinal attenuation depending on the existence or not of the limitation of the propagation loss (see key in the graph)

longitudinal attenuation Da*L

70 without with

60

50

40

30

20

10

0

1 10 100

f(Hz)

1000 10000 100000 f1/3oct (Hz) without with

25

0,3

0,3

31,5

0,5

0,5

40

0,8

0,8

50

1,2

1,2

63

1,9

1,9

80

3,0

3,0

100

4,5

4,5

125

6,8

6,8

160 200

10,2 14,9

10,2 14,9

250 315 400 500 630

21,3 29,3 38,9 49,2 57,9

19,3 25,0 32,4 40,4 46,5

800 1k 1,25k 1,6k 2k 2,5k 3,15k

60,4 56,8 51,9 45,6 34,8 23,5 15,4

4k

10,1

46,7 45,5 42,9 39,1 30,6 21,4 15,4 10,1

5k

6,6

6,6

6,3k

4,3

4,3

8k

2,9

2,9

10k 12,5k 16k

1,9 1,3 0,8

1,9 1,3 0,8

Comment: the existence or not of a limitation of the propagation loss influences sometimes considerably the acoustic performance of

20k

0,6

0,6 the silencer (at least: for some frequencies). The influence of the conditions of propagation inside the lining has already b een pointed out in a previous illustration: attention has also to be paid to the imperfection of the interface between the lining and the duct (leak occurring by-pass)

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Effects of the reflection loss (illustration 1.5.5)

Imput data: a silencer is considered at (test) room pressure and temperature, with an open area ratio of 50%, the splitters having no transverse solid partitions being filled with a single porous medium homogeneous in directions parallel to and perpendicular to its surface, having (at room temperature) a flow resistivity in the direction normal to the axis of the duct σy1=12000Nsm-4, a porosity

ø=0.95 (model M76), with a thickness d=0.1m and a length L=1m. No series cloth is considered, no series perforated protection is considered. The insertion loss is considered with or without the reflection loss.

Illustration of one of the effects: see below the prediction of the insertion loss depending on the existence or not of the reflexion loss

(see key in the graph)

insertion loss Di

35 without with

30

25

20

15

10

5

0

1 10 100

f(Hz)

1000 10000 100000 f1/3oct (Hz) without with

25

0,2

0,4

31,5

0,3

0,4

40

0,4

0,6

50

0,6

0,8

63

1,0

1,3

80

1,5

1,8

100

2,3

2,6

125

3,4

3,7

160

5,1

5,4

200

7,5

7,8

250 315 400 500 630

10,7 14,7 19,5 24,6 29,0

11,1 15,2 20,2 25,5 30,0

800 1k 1,25k 1,6k 2k 2,5k 3,15k

30,2 28,4 26,0 22,8 17,4 11,8 7,7

31,7 30,5 28,6 26,0 21,2 15,8 11,8

4k

5,1

9,2

5k

3,3

7,5

6,3k

2,2

6,4

8k

1,5

5,6

10k 12,5k 16k

1,0 0,7 0,4

5,1 4,8 4,6

20k

0,3

4,5

Comment: the existence or not of the reflection loss influences the acoustic performance of the silencer (at least: for some frequencies).

One should keep in mind that in the evaluation of the reflection loss includes the effect of higher modes with increased prop agation loss in the air passage in the testing conditions used for the used data pool: different on site conditions may involve different reflection loss effects.

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Effects of temperature (illustration 1.5.6)

Imput data: a silencer is considered (at (test) room pressure) on the one hand at (test) room temperature and on the other hand at high temperature with an open area ratio of 50%, the splitters having transverse solid partitions inhibiting the sound propagation along the duct axis inside the non-laminated lining consisting of a single porous medium having (at room temperature) a flow resistivity in the direction normal to the axis of the duct σy1=12400 Nsm-4, a porosity ø=0.95 (model M76), with a thickness d=0.05m. No series cloth is considered, no series perforated protection is considered.

Illustration of one of the effects: see below the prediction of the propagation loss depending on the temperature (see key in the graph)

propagation loss Da

120

20 °C 300 °C 600 °C

100

80

60

40

20

0

1 10 100

f(Hz)

1000 10000 100000 f1/3oct (Hz)

20 °C

300 °C

600 °C

25

0,0

0,0

0,0

31,5

0,1

0,1

0,1

40

0,1

0,1

0,1

50

0,1

0,1

0,1

63

0,2

0,2

0,2

80

0,3

0,3

0,3

100

0,5

0,5

0,5

125

0,9

0,8

0,8

160

1,4

1,3

1,3

200

2,3

2,0

2,0

250

3,8

3,1

3,0

315

6,3

4,9

4,5

400 500

10,5 17,5

7,6

6,7

11,6

9,7

630 800 1k 1,25k 1,6k

29,5 49,9 80,5 99,9 77,0

2k

59,0

2,5k

55,0

3,15k

62,9

4k

32,7

5k

20,8

6,3k

15,0

17,9 26,5 37,3 48,4

13,4 17,8 22,7 28,7

56,5

34,4

59,7

40,1

61,2

46,1

65,6

53,8

70,3

63,6

48,7

69,0

31,1

53,5

8k

8,4

19,4

33,4

10k 12,5k 16k

5,5 3,4 2,1

11,6 7,1

19,7 11,8

4,4

7,0

20k

1,3

2,7

4,3

Comment: the temperature of the application influences sometimes considerably the acoustic performance of the silencer (at least: for some frequencies). For a given material, an increase of the temperature involves - generally speaking - an increase of the flow resistivity (everything else supposed to be equal).In particular, the choice of a flow resistivity of the porous medium (at room temperature) too big compared with the optimum required (at the temperature of the application) - as far as acoustics is concerned - can lead to a degradation of the performance for frequencies possibly within the range of interest.

See also the last paragraph of illustration 1.5.1

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Effects of pressure (illustration 1.5.7)

Imput data: a silencer is considered at (test) room temperature and at a pressure from 100 to 400kPa with an open area ratio of 50%, the splitters having transverse solid partitions inhibiting the sound propagation along the duct axis inside the non -laminated lining consisting of a single porous medium having (at room temperature) a flow resistivity in the direction normal to the axis of the duct

σy1=48000 Nsm-4, a porosity ø=0.95 (model M76), with a thickness d=0.1m. No series cloth is considered, no series perforated protection is considered.

Illustration of one of the effects: see below the prediction of the propagation loss depending on the pressure (see key in the graph)

propagation loss Da

40

35

30

25

20

15

10

100kPa 200kPa 400kPa

5

0

1 10 100

f(Hz)

1000 10000 100000 f1/3oct (Hz)

100kPa

200kPa

400kPa

25

0,4

0,2

0,1

31,5

0,6

0,3

0,2

40

0,9

0,5

0,3

50

1,3

0,8

0,4

63

1,9

1,2

0,7

80

2,6

1,8

1,1

100

3,4

2,8

1,7

125

4,3

4,0

2,6

160

5,2

5,6

4,2

200

6,0

7,6

6,8

250

6,9

315

7,9

400

9,1

500

10,6

9,7 12,1 14,7 17,4

10,7 16,2 23,0 29,3

630 800 1k 1,25k 1,6k

12,8 15,9 20,0 24,8 29,9

2k

31,1

2,5k

20,1

3,15k

11,0

4k

6,2

20,3 23,6 27,9 32,9

32,4 32,1 31,6 33,7

33,7

32,2

25,0

19,9

15,2

12,8

8,8

7,8

5,2

4,7

5k

3,5

3,1

2,9

6,3k

2,1

1,9

1,8

8k

1,2

1,1

1,1

10k 12,5k 16k

0,8 0,5 0,3

0,7

0,7

0,4

0,4

0,3

0,3

20k

0,2

0,2

0,2

Comment: the pressure of the application influences sometimes considerably the acoustic performance of the silencer (at least: for some frequencies). Depending on the frequency range of interest, absorbers with a higher flow resistivity may be selected in case of pressure lines. But the choice of a flow resistivity of the porous medium too big compared with the optimum required (at the pressure of the application) - as far as acoustics is concerned - can lead to a degradation of the performance for frequencies possibly within the range of interest.

See also the last paragraph of illustration 1.5.1

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Effects of a series cloth (illustration 1.5.8)

Imput data: a silencer is considered at (test) room pressure and temperature, with an open area ratio of 50%, the splitters having no transverse solid partitions inhibiting the sound propagation along the duct axis inside the non -laminated lining consisting of a single porous medium homogeneous in directions parallel to and perpendicular to its surface, having a flow resistivity σy=22332Nsm-4, a porosity ø=0.95 (model M76) with a thickness d=0.05m. The cloth consists of an impervious membrane (surface density 125 g/m2)

Illustration of the effect: see below the prediction of the propagation loss without and with the cloth

propagation loss Da

70

60

50

40 without with

30

20

10

0

1 10 100 1000 10000 100000

f(Hz)

f1/3oct (Hz) without with

25

0,1

0,1

31,5

0,1

0,1

40

0,2

0,2

50

0,3

0,3

63

0,5

0,5

80

0,8

0,8

100

1,2

1,2

125

1,9

2,0

160

2,9

3,2

200

4,5

5,2

250

6,8

8,5

315 400 500 630 800 1k 1,25k 1,6k 2k 2,5k 3,15k 4k 5k 6,3k 8k

10,1 14,9 21,3 29,4 39,1 49,8 59,4 62,0 57,1 51,1 44,5 34,3 23,2 15,2 10,0

13,7 22,3 35,1 53,1 57,0 30,7 17,2 10,3 6,4 4,1 2,5 2,6 1,0 0,6 0,4

10k 12,5k 16k

6,6 4,4 2,9

0,3 0,2 0,1

20k

1,9

0,1

Comment: the choice of a series cloth influences sometimes considerably the acoustic performance of the silencer (at least: for some frequencies). In particular, the choice of a permeability of the cloth too small compared with the optimum required - as far as acoustics is concerned - can lead to a degradation of the performance for frequencies possibly within the range of interest (an increase of the performance being often obtained at low frequency due to the presence of a free vibrating foil).

Attention has to be paid to the consequences of the use (in some locations…) of cloths producing possibly linings with a high flow resistance (especially when nothing is known regarding the properties of this materials in terms of flow resistivity,

porosity…).

Attention has to be paid also to dust deposits in a position (in some cases) of involving effects comparable to the effect of a series cloth.

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Effects of a series perforated protection (illustration 1.5.9)

Imput data: a silencer is considered at (test) room pressure and temperature, with an open area ratio of 50%, the splitters the splitters having transverse solid partitions inhibiting the sound propagation along the duct axis inside the non-laminated lining consisting of a single porous medium having a flow resistivity σy=72kNsm-4, a porosity ø=0.95 (model M76) with a thickness d=0.1m. The perforated protection consists of a sheet R3T5 (round holes with an hexagonal arrangement, diameter 3 mm, open area ratio

ε=0.3265) of thickness 1 mm (general model MOI, model for the added impedances ROA)

Illustration of the effect: see below the prediction of the propagation loss without and with the perforated protection

propagation loss Da

35 without with

30

25

20

15

10

5

0

1 10 100

f(Hz)

1000 10000 100000 f1/3oct (Hz) without with

25

0,5

0,5

31,5

0,8

0,8

40

1,1

1,2

50

1,6

1,6

63

2,1

2,1

80

2,6

2,7

100

3,2

3,2

125

3,8

3,8

160

4,3

4,3

200

4,9

4,9

250

5,5

5,5

315

6,3

6,3

400

7,3

7,3

500

8,6

8,6

630

10,2

10,3

800 1k 1,25k 1,6k 2k 2,5k 3,15k

12,4 15,4 19,5 24,7 29,9 25,0 13,2

12,5 15,3 19,0 23,1 25,0 19,4 11,5

4k

7,1

6,5

5k

3,9

3,8

6,3k

2,3

2,2

8k

1,3

1,4

10k 12,5k 16k

0,8 0,5 0,3

0,8 0,5 0,3

Comment: the choice of a perforated protection influences sometimes considerably the acoustic performance of the silencer (at least:

20k

0,2

0,2 for some frequencies). For a given geometry of holes and a given thickness, a decrease of the open area ratio involves - generally speaking - a decrease of the performance. In particular, the choice of a perforated protection with an open area ratio too small compared with the optimum required - as far as acoustics is concerned - can lead to a degradation of the performance for frequencies possibly within the range of interest (in the area of the maximum propagation loss, the performance is degraded in the example above despite a quite high open area ratio).

For a given perforated protection, the performance can decrease notably in case of a non-sufficiently pervious material at the rear: see also the last paragraph of illustration 1.5.1

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Effects of the velocity of air flow (other than regenerated noise) (illustration 1.5.10)

Imput data: a silencer is considered at (test) room pressure and temperature, with an open area ratio of 50%, the splitters having no transverse solid partitions inhibiting the sound propagation along the duct axis inside the non-laminated lining consisting of a single porous medium homogeneous in directions parallel to and perpendicular to its surface, having (at room temperature) a flow resistivity in the direction normal to the axis of the duct σy1=15kNsm-4, a porosity ø=0.95 (model M76), with a thickness d=0.1m and a length

L=2m. No series cloth is considered, no series perforated protection is considered.

Illustration of one of the effects: see below the prediction of the longitudinal propagation depending on the mean flow velocity in the airways (see key in the graph)

longitudinal attenuation Da*L

70 v=0 ms-1 v=-10ms-1 v=+20ms-1

60

50

40

30

20

10

0

1 10 100

f(Hz)

1000 10000 100000 f1/3oct (Hz) v=0 ms-1 v=-10ms-1 v=+20ms-1

25

0,3

0,4

0,3

31,5

0,5

0,6

0,5

40

0,8

0,9

0,8

50

1,3

1,4

1,2

63

2,1

2,2

1,9

80

3,2

3,3

2,9

100

4,8

5,0

4,4

125

7,2

7,5

6,6

160 200 250 315 400 500 630 800 1k 1,25k 1,6k 2k 2,5k 3,15k 4k

10,5 15,0 21,0 28,5 37,1 45,8 52,5 55,7 55,8 54,2 48,9 36,7 24,4 15,8 10,2

11,0 15,6 21,8 29,6 38,5 47,4 54,3 57,3 57,2 55,3 49,4 36,4 24,0 15,5 10,0

9,7 13,8 19,4 26,5 34,6 42,8 49,3 52,6 53,1 52,0 47,8 37,0 25,0 16,4 10,7

5k

6,6

6,5

6,9

6,3k

4,3

4,2

4,5

8k

2,8

2,7

3,0

10k 12,5k 16k

1,9 1,2 0,8

1,8

1,9

1,2

1,3

0,8

0,9

Comment: the flow velocity in the airways influences sometimes considerably the acoustic performance of the silencer (at least: for some frequencies), due to the change that can occur in the propagation loss affecting the longitudinal attenuation (relied to the conditions of propagation of sound in the lining and in the airways). Generally speaking, a negative airflow ( direction of airflow and direction of propagation of sound opposite) involves an increase of the acoustic performance of the silencer when a positive airflow

(same direction for airflow and propagation of sound) lead to a decrease of the acoustic performance of the silencer. In particular, the choice of a free area of the silencer (relied to the front section of the silencer and to the open area ratio) too small comp ared with the optimum required - as far as acoustics is concerned - can lead to a degradation of the performance for frequencies possibly within the range of interest.

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Effects of the velocity of air flow (regenerated noise) (illustration 1.5.11)

Imput data: a silencer is considered at (test) room pressure and temperature, with an open area ratio of 50%, the splitters having no transverse solid partitions inhibiting the sound propagation along the duct axis inside the non -laminated lining consisting of a single porous medium homogeneous in directions parallel to and perpendicular to its surface, having (at room temperature) a flow resistivity in the direction normal to the axis of the duct σy1=15kNsm-4, a porosity ø=0.95 (model M76), with a thickness d=0.1m and a length

L=2m. No series cloth is considered, no series perforated protection is considered. A reflection loss and a limitation of the propagation loss are considered. The considered front section of the silencer is 2.5 m2.A noise source with an acoustic power of 80 dB/oct is considered.

Illustration of one of the effects: see below the prediction of the insertion loss depending on the mean flow velocity in the airways (see key in the graph)

insertion loss Di

50

45

40

35

30

25

20 v=0 ms-1 v=-10ms-1 v=+20ms-1

15

10

5

0

1 10 100

f(Hz)

1000 10000 100000 f1/1oct (Hz) 31 v=0 ms-1 v=-10ms-1

0,8

0,8 v=+20ms-1 0,4

63

2,4

2,3

1,4

125 250 500 1k 2k 4k 8k

7,2 18,3 35,1 46,1 30,4 13,6 7,1

6,9 17,2 28,8 34,5 30,2 13,9 7,2

4,4 8,5 11,6 15,3 19,6 13,7 7,2

16k

5,1

5,1

5,2

Comment: the flow velocity in the airways influences sometimes considerably the acoustic performance of the silencer (at least: for some frequencies) due to the fact that the sound power level at the outlet of a silencer cannot be less than its self noise, leading to a reduction of the insertion loss in case of high sound power level due to the airflow. Attention has to be paid to limit the speed in the airways to acceptable values (taking into account the difference between unsilenced sound power level of the source and the insertion loss without taking into account the self noise) influenced - for a given flow rate - notably by the front area and the open area ratio of the silencer.

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Effects of the unsilenced sound power spectrum (and of other uncertainties) (illustration 1.5.12)

Imput data: a silencer is considered at (test) room pressure and temperature, with an open area ratio of 50%, the splitters having transverse solid partitions inhibiting the sound propagation along the duct axis inside the non -laminated lining consisting of a single porous medium having (at room temperature) a flow resistivity in the direction normal to the axis of the duct σy1=12000kNsm-4, a porosity ø=0.95 (model M76), with a thickness d=0.1m and a length L=1m.. No series cloth is considered, no series perforated protection is considered. The longitudinal attenuation for the 1/1 octave band of central frequency 250 Hz is considered for various sound power spectra of the unsilenced source Lw0, taking into account the propagation loss Da computed (on the occasion of th e first illustration of this §) for the corresponding 1/3 octave bands: 6.8 dB/m at 200 Hz,10.7 dB/m at 250 Hz, 16.3 dB/m at 315 Hz.

Illustration of one of the effects: see below the calculation of the longitudinal attenuation for the 1/1 octave band depending on the sound power spectrum of the unsilenced source (see key in the table)

Case 1

Case 2

Case 3

Lw0 (dB ref1E-12W)

Da*L (dB)

Lw0 - Da*L (dB ref1E-12W)

Lw0 (dB ref1E-12W)

Da*L (dB)

Lw0 - Da*L (dB ref1E-12W)

Lw0 (dB ref1E-12W)

Da*L (dB)

Lw0 - Da*L (dB ref1E-12W)

1/3 octave frequency band central frequency (Hz)

200

75.2

6.8

68.4

250

75.2

10.7

64.5

315

75.2

16.3

58.9 longitudinal attenuation for the 1/1 octave band

68.0 75.0 78.0

6.8 10.7 16.3

61.2 64.3 61.7 longitudinal attenuation for the 1/1 octave band

78.0

6.8

71.2

75.0

10.7

64.3

68.0

16.3

51.7 longitudinal attenuation for the 1/1 octave band

1/1 octave band central frequency

(Hz)

250

80

70.2

9.8

80

67.4

12.6

80

72.0

8.0

Comment: the sound power spectrum of the unsilenced source influences sometimes considerably the acoustic performance of the silencer (at least: for some frequencies) in terms of longitudinal attenuation per 1/1 octave band (and so in terms of insertion loss) due to the combination of possibly high frequential variation on the one hand: of the performance of the silencer and on the other hand: of the spectrum of the source (especially in case of pure tones such as produced by rotating machines). Only in the case of a pink spectrum for the unsilenced noise source is the averaging of 1/3 octave band performance leading to a correct result for the 1/1 octave band longitudinal attenuation.

Attention has to be paid by the user of the software to use an 1/3 octave band spectrum for accurate sizing of dissipative silencers (and to take a safety margin for the uncertainty of the available input data and of the conditions of on-site installation of the silencer).

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Appendix to Section 1: list of symbols

General

f: frequency (Hz)

Lw0: sound power level without soundproofing equipment (dB ref. 1pW)

Lw1: sound power level with soundproofing equipment (dB ref. 1pW) t: time (s)

Set of materials

ilim: limit set index imax: maximum set index

: total number of cloths and perforated protections accounted as porous media i.e. not accounted as series cloth (resp. series perforated protections) using electro acoustic analogie

Dry air

a: diffusivity (m

2

/s) c: (adiabatic) velocity of sound (ms

-1

) c p

: specific heat (capacity) (at constant pressure) (J/kg/K)

C s

: adiabatic compressibility (Pa

-1

C

T

: isothermal compressibility (Pa

)

-1

) k: wave number (rad/m)

K s

: adiabatic bulk modulus (Pa)

K

T

: isothermal bulk modulus (Pa) t: temperature (°C)

P: static/atmospheric pressure (Pa)

Pr: Prandtl number

R: gas constant (J/kg/K)

V: volume (m

3

)

Z: characteristic impedance (Nsm

-3

)

β: coefficient of thermal expansion

: propagation constant (rad. m

-1

)

: dynamical viscosity (Nsm

-2

)

: thermal conductivity (W/m/K)

: wavelength (m)

: kinematic viscosity (m

2

/s)

: density (kg/m3) subscript / superscript subscript superscript for normal conditions for test (room) conditions

0

0

N

* for service conditions front atmosphere rear atmosphere

0

0 **

Porous media

a’, a’’: coefficients for the expression of

 an

 b’, b’’: coefficients for the expression of Z an c

1

, c

2

, c

3

, c

4

, c

5

, c

6

, c

7

, c

8

: coefficients for the expression of

C seff

: adiabatic compressibility (Pa

-1

) an and Z an

E: non-dimensional parameter related to frequency, flow resistivity and density of dry air

K seff

: adiabatic bulk modulus (Pa)

RG: (bulk) density (kg/m

3

)

Z a

: characteristic impedance (Nsm

-3

)

Z an

: normalized characteristic impedance

α’, α’’: exponents for the expression of

β’, β’’: exponents for the expression of Z an

 an

α

: (high frequency limit of the) tortuosity

 a

: propagation constant (rad.m

-1

)

 an

: normalized propagation constant

 ax

: propagation constant in the x-direction (rad.m

 ay

: propagation constant in the y-direction (rad.m

-1

)

-1

)

Λ’: thermal characteristic length (m)

Λ : viscous characteristic length (m)

ρ eff

: effective density (kg/m

3

)

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ø : (open) porosity

σ: (static) air flow resistivity (=specific flow resistance) (Nsm

-4

)

σ1x: (static) air flow resistivity in the x-direction for porous medium of set 1(Nsm

σ1y: (static) air flow resistivity in the y-direction for porous medium of set 1(Nsm

-4

)

-4

)

Note: subscript i for set i except for σ1x and σ1y

Cloths

d’: thickness (m)

M’: surface density (kg/m

2

)

R’: superficial flow resistance (Nsm -3

)

Rp’: parallel resistance (losses due to mounting) (Nsm -3

)

Note: subscript i for set i

Perforated protections

a: diameter of holes / width of slit (m) d’’: thickness (m)

M’’: surface density (kg/m 2

)

R’’: series flow resistance (Nsm -3

)

Rp’’: parallel resistance (losses due to mounting) (Nsm

-3

)

ε: open area ratio

Note: subscript i for set i

Silencer

a: a=h*2*π -0.5

(m)

2a: width of airway (m)(for mounting C0 only) abulk: cf. step [F] (m) alocal: cf. step [F] (m)

A : area of the duct above and below the silencer (m

Af: area of the overall section of the silencer (m

2

)

2

)

Af*: area of the duct above and below the silencer when the area of the duct is not equal to the area of the overall section of the silencer (m

2

)

Ap : free area of the silencer (passage area of the airways) (m

2

)

B: width for mounting R, R’’, RPTR, RPTR’’, RPTL, RPTL’’(m) d: overall thickness of the acoustic structure (m) d=2d/2: for dissipative silencers, thickness of extreme inner lagging (for mountings R, C1, C2 only) = thickness of lining (for mountings Q, C0 only) (m)

2d: for dissipative silencers, thickness of central splitters (for mountings R, R’’) = diameter of central pod (for mountings C1, C2 only)

= thickness of intermediate splitter (for mounting C2 only) (m) dbulk: cf. step [F] (m) dlocal: cf. step [F] (m) d*=2d*/2: for resonant silencers, thickness of extreme inner lagging (for mountings RPTR, RPTL only)

2d*: for resonant silencers, thickness of central splitters (m)

Da: propagation loss (dB/m)

Da.L:longitudinal attenuation (dB)

Di: insertion loss with flow and self noise (dB)

Di’: insertion loss with flow without self noise (dB) (Di’=Da*L+Dk+Dr)

Dk: limitation of the propagation loss (dB/m)

Dr: reflection loss (dB)

D0: overall diameter for mounting C0 (m)

D1: overall diameter for mounting C1 (m)

D2: overall diameter for mounting C2 (m) fco: cut-off frequency of the duct (Hz) h=2h/2: for dissipative silencers, width of extreme air way (for mounting R’’ only) (m)

2h: for dissipative silencers, width of central airways (for mounting R” only) = width of the airways (for mountings R, C1, C2, Q) (m) hbulkl: cf. step [F] (m) hlocal: cf. step [F] (m)

H: height for mounting R, R’’(m)

Hs: for a resonant silencer only (half) airway in the chamber (m)

Hsbulkl: for a resonant silencer only cf. step [F] (m)

Hslocal: for a resonant silencer only cf. step [F] (m)

L: length without aerodynamic extremities (m)

Ls: for a resonant silencer only length of the chamber (m)

M: Mach number

N: for a dissipative silencer only number of central splitters (for mounting R only)

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N’’: for a dissipative silencer only number of central splitters (for mounting R’’only)

N*: for a resonant silencer only number of central splitters (for mounting RPTR, RPTL only)

N’’*: for a resonant silencer only number of central splitters (for mounting RPTR’’, RPTL’’only)

Q: overall width=overall height for mounting Q (m)

Qm: mass flow rate (kg/s)

Qv: volume flow rate (m3/s or m3/h or Nm3/h)

Sa: for a resonant silencer only width between necks of chambers (m)

Ss: for a resonant silencer only width of necks of chambers (m)

T: for resonant silencers only period width such as T=Ss+Sa (m)

Vf: speed of airflow in the area Af (m/s)

Vf*: speed of airflow in the area Af* (m/s)

Vp: speed of airflow in the area Ap (m/s)

Δd: for resonant silencers with a rear lining only thickness such as Δd=d*-d (m)

Λ=d/h

 f: total pressure loss coefficient in relation with airflow speed Vf

 f*: total pressure loss coefficient in relation with airflow speed Vf*

 p: total pressure loss coefficient in relation with airflow speed Vp

: angle of the branches of the Pine Tree spiltters

Miscellaneous

See also corresponding § in General considerations and in Section 2

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Section 1A: computation of silencers with discontinued

splitters (MODULE 1A of the software)

1A.1: Introduction

Terms and definitions

For the needs of the present user’s manual, the following terms and definition apply (see NF EN ISO 14163 Acoustics - Guidelines for noise control by silencers, 1999):

Silencer: device reducing the acoustic transmission in a duct, a pipe or an aperture, without preventing the carriage of the fluid

Dissipative silencer: silencer attenuating the wideband sounds with a relatively low pressure loss and converting partially the acoustic energy into heat by friction on tubes having a porous or fibrous structure

Mountings and geometry

Silencers having rectangular cross sections are frequently used for industrial applications.

For dissipative silencers with discontinued splitters, mountings for which predictions can be done with the software SILDIS are shown in fig.1A1

fig.1A.1 cf. worksheet CODIS-1A

mounting RD

Key of the previous figures

2d: thickness of central splitters (for mountings RD h=2h/2: width of extreme air way (for mounting RD)

2h: width of central airways (for mounting RD)

L: length of the silencer without aerodynamic extremities

Nd: number of central splitters (for mounting RD);

Concerning the area of the duct upstream and downstream (above and below the silencer) A compared to the area of the overall section of the silencer Af, predictions with the software SILDIS can be done:

 for mountings RD with A = Af

Section of the duct above and below the silencer A depending on mounting

A=Af

R, R’’

B*H

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The direction parallel to the axis of the duct is referred to as x, the direction normal to the axis of the duct along the width B is referred to as y, the direction normal to the axis of the duct along the height H is referred to as z according to the fig. 1A.2 below z x fig.1A.2 y

1A.2: Scientific and technical background

The prediction of acoustic and aerodynamic performances of dissipative silencers with SILDIS is founded on a scientific and technical background in relation with: o analytical models for taking into account the properties of materials and various physical phenomena useful on the occasion of the computation o measurement results for feeding some of those models and for allowing the necessary improvement (through correction factors) of the correlation between some calculations and on site observations

For a rectangular silencer, the obtained results are comparable with the standardized measurement with the plane wave excited alone as much as possible: see NF EN ISO 7235 Acoustics - Laboratory measurement procedures for ducted silencers and air terminal units

- Insertion loss, flow noise and total pressure loss (2004).

1A.2.1 Thermodynamics and fluid dynamics:

Steps of the computation

Step [a-1A]

All computations have been gathered in this single step for the sake of simplicity. o

Bibliography (references) :

[a1-1A]

[a2-1A]

[a3-1A]

[a4-1A]

-

[a5-1A] o

Comments in relation with partial derivatives:

Partial derivatives (and related quantities), which are usually employed to measure the equation of state of the fluid near the equilibrium state (with various notations according bibliographic sources) are written for the purpose of the present user’s manual with the following notations:

 the isothermal compressibility of dry air is referred to as C

T

C

T

-

 

= =

V

T

1

∂P

 

T

  

T

with K

T

=1/C

T

 the adiabatic compressibility of dry air is referred to as C s

C s

=

-

1

V

∂V

∂P

=

T

1



∂P

T because C s

= C

T

/

 s

with K s

=1/C s

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 the coefficient of thermal expansion of dry air is referred to as β

β = =

V

∂V

∂T

P o

Other comments:

-

1

∂T

P

 when used the density of dry air

 is computed according various models as shown in the table below: model MAR

MEC

source

[a1-1A] using ideal gas law

(derived from

MARiottes’s law) (*)

[a1-1A] using a regression

* the gas constant of dry air R (J/kg/K) is set to 287 or 287.053 or 287.10 depending on the eponym selected model

 when used the dynamical viscosity of dry air

is computed according various models as shown in the table below: model source limiting temperature

SUT

[a2-1A] using

SUTherland

’s law)

-20 to 800

°C

VER

[a4-1A]

?

MEC

[a1-1A] using a regression

-173.15 to

926.85 °C

IDE

[a2-1A] using a regression

-20 to 800

°C

Conversion factors micropoise centipoise poise

= g/cm/s kg/m/s

= Nsm-2 micropoise

1

10

4

10

6

10

7 centipoise

10

-4

1

10

2

10

3 poise

= g/cm/s

10

-6

10

-2

1

10 kg/m/s

= Nsm-2

10

-7

10

-3

10

-1

1

 when used the kinematic viscosity of dry air

is computed from [a1-1A]

Note :

=

/

Conversion factors centistokes

= mm2/s stokes = cm2/s m2/s centistokes

= mm2/s

1

10

2

10

6 stokes = cm2/s

10

-2

1

10

4 m2/s

10

-6

10

-4

1

 when used the adiabatic exponent of dry air

is computed according various models as shown in the table below: model INV

MEC

source limiting temperature

(*)

-

[a1-1A] using a regression

-73.15

to

926.85 °C

*

 is set to 1.399 or 1.400 or 1.401 or 1.402 depending on the eponym selected model

 when used the specific heat (capacity) (at constant pressure) of dry air c p is computed according various models as shown in the table below:

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MEC

[a1-1A] using a regression for a (the regression for c p

being in error)

-73.15

to

926.85 °C

MEC2

[a1-1A] using a regression for Pr (the regression for c p being in error)

-173.15 to

926.85 °C

KRA

[a3-1A] using a regression

-20 to 800

°C

Conversion factors

J cal

J

1

4.1868 cal

0.2388

1

 the following relation apply:

- 1

β

2

.T

=

S

.c

p

.

C

 when used the thermal conductivity of dry air

is computed according various models as shown in the table below: model

MEC

KRA source limiting temperature

[a1-1A] using a regression

-173.15 to

926.85 °C

[a3-1A] using a regression

-20 to 800

°C

Conversion factors

J cal

J

1

4.1868 cal

0.2388

1

 when used the diffusivity of dry air a is computed from [a1]

Note : a =

/

/c p

 when used the Prandtl number of dry air Pr is computed according various models as shown in the table below: in case of model for c p

MEC

MEC2 KRA source limiting temperature

[a1-1A] from

, c p

and

-73.15

to

926.85 °C

[a1-1A] using a regression

-173.15 to

926.85 °C

[a3-1A] from

, c p and

-20 to 800

°C

Note : Pr =

/a =

/

/a =

.c

p

/

 when used the (adiabatic) sound velocity in dry air c is computed from [a5-1A]

Note : c = (K s

/

)

0.5

 when used the characteristic impedance of dry air Z is computed from [a1-1A]

Note : Z =

 c

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1A.2.2 Acoustics:

Bloc diagram for rectangular dissipative silencers:

the computation scheme for rectangular dissipative silencers is as shown on fig 1A.3 below

Fig. 1A3

Note 1: the service conditions dependence has been omitted for the sake of simplicity. See: report [PhRxx-002x] pages 6 to 7, report

[PhRxx-006x] pages 2 to 3, report [PhRxx-015x]

Note 2: the main steps (the steps involving a physical modeling) being referred to as [A-1A] to [K-1A] have been taken into account for the bloc-diagram above (some of the parameters of the above bloc diagram are not independent); the frequency dependence has been omitted for the sake of simplicity; the calculation is carried out with the hypothesis of plane waves, typically regarded as the least attenuated mode (only for step [H-1A] are other modal contributions taken into account)

Note 3: analytical calculations are involved in steps [A-1A] and [J-1A] to [K-1A]; empirical methods are involved in steps [G-1A] to

[I-1A]

Note 4: step [F-1A] is depending on the conditions of axial sound propagation inside the lining

Note 5: the bloc diagram above is suitable for rectangular dissipative silencers, for the mounting SD .

Steps of the computation

Steps [A-1A] to [F-1A]

Those steps aim at taking into account the properties of the filling of splitters (cf. fig 1A.4)and at calculating the propagation

loss with flow of the silencer.

Sketch Nomenclature land mark element

Airway

E

D

C series perforated protection series cloth porous medium

E D C

Fig. 1A4

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Bibliography (references) :

[A1-1A]

-

- o

Comments :

No comment

Step [G-1A]

This step aims at taking into account a bypass correction (i.e. a limitation of the propagation loss in case of a length of the silencer over 1m: indeed, compared with the estimation obtained with an hypothesis of proportionality of the performance to the length of the silencer, in order to predict an insertion loss). o

Bibliography (references) :

[G1-1A]

-

[G2-1A]

-

[G3-1A] o

Comments :

The bypass correction (Dk in dB) is basically computed at frequency steps of 1/3 octave:

for L≤1m: Dk = 0 and for L>1m: Dk =

D * ( 1 – L ) with

D in dB/m

general case

An extrapolation of the original value of

D mentioned in [G1-1A] is used for SILDIS, allowing calculations in an extended range of values of σy1 for values of Λ=d/h to be précised on the occasion of a future revision of this user’s manual

Note 1: the data pool used for the determination of the original value of

D mentioned in [G1-1A] is related to splitters filled with 1 porous medium with a flow resistivity σx1 =? σy1 from 9 to 15 kNsm

-4

: no influence of the speed of the airflow seems to be taken into account for the computation, no influence of a series cloth seems to be taken into account for the computation, no influence of a series perforated protection seems to be taken into account for the computation

Note 2: in [G3-1A] is mentioned for [G2-1A] basing [G1-1A] complementary information. The data pool used for

D is related to splitters “in 1 piece” with a thickness 2d=0.1 or 2d=0.2 m with Λ=d/h=0.5 to 4

Model

Bypass correction

FRO as above

ZER no limitation

*although at the time of the present user’s manual the conditions of the measurement of the data pool ([G1-

1A],[G2-1A]) are not known with accuracy, one can consider that: Dk = Dk1 + Dk2 (the 2 terms being presently not known separately) with:

Dk1 to be accounted for the vibration transmission along the duct wall, for the sound transmission over the duct wall, for the vibration transmission along the splitter frame (as described in [G1-1A] and for the imperfection of the interface between the lining and the duct

Dk2 to be accounted for the inhomogeneity of the used absorber in directions parallel to and perpendicular to its surface: a unique model is used for taking into account the limitation of propagation whatever σx1/σy1 is (may be that this correction should be used only in the case of an inhomogeneous absorber in directions parallel to and perpendicular to its surface when the hypothesis σx1/σy1=1 is used for the computation).

For those reasons, the value obtained by the means of the unique model FRO has to be considered as a typical general estimation of the limitation of the propagation loss useful when no accurate regression is available for a silencer with a particular filling and particular modalities of construction (this is often the case)

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Step [H-1A]

This step aims at taking into account the reflection loss in the silencer, in order to predict an insertion loss. o

Bibliography (references) :

[H1-1A]

-

[H2-1A]

-

[H3-1A] o

Comments :

The reflection loss (Dr in dB) is basically computed at frequency steps of 1/21 octave (then averaged per 1/3 octave frequency band).

general case: no influence of the speed of the airflow is taken into account for the computation

Model

Reflection loss

MUL (*) as above

(higher modes integrated)

ZER no reflection

* No influence of a series cloth is taken into account for the computation, no influence of a series perforated protection is taken into account for the computation. The data pool used for Dr is related to splitters with a thickness 2d=0.1 or

0.2 or 0.3 m, filled with 1 porous medium with a flow resistivity σx1 = σy1 from 9 to 15 kNsm-4 (an extrapolation of

Dr with a different thickness has been used). At the time of the present user’s manual the conditions of the measurement of the data pool ([H2-1A],[H3-1A]) are not known with accuracy, especially the higher modes propagating in the duct in relation with the characteristics of the testing facility mentioned in [H2-1A] (with a front section from 0.5m*0.5m to 1.3m*0.5m). For those reasons, the value obtained by the means of the unique model

MUL has to be considered as a typical estimation of the reflection loss for a duct of dimensions comparable to testing facility mentioned in [H2-1A] when no accurate information is available regarding the higher order modes (this is often the case).

Step [I-1A]

This step aims at taking into account the self noise of the silencer (noise produced by the airflow).

For dissipative silencers o

Bibliography (references) :

[I1-1A]

[I2-1A]

[I3-1A]

[I4-1A]

[I5-1A]

[I6-1A]

[I7-1A]

[I8-1A]

[I9-1A]

-

[I10-1A]

[I11-1A]

o

Comments: the self noise (acoustic power of flow noise Lw in dB ref 1E-12W) is basically computed at frequency steps of

1/1 octave.

for the mounting of the worksheet CODIS-1A (RD), the determination of the self noise is done according various models as shown in the tables below: model source

DN1

[I1-1A]

DN2

[I1-1A]

NF1

[I2-1A]

NF2

[I2-1A]

(*)

2081A

[I3-1A]

(**) (***)

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2081B

[I4-1A]

(**)(***)

2081R

[I5-1A]

(**)(***)

2081C1

[I5-1A]

(**)(***)

MUN

[I8-1A]

(***)

VER

[I9-1A]

(***)

(*) B (dB) and

(m) are input data (**) with an additional correction for temperature

(***) with an additional correction for pressure

 for the models 2081 and 3733, a spectral correction is used according various models as shown in the tables below: model source

2081

[I5-1A]

FRO

[I11-1A]

3733

[I7-1A]

Warning: at the time of the writing of this manual, all the consequences of the choice of one or the other model are not known with accuracy. The choice of the model can be done by the user allowing tests and feed-back.

Step [J-1A]

This step aims at calculating the insertion loss without taking into account the self noise. o

Bibliography (references) :

[J1-1A]

o

Comments :

The insertion loss without taking into account the self noise (Di’ in dB) is computed at frequency steps of 1/3 octave (then calculated per 1/1 octave frequency band for a reference acoustic power spectrum Lw0 in dB ref 1E-12W).

Di’ = Da * L + Dk + Dr

Step [K-1A]

This step aims at calculating the insertion loss of the silencer including its self noise. o

Bibliography (references) :

[K1-1A]

o

Comments :

The sound power level with silencer including self noise (Lw1 in dB ref 1E-12W) is basically computed at frequency steps of 1/1 octave (in reference to a reference acoustic power spectrum Lw0 ref 1E-12W).

Lw1 = 10 * log [10^ (0.1 * (Lw0 – Di’)) + 10^ (0.1 * Lw)]

Lw being the self noise (acoustic power of flow noise in dB ref 1E-12W)

The insertion loss taking into account the self noise (Di in dB) is basically computed at frequency steps of 1/1 octave (in reference to a reference acoustic power spectrum Lw0 ref 1E-12W).

Di = Lw0 – Lw1

In case of rectangular silencers, the obtained results are comparable with the standardized measurement: see NF EN ISO

7235 Acoustics - Laboratory measurement procedures for ducted silencers and air terminal units- Insertion loss, flow noise and total pressure loss (2004).

Aerodynamics:

Steps of the computation

Step [α-1A]

All computations have been gathered in this single step for the sake of simplicity (this step aims at computing the total pressure

loss due to the silencer).

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Bibliography (references) :

[

α

1-1A]

[

α

2-1A]

-

[

α

3-1A]

[

α

4-1A]

[

α

5-1A]

[

α

6-1A]

[

α

7-1A]

[

α

8-1A] o

Comments :

The total pressure loss due to the silencer is computed with the hypothesis of a uniform air flow (supposed to not be rotational), taking into account the aerodynamics type upstream and downstream (*):

Aerodynamics type downstream R C

mounting RD

Rectangular

1/2 Circle

1/2 Circle for central splitters, 1/4 Circle for extreme inner lagging

1/4 Circle for extreme inner lagging

Aerodynamics type downstream

mounting RD

R

Rectangular

C

1/2 Circle

1/2 Circle for central splitters, 1/4 Circle for extreme inner lagging

P

Profiled according sketch, the dotted line showing either a symmetry plane or an impervious rigid back

(see fig.1A.4)

1/4 Circle for extreme inner lagging various models as shown in the tables below:

Fig.1A.4

for the mounting of the worksheet CODIS-1A (RD), the determination of the total pressure loss is done is done according

Model source

[

FRO MEC 2081C1

BER

α

1-1A] [

α

2-1A] [

α

6-1A] [

α

3-1A]

ISO

[

α

4-1A]

[

α

7-1A]

In case of rectangular silencers, the obtained results are comparable with the standardized measurement: see NF EN ISO 7235

Acoustics - Laboratory measurement procedures for ducted silencers and air terminal units- Insertion loss, flow noise and total pressure loss.

*a safety factor has to be used (by the user) for taking into account the inhomogeneity of the inflow (see [

α

2-1A],[

α

5-1A]) leading to predictions lower than on-site values

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1A. 3: How to use SILDIS

Operating conditions / security level / safety

See corresponding § in the chapter General considerations

For safety reasons, some cells of the original file provided to the user (as mentioned in the table below) for which input data are foreseen to be entered by the user are pre-filled with the value “1/0”, among the yellow cells for which the color orange is used (*).

Worksheet

[in COALA-1A]

Cells

E13, J37

* something like that

[in COSIL-1A]

D25, BD25, D37, D43,

D44, D45

** attention has to be paid to the fact that the considered sheet is not included in the worksheets listed below

Worksheets

Regarding the COmputation of DIssipative Silencers, the software SILDIS is configurated in order to allow the user to access to 4 worksheets being linked as shown in fig.1A.5 (the overview of the worksheets being shown in table below).

Fig. 1A.5

Concerning the worksheet [in COALA-1A]:

 a complementary set (set 0) and a rear atmosphere are displayed: they are none of interest for the COmputation of DIssipative

Silencers (only the case of an impervious rigid back at the rear of set1 applies for the COmputation of SILencers)

 data concerning series thin plates are displayed: they are none of interest for the COmputation of DIssipative Silencers (not taken into account whatever the input data concerning thin plates are in worksheet in [COALA])

Worksheet Suitable for mountings Input data Results

[in COALA-1A]

all --

[in COSIL-1A]

all for sets, for reference spectrum particular conditions for the design of the silencer

--

[in-out CODIS-1A]

RD condition of propagation (of sound) indicators of performance (acoustics

& Aerodynamics)

Input data, alerts and results: the key points

The best use of the software requires the knowledge of some key points in relation with: o the input data

See corresponding § in the chapter General considerations

As far as porous media, series cloths and series perforated protections are concerned, specific data bases (libraries) ( will ) allow the design to be made with in-built engineering data (constants) referred to as “Usual” in the worksheets of the software.

Warning: some properties of the presently referenced materials still not have been checked by reliable sources.

See also report

[PhRxx-015x] Collection of soundproofing constructions systems: a companion to “User’s manual for the software SILDIS”

data base (library) for porous media

 contents of the library: 1 possible reference of material layer

data base (library) for series cloths

 contents of the library: 1 possible reference of material layer

data base (library) for series perforated protections

 contents of the library: 1 possible reference of material layer o some alerts in case of input data involving a warning of the user o the place where (and the way) some results are presented

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Those key points are reviewed worksheet per worksheet hereafter: the cells will be referred to thanks to their EXCEL’s coordinates

(column / line) in the following part of the present user’s manual.

Worksheet [in COALA-1A]

o

Input data :

Item

Cell for input

Foreseen action Comment

Language

Date

Project

Title

Temperature

Pressure

Maximum set index imax

C1

B3

E3

M3

D6

D7

E13 for English input E, for

French input F

Modification of the displayed date

Input a string

Input a string

Input a real number

Input a real positive number

Input an integer from 0 to

4 common value applicable to the fluid, to porous media, to series cloths, to perforated protection common value applicable to the fluid, to porous media, to series cloths, to perforated protection

Reference

G18 to

K18

Select a material (in the proposed list) for each layer of interest for CODIS only: a possible inhomogeneity in directions parallel to and perpendicular to its surface (i.e. different properties - depending on the used model - in directions x and y) is considered for the porous medium of set 1 ( porous media of sets 2 to 4 being considered homogeneous)

Thickness

Reference

Incorporation of the series perforated protection (0/1)

G37 to J37

G45 to J45

G57 to J57

Input a real positive number

Select a reference of element (material in the proposed list) for each layer of interest

For NO press 0, for YES press 1

imax is the maximum set index taken into account for the computation, despite the status of the selection of the parameters related to sets with an index i> imax

Thickness G58 to J58

Input a real positive number taken into account for the computation as a non zero value only if 1 in cell just above

Reference

Incorporation of the series cloths (0/1)

T18 to

W18

T23 to

W23

Select a reference of element (material in the proposed list) for each layer of interest

For NO input 0, for YES input 1

Thickness

Lw0 only known per 1/1 octave frequency band (0/1)

T24 to

W24

R62

Input a real positive number taken into account for the computation as a non zero value only if 1 in cell just above

In case of input “0”: the input data of the table below are not applicable, the next table only must be filled

Lw0

Lw0

B65 to

K65

B70 to P70

B73 to P73

For NO input 0, for YES input 1

Input a real positive number as requested for a

1/1 octave band sound power level

Input a real positive number as requested for a

1/1 octave band sound power level

In case of Lw0 only known per 1/1 octave frequency band, default values are foreseen such as

Lw0 1/3 oct = Lw0 1/1 oct - 4.8 (dB)

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Comments :

 some data of the table above may not be modifiable by the user despite the displayed color of the cell

 data of the second table (below) are not taken into account for the design of dissipative silencers

Item

Cell for input

Foreseen action Comment

Rear atmosphere ? (0/1) O8

For NO input 0, for YES input 1 not taken into account for CODIS

Reference

(1/2)

Model of losses

Model of effective critical frequency

Number of identical plates

Thickness

T31 to

W31

Y31

T36 to

W36

T37 to

W37

T38 to X38

T39 to

W39

Select a reference of element (material in the proposed list) for each layer of interest

Select a number (in the proposed list)

Select a model (in the proposed list)

Select a model (in the proposed list)

Input a real positive number

Input a real positive number select 1 (resp. 2) to get for set 0 the same plate as for set

1 (resp. set 2) taken into account for the computation as a non zero value only if a non zero value in cell just above

Note: temperature (resp. pressure) of cell D6 (resp. D7) also apply to thin plates

 data of the third table (below) are not modifiable by the user despite the displayed color of the cell

Item

Cell for input

Foreseen action Comment

For (test) room conditions below: temperature

For (test) room conditions below: pressure

S48

S49

Input a real number

Input a real positive number common value applicable to the fluid, to porous media, to series cloths, to perforated protection common value applicable to the fluid, to porous media, to series cloths, to perforated protection

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Worksheet [in COSIL-1A]

o

Input data :

Item

Cell for input

Foreseen action Comment

Limit set index ilim

Half airway h (m)

Mass flow rate

Width B (m)

Height H (m)

D18

D25

D37

D43

D44

Input an integer from 1 to

imax

Input a positive real

Input a real

Input a positive real

Input a positive real

imax-

ilim

imax (

being the total number of cloths and perforated protections accounted as porous media)

A positive value is related to a direction of airflow equal to the direction of propagation of sound, a negative value is related to a direction of airflow opposite to the direction of propagation of sound

If a particular value of N’’

(resp. N’’*) is wished then input the value given in

O43 (resp. AQ43). If the extrapolation from mounting R to a particular mounting is wished then input the value given in

R43 (resp. U43, AA43…)

If the extrapolation to a particular mounting is wished then input the value given in R44 (resp.

U44, AA44…)

Without aerodynamics extremities Length L (m)

Model of reflection loss

Model of by-pass correction E51 to G51

Aerodynamics upstream

Aerodynamics downstream

Roughness of lining Δ (m)

Model of total pressure loss

For model NF2 only B (dB)

For model NF2 only



(m)

For all models 2081,3733,

FRO only spectral correction model

Model for the flow acoustic power

D45

G47

D54

D55

AW61

V63

E64

G64

G65

Input a positive real

Select a model (in the proposed list)

Select a model (in the proposed list)

Select a model (in the proposed list)

Select a model (in the proposed list)

Input a positive real

Select a model (in the proposed list)

Input a positive real

Input a positive real

Select a model (in the proposed list)

For the COmputation of DIssipative Silencers with mountings RD

For the COmputation of DIssipative Silencers with mountings RD

Used for the interpolation of a ponderation curve

(generally of secondary importance)

V65

Select a model (in the proposed list)

For the COmputation of DIssipative Silencers only o

Comments :

 some data of the table above may not be modifiable by the user despite the displayed color of the cell

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Worksheets [in-out CODIS-1A]

o

Input data :

Item

Cell for input

Foreseen action Comment

Condition of propagation W182

Select a model (in the proposed list) among the possible conditions of propagation in porous medium of set 1 (for the COmputation of DIssipative

Silencers σx1/σy1=∞, σx1/σy1=1, σx1/σy1=var. o

Comments :

 some data of the table above may not be modifiable by the user despite the displayed color of the cell o

Main displays of the results :

total pressure loss: see lines 98 to 100

Note: the following equation is considered for the definition of total pressure loss coefficients

f,

f*,

p:

pt =

p . 0.5 .



(Vp

2

=

f . 0.5 .



(Vf

2

=

f * . 0.5 .



(Vf*

2

pt: total pressure loss (Pa)

 density of fluid (kgm-3)

Vp: speed in the area Ap (ms-1)

Vf: speed in the area Sf (ms-1)

Vf*: speed in the area Sf (ms-1)

insertion loss without flow: see line 105 per 1/1 octave frequency band and in terms of A weighted global value with reference to the reference acoustic power spectrum.

Note: those results are intermediate/complementary results not equal (generally speaking) to the insertion loss with flow and self noise that the user has to use as the only reliable indicator of performance of the performance of the silencer. Those results are only displayed in order to allow the evaluation of the impact of airflow - other than self noise - by the means of a comparison with results displayed line 106.

insertion loss with flow without flow noise (Di’): see line 106 per 1/1 octave frequency band and in terms of A weighted global value with reference to the reference acoustic power spectrum.

Note 1: those results are intermediate/complementary results not equal (generally speaking) to the insertion loss with flow and self noise that the user has to use as the only reliable indicator of performance of the performance of the silencer. Those results are only displayed in order to allow the evaluation of the impact:

-

- of airflow - other than self noise - by the means of a comparison with results displayed line 105 of flow noise by the means of a comparison with results displayed line 162

Note 2: since the insertion loss is predicted from the sum of the longitudinal attenuation, a bypass correction and reflection loss, the results corresponding to the different terms of the sum are also displayed in order to allow the evaluation of the impact of each one (see table below).

Term of the sum Cells for display Notation Comment

longitudinal attenuation by pass correction reflection loss insertion loss without self noise

A108 to L127

M108 to X127

A129 to L148

M129 to X148

Da.L

Dk

Dr

D’i= Da.L+ Dk+ Dr curve and table of results per 1/3 octave band, per

1/1 octave frequency band and in terms of A weighted global value with reference to the reference acoustic power spectrum

self noise (acoustic power of flow noise): see line 153 per 1/1 octave frequency band and in terms of A weighted global value

not A-weighted acoustic power with silencer (Lw1): see line 156 per 1/1 octave frequency band and in terms of A weighted global value with reference to the reference acoustic power spectrum.

A-weighted acoustic power with silencer: see line 157 per 1/1 octave frequency band

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insertion loss with flow and self noise (Di): see line 162 per 1/1 octave frequency band and in terms of A weighted global value with reference to the reference acoustic power spectrum.

acoustic power without silencer (Lw0) and acoustic power with silencer including self noise (Lw1) versus frequency

see lines 164 to 184 columns A to F per 1/1 octave frequency band and in terms of A weighted global value with reference to the reference acoustic power spectrum.

insertion loss with flow without self noise (Di’) and insertion loss with flow and self noise (Di) versus frequency see

lines 164 to 184 columns G to L per 1/1 octave frequency band and in terms of A weighted global value with reference to the reference acoustic power spectrum.

1A.4: Examples of computation with SILDIS

Example 1A.4.1 dissipative silencer with a rectangular cross section

Envisaged application

It is wished to compute the acoustic and aerodynamic performances of a dissipative silencer with a rectangular cross section (width

B=1200mm [1], height H=1200mm [2], length L=1000mm [3]), having rectangular edged [4] splitters of thickness 2d such as 2d-

2d’1=398.6mm [5] with a open area ratio of 55.5% [6] made of one [7] inhomogeneous in directions parallel to and perpendicular to its surface bulk absorber [8] having the reference DISP (resp. DISN) in the database for porous media of SILDIS [9] with [10] a cloth of thickness d’1=0.5/100 mm [11] having the reference DIS in the series cloths database of SILDIS [12] with a perforated protection of thickness d’1=0.7 mm [12bis] with holes diameter 3 mm spaced by a distance 5 mm with an hexagonal array, referred to as

R3T5in data base [13]

It is foreseen to use the silencer with an air flow rate of 32.645 kg/s [14] at 20 °C [15] at a pressure of 101325 Pa [16].

It is decided to not take into account a limitation of the propagation loss for L>1m [17] and to not take into account the reflection loss

[18].

The reference spectrum is supposed of the type “pink noise” [19] with a sound power level of 130 dB/oct [20]

It is chosen to predict the self noise of the silencer in the way described with the model referred to as 2081B [21]

It is chosen to predict the back pressure with the model referred to as FRO [22]

Input data

The input data required for the computation are listed hereafter in reference with the above data (see figures in brackets in the previous

§, used as placemarks for explaining the selection below).The input cells will be referred to thanks to their EXCEL’s coordinates

(column / line) in the following part of the present user’s manual.

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Worksheet [in COALA-1A] for example 1A.4.1

Item

Cell for input

Foreseen action (see

§1.3)

Temperature D6

Pressure

Maximum set index imax

Reference

Thickness

Reference

Incorporation of the series perforated protections (0/1)

Thickness

Reference

Incorporation of the series cloths (0/1)

Thickness

Lw0 only known per 1/1 octave frequency band (0/1)

Lw0

D7

E13

J18 to K18

J37

J45

J57

J58

W18

W23

W24

R62

B65 to

K65

Input a real number

Input a real positive number

Input an integer from 1 to

4

Select a reference

(material in the proposed list) for each layer of interest

Input a real positive number

Select a reference

(material in the proposed list) for each layer of interest

For NO press 0, for YES press 1

Input a real positive number

Select a material (in the proposed list) for each layer of interest

For NO input 0, for YES input 1

Input a real positive number

For NO input 0, for YES input 1

Input a real positive number as requested for a

1/1 octave band sound power level

Worksheet [in COSIL-1A] for example 1A.4.1 only

Item

Limit set index ilim

Cell for input

D18

Foreseen action (see

§1.3)

Input an integer from 1 to

imax

D25

D37

Input a positive real

Input a real

Half airway

Mass flow rate

Width B (m)

Height H (m)

Length L (m)

D43

D44

D45

Input a positive real

Input a positive real

Model of reflection loss

Model of by-pass correction for L>1m

Aerodynamics upstream

Aerodynamics downstream

Model of total pressure loss

G47

F51

D54

D55

V63

V65

Input a positive real

Select a model (in the proposed list)

Select a model (in the proposed list)

Select a model (in the proposed list)

Select a model (in the proposed list)

Select a model (in the proposed list)

Select a model (in the proposed list)

Model for the flow acoustic power

Input

20

101325

1

DISN, DISP

0.19930

R3T5

1

0.0007

DIS

1

0.00005

1

130

Input

1

0.1

32.645

1.2

1.2

1.0

ZER

ZER

R

R

FRO

2081B

See placemark / comment

[15]

[16]

[7]

[8],[9]

[5]

[13]

[13]

[12bis]

[12]

[10]

[11]

[20]

[20]

See placemark

[7]

Based on [6]

[14]

[1]

[2]

[3]

[18]

[17]

[4]

[4]

[22]

[21]

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Worksheet [in-out CODIS1-1A] for example 1A.4.1 only

Item

Cell for input

Foreseen action (see

§1.3)

Condition of propagation W182

Select a model (in the proposed list)

Screenshots of the worksheets (for the example of computation)

Screenshot of worksheet [in COALA-1A] for example 1A.4.1

Input

σx1/σy1=var

See placemark

[8]

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Screenshot of worksheet [in COSIL-1A] for example 1A.4.1

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Screenshot of worksheet [in-out CODIS1A] for example 1A.4.1 some

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Appendix to Section 1A: list of symbols

General

f: frequency (Hz)

Lw0: sound power level without soundproofing equipment (dB ref. 1pW)

Lw1: sound power level with soundproofing equipment (dB ref. 1pW) t: time (s)

Set of materials

ilim: limit set index imax: maximum set index

: total number of cloths and perforated protections accounted as porous media i.e. not accounted as series cloth (resp. series perforated protections) using electro acoustic analogie

Dry air

a: diffusivity (m

2

/s) c: (adiabatic) velocity of sound (ms

-1

) c p

: specific heat (capacity) (at constant pressure) (J/kg/K)

C s

: adiabatic compressibility (Pa

-1

C

T

: isothermal compressibility (Pa

)

-1

) k: wave number (rad/m)

K s

: adiabatic bulk modulus (Pa)

K

T

: isothermal bulk modulus (Pa) t: temperature (°C)

P: static/atmospheric pressure (Pa)

Pr: Prandtl number

R: gas constant (J/kg/K)

V: volume (m

3

)

Z: characteristic impedance (Nsm

-3

)

β: coefficient of thermal expansion

: propagation constant (rad. m

-1

)

: dynamical viscosity (Nsm

-2

)

: thermal conductivity (W/m/K)

: wavelength (m)

: kinematic viscosity (m

2

/s)

: density (kg/m3) subscript / superscript subscript superscript for normal conditions for test (room) conditions

0

0

N

* for service conditions front atmosphere rear atmosphere

0

0 **

Porous media

a’, a’’: coefficients for the expression of

 an

 b’, b’’: coefficients for the expression of Z an c

1

, c

2

, c

3

, c

4

, c

5

, c

6

, c

7

, c

8

: coefficients for the expression of

C seff

: adiabatic compressibility (Pa

-1

) an and Z an

E: non-dimensional parameter related to frequency, flow resistivity and density of dry air

K seff

: adiabatic bulk modulus (Pa)

RG: (bulk) density (kg/m

3

)

Z a

: characteristic impedance (Nsm

-3

)

Z an

: normalized characteristic impedance

α’, α’’: exponents for the expression of

β’, β’’: exponents for the expression of Z an

 an

α

: (high frequency limit of the) tortuosity

 a

: propagation constant (rad.m

-1

)

 an

: normalized propagation constant

 ax

: propagation constant in the x-direction (rad.m

 ay

: propagation constant in the y-direction (rad.m

-1

)

-1

)

Λ’: thermal characteristic length (m)

Λ : viscous characteristic length (m)

ρ eff

: effective density (kg/m

3

)

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ø : (open) porosity

σ: (static) air flow resistivity (=specific flow resistance) (Nsm

-4

)

σ1x: (static) air flow resistivity in the x-direction for porous medium of set 1(Nsm

σ1y: (static) air flow resistivity in the y-direction for porous medium of set 1(Nsm

-4

)

-4

)

Note: subscript i for set i except for σ1x and σ1y

Cloths

d’: thickness (m)

M’: surface density (kg/m

2

)

R’: superficial flow resistance (Nsm -3

)

Rp’: parallel resistance (losses due to mounting) (Nsm -3

)

Note: subscript i for set i

Perforated protections

a: diameter of holes / width of slit (m) d’’: thickness (m)

M’’: surface density (kg/m 2

)

R’’: series flow resistance (Nsm -3

)

Rp’’: parallel resistance (losses due to mounting) (Nsm

-3

)

ε: open area ratio

Note: subscript i for set i

Silencer

abulk: cf. step [F-1A] (m) alocal: cf. step [F-1A] (m)

A : area of the duct above and below the silencer (m

2

)

Af: area of the overall section of the silencer (m

2

)

Ap : free area of the silencer (passage area of the airways) (m

2

)

B: width for mounting RD (m) d: overall thickness of the acoustic structure (m)

2d: for dissipative silencers, thickness of central splitters (for mounting RDdbulk: cf. step [F-1A] (m) dlocal: cf. step [F] (m)

Da: propagation loss (dB/m)

Da.L:longitudinal attenuation (dB)

Di: insertion loss with flow and self noise (dB)

Di’: insertion loss with flow without self noise (dB) (Di’=Da*L+Dk+Dr)

Dk: limitation of the propagation loss (dB/m)

Dr: reflection loss (dB) fco: cut-off frequency of the duct (Hz) h=2h/2: for dissipative silencers, width of extreme air way (for mounting RD only) (m)

2h: for dissipative silencers, width of central airways (for mounting RD only) hbulkl: cf. step [F-1A] (m) hlocal: cf. step [F-1A] (m)

H: height for mounting RD(m)

L: length without aerodynamic extremities (m)

M: Mach number

Nd: for a dissipative silencer only number of central splitters (for mounting RD only)

Qm: mass flow rate (kg/s)

Qv: volume flow rate (m3/s or m3/h or Nm3/h)

Vf: speed of airflow in the area Af (m/s)

Vf*: speed of airflow in the area Af* (m/s)

Vp: speed of airflow in the area Ap (m/s)

Λ=d/h

 f: total pressure loss coefficient in relation with airflow speed Vf

 f*: total pressure loss coefficient in relation with airflow speed Vf*

 p: total pressure loss coefficient in relation with airflow speed Vp

Miscellaneous

See also corresponding § in General considerations

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Section 2: computation of plane partitions

(MODULE 2 of the software)

2.1: Introduction

Terms and definitions

For the needs of the present user’s manual, the following terms and definition apply:

Partition: acoustic structure (see corresponding § in Section 0), regardless of what is on the back (atmosphere or impervious rigid back).

Plane partition: partition for which the shape of the surfaces on the one hand: facing the front atmosphere and on the other hand: at the rear are sufficiently close to a plane (for example: including corrugated plates and profiled claddings, but excluding cylindrical shells or pipes)

Sound reduction index: 10 times the decimal logarithm of the ratio of the acoustic power impinging on a partition under test to the acoustic power transmitted by the sample [see NF EN ISO 140-3 Acoustics - Measurement of sound insulation in buildings and of building elements – Part 3: Laboratory measurement of airborne sound insulation of building elements (1995)]

Rstat: with a statistic incidence (i.e. all possible incidence with an equal probability between angular limits)

Rdif: for a diffuse field

Sound absorption factor (

0): ratio of the acoustic power absorbed by the surface of the sample under test (no way back) to the incident acoustic power, for a plane wave at normal incidence [see ISO 10534-1 Acoustics – Determination of sound absorption coefficient and impedance in impedance tubes – Part 1: Method using standing wave ratio (1996)]

Sound absorption coefficient for a statistic incidence (

 stat): ratio of the acoustic power absorbed by the surface of the sample to the incident acoustic power, for a plane wave with a statistic incidence (i.e. all possible incidence with an equal probability between angular limits)

Sabine’s factor (

 sab): ratio of the equivalent acoustic area of a sample to the area of the sample [see NF EN ISO 354 Acoustics –

Measurement of sound absorption in a reverberation room (1993)]

Geometry

The geometry used for the design of plane partitions with the program SILDIS is shown in figure 2.1 (illustrating the case of a profiled cladding).

x: in case of an orthotropic plate, direction of highest bending stiffness (xx: axis about which an orthotropic plate is least stiff )

y: direction of the thickness of the partition (yy: axis normal to the partition surface)

z: in case of an orthotropic plate, direction of lowest bending stiffness (zz: axis about which an orthotropic plate is the stiffest )

O

rientation: (useful in case of an orthotropic plate) the angle

(may be displayed: fi) of the projection (on the surface of the acoustic structure) of the direction of propagation of the waves in the front atmosphere is considered with respect to the axis xx (for example, for a corrugated acoustic structure, it is with respect to the axis parallel to the corrugations as shown on the figure)

Incidence: the angle

(may be displayed: teta) of the direction of propagation of the waves in the front atmosphere is considered with respect to the axis yy

Fig. 2.1

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In case of a partition surrounded by a baffle (in which the partition is symmetrically mounted), the geometry used is shown in figure

2.2

Fig. 2.2

For Lx ≠ lx the following limitation of the input data is required: Int [

0.5

* Lx * 20000 / c

0

] ≤ 464 ; for Lz ≠ lz the following limitation of the input data is required: Int [

 0.5

* Lz * 20000 / c

0

] ≤ 464 where c

0 is the speed of sound in air (m/s). Note: For Lx ≠ lx (resp. Lz

≠ lz) the the following limitation of the input data is required for Lx (resp. Lz): 4.500 m when c

0

=343.3 m/s

2.2: Scientific and technical background

The prediction of acoustic performances of plane partitions with SILDIS is founded on a scientific and technical background in relation with: o analytical models for taking into account the properties of materials and various physical phenomena useful on the occasion of the computation o measurement results for feeding some of those models and for allowing the necessary improvement (through correction factors) of the correlation between some calculations and on site observations

In case of an atmospheric back, the obtained results are comparable with the standardized measurement: see NF EN ISO 140-3

Acoustics - Measurement of sound insulation in buildings and of building elements – Part 3: Laboratory measurement of airborne sound insulation of building elements (1995) and (in case of rigid impervious back) see NF EN ISO 354 Acoustics – Measurement of sound absorption in a reverberation room (1993) and also ISO 10534-1 Acoustics – Determination of sound absorption coefficient and impedance in impedance tubes – Part 1: Method using standing wave ratio (1996).

2.2.1Thermodynamics and fluid dynamics:

Steps of the computation

Step [a]

All computations have been gathered in this single step for the sake of simplicity. See corresponding § in Section 1

2.2.2 Acoustics:

Bloc diagram :

The computation scheme of plane partitions is according the bloc-diagram below (cf fig. 2.3):

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fig. 2.3

Note 1: the service conditions dependence has been omitted for the sake of simplicity. See: report [PhRXX-015]

Note 2: the main steps (the steps involving a physical modeling) being referred to from [A] to [T] have been taken into account for the bloc-diagram above (some of the parameters of the above bloc diagram are not independent); the frequency dependence has been omitted for the sake of simplicity

Note 3: analytical calculations are involved in steps [B] to [T] with the exception of step [R] for which empirical methods are involved

Steps of the computation

Step [A]

This step aims at taking into account what is on the back (i.e. at the rear of the acoustic structure ). See corresponding § in

Section 1 o

Bibliography (complementary sources) :

[A2]

[A3]

Step [B]

This step aims at taking into account porous media used in the acoustic structure. See corresponding § in Section 1

Step [C]

This step aims at taking into account series cloths used in the acoustic structure. See corresponding § in Section 1

Step [D]

This step aims at taking into account series perforated protections used in the acoustic structure. See corresponding § in

Section 1

Step [E]

This step aims at predicting the surface impedance of a multilayered acoustic structure (including porous media, series cloths and series perforated protections with a back selected in a way appropriate for the considered simulation): see corresponding § in

Section 1) including also thin plates at the front of the series cloths (bibliography unchanged).

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Comments :

It has been taken into account:

 that the most sophisticated partition of interest for the applications foreseen at ITS or elsewhere consists of a multilayer filling - from inside to outside - (see report [PhRxx-006x]):

-

-

-

-

1 layer of perforated sheet (being presently with diameter of holes 3mm in a hexagonal array with a perforation rate of 32 % thickness 1.5mm)

1 layer of cloth (being presently : to be précised)

1 layers of porous media (being presently: to be precised)

1 steel plate

-

-

Air

1 layer of perforated sheet (being presently with diameter of holes 3mm in a hexagonal array with a perforation rate of 32 % thickness 0.8mm)

1 layer of cloth (being presently : to be precised)

-

-

-

1 layers of porous media (being presently: to be precised)

1 steel plate

 the rear boundary condition for the arrangement of materials of interest for the COmputation of Plane PArtitions

(being an atmospheric back for the derivation of the sound reduction index )

 possible other useful arrangements of materials (for other predictions to be done in relation with the COmputation of

Acoustic LAyers, not only in the context of COmputation of Plane PArtitions)

 possible other useful rear boundary conditions for the arrangements of materials: impervious rigid back for Sabine’s factor for example (also for other predictions to be done in relation with the COmputation of Acoustic LAyers, not only in the context of COmputation of Plane PArtitions)

Consequently (see figure 2.4 below showing the most sophisticated acoustic structure available under the condition – presently not fulfilled - of complete implementation of the software):

 a variable (from 1 to 4) number of sets of elements is considered for the computation, the sets being indexed from an impervious rigid back to the front (airway side): 1 to 4

 a complementary set (set 0) is used (at the rear of set 1) consisting of up to 1 thin plate (indeed 1 or several identical thin plates) backed by atmosphere or 1 backed by an impervious rigid wall, the selection being made by the user, depending on the considered application for which the computation is performed.

Remark: the set 0 has still not been 100 % implemented in the considered revision of the software (work on progress but considerable unsolved difficulties faced in relation with a computational overload)

For the total thickness of the acoustic structure d the following formula apply:



d = imax

∑ d i

+ imax

I’ i

* d’ i

+ imax

I’’ i

* d’’ i

+ imax

∑ n i

* d’’’ i i = 1 i = 1 i = 1 i = 0

d i

(resp. d’ i

, d’’ i and d’’’ i

) = thickness of the porous medium (resp. the series cloth, the series perforated protection and the thin plate) of set i

I’ i

(resp.Id’’ i

) = 0 or 1 depending on the incorporation (or not) of the considered element of set i in the acoustic structure

(omitted in the worksheets displays of the software for the sake of simplicity) n i

= number of identical thin plates of set i (omitted in the worksheets displays of the software for the sake of simplicity)

For the total surface density of the acoustic structure d the following formula apply:



= M i

+

I’ i

* M’ i

+

I’’ i

* M’’ i

+ n i

* M’’’ i imax

∑ imax

∑ imax

∑ imax

∑ i = 1 i = 1 i = 1 i = 0

M i

(resp. M’ i

, M’’ i and M’’’ i

) = surface density of the porous medium (resp. the series cloth, the series perforated protection and the thin plate) of set i

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I’ i

(resp.Id’’ i

) = 0 or 1 depending on the incorporation (or not) of the considered element of set i in the acoustic structure

(omitted in the worksheets displays of the software for the sake of simplicity) n i

= number of identical thin plates of set i (omitted in the worksheets displays of the software for the sake of simplicity)

set 4 set 3 set 2 set 1 set 0

Fig. 2.4 atmospheric back or impervious rigid back

 each set (from 1 to 4) consists (from the rear to the front) of up to 1 porous medium, up to 1 series cloth and up to 1 series perforated protection , up to 1 series thin plate (using electro-acoustic analogies): see figure 2.5 below.

?

set 1 to 4: zoom

fig. 2.5 porous medium

. series cloth series thin plate series perforated protection

 each thin plate can be either profiled (when monolithic) or with an extensional damping or with a constrained damping

(see fig. 2.6 and 2.7)

 the surface impedance of the acoustic structure with an impervious rigid back or with an atmospheric back is calculated above the set imax: the COmputation of the Plane PArtitions is performed for an acoustic structure (with an impervious rigid back or with an atmospheric back) including sets from 0 to imax (with 0

imax

4)

Note: for the considered version of SILDIS, calculations with the routine COPPA are possible for imax = 0 or for imax

=1or for imax = 2

The less complicated models available for taking into account the physical properties of a porous medium are based on the hypothesis of homogeneity in directions parallel to and perpendicular to the surface of the material (i.e. same properties in directions x, y and z). Although some porous media (including some stone wools, some glass wools) are known to be non homogeneous in directions parallel to and perpendicular to the surface of the material having (in particular) an airflow resistivity normal to laminae of fibers σ

N

and an airflow resistivity parallel to laminae of fibers σ

P that can notably differ (with σ

P

reaching only 0.5*σ

N sometimes), no possible inhomogeneity of porous media in directions parallel to and perpendicular to its surface (i.e. no different properties - depending on the used model - in directions x and y) is considered (for the routine COmputation of

Plane PArtitions).

Note 1: each layer is assumed to not be glued to another

Note 2: concerning the perforated protection of the set i, the porous medium taken into account with the models of added impedance ROA and RDE is:

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 at the rear: the porous medium of set i

 at the front: the porous medium of set i+1 if i<4 (even if i+1>imax: the selection of a reference different of AIR for the porous media of set i such as i>imax is highly discouraged) or the front atmosphere if i=4

Note 3: the use in practical cases (and the corresponding prediction of performance) of a perforated protection in contact with something else than a porous medium (that can be air at the front or a thin wire mesh spacer at the rear in some cases) is highly discouraged

Step [M]

This steps aims at taking into account series thin plates used in the acoustic structure. o

Bibliography (references) :

thin plate

[M1]

[M2]

[M3]

-

[M4]

-

[M5]

-

[M6]

-

[M7]

-

[M8]

-

[M9]

- o

Comments :

The following governing equation is considered (with notations adapted from various sources: will be specified on the occasion of a future revision of this user’s manual)

:

 w

D

11

∂x



12

+ 2D

66

where

M’’’: surface density (kg/m2)

∂x w

∂z

2 22

∂z w



∂t

 w



 p: pressure (Pa) t: time (s) w: lateral (transverse) displacement (m)

and where the bending stiffnesses Dij (i and j varying from 1 to 2) (Nm) can be expressed as:

D

11

= D’x =D

2 ( D

12

+ 2D

66

) = 2 D’xz = 2 H = 2D, where = D’xz = (D’x D’z) 0.5

= D

D

22

= D’z = D

The loss factor of plates

is computed according various models as shown in the table below:

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INT

TOT source

of the material

[M5]

When used, the frequency corresponding to the mode (1,1) of thin plates f

11

(may be displayed f11) is computed according various models as shown in the table below: model HAN

HEA

source [M4] [M6]

The critical frequency fc is derived as:

fc =

c



M’’’

D

0.5

consider the plate as a thin plate ) is computed according various models as shown in the table below: model GER NF

NAT

source [M7], [M8] [M9] fceff=fc

Step [M’]

This step, being a complementary feature associated with step [M], aims at calculating the properties of series perforated plates in the acoustic structure.

This steps aims at taking into account series thin plates used in the acoustic structure. perforated plate

In order to include the calculations in the general layout of the program, an equivalent series thin plate is considered, referenced

PERFO, available in the list of thin plates of the worksheet [in COALA], for which the corresponding parameters are first derived from the input data of the layer, by the use (before using the worksheet [in COALA]) of a complementary worksheet referenced [inout COPERF] (COmputation of PERForated plates). o

Bibliography (references) :

[M’1] o

Comments :

The Young’s modulus of the equivalent plate (depending on open area ratio

) is computed according various models as shown in the table below model MEC source [M’1]

The density of the equivalent plate (depending on open area ratio

) is computed as for a monolithic plate of same surface density and of same thickness.

The Poisson’s ratio of the equivalent plate is set to the Poisson’s ratio of the (thin) base plate.

The loss factor of the equivalent plate is set to the loss factor of the base (thin) plate.

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Step [M’’]

This step, being a complementary feature associated with step [M], aims at calculating the properties of damped plates made of a

(thin) base plate and of an unconstrained layer of damping material in the acoustic structure (extensional damping) as shown of figure 2.8 below fig. 2.8

damping plate base plate

In order to include the calculations in the general layout of the program, an equivalent series thin plate (composite) is considered, referenced 2-PLY, available in the list of thin plates of the worksheet [in COALA], for which the corresponding parameters are first derived from the input data of each layer of the composite, by the use (before using the worksheet [in COALA]) of a complementary worksheet referenced [in-out CODAP] (COmputation of DAmped Plates). o

Bibliography (references) :

[M’’1]

[M’’2]

-

[M’’3]

-

[M’’4]

[M’’5]

[M’’6]

[M’’7]

- o

Comments :

The Young’s modulus and the loss factor of the equivalent plate are computed according various models as shown in the table below: model BER MOI AB source

[M’’1]

[M’’2]

[M’’4]

[M’’3]

[M’’4]

[M’’7]

The density of the equivalent plate is computed as for a monolithic plate of same surface density and of same total thickness

(the sum of the thicknesses of the 2 layers of the composite - as displayed in worksheet [in-out CODAP] - is required as an input in the worksheet [in COALA] for the thickness of the thin plate referenced 2-PLY).

The Poisson’s ratio of the equivalent plate is set to the Poisson’s ratio of the (thin) base plate. The use of results of computations involving damping materials with Poisson’s ratio not sufficiently close of the Poisson’s ratio of the (thin) base plate is discouraged.

Step [M’’’]

This step, being a complementary feature associated with step [M], aims at calculating the properties of damped plates made of a

1st thin plate (base plate), a damping material and a 2 nd

thin plate (constraining layer) in the acoustic structure (constrained

damping) as shown of figure 2.9 below

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constraining plate base plate damping plate

In order to include the calculations in the general layout of the program, an equivalent series thin plate (composite) is considered, referenced 3-PLY, available in the list of thin plates of the worksheet [in COALA], for which the corresponding parameters are first derived from the input data of each layer of the composite, by the use (before using the worksheet [in COALA]) of a complementary worksheet referenced [in-out CODAP] (COmputation of DAmped Plates).

At the date of writing of the present user’s manual, it has not been checked in a satisfying way the accuracy of the software for the computation of the performances of sandwich panels with a thickness of the core much greater than the thickness of the laminates and/or with any extensional stiffness.

At the date of writing of the present user’s manual, it has not been checked in a satisfying way the accuracy of the software for all the possible models involved in the step [P’] when the reference 3-PLY is used for the plate. o

Bibliography (references) :

[M’’’1]

[M’’’2]

-

[M’’’3]

-

[M’’’4]

[M’’’5]

[M’’’6]

[M’’’7]

- o

Comments :

The Young’s modulus and the loss factor of the equivalent plate referenced 3-PLY are computed according various models as shown in the table below: model BER MOI MAX source

[M’’’1]

[M’’’2]

[M’’’3]

[M’’’4]

(*)

*combining models BER and MOI

The density of the equivalent plate is computed as for a monolithic plate of same surface density and of same total thickness

(the sum of the thicknesses of the 3 layers of the composite - as displayed in worksheet [in-out CODAP] - is required as an input in the worksheet [in COALA] for the thickness of the thin plate referenced 3-PLY).

The Poisson’s ratio of the equivalent plate is set to the Poisson’s ratio of the base (thin) plate. The use of results of computations involving damping materials with Poisson’s ratio not sufficiently close of the Poisson’s ratio of the base (thin) plate is discouraged.

Step [M’’’’]

This step, being a complementary feature associated with step [M], aims at calculating the properties of series orthotropic

plates in the acoustic structure (i.e. plates for which the bending stiffness is dependent upon the direction of wave propagation).

In order to include the calculations in the general layout of the program, an equivalent series thin plate is considered, referenced

ORTHO, available in the list of thin plates of the worksheet [in COALA], for which the corresponding parameters are first der ived from the input data of the layer, by the use (before using the worksheet [in COALA]) of a complementary worksheet referenced [inout COORT] (COmputation of ORThotropic plates).

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At the date of writing of the present user’s manual, it has not been checked in a satisfying way the accuracy of the software for models different of the model INT involved in the step [P’] when the reference ORTHO is used for the plate. o

Bibliography (references) :

[M’’’’1]

[M’’’’2]

-

[M’’’’3]

-

[M’’’’4]

[M’’’’5]

-

[M’’’’6]

[M’’’’7]

-

[M’’’’8]

- o

Comments :

The bending stiffness D’x (D’zz) in the direction x of highest bending stiffness of the plate (about the zz-axis about which the panel is the stiffest) and the bending stiffness D’z (D’xx) in the direction z of lowest bending stiffness of the plate (about the

xx-axis about which the panel is the least stiff), of the equivalent plate referenced ORTHO are computed according various models as shown in the table below (cf. fig 2.10): model COR RIB CLA MOI source

[M’’’’1] [M’’’’1]

(*) (**)

*For the model CLA, the bending stiffness are computed according various models as shown in the table below : model SAY HAN source

[M’’’’2],

[M’’’’3]

[M’’’’6],

[M’’’’7]

**D’x (D’zz) and D’z (D’xx) are input data model COR model RIB model CLA

Fig. 2.10

The following governing equation is considered (with notations adapted from various sources: will be specified on the occasion of a future revision of this user’s manual)

:

D

11

∂x w



12

+ 2D

66

∂x w

∂z

2 22

 w

∂z



∂t

 w



+ M’’’ = p (x, z, t)

 

where

  

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M’’’: surface density (kg/m2) p: pressure (Pa) t: time (s) w: lateral (transverse) displacement (m)

and where the bending stiffnesses Dij (i and j varying from 1 to 2) (Nm) can be expressed as:

D

11

= D’x

2 ( D

12

+ 2D

66

) = 2 D’xz = 2 H, where = D’xz = (D’x D’z)

0.5

with the exception of the model MOI where D’xz is an input data

D

22

= D’z

When used, the frequency corresponding to the mode (1,1) of thin plates f

11

(may be displayed f11) is computed according various models as shown in the table below: model HAN

HEA

source [M’’’’6] [M’’’’8]

The Young’s modulus of the equivalent plate referenced ORTHO is set to the Young’s modulus of the base (thin) plate.

The density of the equivalent plate is computed as for a monolithic plate of same surface density and of same total thickness

(the overall thicknesses of the plate - as displayed in worksheet [in-out COORT] - is required as an input in the worksheet [in

COALA] for the thickness of the thin plate referenced ORTHO).

The Poisson’s ratio of the equivalent plate is set to the Poisson’s ratio of the base (thin) plate.

The loss factor of the equivalent plate is set to the loss factor of the base (thin) plate.

The lowest critical frequency fcx is derived as:

fcx =

c



M’’’

D’x

0.5

fcz =

c



M’’’

D’z

0.5

Step [N]

 

This steps aims at calculating the sound absorption coefficient at normal incidence of the acoustic structure assumed to be locally reacting o

Bibliography (references) :

[N1]

[N2]

[N3] o

Comments :

The sound absorption coefficient at normal incidence derived by the means of the present step is referred to as

0 (may be displayed: alpha 0). o

Remarks in relation with the displayed results:

In case of rigid impervious back, at the room conditions of temperature and pressure, the displayed results in terms of values per 1/3 octave frequency band (computed from 1/21 octave frequency band values) are comparable with the standardized measurement: see standard ISO 10534-1 Acoustics – Determination of sound absorption coefficient and impedance in impedance tubes – Part 1: Method using standing wave ratio.

The values per 1/1 octave frequency band are obtained with SILDIS by averaging the results per 1/3 octave band

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Step [O]

This steps aims at calculating the sound absorption coefficient for a statistic incidence of the acoustic structure o

Bibliography (references) :

[O1]

[O2]

[O3]

[O4]

-

[O5]

-

[O6] o

Comments :

The sound absorption coefficient for a statistic incidence derived by the means of the present step is referred to as

stat

(may be displayed: alpha stat). o

Remarks in relation with the angular integration (see § Geometry in Section 2)

The sound absorption coefficient for a statistic incidence is calculated (per frequency band) by angular integration according to the generalized (customized) formula below (see notations farther): min (

max,

L)

min



,

)*cos(

)*sin(

)*d



stat =

1

N

N

min (

max,

L) i = 1

min cos(

)*sin(

)*d

 with the notable exception of the model DAV where the denominator is replaced by 0.5

with respect to the orientation (angle

): the integration is performed from

min to

max as selected by the user (in order to match field considerations) in a proposed list (for the present version of the program, angles from 5.625 to

84.375° with a step of 11.25° i.e. N=8 angles)

Recall: orientation (angle

) is of interest in case of an orthotropic plate included in the acoustic structure

regarding the incidence (angle

): the integration is performed from

min to min (

max,

L)

-

min and

max are selected by the user (in order to match field considerations) in a proposed list (for the present version of the program, angles from 0 to 89.375° with a step of 1.25° i.e. 73 angles)

-

L is taken into account according various models as shown in the table below: model 90° DAV MOI

[O4] [O5]

[O6] source (*) [O4] [O5]

*

L = 90°

Accordingly:

with respect to the orientation (angle

):

 for a simulation between 2 limiting angles of incidence (to choose), the user will input (by the means of the proposed lists) a value for

min and a value for

max

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 for a simulation of a diffuse incidence (with respect to the orientation angle

), the user will input (by the means of the proposed lists) 5.625° for

min and 84.375° for

max

regarding the incidence (angle

):

 for a simulation between 2 limiting angles of incidence (to choose), without other consideration, the user will input (by the means of the proposed lists):

 a value for

min and a value for

max

 the model for

L: 90°

 for a simulation of a field (diffuse ?) incidence (with respect to the incidence angle

)

 using the (classical) approach consisting (for a partition of undefined extent) in using a unique limiting value of the angle of incidence (78°, 80°, 85° … in any case below 90° in order to reduce the discrepancies between prediction and measurement results especially at low frequency), the user will input (by the means of the proposed lists):

- 0° for

min

- the closer (to the wished limiting angle) value for

max

- the model for

L: 90°

 using the “pure” approach basing the model referred to as “DAV” (taking into account the dimensions of the partition), the user will input (by the means of the proposed lists):

- 0° for

min

- 90° for

max and

- the model for

L: DAV

 preferring not replacing by 0.5 the denominator of the formula above, but being interested by the approach basing the model referred to as “DAV” the user will input (by the means of the proposed lists):

- 0° for

min

- 90° for

max and

- the model for

L: MOI o

Remarks in relation with the displayed results:

In case of rigid impervious back, at the room conditions of temperature and pressure and with an appropriate selection of values of limiting angles of integration the displayed result(s):

 in terms of values per 1/3 octave frequency band (computed from 1/21 octave frequency band values) and in term of values per 1/1 octave frequency band are comparable with the standardized measurement: see standard NF EN ISO

354 Acoustics – Measurement of sound absorption in a reverberation room.

 in terms of the unique index

 w is comparable with the standardized measurement: see standard NF EN ISO 11654

Acoustics – Sound absorbers for use in buildings – Rating of sound absorption.

Step [O’]

This step, being a complementary feature associated with step [O], aims at calculating the Sabine’s factor of the acoustic structure o

Bibliography (references) :

[O’1] o

Comments :

The sound absorption coefficient derived by the means of the present step is referred to as

sab (may be displayed: alpha

sab).

When alpha stat reaches 1,

sab is set to an (upper) (finite) limiting value being chosen by the user for the considered version of the software o

Remarks in relation with the angular integration (see § Geometry in Section 2)

The Sabine’s factor is derived (per frequency band) from the sound absorption coefficient for a statistic incidence: attention has to be paid to angular limits of integration appropriate for a diffuse field (see corresponding § at step

[O])

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Remarks in relation with the displayed results:

see corresponding § at step

[O]

Note: in case of rigid impervious back only makes the results displayed for

sab sense

Step [P]

This steps aims at calculating the sound reduction index for coupling 0 % without sound leaks o

Bibliography (references) :

[P1]

[P2]

[P3]

-

[P4]

-

[P5]

-

[P6] o

Comments:

The transmission loss for a statistic incidence derived by the means of the present step is referred to as R stat = -

10log(

stat) where

stat is the transmission factor for a statistic incidence o

Remarks in relation with the angular integration (see § Geometry in Section 2)

The transmission factor for a statistic incidence is calculated (per frequency band) by angular integration according to the generalized (customized) formula below (see notations farther): min (

max,

L)

min



,

)*cos(

)*sin(

)*d



stat

=

1

N

N

min (

max,

L) i = 1

min cos(

)*sin(

)*d

 with the notable exception of the model DAV where the denominator is replaced by 0.5

with respect to the orientation (angle

): the integration is performed from

min to

max as selected by the user (in order to match field considerations) in a proposed list (for the present version of the program, angles from 5.625 to

84.375° with a step of 11.25° i.e. N=8 angles)

Recall: orientation (angle

) is of interest in case of an orthotropic plate included in the acoustic structure

regarding the incidence (angle

): the integration is performed from

min to min (

max,

L)

-

min and

max are selected by the user (in order to match field considerations) in a proposed list (for the present version of the program, angles from 0 to 89.375° with a step of 1.25° i.e. 73 angles)

-

L is taken into account according various models as shown in the table below: model 90° DAV MOI

[O4] [O5]

[O6] source (*) [O4] [O5]

*

L = 90°

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Accordingly:

with respect to the orientation (angle

):

 for a simulation between 2 limiting angles of incidence (to choose), the user will input (by the means of the proposed lists) a value for

min and a value for

max

 for a simulation of a diffuse incidence (with respect to the orientation angle

), the user will input (by the means of the proposed lists) 5.625° for

min and 84.375° for

max

regarding the incidence (angle

):

 for a simulation between 2 limiting angles of incidence (to choose), without other consideration, the user will input (by the means of the proposed lists):

 a value for

min and a value for

max

 the model for

L: 90°

 for a simulation of a field (diffuse ?) incidence (with respect to the incidence angle

)

 using the (classical) approach consisting (for a partition of undefined extent) in using a unique limiting value of the angle of incidence (78°, 80°, 85° … in any case below 90° in order to reduce the discrepancies between prediction and measurement results especially at low frequency), the user will input (by the means of the proposed lists):

- 0° for

min

- the closer (to the wished limiting angle) value for

max

- the model for

L: 90°

 using the “pure” approach basing the model referred to as “DAV” (taking into account the dimensions of the partition), the user will input (by the means of the proposed lists):

- 0° for

min

- 90° for

max and

- the model for

L: DAV

 preferring not replacing by 0.5 the denominator of the formula above, but being interested by the approach basing the model referred to as “DAV” the user will input (by the means of the proposed lists):

- 0° for

min

- 90° for

max and

- the model for

L: MOI o

Remarks in relation with the displayed results:

The sound reduction index is computed at frequency steps of 1/3 octave (from 1/21 octave frequency band values) and then calculated per 1/1 octave frequency band for a reference acoustic power spectrum Lw0 in dB ref 1E-12W).

In case of a rear atmosphere at the room conditions of temperature and pressure, the obtained (with an appropriate selection of values of limiting angles of integration) result(s):

 in terms of sound reduction index per 1/3 octave frequency band are comparable with the standardized measurement: see

NF EN ISO 10140-2 Acoustics. Laboratory measurement of sound insulation of building elements. Measurement of airborne sound insulation

 in terms of sound reduction index per 1/1 octave frequency band are comparable with the same standard when obtained with SILDIS by the use of a pink power spectrum for Lw0.

 in terms of the unique index Rw is comparable with the standardized measurement: see standard NF EN ISO 717-1

Acoustics – Rating of sound insulation in buildings and of building elements – Part 1: Airborne sound insulation.

Step [P’]

This step, being a complementary feature associated with step [P], aims at calculating the sound reduction index of a single-

leaf (rectangular) (plane) partition (thin plate 0) with sound leaks, allowing an extended integration of various parameters (1 plate alone such as those of set 0, regardless of the selected quantity of such plates for set 0, regardless of the selected quantities of other elements, and with atmosphere at the front and at the rear regardless of the selected input data)

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Bibliography (references) :

[P’1]

-

[P’2]

-

[P’9]

-

[P’10]

-

[P’11]

[P’12]

[P’13]

-

[P’14]

-

[P’15]

-

[P’3]

-

[P’4]

[P’5]

-

[P’6]

-

[P’7]

-

[P’8]

o

Comments :

 when used, the boundary conditions are taken into account according various models as shown in the table below: model condition

SSE

Simply

Supported

Edges

CE

Clamped

Edges

MID

MIDSay between SSE and CE

 when used, the free bending waves radiation ratio

 rad is computed according various models as shown in the table below: model MAI NF source

[P’1][P’2]

[P’3] [P’4]

[P’5] (*)

[P’1][P’2]

[P’3] [P’4]

[P’5]

*although not mentioned in references [P’1 and [P’2], considerations in relation with the eigen frequency corresponding to the mode (1,1) of the plate (f

11

) are also considered. The models MAI and NF differ only by the result obtained in the area of the critical frequency.

 when used, the transmission factor for normal incidence TO is computed either with a simplified model (1/TO proportional to the frequency) or not simplified

 when used, the loss factor

 is taken into account in the way described for step [M]

 the transmission factor is computed according various models taking into account (resp. taking not into account) various parameters as shown in the table below:

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SHA(*)

MOI

[P’6] (**) parameters forced transmission resonant transmission yes yes/no no yes/no partition in a baffle / niche effect no yes/no

*not appropriate for computations with the plate referenced 3-PLY **see below

 when used, the general model MOI allows to compute the sound reduction index R as a function of frequency f as follows:

below the critical frequency fc :

 for f sufficiently below fc, the forced transmission factor

 forced is derived according various models as shown in the table below: model 4TO 3TO SEW BAL source

[P’7] [P’5]

INT

[P’5]

(*)

[P’8] [P’9]

DAV

[P’6]

[P’10] model JOS GER NF NI1 (**) NI2 (**) ZER source

[P’11] [P’12] [P’13]

[P’3]

[P’14] [P’15]

 forced=0

* see step [M] (in case of a non “pure” thin plate see also steps [M’] to [M’’’], see remarks in relation with the angular integration: below) ** the use of this model is highly discouraged if the same choice of model is not made for resonant transmission

 for f sufficiently below fc, the resonant transmission factor

 res is derived according various models as shown in the table below: model SEA JOS NF NI1 NI2 ZER source

[P’4] [P’5]

[P’11]

[P’12]

[P’3]

[P’14]

(*)

[P’15]

(*)

 res=0

* the use of this model is highly discouraged if the same choice of model is not made for forced transmission

 for f

≈ fc the transmission factor is derived (for a frequency range chosen by the user in terms of a number of 1/3 of octave below fc) according various models as shown in the table below: model JOS NF NAT source

[P’11]

[P’12]

[P’3]

(*)

* the transmission factor is derived as for the general case f < fc

at and above the critical frequency fc:

 for f sufficiently above fc the transmission factor

is derived according various models as shown in the table below: model INT SEA CRE JOS NF NIL source

[P’5](*) [P’2] [P’5]

[P’6] [P’11]

[P’3]

[P’14]

[P’15]

* see step [M] (in case of a non “pure” thin plate see also steps [M’] to [M’’’], see remarks in relation with the direction of the waves impinging the partition: below)

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 for f ≈ fc the transmission factor is derived (for a frequency range chosen by the user in terms of a number of 1/3 of octave above fc) according various models as shown in the table below: model JOS NF NI2 NAT source

[P’11]

[P’12]

[P’3] [P’15] (*)

(**)

* to be used only with model NI2 for forced and resonant transmission, and with model NIL for transmission above fc ** the transmission factor is derived as for the general case f

fc

in order to retrieve some (not always comprehensive) presentations given in various bibliographic sources

with the general model MOI: source models

[P’2] [P’3] [P’5] [P’8] [P’9] boundary conditions radiation ratio (of free bending waves) simplified transmission factor for normal incidence for f < for f >

fc

fc model of forced transmission model of resonant transmission model of transmission

SSE/CE

MAI yes

ZER

SEA

SEA

SSE/CE

NF yes

NF

NF

NF

SSE/CE

MAI no/yes

INT

SEA

INT/SEA

?

? yes

SEW

SEA?

SEA?

-

- yes

BAL

ZER

CRE source models

[P’10] [P’11] [P’13] [P’14] boundary conditions radiation ratio (of free bending waves) simplified transmission factor for normal incidence model of forced for f <

fc transmission model of resonant transmission for f >

fc model of transmission

-

- no

DAV

ZER

CRE

SSE/CE

? yes

JOS

JOS

JOS

SSE/CE

? no/yes

GER

JOS

JOS

in order to retrieve the results of step [P] (with other appropriate input data :

SSE/CE

- yes

NI1

NI1

NIL

[P’15]

SSE/CE

- yes

NI2

NI2

NIL source models boundary conditions radiation ratio (of free bending waves) simplified transmission factor for normal incidence step [P]

-

- no model of forced transmission INT for f <

fc model of resonant transmission 0 for f >

fc model of transmission INT

The sound reduction index derived by the means of the present step is referred to as R dif (assuming a diffuse field).

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In case of use of the model INT, attention has to be paid to an appropriate selection of limiting angles for the angular integration in order to match field considerations. o

Remarks in relation with the angular integration:

in case of use of the model INT: see corresponding § at step [P] o

Remarks in relation with the displayed results:

see corresponding § at step [P]

Step [Q]

This steps aims at calculating the sound reduction index for coupling 100 % without sound leaks o

Bibliography (references) :

See comments below o

Comments :

The approach of step [P] is extented to the case of a partition for which the behavior is only controlled by the (total) mass

(law). The sound reduction index derived by the means of the present step is referred to as R stat. o

Remarks in relation with the angular integration:

see corresponding § at step [P] o

Remarks in relation with the displayed results:

see corresponding § at step [P]

Step [R]

This steps aims at calculating the sound reduction index with connections without sound leaks o

Bibliography (references) :

[R1]

-

[R2]

-

[R3]

[R4]

-

-

[R5]

-

[R6]

-

Comments :

Connections (for a double shell partition consisting of thin plates of set 0 and 2) are taken into account according various models:

- a general model (concerning the computation) for Rdif as shown in the tables below: model FAH DAV SHA1 SHA2 SHA3 source number of identical plates for each leaf

[R1]

1

[R1]

1

[R1][R2] according input data

[R1] [R2] according input data

[R1]

1

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- for the general model DAV only, a sub model for Rdif as shown in the tables below: model 1990 2009 2012 source [R4] [R5] [R6]

- for the general model DAV only, a sub model for Rdif as shown in the tables below: model BYO PWL ZER source comment

-

Bring Your

Own

[R6]

Plasterboar d Walls

Leaves

-

ZERo

- for the general models SHA1, SHA2, SHA3 only, a model for connections as shown in the tables below: model source

L-L

[R1][R1]

Line-Line

L-P P-P

[R1] [R1][R2]

Line-Point Point-Point comment

Note: for the present revision of the software vibration transmission factor input data are not used for the computation (to be continued: work on progress) o

Remarks in relation with the angular integration:

in case of use of the model INT for plates of set 0 (general models SHA1 and SHA 2): see corresponding § at step [P] o

Remarks in relation with the displayed results:

see corresponding § at step [P]

To be continued

Step [S]

This steps aims at calculating the sound reduction index of sound leaks o

Bibliography (references) :

[S1]

[S2]

o

Comments :

In order to include the calculations in the general layout of the program, the following bibliographic source have not been used:

[S3]

-

(slit-shaped) leaks are taken into account according various models as shown in the tables below: model

GOM

UNI source

[S1][S2] (*)

*the transmission factor is considered equal to unity

To be continued

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Step [S’]

This steps aims at calculating the sound reduction index of sound leaks for 1 leaf i.e. when is considered: not sets 0 to imax

(as it is considered for step [S] ) but 1 plate alone such as those of set 0, regardless of the selected quantity of such plates for set 0, regardless of the selected quantities of other elements, and with atmosphere at the front and at the rear regardless of the corresponding input data o

Bibliography (references) :

see corresponding § of step [S] o

Comments :

see corresponding § of step [S] To be continued

Step [T]

This steps aims at calculating the sound reduction index for coupling 0 % with sound leaks o

Bibliography (references) :

[T1] o

Comments :

The sound reduction index derived by the means of the present step is referenced R stat. o

Remarks in relation with the angular integration:

in case of use of the model INT: see corresponding § of step [P] o

Remarks in relation with the displayed results:

see corresponding § of step [P]

To be continued

Step [T’]

This steps aims at calculating the sound reduction index with sound leaks for 1 leaf i.e. when is considered: not sets 0 to imax

(as it is considered for step [T] ) but 1 plate alone such as those of set 0, regardless of the selected quantity of such plates for set

0, regardless of the selected quantities of other elements, and with atmosphere at the front and at the rear regardless of the corresponding input data o

Bibliography (references) :

see corresponding § of step [T] o

Comments :

see corresponding § of step [T]

To be continued

Step [U]

This steps aims at calculating the insertion loss for coupling 0 % with sound leaks o

Comments :

The insertion loss derived by the means of the present step is referred to as IL stat.

IL stat is not the insertion loss of the (total) acoustic structure. IL stat = R statR’ stat where R’stat is the sound reduction index of 1 plate alone such as those of set 0, regardless of the selected quantity of such plates for set 0, regardless of the selected quantities of other elements, and with atmosphere at the front and at the rear regardless of the selected input data

To be continued

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Step [V]

This steps aims at calculating the sound reduction index for coupling 100 % with sound leaks o

Bibliography (references) :

See corresponding § of step [T] o

Comments :

The sound reduction index derived by the means of the present step is referred to as R stat. o

Remarks in relation with the angular integration:

in case of use of the model INT: see corresponding § of step [P] o

Remarks in relation with the displayed results:

see corresponding § of step [P]

To be continued

Step [W]

This steps aims at calculating the sound reduction index with connections with sound leaks (2 leaves) o

Bibliography (references) :

See corresponding § of step [T] o

Comments :

The sound reduction index derived by the means of the present step is referred to as R stat. o

Remarks in relation with the angular integration:

in case of use of the model INT: see corresponding § at step [P] o

Remarks in relation with the displayed results:

see corresponding § at step [P] To be continued

2.3: How to use SILDIS

Operating conditions / security level / safety

See corresponding § in the chapter General considerations

For safety reasons, some cells of the original file provided to the user (as mentioned in the table below) for witch input data are foreseen to be entered by the user are pre-filled with the value “1/0”, among the yellow cells for which the color orange is used (*).

Worksheet Cells

[in COALA]

E13, J37, W39

* something like that

[in-out CODAP]

[in-out COPPA]

W23

X53, X54

Worksheets

Regarding the COomputation of Plane Partitions, the software SILDIS is configurated in order to allow the user to access to 4 worksheets being linked as shown in fig.2.11 (the overview of the worksheets being shown in table below).

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Fig. 2.11

Note concerning the worksheet [in COALA]: a rear atmosphere or an impervious rigid back are displayed, to be selected by the user depending on the conditions of the application for which the simulation is performed

Worksheet Suitable for mountings Input data Results

[in-out COPERF]

[in-out CODAP]

[in-out COORT]

[in COALA]

perforated plates damped plates orthotropic plates all for base plate for layers of the composite for the base plate and the geometry for elements of sets, for reference spectrum some of the parameters of the equivalent plate some of the parameters of the equivalent plate some of the parameters of the equivalent plate

--

[in-out COPPA]

[in-out COPPA0]

[in-out COPPA1]

all (i.e. for the total acoustic structure as selected, with an impervious rigid back or with an atmospheric back as selected) with 0 leaf (without leaf), with an impervious rigid back with 1leaf, with an atmospheric back *) for limits of integration, for dimensions no input data (for the time being) for specific complementary models sound absorption and sound transmission indicators sound absorption and sound transmission indicators sound transmission indicators with 2 leaves, with an for specific complementary

[in-out COPPA2]

atmospheric back

*

regardless of corresponding input data

Input data, alerts and results: the key points

models, for connections

The best use of the software requires the knowledge of some key points in relation with: o the input data : see corresponding § in Section 1 sound transmission indicators

As far as thin plates are concerned, specific data bases (libraries) ( will ) allow the design to be made with in-built engineering data (constants) referred to as “Usual” in the worksheets of the software. Warning: some properties of the presently referenced materials still not have been checked by reliable sources.

See also report [PhRxx-015x] Collection of soundproofing constructions systems: a companion to “User’s manual for the software SILDIS”

data base (library) for thin plates (available in worksheet in COALA)

 contents of the library: 21 possible references of material layers among those references: 2-PLY and 3-PLY (reported from worksheet CODAP) and ORTHO (reported from worksheet COORT)

data base (library) for layers constituting the damped plates (available in worksheet in CODAP)

 contents of the library: 21 possible references of material layers

data base (library) for the base plate used for defining orthotropic plates (available in worksheet in COORT)

 contents of the library: 21 possible references of material layers

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Those key points are reviewed worksheet per worksheet hereafter: the cells will be referred to thanks to their EXCEL’s coordinates

(column / line) in the following part of the present user’s manual.

Worksheet [in-out COPERF]

o

Input data :

Item

Cell for input

Foreseen action Comment

Date

Project

Configuration

Comments

Reference

Open area ratio

B3

D3

L3

T3

U16

U22

Modification of the displayed date possible

Input a name for the considered project

Input a name for the considered configuration

Input a comment

Select a reference of material (in the proposed list) for each layer of interest

Input a real positive number o

Comments :

Item

Temperature

Pressure

Cell for input

D5

D6

Foreseen action

--

--

Comment

Value reported from worksheet [in COALA] cell D6

Value reported from worksheet [in COALA] cell D7 o

Main displays of the results for the perforated plate (table of results):

Tables of results for the reference PERFO:

Young’s modulus of the composite: see cell U28

density of the composite: see cell U29

Poisson’s ratio of the composite: see cell U30

loss factor of the composite: see cell U31

Worksheet [in-out CODAP]

o

Input data :

Item

Cell for input

Foreseen action

Date B3

Modification of the displayed date possible

Project

Configuration

Comments

Reference

D3

L3

T3

V17 to

W17; U48 to W48

Input a name for the considered project

Input a name for the considered configuration

Input a comment

Select a reference of material (in the proposed list) for each layer of interest

Thickness

V23 to

W23; U54 to W54

Input a real positive number

Model of composite L31;L41

Select a model (in the proposed list)

Comment

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Comments :

Item

Temperature

Pressure

Cell for input

D5

D6

Foreseen action

--

--

Comment

Value reported from worksheet [in COALA] cell D6

Value reported from worksheet [in COALA] cell D7 o

Main displays of the results for the composite (table of results):

Tables of results for the reference 2-PLY:

Young’s modulus of the composite: see cell V29

density of the composite: see cell V30

Poisson’s ratio of the composite: see cell V31

loss factor of the composite: see cell V32

thickness (overall) of the composite: see cell V34

Tables of results for the reference 3-PLY:

Young’s modulus of the composite: see cell V39 (*)

density of the composite: see cell V40

Poisson’s ratio of the composite: see cell V41

loss factor of the composite: see cell V42 (*)

thickness (overall) of the composite: see cell V44

*limit at low frequency is displayed for the composite reference 3-PLY

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Worksheet [in-out COORT]

o

Input data :

Item

Cell for input

Foreseen action Comment

Date

Project

Configuration

Comments

To get fc* (Hz)

To get fc*.h =

Reference of base plate

Thickness

Model of orthotropic plate hw l r

T

Surface density

Overall thickness

B3

D3

M3

U3

M8

P8

L9

J15

J17

J23

J24

J25

J26

L28

L29

Modification of the displayed date possible

Input a name for the considered project

Input a name for the considered configuration

Input a comment

Input a real positive number

Input a real positive number

Select a reference of layer

(in the proposed list) for each layer of interest

Input a real positive number

Select a model (in the proposed list)

Input a real positive number

Input a real positive number

Input a real positive number

Input a real positive number

Input a real positive number

Input a real positive number

Input a real positive number

Input a real positive number no compulsory input data

If a particular value of fc* is wished

If a particular value of fc*.h is wished

The thickness of the plate used before profiling is considered (not the overall thickness after profiling) for model RIB only for model CLA only for model MOI only

To get fcz* (Hz)

To get M’’’.fcz* (kg.Hz) =

To get M’’’.2

π.fcz*/Z

0

* =

To get fcz*.d’’’ =

To get Zm=M’’’.fcz*/Z

0

=

M30

N30

O30

P30

Q30

Input a real positive number

Input a real positive number

Input a real positive number for model MOI only (no compulsory input data)

If a particular value of fc* is wished

If a particular value of

M’’’.fcz* is wished

If a particular value of

M’’’.2.πi.fcz*/Z

0

* is wished

If a particular value of fcz*.d’’’ is wished

If a particular value of

Zm=M’’’.fcz*/Z

0

is wished

Bending stiffness (per unit width) in the x-direction

(maximum) D’x = D’zz =

D

11

L31

Input a real positive number

Bending stiffness (per unit width) in the z-direction

(minimum) D’z = D’xx = D

22

L32

Input a real positive number for model MOI only

If a particular value of fcz* (resp. M’’’.fcz*,

M’’’.2.

π.fcz*/Z

0

, fcz*.d’’’,

Zm=M’’’.fcz*/Z

0

is wished input the value given in M32 (resp. N32,

O32, P32, Q32)

Torsional rigidity (per unit width) D

12

+2D

66

Model of bending stiffness: maximum

Model of bending stiffness: minimum

L35

J50

J51

Input a real positive number

Select a model (in the proposed list)

Select a model (in the proposed list) for model MOI only for model CLA only for model CLA only

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Comments :

Item

Temperature

Pressure

Cell for input

D5

D6

Foreseen action

--

--

Comment

Value reported from worksheet [in COALA] cell D6

Value reported from worksheet [in COALA] cell D7 o

Main displays of the results for the equivalent plate (not for the model MOI):

surface density of the equivalent plate: see cell J28

overall thickness of the equivalent plate: see cell J29

bending stiffness (per unit width) in the x-direction (maximum): see cell J31

bending stiffness (per unit width) in the z-direction (minimum): see cell J32

torsional rigidity (per unit width): see cell J35

Worksheet [in COALA]

See corresponding § in Section 1

Worksheet [in-out COPPA]

o

Input data :

Item

Cell for input

Foreseen action Comment

Limitation of radiation ?

(0/1)

Large power used for the calculation

Size of the baffle in which the partition is symmetrically mounted along the xdirection

Size of the baffle in which the partition is symmetrically mounted along the zdirection

Size of the partition along the x-direction

Size of the partition along the z-direction

Model for the calculation of f11

E8

E9

X49

X50

X53

X54

For NO input 0, for YES input 1

Input a positive real

Input a positive real

Input a positive real

Input a positive real

Input a positive real

Fi min (°)

Fi max (°)

Teta min (°)

Teta max (°)

Model for teta L alpha sab max length of slit (m) width of slit (m) model

X56

I71

K71

P71

R71

U71

AF94

E97

H97

K97

Select a model (in the proposed list)

Select a value (in the proposed list)

Select a value (in the proposed list)

Select a value (in the proposed list)

Select a value (in the proposed list)

Select a model (in the proposed list)

Input a positive real

Input a positive real

Input a positive real

Select a model (in the proposed list) o

Main displays of the results :

Tables of results:

lowest critical frequency of the thin plates: see line 41 (columns T to Y)(not displayed for the reference 3-PLY because depending on frequency)

highest critical frequency of the thin plates: see line 42 (columns T to Y)(not displayed for the reference 3-PLY because depending on frequency)

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Tables of results and graphs for the partition

absorption coefficient for normal incidence: see lines 73 to 91 (columns A to L)

Tables of results and graphs for the partition, with an integration within selected limits for orientation & incidence

absorption coefficient for a statistic incidence: see lines 73to 94 (columns M to Z)

Sabine’s factor: see lines 73 to 94 (columns AA to AN)

Tables of results and graphs for the partition (except for insertion loss: see below), with an integration within

selected limits for orientation & incidence, with sound leaks

sound reduction index (coupling 0 %): see lines 99 to 121 (columns A to L)

insertion loss (coupling 0 %): see lines 99 to 118 (columns M to Z)

Nota: the considered insertion loss is not the insertion loss of the partition i.e. the (total) acoustic structure. The insertion loss IL stat is defined as IL stat = R stat – R’ stat with R’ stat: sound reduction index of 1 plate such as those of set 0 whatever the quantity of such plates selected for set 0 is (angular integration & sound leaks included)

acoustic power without (resp. with) the partition (coupling 0 %): see lines 99 to 117 (columns AA to AJ)

Worksheet [in-out COPPA0]

o

Input data : no input data required o

Main displays of the results :

Tables of results and graphs for sets 1 to imax, without thin plate(s), with an impervious rigid back

surface impedance at normal incidence: see lines 47 to 65 (columns A to L for real part, columns M to X for imaginary part)

normalized surface impedance at normal incidence: see lines 67 to 85 (columns A to L for real part, columns M to

X for imaginary part)

absorption coefficient for normal incidence: see lines 87 to 105 (columns A to L)

Worksheet [in-out COPPA1]

o

Input data :

Item

Cell for input

Foreseen action Comment

boundary conditions model of radiation ratio (of free bending waves)

Simplified transmission factor for normal incidence

(0/1)

E77

K77

G81

Select a model (in the proposed list)

Select a model (in the proposed list)

For NO input 0, for YES input 1

General model (for R) model of forced transmission model of resonant transmission model of transmission

K81

E85

E90, K90

E95, K95 frequency range where f

fc E99, K99

Select a model (in the proposed list)

Select a model (in the proposed list)

Select a model (in the proposed list)

Select a model (in the proposed list)

Select a number of 1/3 octave bands

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Comments :

Item

STOP 3-PLY not exact for f < fc

STOP: valid model NI1

STOP: valid model NI2

STOP: radiation ratio not valid

STOP: radiation ratio not valid

STOP: valid model NI1

STOP: valid model NI2

STOP: radiation ratio not valid

Cell

L81, L82

C86, D86

B87

D87

D91

J91

B92

D92

J96

Foreseen action

--

--

--

--

--

--

--

--

--

Comment

In case of such an alert, the accuracy of the program with all the models has not been checked

In case of such an alert, the user has to be prepared to get approximate results below the frequency displayed due to imperfections of the chosen model

In case of such an alert, the model has to be changed for the same model as in cell E90

In case of such an alert, the model has to be changed for the same model as in cell E90

In case of such an alert, the input data of cell K77 has to be changed

In case of such an alert, the input data of cell K77 has to be changed

In case of such an alert, the model has to be changed for the same model as in cell E85

In case of such an alert, the model has to be changed for the same model as in cell E85

In case of such an alert, the input data of cell K77 has to be changed o

Main displays of the results :

Tables of results and graphs for 1 plate such as those of set 0 alone (whatever the quantity of such plates selected for set 0 is):

radiation ratio (of free bending waves): see lines 75 to 99 (columns M to Z)

sound reduction index: see lines 75 to 103 (columns AA to AN)

Worksheet [in-out COPPA2]

o

Input data :

Item

Cell for input

Foreseen action Comment

general model (for Rdif) K76

K80

Select a model (in the proposed list)

Select a model (in the proposed list) sub-model (for general model

DAV) model for connections (for general models

SHA1,SHA2,SHA3) distance between line-type connections (m) vibration transmission factor

(not for general models

FAH,DAV,SHA1,SHA2,SHA3) compliance of connections for the general model DAV, for the compliance model BYO (in mN-

1) model of compliance (for general model DAV) number of connections per m2

(m-2) vibration transmission factor

(not for general models

FAH,DAV,SHA1,SHA2,SHA3) compliance of connections for the general model DAV, for the compliance model BYO (in mN-

1)

K82

K85

K86

K87

K89

K92

K93

K94

Select a model (in the proposed list)

Input a positive real

Input a positive real

Input a positive real

Select a model (in the proposed list)

Input a positive real

Input a positive real

Input a positive real

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Comments :

no comment o

Main displays of the results :

Tables of results and graphs of a double-leaf partition with connections between thin plates of sets 0 and 2 (for imax= 2):

sound reduction index: see lines 74 to 98 (columns AA to AN)

2.4: Examples of computation with SILDIS

Example 2.4.0 porous medium with series cloth

Envisaged application

It is wished to compute the absorption coefficient of the lining considered in the corresponding § in Section 1 (with an impervious rigid back) for a normal incidence.

Input data

The input data required for the computation are listed hereafter in reference with the above data (see placemarks).

The input cells will be referred to thanks to their EXCEL’s coordinates (column / line) in the following part of the present user’s manual.

Worksheet [in COALA] for example 2.4.0 only

See corresponding § in Section 1

Worksheet [in-out COPERF] for example 2.4.0

No input data required for the example of computation

Worksheet [in-out CODAP] for example 2.4.0 and for example 2.4.1

Item

Cell for input

Foreseen action Input

See placemark

/ comment

Thickness W23

Input a real positive number

0.001 (*)

-

*see § 2. 3: How to use SILDIS Operating conditions / security level / safety

Worksheet [in-out COORT] for example 2.4.0

No input data required for the example of computation

Worksheet [in-out COPPA] for example 2.4.0

No input data required for the example of computation

Worksheet [in-out COPPA0] for example 2.4.0

No input data required for the example of computation

Worksheet [in-out COPPA1] for example 2.4.0

No input data required for the example of computation

Worksheet [in-out COPPA2] for example 2.4.0

No input data required for the example of computation

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Screenshots of the worksheets (for the example of computation)

Screenshot of worksheet [in COALA] for example 2.4.0 only

See corresponding § in Section 1

Screenshot of worksheet [in-out COPPA0] for example 2.4.0

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Example 2.4.1a single isotropic plate (general method)

Envisaged application

It is foreseen to use the following conditions: temperature 20 °C [15], pressure 101325 Pa [16].

The reference spectrum is supposed of the type “pink noise” [19] with a sound power level of 130 dB/oct [20]

It is wished to compute the sound reduction index (with an atmospheric back) [24] of 1 [25] aluminium plate [26] of thickness 2mm

[27], the (intrinsic) losses of the material being considered [28] with a infinite extend [29] and by an integration of the transmission factor between 0 and 90° [30]. No sound leak is considered [31].

Input data

The input data required for the computation are listed hereafter in reference with the above data (see placemarks).

The input cells will be referred to thanks to their EXCEL’s coordinates (column / line) in the following part of the present user’s manual.

Worksheet [in COALA] for example 2.4.1a

Item

Temperature

Pressure

Rear atmosphere ? (0/1)

Maximum set index imax

Reference

Incorporation of the series perforated protections (0/1)

Incorporation of the series cloths (0/1)

Reference

Model of losses

Model of effective critical frequency

Number of identical plates

Thickness

Lw0 only known per 1/1 octave frequency band (0/1)

Lw0

Cell for input

D6

D7

O8

E13

J18 to K18

J57

W23

W31

W36

W37

W38

W39

R62

B65 to

K65

Foreseen action (see

§1.3)

Input a real number

Input a real positive number

For NO input 0, for YES input 1

Input an integer from 1 to

4

Select a reference

(material in the proposed list) for each layer of interest

For NO press 0, for YES press 1

For NO input 0, for YES input 1

Select a reference (in the proposed list)

Select a model (in the proposed list)

Select a model (in the proposed list)

Input a real positive number

Input a real positive number

For NO input 0, for YES input 1

Input a real positive number as requested for a

1/1 octave band sound power level

Input

20

101325

1

1

AIR

0

0

ALU

INT

1

0.002

1

130

See placemark / comment

[15]

[16]

[24]

[25]

-

-

-

[26]

[28]

[25]

[27]

[20]

[20]

Worksheet [in-out COPERF] for example 2.4.1a

No input data required for the example of computation

Worksheet [in-out CODAP] for example 2.4.1a

See corresponding § for

example 2.4.0

Worksheet [in-out COORT] for example 2.4.1a

No input data required for the example of computation

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Worksheet [in-out COPPA] for example 2.4.1a

Item

Cell for input

Foreseen action

Size of the baffle in which the partition is symmetrically mounted along the xdirection

Size of the baffle in which the partition is symmetrically mounted along the zdirection

Size of the partition along the x-direction

Size of the partition along the z-direction

X49

X50

X53

X54

Input a positive real

Input a positive real

Input a positive real

Input a positive real

Fi min (°)

Fi max (°)

Teta min (°)

Teta max (°)

Model for teta L length of slit (m) width of slit (m) model

I71

K71

P71

R71

U71

E97

H97

K97

Select a value (in the proposed list)

Select a value (in the proposed list)

Select a value (in the proposed list)

Select a value (in the proposed list)

Select a model (in the proposed list)

Input a positive real

Input a positive real

Select a model (in the proposed list)

*see § 2. 3: How to use SILDIS Operating conditions / security level / safety

Input

4.5

3.5

1

1

5.625

84.375

0

89.375

90°

1E-50

1E-50

-

See placemark

/ comment

Worksheet [in-out COPPA0] for example 2.4.1a

No input data required for the example of computation

Worksheet [in-out COPPA1] for example 2.4.1a

No input data required for the example of computation

Worksheet [in-out COPPA2] for example 2.4.1a

No input data required for the example of computation

(*)

(*)

(*)

(*)

-

-

[30]

[30]

[29]

[31]

[31]

[31]

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Screenshots of the worksheets (for the example of computation)

Screenshot of worksheet [in COALA] for example 2.4.1a only

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Screenshot of worksheet [in-out COPPA] for example 2.4.1a only

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Example 2.4.1b single isotropic plate (alternative method)

Envisaged application

It is foreseen to use the following conditions: temperature 20 °C [15], pressure 101325 Pa [16].

The reference spectrum is supposed of the type “pink noise” [19] with a sound power level of 130 dB/oct [20]

It is wished to compute the sound reduction index (with an atmospheric back) [24] of 1 [25] aluminium plate [26] of thickness 2mm

[27], the (intrinsic) losses of the material being considered [28] with a infinite extend [29] and by an integration of the transmission factor between 0 and 90° [30]. No sound leak is considered [31].

Input data

The input data required for the computation are listed hereafter in reference with the above data (see placemarks).

The input cells will be referred to thanks to their EXCEL’s coordinates (column / line) in the following part of the present user’s manual.

Worksheet [in COALA] for example 2.4.1b

Item

Temperature

Cell for input

D6

Foreseen action (see

§1.3)

Input a real number

Pressure

Reference

(1/2)

Model of losses

Model of effective critical frequency

Number of identical plates

Thickness

Lw0 only known per 1/1 octave frequency band (0/1)

Lw0

D7

W31

Y31

W36

W37

X38

W39

R62

B65 to

K65

Input a real positive number

Select a reference (in the proposed list)

Select a number (in the proposed list)

Select a model (in the proposed list)

Select a model (in the proposed list)

Input a real positive number

Input a real positive number

For NO input 0, for YES input 1

Input a real positive number as requested for a

1/1 octave band sound power level

Input

20

101325

ALU select 1

INT

1

0.002

1

130

See placemark / comment

[15]

Worksheet [in-out COPERF] for example 2.4.1b

No input data required for the example of computation

Worksheet [in-out CODAP] for example 2.4.1b

See corresponding § for

example 2.4.0

Worksheet [in-out COORT] for example 2.4.1b

No input data required for the example of computation

[16]

[26]

-

[28]

[25]

[27]

[20]

[20]

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Worksheet [in-out COPPA] for example 2.4.1b

Item

Cell for input

Foreseen action

Size of the baffle in which the partition is symmetrically mounted along the xdirection

Size of the baffle in which the partition is symmetrically mounted along the zdirection

Size of the partition along the x-direction

Size of the partition along the z-direction

Model for the calculation of f11

X49

X50

X53

X54

X56

Input a positive real

Input a positive real

Input a positive real

Input a positive real

Fi min (°)

Fi max (°)

Teta min (°)

Teta max (°)

Model for teta L length of slit (m) width of slit (m) model

I71

K71

P71

R71

U71

E97

H97

K97

Select a model (in the proposed list)

Select a value (in the proposed list)

Select a value (in the proposed list)

Select a value (in the proposed list)

Select a value (in the proposed list)

Select a model (in the proposed list)

Input a positive real

Input a positive real

Select a model (in the proposed list)

Input

4.5

3.5

1

1

-

5.625

84.375

0

89.375

90°

1E-50

1E-50

-

See placemark / comment

(*)

(*)

(*)

(*)

-

-

-

[30]

[30]

[29]

[31]

[31]

[31]

Worksheet [in-out COPPA0] for example 2.4.1b

No input data required for the example of computation

Worksheet [in-out COPPA1] for example 2.4.1b

No input data required for the example of computation

Item

Cell for input

Foreseen action Input

See placemark / comment

Simplified transmission factor for normal incidence

(0/1)

G81

For NO input 0, for YES input 1

0

-

General model (for R) model of forced transmission

K81

E85

Select a model (in the proposed list)

Select a model (in the proposed list)

MOI

INT

[30]

[30] model of resonant transmission

E90, K90 ZER, INT [30] model of transmission E95, K95 frequency range where f

fc E99, K99

Select a model (in the proposed list)

Select a model (in the proposed list)

Select a number of 1/3 octave bands

NAT, NAT

-, -

[30]

-

Worksheet [in-out COPPA2] for example 2.4.1b

No input data required for the example of computation

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Screenshots of the worksheets (for the example of computation)

Screenshot of worksheet [in COALA] for example 2.4.1b only

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Screenshot of worksheet [in-out COPPA1] for example 2.4.1b only

Example 2.4.2 double leaf partition with connections

Envisaged application

It is foreseen to use the following conditions: temperature 20 °C [15], pressure 101325 Pa [16].

The reference spectrum is supposed of the type “pink noise” [19] with a sound power level of 130 dB/oct [20]

It is wished to compute the sound reduction index (with an atmospheric back) [24] of a double-leaf partition consisting of:

-1 [25] aluminium plate [26] of thickness 2mm [27], the (intrinsic) losses of the material being considered [28]

-1 [32] steel plate [33] of thickness 2mm [34], the (intrinsic) losses of the material being considered [35] with a infinite extend [29] and by an integration of the transmission factor between 0 and 90° [30]. No sound leak is considered [31 ].

The interspace is assumed to be filled with the porous medium reference DEMO [36], with a thickness of 100mm [37]

The general model SHA3 is considered [38] for Line-Line connections [39] having a distance of 600mm [40]

Input data

The input data required for the computation are listed hereafter in reference with the above data (see placemarks).

The input cells will be referred to thanks to their EXCEL’s coordinates (column / line) in the following part of the present user’s manual.

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Worksheet [in COALA] for example 2.4.2

Item

Cell for input

Foreseen action (see

§1.3)

Temperature D6

Pressure

Rear atmosphere ? (0/1)

Maximum set index imax

Reference

Thickness

Incorporation of the series perforated protections (0/1)

Incorporation of the series cloths (0/1)

Reference

(1/2)

Model of losses

Model of effective critical frequency

Number of identical plates

Thickness

Lw0 only known per 1/1 octave frequency band (0/1)

Lw0

D7

O8

E13

J18 to K18

I37,J37

I57,J57

V23,W23

V31,W31

Y31

V36,W36

V37,W37

V38,X38

V39,W39

R62

B65 to

K65

Input a real number

Input a real positive number

For NO input 0, for YES input 1

Input an integer from 1 to

4

Select a reference

(material in the proposed list) for each layer of interest

Input a real positive number

For NO press 0, for YES press 1

For NO input 0, for YES input 1

Select a reference (in the proposed list)

Select a number (in the proposed list)

Select a model (in the proposed list)

Select a model (in the proposed list)

Input a real positive number

Input a real positive number

For NO input 0, for YES input 1

Input a real positive number as requested for a

1/1 octave band sound power level

Input

20

101325

1

2

DEMO

0.05,0.05

0

0

STEEL,ALU select 1

INT,INT

1,1

0.002,0.002

1

130

See placemark / comment

[15]

Worksheet [in-out COPERF] for example 2.4.2

No input data required for the example of computation

Worksheet [in-out CODAP] for example 2.4.2

See corresponding § for

example 2.4.0

Worksheet [in-out COORT] for example 2.4.2

No input data required for the example of computation

[16]

[24]

-

[36]

[37]

-

-

[33],[26]

-

[35],[28]

[32],[25]

[34], [27]

[20]

[20]

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Worksheet [in-out COPPA] for example 2.4.2

Item

Cell for input

Foreseen action

Size of the baffle in which the partition is symmetrically mounted along the xdirection

Size of the baffle in which the partition is symmetrically mounted along the zdirection

Size of the partition along the x-direction

Size of the partition along the z-direction

Model for the calculation of f11

X49

X50

X53

X54

X56

Input a positive real

Input a positive real

Input a positive real

Input a positive real

Fi min (°)

Fi max (°)

Teta min (°)

Teta max (°)

Model for teta L length of slit (m) width of slit (m) model

I71

K71

P71

R71

U71

E97

H97

K97

Select a model (in the proposed list)

Select a value (in the proposed list)

Select a value (in the proposed list)

Select a value (in the proposed list)

Select a value (in the proposed list)

Select a model (in the proposed list)

Input a positive real

Input a positive real

Select a model (in the proposed list)

Input

4.5

3.5

1

1

-

5.625

84.375

0

89.375

90°

1E-50

1E-50

-

See placemark / comment

(*)

(*)

(*)

(*)

-

-

-

[30]

[30]

[29]

[31]

[31]

[31]

Worksheet [in-out COPPA0] for example 2.4.2

No input data required for the example of computation

Worksheet [in-out COPPA1] for example 2.4.2

No input data required for the example of computation

Worksheet [in-out COPPA2] for example 2.4.2

Cell for

Item Foreseen action input

general model (for Rdif) K76

Select a model (in the proposed list)

Input

SHA3

See placemark / comment

[38]

K80

Select a model (in the proposed list)

- sub-model (for general model

DAV) model for connections (for general models

SHA1,SHA2,SHA3) distance between line-type connections (m) vibration transmission factor

(not for general models

FAH,DAV,SHA1,SHA2,SHA3) compliance of connections for the general model DAV, for the compliance model BYO (in mN-

1) model of compliance (for general model DAV) number of connections per m2

(m-2) vibration transmission factor

(not for general models

FAH,DAV,SHA1,SHA2,SHA3) compliance of connections for the general model DAV, for the compliance model BYO (in mN-

1)

K82

K85

K86

K87

K89

K92

K93

K94

Select a model (in the proposed list)

Input a positive real

Input a positive real

Input a positive real

Select a model (in the proposed list)

Input a positive real

Input a positive real

Input a positive real

L-L

0.6

-

-

-

-

-

-

[39]

[40]

-

-

-

-

-

-

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Screenshot of worksheet [in COALA] for example 2.4.2

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Screenshot of worksheet [in-out COPPA2] for example 2.4.2

Example 2.4.3 perforated plate

Envisaged application

It is foreseen to compute the engineering constants for a perforated plate consisting of a steel plate [41] with an open area ratio of

32.65 % [42].

Input data

The input data required for the computation are listed hereafter in reference with the above data (see placemarks).

The input cells will be referred to thanks to their EXCEL’s coordinates (column / line) in the following part of the present user’s manual.

Worksheet [in-out COPERF] for example 2.4.3

Item

Cell for input

Foreseen action

Reference

Open area ratio

U16

U22

Select a reference of material (in the proposed list) for each layer of interest

Input a real positive number

Input

STEEL

0.03265

See placemark / comment

[41]

[42]

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Screenshot of worksheet [in-out COPERF] for example 2.4.3

Example 2.4.4 plate with an extensional damping

Envisaged application

It is foreseen to compute the engineering constants for a damped plate consisting of:

-1 aluminum plate [43] of thickness 2mm [44]

-1 viscoelastic plate (reference VSCO in the database) [45] of thickness 2mm [46]

The model of composite MOI is considered [47]

Input data

The input data required for the computation are listed hereafter in reference with the above data (see placemarks).

The input cells will be referred to thanks to their EXCEL’s coordinates (column / line) in the following part of the present user’s manual.

Worksheet [in-out CODAP] for example 2.4.4

Item

Cell for input

Foreseen action

Reference

V17 to

W17

Select a reference of material (in the proposed list) for each layer of interest

Thickness

Model of composite

V23 to

W23

L31

Input a real positive number

Select a model (in the proposed list)

Input

VISCO, ALU

0.002;0.002

MOI

See placemark / comment

[43],[45]

[44],[46]

[47]

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Screenshots of the worksheets (for the example of computation)

Screenshot of worksheet [in-out CODAP] for example 2.4.4

Example 2.4.5 plate with a constrained damping

Envisaged application

It is foreseen to compute the engineering constants for a damped plate consisting of:

-1 GLASS plate [48] of thickness 4mm [49]

-1 viscoelastic plate (reference PVB in the database) [50] of thickness 0.5mm [51]

-1 GLASS plate [52] of thickness 4mm [53]

The model of composite MAX is considered [54]

Input data

The input data required for the computation are listed hereafter in reference with the above data (see placemarks).

The input cells will be referred to thanks to their EXCEL’s coordinates (column / line) in the following part of the present user’s manual.

Worksheet [in-out CODAP] for example 2.4.5

Item

Cell for input

Foreseen action

Reference

Thickness

Model of composite

U48 to

W48

U54 to

W54

L41

Select a reference of material (in the proposed list) for each layer of interest

Input a real positive number

Select a model (in the proposed list)

Input

GLASS, PVB, GLASS

0.004,0.0005,0.004

MAX

See placemark / comment

[48], [50], [52]

[49], [51], [53]

[54]

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Screenshots of the worksheets (for the example of computation)

Screenshot of worksheet [in-out CODAP] for example 2.4.5

Example 2.4.6 orthotropic plate

Envisaged application

It is foreseen to compute the engineering constants for a cladding [55] consisting of an aluminium plate [56] of thickness 1mm [57] with an overall thickness 30 mm [58] with a periodic length l=300 mm [59], with lengths of the corrugation T=b=100mm [60].

The model HAN [61] is considered.

Input data

The input data required for the computation are listed hereafter in reference with the above data (see placemarks).

The input cells will be referred to thanks to their EXCEL’s coordinates (column / line) in the following part of the present user’s manual.

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Worksheet [in-out COORT] for example 2.4.6

Item

Cell for input

Foreseen action

Reference of base plate

Thickness

Model of orthotropic plate hw l

T

Model of bending stiffness: maximum

Model of bending stiffness: minimum

L9

J15

J17

J23

J24

J26

J50

J51

Select a reference of layer

(in the proposed list) for each layer of interest

Input a real positive number

Select a model (in the proposed list)

Input a real positive number

Input a real positive number

Input a real positive number

Select a model (in the proposed list)

Select a model (in the proposed list)

Screenshots of the worksheets (for the example of computation)

Screenshot of worksheet [in-out COORT] for example 2.4.6

Input

ALU

0.001

CLA

0.03

0.3

0.1 for model CLA only for model CLA only

See placemark / comment

[56]

[57]

[55]

[58]

[59]

[60]

[61]

[61]

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2.5: Illustrations of effects taken into account with SILDIS

Introduction

The prediction of acoustic performances of plane partitions with the software SILDIS is founded on a scientific and technical background as presented in § 2.2 of this user’s manual, combining various knowledges in relation with physics. Some (future possible) users may not be perfectly familiar with some aspects of this background: in order to be anyway in a position of making the best use of this calculation tool, attention has to be paid by such users to some particular effects taken into account for the predictions thanks to illustrations given in this section of the user’s manual. The intention is not to give a comprehensive list of the various effects of each parameter that may (alone or coupled with others) influence the acoustic performance of a partition, what would be very difficult to do. The goal is (thanks to examples): highlighting major key-points (considered separately) of the design of partitions, given some known laws of the physics, some of the input data being chosen in order to be as demonstrative as possible, given the plausible field of typical engineering applications.

All the numerical results below have been obtained using the software SILDIS with some post treatment for comparisons notably

(some of those results can not be obtained by the user in the presented form for a sake of simplicity of the software).

Effects of the properties of a porous medium in a non-laminated lining (illustration 2.5.1)

Imput data: a lining is considered at (test) room pressure and temperature, (with an impervious rigid back), consisting of a single porous medium having (at room temperature) a flow resistivity in the direction normal to its surface σy1 variable from 8 to 72 kNsm-

4, a porosity ø=0.95 (model M76), with a thickness d=0.1m. No series cloth is considered, no series perforated protection is considered.

Illustration of one of the effects: see below the prediction of the absorption coefficient at normal incidence depending on the flow resistivity of the porous medium (see key in the graph)

absorption coefficient at normal incidence alpha0

1,20

1,00

0,80

0,60

8kNsm-4

12kNsm-4

16kNsm-4

24kNsm-4

48kNsm-4

72kNsm-4

0,40

0,20

0,00 f1/3oct (Hz)

8kNsm-4

12kNsm-4

16kNsm-4

24kNsm-4

48kNsm-4

72kNsm-4

1 10

25 31,5 40 50 63 80 100 125 160 200

0,01 0,02 0,03 0,04 0,07 0,10 0,15 0,23 0,34 0,46

0,02 0,02 0,04 0,06 0,09 0,13 0,20 0,29 0,39 0,52

0,02 0,03 0,05 0,07 0,11 0,16 0,24 0,33 0,44 0,55

0,03 0,04 0,07 0,10 0,15 0,21 0,29 0,38 0,48 0,56

0,05 0,08 0,11 0,16 0,21 0,27 0,33 0,39 0,43 0,47

0,07 0,10 0,14 0,18 0,22 0,27 0,30 0,34 0,37 0,39

100

f(Hz)

1000 10000 100000

250 315 400 500 630 800 1k 1,25k 1,6k 2k 2,5k 3,15k

0,60 0,74 0,85 0,93 0,98 0,99 0,98 0,96 0,96 0,99 0,99 0,99

4k

1,00

5k

1,00

6,3k

1,00

8k

1,00

10k

1,00

12,5k

1,00

16k

1,00

20k

1,00

0,65 0,77 0,86 0,92 0,95 0,96 0,95 0,94 0,96 0,98 0,99

0,66 0,76 0,84 0,88 0,91 0,91 0,92 0,93 0,95 0,97 0,98

0,64 0,70 0,75 0,79 0,82 0,84 0,87 0,90 0,93 0,95 0,96

0,51 0,54 0,57 0,61 0,65 0,71 0,76 0,81 0,84 0,88 0,91

0,42 0,45 0,49 0,53 0,58 0,62 0,67 0,72 0,77 0,82 0,85

0,99

0,98

0,97

0,99

0,99

0,98

0,99

0,99

0,98

1,00

0,99

0,99

1,00

1,00

0,99

1,00

1,00

0,99

1,00

1,00

1,00

1,00

1,00

1,00

1,00

1,00

1,00

0,93 0,95 0,96 0,97 0,98 0,98 0,99 0,99 0,99

0,89 0,91 0,93 0,95 0,96 0,97 0,98 0,98 0,99

Comment: the choice of the flow resistivity of the porous medium influences sometimes considerably the acoustic performance of the lining (at least: for some frequencies). In particular, the choice of a flow resistivity of the porous medium too big compared with the optimum required - as far as acoustics is concerned - can lead to a degradation of the performance for frequencies possibly within the range of interest. This comment would also apply for the absorption coefficient for a statistic incidence.

For a given porous medium, an increase of the density involves - generally speaking - an increase of the flow resistivity (everything else supposed to be equal): for example, attention has to be paid to the consequences of the use (in some locations…) of high

density rock wools using bonded short fibers producing possibly linings with a high flow resistance in some cases (especially

when nothing is known regarding the properties of those materials in terms of flow resistivity, porosity…).

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Effects of the properties of porous media in a laminated lining (illustration 2.5.2)

Imput data: a lining is considered at (test) room pressure and temperature (with an impervious rigid back), consisting of:

- a surface layer being a porous medium having (at room temperature) a flow resistivity in the direction normal to its surface

σy1=72 kNsm-4, a porosity ø=0.95 (model M76), with a thickness ds=0.02m. No series cloth is considered, no series perforated protection is considered.

- a core layer being a porous medium having (at room temperature) a flow resistivity in the direction normal to its surface σy1=12 kNsm-4, a porosity ø=0.95 (model M76), with a thickness dc=0.08m. No series cloth is considered, no series perforated protection is considered.

Illustration of one of the effects: see below the prediction of the absorption coefficient at normal incidence of the mix (laminated lining) and the comparison with a non-laminated lining made (with a thickness d=ds+dc=0.10m) either 100 % of the material of the surface layer or 100 % of the material of the core layer (see key in the graph)

absorption coefficient at normal incidence alpha0

1,00

0,90

0,80

0,70

0,60

0,50

0,40

0,30

0,20

0,10

12kNsm-4

72kNsm-4 mix

0,00

1 10 100

f(Hz)

1000 10000 100000 f1/3oct (Hz)

12kNsm-4

72kNsm-4 mix

25 31,5 40 50 63

0,02 0,02 0,04 0,06 0,09

0,07 0,10 0,14 0,18 0,22

0,05 0,07 0,10 0,15 0,21

80 100 125 160 200

0,13 0,20 0,29 0,39 0,52

0,27 0,30 0,34 0,37 0,39

0,28 0,36 0,43 0,49 0,54

250 315 400 500 630

0,65 0,77 0,86 0,92 0,95

0,42 0,45 0,49 0,53 0,58

0,58 0,61 0,62 0,63 0,64

800 1k 1,25k 1,6k 2k 2,5k 3,15k

0,96 0,95 0,94 0,96 0,98 0,99 0,99

4k

0,99

5k

0,99

6,3k

1,00

8k

1,00

0,62 0,67 0,72 0,77 0,82 0,85 0,89 0,91 0,93 0,95 0,96

0,64 0,66 0,69 0,75 0,80 0,83 0,88 0,91 0,94 0,95 0,96

10k 12,5k 16k 20k

1,00 1,00 1,00 1,00

0,97 0,98 0,98 0,99

0,97 0,98 0,98 0,99

Comment: in case of a laminated lining, the choice of the flow resistivity of the porous media influences sometimes considerably the acoustic performance of the lining (at least: for some frequencies). In particular, the choice of a flow resistivity of the porous medium for the surface layer too big compared with the optimum required - as far as acoustics is concerned - can (even with a thickness small compared to the total thickness of the lining) lead to a degradation of the performance for frequencies possibly within the range of interest. This comment would also apply for the absorption coefficient for a statistic incidence.

See also the last paragraph of illustration 2.5.1

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Effects of temperature (illustration 2.5.3)

Imput data: a lining is considered at (test) room pressure on the one hand at (test) room temperature and on the other hand at high temperature, (with an impervious rigid back), consisting of a single porous medium having (at room temperature) a flow resistivity in the direction normal to its surface σy1=12400 Nsm-4, a porosity ø=0.95 (model M76), with a thickness d=0.05m. No series cloth is considered, no series perforated protection is considered.

Illustration of one of the effects: see below the prediction of the absorption coefficient at normal incidence depending on the temperature (see key in the graph)

absorption coefficient at normal incidence alpha0

1,20

20 °C 300 °C 600 °C

1,00

0,80

0,60

0,40

0,20

0,00

1 10 100

f(Hz)

1000 10000 100000 f1/3oct (Hz)

20 °C

300 °C

600 °C

25 31,5

0,00 0,00

0,00 0,00

0,00 0,00

40 50 63 80

0,01 0,01 0,01 0,02

0,01 0,01 0,01 0,02

0,01 0,01 0,01 0,02

100 125 160 200

0,04 0,06 0,09 0,14

0,03 0,05 0,08 0,12

0,03 0,05 0,08 0,12

250 315 400 500

0,21 0,31 0,43 0,56

0,18 0,26 0,36 0,48

0,18 0,25 0,34 0,43

630 800 1k 1,25k 1,6k

0,70 0,82 0,92 0,98 1,00

2k

0,99

2,5k

0,96

3,15k

0,96

4k

0,98

5k

1,00

6,3k

0,99

8k

1,00

0,61 0,73 0,82 0,89

0,53 0,61 0,68 0,74

0,92

0,79

0,93

0,82

0,93

0,84

0,93

0,87

0,95

0,90

0,97

0,92

0,98

0,95

0,98

0,96

10k 12,5k 16k 20k

1,00 1,00 1,00 1,00

0,99 0,99 0,99 1,00

0,97 0,98 0,98 0,99

Comment: the temperature of the application influences sometimes considerably the acoustic performance of the lining (at least: for some frequencies). For a given material, an increase of the temperature involves - generally speaking - an increase of the flow resistivity (everything else supposed to be equal).In particular, the choice of a flow resistivity of the porous medium (at r oom temperature) too big compared with the optimum required (at the temperature of the application) - as far as acoustics is concerned - can lead to a degradation of the performance for frequencies possibly within the range of interest. This comment would also apply for the absorption coefficient for a statistic incidence.

See also the last paragraph of illustration 2.5.1

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Effects of pressure (illustration 2.5.4)

Imput data: a lining is considered at (test) room temperature and at a pressure from 100 to 400kPa (with an impervious rigid back), consisting of a single porous medium having (at room temperature) a flow resistivity in the direction normal to its surface σy1=48000

Nsm-4, a porosity ø=0.95 (model M76), with a thickness d=0.1m. No series cloth is considered, no series perforated protection is considered.

Illustration of one of the effects: see below the prediction of the absorption coefficient at normal incidence depending on the pressure

(see key in the graph)

absorption coefficient at normal incidence alpha0

1,20

100kPa 200kPa 400kPa

1,00

0,80

0,60

0,40

0,20

0,00

1 10 100

f(Hz)

1000 10000 100000 f1/3oct (Hz)

100kPa

200kPa

400kPa

25 31,5

0,05 0,08

0,03 0,04

0,01 0,02

40 50 63 80

0,11 0,16 0,21 0,27

0,07 0,10 0,15 0,21

0,04 0,06 0,09 0,13

100 125 160 200

0,33 0,39 0,43 0,47

0,29 0,38 0,48 0,56

0,19 0,28 0,39 0,52

250 315 400 500

0,50 0,54 0,57 0,61

0,64 0,69 0,75 0,79

0,65 0,77 0,86 0,92

630 800 1k 1,25k 1,6k

0,65 0,70 0,76 0,80 0,84

2k

0,88

2,5k

0,90

3,15k

0,93

4k

0,94

5k

0,96

6,3k

0,97

8k

0,98

0,82 0,84 0,87 0,90

0,95 0,95 0,95 0,94

0,93

0,96

0,95

0,98

0,96

0,98

0,97

0,99

0,98

0,99

0,98

0,99

0,99

1,00

0,99

1,00

10k 12,5k 16k 20k

0,98 0,99 0,99 0,99

0,99 1,00 1,00 1,00

1,00 1,00 1,00 1,00

Comment: the pressure of the application influences sometimes considerably the acoustic performance of the lining (at least: for some frequencies). Depending on the frequency range of interest, absorbers with a higher flow resistivity may be selected in case of pressure lines. But the choice of a flow resistivity of the porous medium too big compared with the optimum required (at the pressure of the application) - as far as acoustics is concerned - can lead to a degradation of the performance for frequencies possibly within the range of interest. This comment would also apply for the absorption coefficient for a statistic incidence.

See also the last paragraph of illustration 2.5.1

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Effects of a series cloth (illustration 2.5.5)

Imput data: a lining is considered at (test) room pressure and temperature, (with an impervious rigid back), consisting of a single porous medium homogeneous in directions parallel to and perpendicular to its surface, having a flow resistivity σy=22332Nsm-4, a porosity ø=0.95 (model M76) with a thickness d=0.05m. The cloth consists of an impervious membrane (surface density 125 g/m2)

Illustration of the effect: see below the prediction of the absorption coefficient at normal incidence without and with the cloth

absorption coefficient at normal incidence alpha0

1,20

1,00 without with

0,80

0,60

0,40

0,20

0,00

1 10 100 1000 10000 100000 f1/3oct (Hz) without with

f(Hz)

25 31,5 40 50 63 80 100 125 160 200 250 315 400 500 630 800 1k 1,25k 1,6k 2k 2,5k 3,15k 4k 5k 6,3k 8k 10k 12,5k 16k 20k

0,00 0,01 0,01 0,01 0,02 0,04 0,05 0,08 0,13 0,19 0,27 0,38 0,51 0,65 0,77 0,87 0,93 0,96 0,96 0,95 0,95 0,96 0,98 0,99 0,99 0,99 0,99 1,00 1,00 1,00

0,00 0,01 0,01 0,01 0,02 0,04 0,06 0,09 0,14 0,22 0,34 0,51 0,73 0,93 0,99 0,89 0,72 0,55 0,42 0,32 0,22 0,13 0,08 0,05 0,03 0,02 0,01 0,01 0,00 0,00

Comment: the choice of a series cloth influences sometimes considerably the acoustic performance of the lining (at least: for some frequencies). In particular, the choice of a permeability of the cloth too small compared with the optimum required - as far as acoustics is concerned - can lead to a degradation of the performance for frequencies possibly within the range of interest (an increase of the performance being often obtained at low frequency due to the presence of a free vibrating foil).

Attention has to be paid to the consequences of the use (in some locations…) of cloths producing possibly linings with a high flow resistance (especially when nothing is known regarding the properties of this materials in terms of flow resistivity,

porosity…).

Attention has to be paid also to dust deposits in a position (in some cases) of involving effects comparable to the effect of a series cloth.

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Effects of a series perforated protection (illustration 2.5.6)

Imput data: a lining is considered at (test) room pressure and temperature, (with an impervious rigid back),consisting of a single porous medium having a flow resistivity σy=72kNsm-4, a porosity ø=0.95 (model M76) with a thickness d=0.1m. The perforated protection consists of a sheet R3T5 (round holes with an hexagonal arrangement, diameter 3 mm, open area ratio ε=0.3265) of thickness 1 mm (general model MOI, model for the added impedances ROA)

Illustration of the effect: see below the prediction of the absorption coefficient at normal incidence without and with the perforated protection

absorption coefficient at normal incidence alpha0

1,20 without with

1,00

0,80

0,60

0,40

0,20

0,00

1 10 100

f(Hz)

1000 10000 100000 f1/3oct (Hz) without with

25 31,5 40 50 63

0,07 0,10 0,14 0,18 0,22

0,07 0,10 0,14 0,18 0,23

80 100 125 160 200

0,27 0,30 0,34 0,37 0,39

0,27 0,31 0,34 0,37 0,39

250 315 400 500 630

0,42 0,45 0,49 0,53 0,58

0,42 0,46 0,49 0,54 0,58

800 1k 1,25k 1,6k 2k 2,5k 3,15k

0,62 0,67 0,72 0,77 0,82 0,85 0,89

4k

0,91

5k

0,93

6,3k

0,95

8k

0,96

0,63 0,68 0,74 0,79 0,84 0,89 0,92 0,94 0,96 0,96 0,94

10k 12,5k 16k 20k

0,97 0,98 0,98 0,99

0,90 0,83 0,75 0,65

Comment: the choice of a perforated protection influences sometimes considerably the acoustic performance of the lining (at least: for some frequencies). For a given geometry of holes and a given thickness, a decrease of the open area ratio involves - generally speaking

- a decrease of the performance. In particular, the choice of a perforated protection with an open area ratio too small compared with the optimum required - as far as acoustics is concerned - can lead to a degradation of the performance for frequencies possibly within the range of interest (in high frequency the performance is degraded in the example above despite a quite high open area ratio).

For a given perforated protection, the performance can decrease notably in case of a non-sufficiently pervious material at the rear: see also the last paragraph of illustration 2.5.1

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Effects of membrane resonator (illustration 2.5.7)

Imput data: a membrane resonator is considered at (test) room pressure and temperature, consisting of an aluminium plate of thickness 0.0006 m installed in front of an rigid impervious back (distance d=0.1 m) accounted as a series cloth of infinite flow resistance. No porous medium (except air in the cavity) is considered, no series cloth (except the membrane) is considered, n o series perforated protection is considered.

Illustration of one of the effects: see below the prediction of the absorption coefficient at normal incidence depending on a parallel resistance (normalized to the characteristic impedance of air r=Rp/Z0: see key in the graph) accounting for losses in relation with mounting conditions

absorption coefficient at normal incidence alpha0

1,00

0,90

0,80

0,70

0,60

0,50

0,40

0,30

0,20

0,10 r=0,05 r=0,20 r=1,00

0,00

1 10 100

f(Hz)

1000 10000 100000 f1/3oct (Hz) r=0,05 r=0,20 r=1,00

25 31,5 40 50 63

0,00 0,00 0,00 0,00 0,00

0,00 0,00 0,00 0,01 0,02

0,01 0,01 0,02 0,04 0,07

80 100 125 160 200

0,01 0,02 0,09 0,14 0,04

0,03 0,08 0,29 0,44 0,13

0,14 0,32 0,73 0,90 0,45

250 315 400 500 630

0,01 0,01 0,00 0,00 0,00

0,05 0,02 0,01 0,01 0,00

0,20 0,10 0,05 0,03 0,02

800 1k 1,25k 1,6k 2k 2,5k 3,15k

0,00 0,00 0,00 0,00 0,00 0,00 0,00

4k

0,00

5k

0,00

6,3k

0,00

8k

0,00

0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

0,01 0,01 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00

10k 12,5k 16k 20k

0,00 0,00 0,00 0,00

0,00 0,00 0,00 0,00

0,00 0,00 0,00 0,00

Comment: the use of a membrane absorber allows an absorption coefficient at normal incidence in a very narrow frequency band. The choice of a parallel resistance accounting for losses in relation with mounting conditions influences sometimes considerably the acoustic performance (at least: for some frequencies). The way the membrane is fixed on site onto the cavity (limit condition s, properties of the interface), influencing the effective losses, differs of foreseenable cases (furthermore, the stiffness of the membrane itself is disregarded when accounted as a series cloth, what is not important only for sufficiently large plates). Due to those uncertainties, experimental determination of performances are required in the present status of the Art.

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Effects of back (illustration 2.5.8)

Imput data: a lining is considered at (test) room pressure and temperature, consisting of a single porous medium having (at room temperature) a flow resistivity in the direction normal to its surface σy1=12.5 kNsm-4, a porosity ø=0.95 (model M76), with a thickness d=0.1m. A series cloth with a superficial flow resistance Rs=30 Nsm-3 and a surface density ms=0.090 kg/m2 is considered. No series perforated protection is considered.

Illustration of one of the effects: see below the prediction of the absorption coefficient at normal incidence depending on the backing of the porous medium (see key in the graph)

absorption coefficient at normal incidence alpha0

1,20

1,00

0,80

0,60

0,40 impervious rigid back atmospheric back

0,20

0,00

1 10 100

f(Hz)

1000 10000 100000 f1/3oct (Hz) 25 31,5 40 50 63 80 100 125 160 200 250 315 400 500 630 800 1k 1,25k 1,6k 2k 2,5k 3,15k 4k 5k 6,3k 8k 10k 12,5k 16k 20k impervious rigid back 0,02 0,03 0,04 0,06 0,10 0,15 0,22 0,31 0,42 0,54 0,67 0,78 0,87 0,92 0,94 0,94 0,94 0,94 0,96 0,98 0,98 0,98 0,99 0,99 0,99 0,99 0,99 1,00 1,00 1,00 atmospheric back 0,64 0,64 0,64 0,64 0,64 0,65 0,65 0,66 0,67 0,69 0,72 0,76 0,80 0,84 0,88 0,92 0,94 0,96 0,96 0,97 0,98 0,98 0,99 0,99 0,99 0,99 0,99 1,00 1,00 1,00

Comment: the choice of the backing influences sometimes considerably the acoustic performance of the lining (at least: for some frequencies). This comment would also apply for the absorption coefficient for a statistic incidence.

Attention has to be paid to the use of results obtained with an impervious rigid back (for example in an impedance tube or in a reverberant room) in case of on site atmospheric back.

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Appendix to Section 2: list of symbols

General

Cf. corresponding § in Section 1

Partition

x: direction of highest bending stiffness

ILstat: insertion loss for a statistic incidence lx : size of the partition along the x-direction (m) lz : size of the partition along the z-direction (m)

Lx : length of the baffle in which the partition is symmetrically mounted along the x-direction (m)

Lz : width of the baffle in which the partition is symmetrically mounted along the z-direction (m)

Rdif: sound reduction index for a diffuse field

Rstat: sound reduction index for statistic incidence

0: absorption coefficient for normal incidence

 stat: absorption coefficient for statistic incidence

 sab: Sabine’s factor

: angle of orientation

 min: minimum angle of orientation for angular integration

 max: maximum angle of orientation for angular integration

: angle of incidence

 min: minimum angle of incidence for angular integration

 max: maximum angle of incidence for angular integration

 stat: transmission factor for statistic incidence

Plates

d’’’ : overall thickness (m)

D’x: highest bending stiffness per unit width (Nm)

D’z: lowest bending stiffness per unit width (Nm)

E: Young’s modulus (N/m2) fc: critical frequency for an isotropic plate (Hz) Note: superscript * for (test) room conditions fceff: effective critical frequency for an isotropic plate (Hz) Note: superscript * for (test) room conditions fcx: lowest critical frequency (Hz) Note: superscript * for (test) room conditions fcz: upper critical frequency (Hz) Note: superscript * for (test) room conditions f

11

: frequence corresponding to the mode (1,1) of the plate (Hz)

M’’’: mass density (kg/m2) w: lateral (transverse) displacement (m)

: loss factor

: Poisson’s coefficient

ρ : density (kg/m3)

Note: subscript i for set i

Perforated plates

ε: open area ratio

Miscellaneous

See also corresponding § in General considerations and in Section 1

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Section 3: computation of duct walls

(MODULE 3 of the software)

3.1: Introduction

Terms and definitions

For the needs of the present user’s manual, the following terms and definition apply:

No particular term or definition.

Mountings and geometry

The geometry used for the design of ducts with the program SILDIS is shown in figure 3.1

rectangular duct wall circular duct wall

cf. worksheet CORED cf. worksheet COCID

fig 3.1

Key of the previous figures a: biggest (inner) dimension of the cross section of a rectangular duct b: smallest (inner) dimension of the cross section of a rectangular duct

D: (inner) diameter of a rectangular duct

3.2: Scientific and technical background

The prediction of acoustic performances of ducts with SILDIS is founded on a scientific and technical background in relation with: o analytical models for taking into account the properties of materials and various physical phenomena useful on the occasion of the computation o measurement results for feeding some of those models and for allowing the necessary improvement (through correction factors) of the correlation between some calculations and on site observations

The obtained results are not comparable with standardized measurement due to the lack of such documents.

3.2.1Thermodynamics and fluid dynamics:

Steps of the computation

Step [a]

All computations have been gathered in this single step for the sake of simplicity. See corresponding § in Section 1

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3.2.2 Acoustics:

3.2.2.1 Acoustics: rectangular ducts

3.2.2.1.a Acoustics: rectangular ducts, break out noise

Bloc diagram for rectangular duct walls break out noise

The computation scheme of rectangular duct walls is according the bloc-diagram below (cf. fig. 3.3):

fig. 3.3

Note 1: the service conditions dependence has been omitted for the sake of simplicity. See: report [PhRXX-015]

Note 2: the main steps (the steps involving a physical modeling) being referred to from [A] to [AB] have been taken into account for the bloc-diagram above (some of the parameters of the above bloc diagram are not independent); the frequency dependence has been omitted for the sake of simplicity

Steps of the computation for rectangular duct walls break out noise

Steps [A] to [V]

See corresponding § in Section 2, as far as sound reduction index of plates is concerned (used for step [X])

Preliminary remarks common to step [X] and step [X’]

o

Comments :

 the size of the cross section of the duct, the length of the duct, the flow rate are not related to the values selected in the worksheet [in-out COSIL] for B and H: corresponding input data are entered in worksheet [in-out CORED IN->OUT])

Step [X]

This step aims at calculating the sound reduction index of a single-leaf (rectangular) duct made of 1 plate alone such

as plates of set 0, regardless of the selected quantity of such plates for set 0, regardless of the selected quantities of other elements, and with atmosphere at the front and at the rear regardless of the selected input data) o

Bibliography (references) :

[X1]

-

[X2]

[X3]

[X4]

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Comments :

 when used, the cut off frequency for the first higher mode fco is computed depending on the speed of sound c, the

Mach number in the airways M, and the geometry of the duct, according to various models as shown in the table below: model

HAN

MUN source [X1] [X2]

 the cross over frequency fcr is computed depending on the speed of sound c, the Mach number in the airways M, and the geometry of the duct, according to various models as shown in the table below: model HAN NAS

SMA

source [X1] [X3] [X4]

 for f < fcr, the model of transmission (of sound) is selected as shown in the table below: model HAN NAS

SMA

source [X1] [X3] [X4]

 for f > fcr, the model of transmission (of sound) is selected as shown in the table below: model HAN NAS

SMA

source [X1] [X3] [X4]

 the model of minimum for Rdif is selected as shown in the table below: model HAN ZER source [X1] =0

 the model of maximum for Rdif is selected as shown in the table below: model source

HAN

[X1]

NAT

(*)

* the sound reduction index is derived as for the general case

Step [X’]

This step, being a complementary feature associated with step [X], aims at calculating the sound reduction index of a single-

leaf (rectangular) duct made of 1 steel plate alone with a thickness such as those of set 0, regardless of the other selected parameters of such plates for set 0, regardless of the selected quantity of such plates for set 0, regardless of the selected quantities of other elements, and with atmosphere at the front and at the rear regardless of the selected input data) o

Bibliography (references) :

[X’1]

[X’2]

- o

Comments :

 the model of minimum for Rdif is selected as shown in the table below:

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KOP

[X’2]

NAT

(*)

* the sound reduction index is derived as for the general case (cf. [X’1])

Step [Z]

This step aims at calculating the insertion loss of set 1 when compared to set 0 with atmosphere at the front and at the rear regardless of the selected input data o

Bibliography (references) :

[Z1] o

Comments :

 the model of cover is selected as shown in the table below: model RIG LIM source

[Z1]

RIG=RIGid

[Z1]

LIM=LIMp

Step [AA]

This step aims at calculating the transmission loss with sound leaks with atmosphere at the front and at the rear regardless of the selected input data o

Bibliography (references) :

No particular bibliography has been considered o

Comments :

 if IL stat is accounted TL out = R dif + IL stat else TL out = R dif

 the model for Rdif is selected as shown in the table below: model source

1 2 cf. step [X] cf. step [X’]

Step [AB]

This step aims at calculating the break out sound power level with atmosphere at the front and at the rear regardless of the selected input data

First approach

o

Bibliography (references) :

[AB1]

[AB2]

- o

Comments :

 the model for TL out is selected as shown in the table below: model source

2081

[AB1]

HAN

[AB2]

ASH

[AB2] (*)

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* the correction factor to account for gradually decreasing values of the sound power level inside the duct as the distance from the sound source increases only accounts the sound attenuation Δ (dB/m) due to internal ductwork losses which is entered in worksheet [in-out CORED IN->OUT])

Second approach

o

Bibliography (references) :

[AB3]

[AB4]

- o

Comments :

 the model for TL out is selected as shown in the table below: model source

3733

[AB3]

MIX

[AB3](*)

* the way to account for gradually decreasing values of the sound power level inside the duct as the distance from the sound source increases is not as accounted with [AB3] (where is related to thermodynamics and frequency), being accounted by the means of the sound attenuation Δ (dB/m) due to internal ductwork losses as entered in worksheet [in-out CORED IN->OUT])

 the model for diffusivity factor Kd=Km is selected as shown in the table below: model source

SIN

[AB4]

3

=3

3.2.2.1.b Acoustics: rectangular ducts, break in noise

Bloc diagram for rectangular duct walls break in noise

The computation scheme of rectangular duct walls is according the bloc-diagram below (cf. fig. 3.4):

fig. 3.4

Note 1: the service conditions dependence has been omitted for the sake of simplicity. See: report [PhRxx-015x]

Note 2: the main steps (the steps involving a physical modeling) being referred to from [A] to [AG] have been taken into account for the bloc-diagram above (some of the parameters of the above bloc diagram are not independent); the frequency dependence has been omitted for the sake of simplicity

Steps of the computation for rectangular duct walls break in noise

Steps [A] to [V]

See corresponding § in Section 2, as far as sound reduction index of plates is concerned (used for step [X])

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Preliminary remarks common to step [AC] and step [AC’]

o

Comments :

 the size of the cross section of the duct, the length of the duct, the flow rate are not related to the values selected in the worksheet [in-out COSIL] for B and H: corresponding input data are entered in worksheet [in-out CORED IN->OUT])

Step [AC]

This step aims at calculating the sound reduction index of a single-leaf (rectangular) duct made of 1 plate alone such as

plates of set 0, regardless of the selected quantity of such plates for set 0, regardless of the selected quantities of other elements, and with atmosphere at the front and at the rear regardless of the selected input data) o

Bibliography (references) :

[AC1]

-

[AC2]

[AC3]

[AC4] o

Comments :

 when used, the cut off frequency for the first higher mode fco is computed depending on the speed of sound c, the

Mach number in the airways M, and the geometry of the duct, according to various models as shown in the table below: model

HAN

MUN source [AC1] [AC2]

 the cross over frequency fcr is computed depending on the speed of sound c, the Mach number in the airways M, and the geometry of the duct, according to various models as shown in the table below: model HAN NAS SMA source [AC1] [AC3] [AC4](*)

*[AC4] seems to be in error

Step [AC’]

This step, being a complementary feature associated with step [X], aims at calculating the sound reduction index of a single-

leaf (rectangular) duct made of 1 steel plate alone with a thickness such as those of set 0, regardless of the other selected parameters of such plates for set 0, regardless of the selected quantity of such plates for set 0, regardless of the selected quantities of other elements, and with atmosphere at the front and at the rear regardless of the selected input data o

Bibliography (references) :

[AC’1]

[AC’2]

- o

Comments :

 the model of ratio a/b is selected as shown in the table below – whatever the corresponding input data of a and b are model 1 2 4 source a/b=1 a/b=2 a/b=4

Step [AE]

This step aims at calculating the insertion loss of set 1 when compared to set 0 with atmosphere at the front and at the rear regardless of the selected input data

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Bibliography (references) :

[AE1] o

Comments :

Cf. step [Z]

Step [AF]

This step aims at calculating the transmission loss with sound leaks with atmosphere at the front and at the rear regardless of the selected input data o

Bibliography (references) :

No particular bibliography has been considered o

Comments :

 if IL stat is accounted TL out = R dif + IL stat else TL out = R dif

 the model for Rdif is selected as shown in the table below: model 1 2 source cf. step

[AC] cf. step

[AC’]

Step [AG]

This step aims at calculating the break in sound power level with atmosphere at the front and at the rear regardless of the selected input data o

Bibliography (references) :

[AG1]

[AG2]

- o

Comments :

 the model for TL out is selected as shown in the table below: model source

2081

[AG1]

HAN

[AG2]

3.2.2.2 Acoustics: circular ducts

3.2.2.2.a Acoustics: circular ducts, break out noise

Bloc diagram for circular duct walls break out noise

The computation scheme of circular duct walls is according the bloc-diagram below (cf. fig. 3.5):

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Note 1: the service conditions dependence has been omitted for the sake of simplicity. See: report [PhRxx-015x]

fig. 3.5

Note 2: the main steps (the steps involving a physical modeling) being referred to from [A] to [AL] have been taken into account for the bloc-diagram above (some of the parameters of the above bloc diagram are not independent); the frequency dependence has been omitted for the sake of simplicity

Steps of the computation for circular duct walls break out noise

Steps [A] to [V]

See corresponding § in Section 2, as far as sound reduction index of plates is concerned ( use to be précised on the occasion of a future revision of this user’s manual

)

Preliminary remarks common to step [AH] and step [AH’]

o

Comments :

 the size of the cross section of the duct, the length of the duct, the flow rate are not related to the values selected in the worksheet [in-out COSIL] for D: corresponding input data are entered in worksheet [in-out COCID IN->OUT])

Step [AH]

This step aims at calculating the sound reduction index of a single-leaf (circular) duct made of 1 layer alone such as plates

of set 0, regardless of the selected quantity of such plates for set 0, regardless of the selected quantities of other elements, and with atmosphere at the front and at the rear regardless of the selected input data) o

Bibliography (references) :

[AH1]

-

[AH2]

[AH3] o

Comments :

 when used, the cut off frequency for the first higher mode fco is computed depending on the speed of sound c, the

Mach number in the airways M, and the geometry of the duct, according to various models as shown in the table below: model

HAN

MUN source [AH1] [AH2]

 the model of mounting is selected as shown in the table below:

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PhR15-008A 01-04-2015 173/262 model mounting (source [AH3]) a) welded pipe with an average of one bend per approximately 20D length b) welded straight pipe from approximately 20D length behind the source c) d) e) welded, average value from a) and b), if not to be specified more precisely as b) but pipe flanged at a distance from 2m to 6m pipe up to approximately 20D length behind the valve with customary solid-borne sound coupling between valve and flanged pipe

Step [AH’]

This step, being a complementary feature associated with step [X], aims at calculating the sound reduction index of a single-

leaf (circular) folded-spiral seam duct made of 1 layer alone such as plates of set0, regardless of the selected quantity of such plates for set 0, regardless of the selected quantities of other elements, and with atmosphere at the front and at the r ear regardless of the selected input data) o

Bibliography (references) :

[AH’1]

-

[AH’2]

[AH’3]

[AH’4]

-

Comments :

 when used, the cut off frequency for the first higher mode fco is computed depending on the speed of sound c, the

Mach number in the airways M, and the geometry of the duct, according to various models as shown in the table below: model source

HAN

[AH’1]

MUN

[AH’2]

 when used, the annular expansion frequency fRokt is selected as shown in the table below: model source

NAT

(*)

OCT

[AH’3]

* the annular expansion frequency is derived as for the general case (i.e.: not converted in 1/1 octave central frequency)

 the model of HF (High Frequency) limitation is selected as shown in the table below: model 2081

MOI

source

[AH’3]

(*)

* the HF limitation is derived as a corrected value

Step [AJ]

This step aims at calculating the insertion loss of set 1 when compared to set 0 with atmosphere at the front and at the rear regardless of the selected input data o

Bibliography (references) :

[AJ1]

-

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Comments :

 the model of insertion loss is selected as shown in the table below: model HAL MIC source

[AJ1]

HAL=HAL

[AJ1]

MIC=MICh e elsen

Step [AK]

This step aims at calculating the transmission loss with sound leaks with atmosphere at the front and at the rear regardless of the selected input data o

Bibliography (references) :

No particular bibliography has been considered o

Comments :

 if IL stat is accounted TL out = R dif + IL stat else TL out = R dif

 the model for Rdif is selected as shown in the table below: model 1 2

[AL]

[AL2]

- o

Comments :

source cf. step

[AH] cf. step

[AH’]

Step [AL]

This step aims at calculating the break out sound power level with atmosphere at the front and at the rear regardless of the selected input data

First approach

o

Bibliography (references) :

 the model for TL out is selected as shown in the table below: model source

2081

[AL]

HAN

[AL2]

ASH

[AL2] (*)

Second approach

o

Bibliography (references) :

[AL3]

[AL4]

-

* the correction factor to account for gradually decreasing values of the sound power level inside the duct as the distance from the sound source increases only accounts the sound attenuation Δ (dB/m) due to internal ductwork losses which is entered in worksheet [in-out COCID IN->OUT])

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Comments :

 the model for TL out is selected as shown in the table below: model source

3733

[AL3]

MIX

[AL3](*)

* the way to account for gradually decreasing values of the sound power level inside the duct as the distance from the sound source increases is not as accounted with [AL3] (where is related to thermodynamics and frequency), being accounted by the means of the sound attenuation Δ (dB/m) due to internal ductwork losses as entered in worksheet [in-out COCID IN->OUT])

 the model for diffusivity factor Kd=Km is selected as shown in the table below: model SIN 3 source [AL4] =3

3.2.2.2.b Acoustics: circular ducts, break in noise

Bloc diagram for circular duct walls break in noise

fig. 3.6

Note 1: the service conditions dependence has been omitted for the sake of simplicity. See: report [PhRxx-015x]

Note 2: the main steps (the steps involving a physical modeling) being referred to from [A] to [AQ] have been taken into account for the bloc-diagram above (some of the parameters of the above bloc diagram are not independent); the frequency dependence has been omitted for the sake of simplicity

Steps of the computation for circular duct walls break in noise

Steps [A] to [V]

See corresponding § in Section 2, as far as sound reduction index of plates is concerned ( use to be précised on the occasion of a future revision of this user’s manual

)

Preliminary remarks common to step [AP] and step [AQ]

o

Comments :

 the size of the cross section of the duct, the length of the duct, the flow rate are not related to the values selected in the worksheet [in-out COSIL] for D: corresponding input data are entered in worksheet [in-out COCID IN->OUT])

Step [AP]

This step aims at calculating the transmission loss with sound leaks with atmosphere at the front and at the rear regardless of the selected input data

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Bibliography (references) :

No particular bibliography has been considered o

Comments :

 if IL stat is accounted TL out = R dif + IL stat else TL out = R dif

 the model for Rdif is selected as shown in the table below: model 1 2 source cf. step

[AN] cf. step

[AN’]

Step [AQ]

This step aims at calculating the break out sound power level with atmosphere at the front and at the rear regardless of the selected input data o

Bibliography (references) :

[AQ1]

[AQ2]

- o

Comments :

 the model for TL out is selected as shown in the table below: model source

2081

[AB1]

HAN

[AB2]

3. 3: How to use SILDIS

Operating conditions / security level / safety

See corresponding § in the chapter General considerations

For safety reasons, some cells of the original file provided to the user (as mentioned in the table below) for which input data are foreseen to be entered by the user are pre-filled with the value “1/0”, among the yellow cells for which the color orange is used (*).

Worksheet

[in COALA]

[in CODAP]

[in-out COPPA]

Cells

E13, J37, W38

W23

X53, X54 (**)

* something like that

** attention has to be paid to the fact that the considered sheet is not included in the worksheets listed below

Worksheets

Regarding the COmputation of Duct Walls, the software SILDIS is configurated in order to allow the user to access to various worksheets being linked as shown in fig.3.5 (the overview of the worksheets being shown in table below).

Fig. 3.5

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Note: a partly common background is required for several steps of the computation schemes of different acoustic components

(insertion loss of a silencer, absorption coefficient / sound reduction index of a plane partition, sound reduction index of a duct wall...).

For this reason worksheets [in COALA] and [in COSIL] are distinct due to the existence of other calculations (by the means of

SILDIS) using the routine COALA (COmputation of Acoustic LAyers) but not using the routine COSIL (COmputation of SILencers).

Worksheet

[in COALA]

[in-out CORED IN->OUT]

Suitable for mountings

all

REctangular Duct, break out transmission

Input data

for sets, for reference spectrum for duct: dimensions, flow rate

Results

--

[in-out CORED OUT->IN]

REctangular Duct, break in transmission

[in-out COCID IN->OUT]

for duct: dimensions, flow rate indicators of performance (acoustics)

CIrcular Duct, break out transmission

CIrcular Duct, break in

[in-out COCID OUT->IN]

transmission

Input data, alerts and results: the key points

The best use of the software requires the knowledge of some key points in relation with: o the input data

See corresponding § in the chapter General considerations

As far as plates (to which the layer of material of the considered wall is equal) are concerned, specific data bases (libraries) ( will ) allow the design to be made with in-built engineering data (constants) referred to as “Usual” in the worksheets of the software.

Warning: some properties of the presently referenced materials still not have been checked by reliable sources.

See also report

[PhRxx-015x] Collection of soundproofing constructions systems: a companion to “User’s manual for the software SILDIS”

data base (library) for thin plates (available in worksheet in COALA)

 contents of the library: 21 possible references of material layers among those references: 2-PLY (reported from worksheet CODAP)

data base (library) for layers constituting the damped plates (available in worksheet in CODAP)

 contents of the library: 21 possible references of material layers o some alerts in case of input data involving a warning of the user o the place where (and the way) some results are presented

Those key points are reviewed worksheet per worksheet hereafter: the cells will be referred to thanks to their EXCEL’s coordinates

(column / line) in the following part of the present user’s manual.

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Worksheet [in-out CORED IN->OUT]

o

Input data :

Item

Biggest dimension a

Smallest dimension b

Length L

Mass flow rate

Model of cut-off frequency fco

Model of cross over frequency fcr

For f<fcr model of transmission

For f>fcr model of transmission

Model of minimum for Rdif

Model of maximum for Rdif

Model of minimum for Rdif

Model

Limitation of IL for HF

Model for Rdif

Accounting IL stat (0/1)

Cell for input

AH49

AH50

AH51

AH53

AH64

R81

R85

R90

R95

R99

R108

R131

R133

R149

R151

Foreseen action

Input a positive real

Input a positive real

Input a positive real

Input a positive real

Select a model (in the proposed list)

Select a model (in the proposed list)

Select a model (in the proposed list)

Select a model (in the proposed list)

Select a model (in the proposed list)

Select a model (in the proposed list)

Select a model (in the proposed list)

Select a model (in the proposed list)

Input a positive real

Select a model (in the proposed list)

For NO input 0, for YES input 1

Comment

Limitation of Insertion Loss for High Frequency

1= first approach displayed in the same worksheet

2= second approach displayed in the same worksheet

Δ (dB / m)

AB154 to

AL154

Input a positive real model model

R158

R164

Select a model (in the proposed list)

Select a model (in the proposed list)

Model for diffusivity factor

Kd=Km

Length of duct

R168

Select a model (in the proposed list)

Input a positive real R172 o

Main displays of the results :

Tables of results and graphs for a rectangular duct: 1 plate alone such as those of set 0

break out sound reduction index: see lines 75 to 100 (columns AA to AN)

Tables of results and graphs for a rectangular duct: 1 steel plate alone, thickness such as those of set 0

break out sound reduction index: see lines 102 to 123 (columns AA to AN)

Tables of results and graphs for a rectangular duct: set 1/ set 0: coupling 0%

insertion loss: see lines 125 to 145 (columns AA to AN)

Tables of results for a rectangular duct: TL out = Rdif +? ILstat

break out transmission loss: see lines 147 to 151 (columns AA to AN)

Tables of results for a rectangular duct: Lw out

break out sound power level: see lines 156 to 160 (columns AA to AN)

Tables of results for a rectangular duct: Lw out

break out sound power level: see lines 162 to 166 (columns AA to AN)

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Worksheet [in-out CORED OUT->IN]

o

Input data :

Item

Cell for input

Foreseen action Comment

Model of cross over frequency fcr

Model of ratio a/b

Model for Rdif

Accounting IL stat (0/1) model

X81

X113

X149

X151

X158

Select a model (in the proposed list)

Select a model (in the proposed list)

Select a model (in the proposed list)

For NO input 0, for YES input 1

Select a model (in the proposed list)

1= first approach displayed in the same worksheet

2= second approach displayed in the same worksheet o

Main displays of the results :

Tables of results and graphs for a rectangular duct: 1 plate alone such as those of set 0

break in sound reduction index: see lines 75 to 100 (columns AA to AN)

Tables of results and graphs for a rectangular duct: 1 steel plate alone, thickness such as those of set 0

break in sound reduction index: see lines 102 to 123 (columns AA to AN)

Tables of results and graphs for a rectangular duct: set 1/ set 0: coupling 0%

insertion loss: see lines 125 to 145 (columns AA to AN)

Tables of results for a rectangular duct: TL out = Rdif +? ILstat

break in transmission loss: see lines 147 to 151 (columns AA to AN)

Tables of results for a rectangular duct: Lw out

break in sound power level: see lines 156 to 160 (columns AA to AN)

Tables of results for a rectangular duct: Lw out

break in sound power level: see lines 162 to 166 (columns AA to AN)

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Worksheet [in-out COCID IN->OUT]

o

Input data :

Item

Diameter D

Length L

Mass flow rate

Model of cut-off frequency fco

Model of mounting

Model of annular expansion frequency fRokt

Model of HF limitation

Model

Model for Rdif

Accounting IL stat (0/1)

Cell for input

AH49

AH51

AH53

AH64

R85

R108

R113

R131

R149

R151

Foreseen action

Input a positive real

Input a positive real

Input a positive real

Select a model (in the proposed list)

Select a model (in the proposed list)

Select a model (in the proposed list)

Select a model (in the proposed list)

Select a model (in the proposed list)

Select a model (in the proposed list)

For NO input 0, for YES input 1

Comment

1= first approach displayed in the same worksheet

2= second approach displayed in the same worksheet

Δ (dB / m)

AB154 to

AL154

Input a positive real model model

Model for diffusivity factor

Kd=Km

Length of duct

R158

R164

R168

R172

Select a model (in the proposed list)

Select a model (in the proposed list)

Select a model (in the proposed list)

Input a positive real o

Main displays of the results :

Tables of results and graphs for a rectangular duct: 1 plate alone such as those of set 0

break out sound reduction index: see lines 75 to 100 (columns AA to AN)

Tables of results and graphs for a rectangular duct: 1 steel plate alone, thickness such as those of set 0

break out sound reduction index: see lines 102 to 123 (columns AA to AN)

Tables of results and graphs for a rectangular duct: set 1/ set 0: coupling 0%

insertion loss: see lines 125 to 145 (columns AA to AN)

Tables of results for a rectangular duct: TL out = Rdif +? ILstat

break out transmission loss: see lines 147 to 151 (columns AA to AN)

Tables of results for a rectangular duct: Lw out

break out sound power level: see lines 156 to 160 (columns AA to AN)

Tables of results for a rectangular duct: Lw out

break out sound power level: see lines 162 to 166 (columns AA to AN)

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Worksheet [in-out COCID OUT->IN]

o

Input data :

Item

Cell for input

Foreseen action Comment

Model for Rdif X149

Select a model (in the proposed list)

1= first approach displayed in the same worksheet

2= second approach displayed in the same worksheet

Accounting IL stat (0/1) model

X151

X158

For NO input 0, for YES input 1

Select a model (in the proposed list) o

Main displays of the results :

Tables of results and graphs for a rectangular duct: 1 plate alone such as those of set 0

break in sound reduction index: see lines 75 to 100 (columns AA to AN)

Tables of results and graphs for a rectangular duct: 1 steel plate alone, thickness such as those of set 0

break in sound reduction index: see lines 102 to 123 (columns AA to AN)

Tables of results and graphs for a rectangular duct: set 1/ set 0: coupling 0%

insertion loss: see lines 125 to 145 (columns AA to AN)

Tables of results for a rectangular duct: TL out = Rdif +? ILstat

break in transmission loss: see lines 147 to 151 (columns AA to AN)

Tables of results for a rectangular duct: Lw out

break in sound power level: see lines 156 to 160 (columns AA to AN)

Tables of results for a rectangular duct: Lw out

break in sound power level: see lines 162 to 166 (columns AA to AN)

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3.4: Examples of computation with SILDIS

Example 3.4.1 rectangular duct wall

Envisaged application

It is wished to compute the breakout transmission loss of a rectangular duct wall for room conditions. The duct is made of steel [1] with a thickness 0.567 mm [2]. A cross section B=151 mm [3]*H=151 mm [4] is considered. Regarding models of computation: the procedures of the model referred to as SMA are selected [5].

Input data

The input data required for the computation are listed hereafter in reference with the above data (see placemarks).

The input cells will be referred to thanks to their EXCEL’s coordinates (column / line) in the following part of the present user’s manual.

Worksheet [in COALA]

Item

Cell for input

Foreseen action

Reference g)

Thickness

W31

Y31

W38

Select a reference

(material in the proposed list)

Select 1 or 2 in the proposed list

Input a real positive number

Worksheet [in-out CORED1 IN->OUT]

Item

Cell for input

Biggest dimension a

Smallest dimension b

Length L

Mass flow rate

Model of cut-off frequency fco

Model of cross over frequency fcr

For f<fcr model of transmission

For f>fcr model of transmission

AH49

AH50

AH51

AH53

AH60

R81

R85

R90

Model of minimum for Rdif

Model of maximum for Rdif

R95

R99

Foreseen action

Input a positive real

Input a positive real

Input a positive real

Input a positive real

Select a model (in the proposed list)

Select a model (in the proposed list)

Select a model (in the proposed list)

Select a model (in the proposed list)

Select a model (in the proposed list)

Select a model (in the proposed list)

Input

STEEL

1

0.567E-3

Input

0.151

0.151

-

-

-

SMA

SMA

SMA

ZER

NAT

See placemark / comment

[1]

[2]

See placemark

[3]

[3]

[5]

[5]

[5]

[5]

[5]

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Screenshots of the worksheets (for the example of computation)

Screenshot of worksheet [in-out COALA]

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Screenshot of worksheet [in-out CORED IN->OUT]

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Example 3.4.2 circular duct wall (pipe)

Envisaged application

It is wished to compute the breakout transmission loss of a circular duct wall (pipe) for service conditions: temperature 100°C [1], pressure 1E6 Pa [2]. The duct is made of steel [3], for which the natural effective critical frequency is considered [4] with a thickness

10 mm [5], with a diameter D=300mm [6]. Regarding models of computation: the procedures basing the model referred to as 3733 are selected [7] with an average value for accounting mounting [8]

Input data

The input data required for the computation are listed hereafter in reference with the above data (see placemarks).

The input cells will be referred to thanks to their EXCEL’s coordinates (column / line) in the following part of the present user’s manual.

Worksheet [in COALA]

Item

Temperature

Pressure

Reference g)

Model of effective critical frequency

Thickness

Worksheet [in-out COCID IN->OUT]

Item

Diameter D

Cell for input

AH49

Length L

Mass flow rate

Model of cut-off frequency fco

AH51

AH53

AH64

Model of mounting

Cell for input

D6

D7

W31

Y31

W37

W38

R85

Foreseen action

Input a real number

Input a real positive number

Select a reference

(material in the proposed list)

Select 1 or 2 in the proposed list

Select a model (in the proposed list)

Input a real positive number

Foreseen action

Input a positive real

Input a positive real

Input a positive real

Select a model (in the proposed list)

Select a model (in the proposed list)

Input

20

100000

STEEL

1

NAT

0.010

Input

0.3

-

-

- c)

See placemark / comment

[1]

[2]

[3]

[4]

[5]

See placemark

[6]

[8]

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Screenshots of the worksheets (for the example of computation)

Screenshot of worksheet [in-out COALA]

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Screenshot of worksheet [in-out COCID IN->OUT]

FAIST

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Example 3.4.3 circular duct wall (spiral-seam pipe)

Envisaged application

It is wished to compute the breakout transmission loss of a circular duct wall (spiral-seam pipe) for room conditions: temperature

17°C [1], pressure 1E5 Pa [2]. The duct is made of steel [3], for which the natural effective critical frequency is considered [4] with a thickness 0.65 mm [5], with a diameter D=250mm [6]. The length of the duct is 1 m [7]. The flow rate is 1400 m3/h [8]. The sound velocity in steel is accounted as 5100 m/s. Regarding models of computation: the procedures basing the model referred to as 2081 are selected [9] except for the high frequency [10].

Input data

The input data required for the computation are listed hereafter in reference with the above data (see placemarks).

The input cells will be referred to thanks to their EXCEL’s coordinates (column / line) in the following part of the present user’s manual.

Worksheet [in COALA]

Item

Temperature

Pressure

Reference g)

Model of effective critical frequency

Thickness

Cell for input

D6

D7

W31

Y31

W37

W38

Reference acoustic power spectrum

D65 to

K65

Worksheet [in-out COCID IN->OUT]

Item

Diameter D

Cell for input

AH49

AH51

AH53

Length L

Mass flow rate

Model of cut-off frequency fco model of annular expansion frequency fRokt

AH64

R108 model of HF limitation model for Rdif

R113

R149

Foreseen action

Input a real number

Input a real positive number

Select a reference

(material in the proposed list)

Select 1 or 2 in the proposed list

Select a model (in the proposed list)

Input a real positive number

Input numbers

Foreseen action

Input a positive real

Input a positive real

Input a positive real

Select a model (in the proposed list)

Select a model (in the proposed list)

Select a model (in the proposed list)

Select a model (in the proposed list)

Input

17

100000

STEEL

1

NAT

0.00065

73.6; 61.6; 49.5; 44.0;

38.3; 33.8; 35.5; 30.5

Input

0.25

1

=1400/3600*AH58

-

NAT

MOI

2

See placemark / comment

[1]

[2]

[3]

[4]

[5]

[11]

See placemark

[6]

[7]

[8]

-

[9]

[9]

-

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Screenshots of the worksheets (for the example of computation)

Screenshot of worksheet [in-out COALA]

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Screenshot of worksheet [in-out COCID IN->OUT]

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Appendix to Section 3: list of symbols

General

Cf. corresponding § in Section 1 and 2

Duct wall

a: biggest (inner) dimension of the cross section of a rectangular duct b: smallest (inner) dimension of the cross section of a rectangular duct

D: (inner) diameter of a rectangular duct fco: cut-off frequency of the duct (Hz) fcr: cross over frequency (Hz) fR: annular expansion frequency (Hz)

Miscellaneous

See also corresponding § in General considerations and in Section 1 and 2

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Section 4: computation of duct straight runs

(MODULE 4 of the software)

4.1: Introduction

Terms and definitions

For the needs of the present user’s manual, the following terms and definition apply:

No particular term or definition (cf. section 1, section 2, cf. section 3)

Mountings and geometry

The geometry used for the computation of duct straight runs is as follows:

cross section

rectangular circular

4.2: Scientific and technical background

The prediction of acoustic performances of ducts straight runs with SILDIS is founded on a scientific and technical background in relation with: o analytical models for taking into account the properties of materials and various physical phenomena useful on the occasion of the computation o measurement results for feeding some of those models and for allowing the necessary improvement (through correction factors) of the correlation between some calculations and on site observations

The obtained results are not comparable with standardized measurement due to the lack of such documents.

4.2.1Thermodynamics and fluid dynamics:

Steps of the computation

Step [a]

All computations have been gathered in this single step for the sake of simplicity. See corresponding § in Section 1

4.2.2 Acoustics:

Bloc diagram

on fig 4.1 below

Fig. 4.1

Note 1: the service conditions dependence has been omitted for the sake of simplicity. See: report [PhRxx-015x]

Note 2: the main steps (the steps involving a physical modeling) being referred to from [AR] to [AU] have been taken into account for the bloc-diagram above (some of the parameters of the above bloc diagram are not independent); the frequency dependence has been omitted for the sake of simplicity

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Steps of the computation

Step [AR] only for applications related to air conditioning systems made of thin duct walls (i.e. not for applications involving stacks made of thick duct walls)

This step aims at calculating the (longitudinal) attenuation (per unit length) of duct straight runs o

Bibliography (references) :

[AR1]

-

[AR2]

[AR3]

[AR4]

[AR5] o

Comments :

 when used, the cut off frequency for the first higher mode fco is computed depending on the speed of sound c, the

Mach number in the airways M, and the geometry of the duct, according to various models as shown in the table below: model

HAN

MUN source [AR1] [AR2]

 when used, the model of (longitudinal)

attenuation (per unit length) is selected among various models as shown in the table below:

 rectangular duct model source comment

2081-R

[AR3] thickness 1 mm,

(rectangular) dimension

0.10 m up to

1.00 m

SMA-R

[AR4]

(rectangular)

ASH

150*150

[AR5] for

(rectangular) cross section

150 mm *

150 mm

ASH

305*305

[AR5] for

(rectangular) cross section

305 mm *

305 mm

ASH

305*610

[AR5] for

(rectangular) cross section

305 mm *

610 mm model source comment

 circular duct

ASH

610*610

[AR5]

For

(rectangular) cross section

610 mm *

610 mm

ASH

1220*1220

[AR5] for

(rectangular) cross section

1220 mm *

1220 mm

ASH

1830*1830

[AR5] for

(rectangular) cross section

1830 mm *

1830 mm

ZER

ZERo attenuation model source comment

2081-C

[AR3] thickness 1 mm,

(rectangular) diameter

0.10 m up to

1.00 m

ASH D≤180

[AR5] for circular cross section diameter D ≤

180 mm

ASH

180<D≤380

[AR5] for circular cross section

180 mm < D

≤ 380 mm

ASH

380<D≤760

[AR5] for circular cross section

380 mm < D

≤ 760 mm

ASH

760<D≤1520

[AR5] for circular cross section

760 mm < D

≤ 1520 mm

ZER

ZERo attenuation

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Step [AS]

This step aims at calculating the insertion loss without self noise of duct straight runs o

Bibliography (references) :

[AS1] o

Comments :

 the insertion loss without flow noise D’i is computed according to various models as shown in the table below: model source comment

3733G

[AS1] only for applications involving stacks made of thick duct walls (based on graphic displayed in

[AS1])

3733T

[AS1] only for applications involving stacks made of thick duct walls (based on table displayed in

[AS1])

COEDLA step [AR] only for applications related to air conditioning systems made of thin duct walls cf. step [AR]

Step [AT]

This step aims at taking into account the self noise of duct straight runs (noise produced by the airflow).

For dissipative silencers o

Bibliography (references) :

[AT1]

[AT2]

[AT3]

[AT4]

[AT5]

- o

Comments: the self noise (acoustic power of flow noise Lw in dB ref 1E-12W) is basically computed at frequency steps of

1/1 octave.

for rectangular cross sections as well as for circular cross sections, the determination of the self noise is done according various models as shown in the tables below: model source

2081B

[AT1]

(**)(***)

3733A1

[AT2]

(**)(***)

3733A2

[AT3]

(**)(***)

3733B

[AT4]

(**)(***)

 for the models 2081 and 3733, a spectral correction is used according various models as shown in the tables below: model source

2081

[AT4]

FRO

[AT5]

3733

[AT3]

Warning: at the time of the writing of this manual, all the consequences of the choice of one or the other model are not known with accuracy. The choice of the model can be done by the user allowing tests and feed-back.

Step [AU]

This step aims at calculating the insertion loss of the duct including its self noise. o

Bibliography (references) :

[AU1]

-

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Comments :

The sound power level downstream of the straight duct including self noise (Lw1 in dB ref 1E-12W) is basically computed at frequency steps of 1/1 octave (in reference to a reference acoustic power spectrum Lw0 ref 1E-12W).

Lw1 = 10 * log [10^ (0.1 * (Lw0 – Di’)) + 10^ (0.1 * Lw)]

Lw being the self noise (acoustic power of flow noise in dB ref 1E-12W)

The insertion loss taking into account the self noise (Di in dB) is basically computed at frequency steps of 1/1 octave (in reference to a reference acoustic power spectrum Lw0 ref 1E-12W).

Di = Lw0 – Lw1

In case of rectangular ducts, the obtained results are comparable with the standardized measurement: see NF EN ISO 7235

Acoustics - Laboratory measurement procedures for ducted silencers and air terminal units- Insertion loss, flow noise and total pressure loss (2004).

4.3: How to use SILDIS

Operating conditions / security level / safety

See corresponding § in the chapter General considerations

For safety reasons, some cells of the original file provided to the user (as mentioned in the table below) for which input da ta are foreseen to be entered by the user are pre-filled with the value “1/0”, among the yellow cells for which the color orange is used (*).

Worksheet

[in COALA]

Cells

E13, J37, W38

* something like that

Worksheets

** attention has to be paid to the fact that the considered sheet is not included in the worksheets listed below

Regarding the COmputation of BENDs, the software SILDIS is configurated in order to allow the user to access to various worksheets being linked as shown in fig.4.2 (the overview of the worksheets being shown in table below).

Fig. 4.2

Note: temperature and pressure conditions as well as reference spectrum one should enter in worksheet in COALA

Worksheet Suitable for mountings Input data Results

[in COALA]

all for climatic conditions, for reference spectrum

--

[in-out COEDLA]

COmputation of Empty

Ducts Longitudinal

Attenuation for duct: dimensions indicators of performance (acoustics)

COmputation of STraigtht

[in-out COSTDUC]

DUcts

Input data, alerts and results: the key points for duct: dimensions, flow rate indicators of performance (acoustics)

Worksheet [in-out COEDLA]

o

Input data :

Item

mass flow rate Qm (kg/s) model of cut-off frequency fco

Cell for input

I5

P5

Foreseen action

Input a real

Select a model (in the proposed list)

Comment

useless input data given the development of SILDIS useless input data given the development of SILDIS

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Only in case of a rectangular cross section

Item

biggest dimension (m)

Cell for input

P23

Foreseen action

Input a real smallest dimension (m) model of attenuation

Input a real

Select a model (in the proposed list)

Only in case of a circular cross section

Item

P24

P32

Cell for input

Foreseen action

diameter (m) model of attenuation

P47

P57

Input a real

Select a model (in the proposed list)

Worksheet [in-out COSTDU]

o

Input data :

Item

mass flow rate Qm (kg/s)

Cell for input

I5

Foreseen action

model of cut-off frequency fco model of insertion loss

N5

S5

Input a real

Select a model (in the proposed list)

Select a model (in the proposed list)

Input a real duct length (m) X5 model of self noise model of spectral correction

Select a model (in the proposed list)

Select a model (in the proposed list)

Only in case of a rectangular cross section

Item

AC5

AC10

Cell for input

Foreseen action

Comment

Comment

Comment

Comment

biggest dimension (m) smallest dimension (m)

Item

P23

P24

Only in case of a circular cross section

Cell for input

Input a real

Input a real

Foreseen action

diameter (m) o

Main displays of the results :

P47 Input a real

Worksheet [in-out COEDLA]

Table of results in case of rectangular cross section

longitudinal attenuation Δ: see lines 21 to 24 (columns S to AC)

Tables of results in case of circular cross section

longitudinal attenuation Δ: see lines 44 to 47 (columns S to AC)

Comment

Worksheet [in-out COSTDU]

Tables of results in case of rectangular cross section

insertion loss without self noise Di’: see lines 21 to 24 (columns S to AD)

self noise Lw: see lines 26 to 30 (columns S to AD)

sound power level downstream of straight duct section: see lines 32 to 36 (columns S to AD)

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insertion loss with self noise Di: see lines 38 to 41 (columns S to AD)

Tables of results in case of circular cross section

insertion loss without self noise Di’: see lines 44 to 47 (columns S to AD)

self noise Lw: see lines 49 to 53 (columns S to AD)

sound power level downstream of straight duct section: see lines 55 to 59 (columns S to AD)

insertion loss with self noise Di: see lines 61 to 64 (columns S to AD)

4.4: Examples of computation with SILDIS

Example 4.4.1 rectangular straight duct (air conditioning system)

Envisaged application

It is wished to compute the sound power level downstream of a rectangular straight duct for room conditions: temperature 17°C [1], pressure 1E5 Pa [2]. The duct is made of steel [3], with a thickness 1 mm [4], with a width B=0.5 m [5], and with a height H= 0.4 m

[6]. The length of the duct is 4 m [7]. The flow rate is 4200 m3/h [8]. Regarding models of computation: the procedures basing the model referred to as 2081 are selected [9].

Note: the sound power spectrum upstream of the considered straight duct section is as shown in the table below [10].

F(Hz) 63 125 250 500 1000 2000 4000 8000

80.8 68.3 48.9 44.9 40.2 39.5 44.0 39.1 Lw0 (dB ref 1pW)

Input data

The input data required for the computation are listed hereafter in reference with the above data (see placemarks).

The input cells will be referred to thanks to their EXCEL’s coordinates (column / line) in the following part of the present user’s manual.

Worksheet [in COALA]

Item

Cell for input

D6

Foreseen action

Temperature

Pressure D7

Input a real number

Input a real positive number

Reference acoustic power spectrum

Input numbers

Worksheet [in-out COEDLA]

Item

mass flow rate Qm (kg/s)

Cell for input

I5

Foreseen action

model of attenuation P32

Input a real model of cut-off frequency fco

P5

Only in case of a rectangular cross section

Select a model (in the proposed list)

Item

biggest dimension (m)

Cell for input

P23

Foreseen action

Input a real smallest dimension (m) P24 Input a real

Select a model (in the proposed list)

D65 to

K65

Input

17

100000

80.8 ; 68.3 ; 48.9 ; 44.9 ;

40.2 ; 39.5 ; 44.0 ; 39.1

Input

-

-

Input

0.5

0.4

2081-R

See placemark / comment

[1]

[2]

[10]

See placemark / comment

See placemark / comment

[5]

[6]

[9]

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Worksheet [in-out COSTDU]

Item

mass flow rate Qm (kg/s)

Cell for input

I5

Foreseen action

model of cut-off frequency fco model of insertion loss

N5

S5

Input a real

Select a model (in the proposed list)

Select a model (in the proposed list)

Input a real duct length (m) X5 model of self noise model of spectral correction

Select a model (in the proposed list)

Select a model (in the proposed list)

Only in case of a rectangular cross section

Item

AC5

AC10

Cell for input

Foreseen action

biggest dimension (m) smallest dimension (m)

P23

P24

Input a real

Input a real

Screenshots of the worksheets (for the example of computation)

Screenshot of worksheet [in-out COALA]

Input

=4200/3600*I10

HAN

COEDLA

4

2081B

2081

Input

0.5

0.4

See placemark / comment

[8]

[7]

[9]

[9]

See placemark / comment

[5]

[6]

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Screenshot of worksheet [in-out COEDLA]

Screenshot of worksheet [in-out COSTDU]

Example 4.4.2 circular straight duct (air conditioning system)

Envisaged application

It is wished to compute the sound power level downstream of a circular straight duct for room conditions: temperature 17°C [1], pressure 1E5 Pa [2]. The duct is made of steel [3], with a thickness 1 mm [4], with a diameter D=0.25 m [5]. The length of the duct is

7 m [6]. The flow rate is1400 m3/h [7]. Regarding models of computation: the procedures basing the model referred to as 2081 are selected [8].

Note: the sound power spectrum upstream of the considered straight duct section is as shown in the table below [9].

F(Hz) 63 125 250 500 1000 2000 4000 8000

Lw0 (dB ref 1pW)

73.6 61.3 45.7 42.1 38.4 36.1 38.8 33.9

Input data

The input data required for the computation are listed hereafter in reference with the above data (see placemarks).

The input cells will be referred to thanks to their EXCEL’s coordinates (column / line) in the following part of the present user’s manual.

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Worksheet [in COALA]

Item

Cell for input

D6

Foreseen action

Temperature

Pressure D7

Input a real number

Input a real positive number

Reference acoustic power spectrum

D65 to

K65

Input numbers

Worksheet [in-out COEDLA]

Item

Cell for input

Foreseen action

mass flow rate Qm (kg/s) model of cut-off frequency fco

I5

P5

Input a real

Select a model (in the proposed list)

Only in case of a circular cross section

Item

Cell for input

Foreseen action

diameter (m) model of attenuation

P47

P57

Input a real

Select a model (in the proposed list)

Input

17

100000

73.6 ; 61.3 ; 45.7 ; 42.1 ;

38.4 ; 36.1 ; 38.8 ; 33.9

Input

-

-

Input

0.250

2081-C

See placemark / comment

[1]

[2]

[9]

See placemark / comment

See placemark / comment

[5]

[8]

Worksheet [in-out COSTDU]

Item

mass flow rate Qm (kg/s) model of cut-off frequency fco model of insertion loss duct length (m) model of self noise model of spectral correction

Cell for input

I5

N5

S5

X5

AC5

AC10

Foreseen action

Input a real

Select a model (in the proposed list)

Select a model (in the proposed list)

Input a real

Select a model (in the proposed list)

Select a model (in the proposed list)

Input

=1400/3600*I10

HAN

COEDLA

7

2081B

2081

See placemark / comment

[7]

[6]

[8]

[8]

Only in case of a circular cross section

Item

Cell for input

Foreseen action

diameter (m) P47 Input a real

Input

0.250

See placemark / comment

[5]

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Screenshots of the worksheets (for the example of computation)

Screenshot of worksheet [in-out COALA]

Screenshot of worksheet [in-out COEDLA]

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Screenshot of worksheet [in-out COSTDU]

Example 4.4.3 circular straight duct (exhaust stack)

Envisaged application

It is wished to compute the sound power level at the mouth of a circular stack for service conditions: temperature 109.85°C [1], pressure 1E5 Pa [2]. The duct is with a diameter D=6 m [3]. The height of the stack is 135 m [4]. The flow rate is 384.615 kg/s [5].

Regarding models of computation: the procedures basing the model referred to as 3733G are selected [6].

Input data

The input data required for the computation are listed hereafter in reference with the above data (see placemarks).

The input cells will be referred to thanks to their EXCEL’s coordinates (column / line) in the following part of the present user’s manual.

Worksheet [in COALA]

Item

Temperature

Cell for input

D6

Foreseen action Input

109.85

See placemark / comment

[1]

Pressure D7

Input a real number

Input a real positive number

100000 [2]

Worksheet [in-out COSTDU]

Item

Cell for input

mass flow rate Qm (kg/s) model of cut-off frequency fco

I5

N5

Foreseen action Input

384.615

-

See placemark / comment

[5] model of insertion loss duct length (m) model of self noise model of spectral correction

S5

X5

AC5

AC10

Input a real

Select a model (in the proposed list)

Select a model (in the proposed list)

Input a real

Select a model (in the proposed list)

Select a model (in the proposed list)

3733G

135

-

-

[5]

[6]

-

-

Only in case of a circular cross section

Item

diameter (m)

Cell for input

P47

Foreseen action

Input a real

Input

6

See placemark / comment

[3]

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Screenshots of the worksheets (for the example of computation)

Screenshot of worksheet [in-out COALA]

Screenshot of worksheet [in-out COSTDU]

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Appendix to Section 4: list of symbols

General

Cf. corresponding § in Section 1,2 and 3

Straight duct

Lw0: sound power level without soundproofing equipment (dB ref. 1pW) i.e. in the entrance plane of the duct (casing) section of interest

Lw1: sound power level with soundproofing equipment (dB ref. 1pW) i.e. in the exit plane of the duct (casing) section of interest

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Section 5: computation of break-out noise

(MODULE 5 of the software)

5.1: Introduction

Terms and definitions

For the needs of the present user’s manual, the following terms and definition apply:

No particular term or definition (cf. section 1, section 2, cf. section 3, cf. section 4)

Mountings and geometry

The geometry used for the design of silencer casings with the program SILDIS is as shown in section 1, section 2, cf. section 3

5.2: Scientific and technical background

The prediction of acoustic performances of ducts with SILDIS is founded on a scientific and technical background in relation with: o analytical models for taking into account the properties of materials and various physical phenomena useful on the occasion of the computation o measurement results for feeding some of those models and for allowing the necessary improvement (through correction factors) of the correlation between some calculations and on site observations

The obtained results are not comparable with standardized measurement due to the lack of such documents.

5.2.1Thermodynamics and fluid dynamics:

Steps of the computation

Step [a]

All computations have been gathered in this single step for the sake of simplicity. See corresponding § in Section 1

5.2.2 Acoustics:

Bloc diagram in case of a silencer

on fig 5.1.1 below

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Fig. 5.1.1

Bloc diagram in case of an empty duct

on fig 5.1.2 below

Fig. 5.1.2

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Note 1: the service conditions dependence has been omitted for the sake of simplicity. See: report [PhRxx-015x]

Note 2: the main steps (the steps involving a physical modeling) being referred to as [AV] have been taken into account for the blocdiagram above (some of the parameters of the above bloc diagram are not independent); the frequency dependence has been omitted for the sake of simplicity

Steps of the computation

Step [AV]

This step aims at calculating the sound power level radiated by duct (or casing) walls with atmosphere at the front and at the rear regardless of the selected input data o

Bibliography (references) :

[AV1]

[AV2]

[AV3]

-

[AV4]

Comments :

 when used, the duct (or casing) walls sound transmission loss referred to as TL out is selected according to various models as shown in the table below: model source

COPPA as derived & displayed in worksheet

COPPA

COPPA1 as derived & displayed in worksheet

COPPA1

COPPA2 as derived & displayed in worksheet

COPPA2

CORED as derived & displayed in worksheet

CORED IN-

>OUT

COCID as derived & displayed in worksheet

COCID IN-

>OUT

BYO

TL out figures to be entered by user (BYO =

Bring Your

Own)

 when used, the model of silencer (i.e. the model of silencer insertion loss referred to as Di) is selected according to various models as shown in the table below: model CODIS1 CODIS2 CORESPTR CORESPTL ZER BYO source as derived & displayed in worksheet

CODIS1 as derived & displayed in worksheet

CODIS1 as derived & displayed in worksheet

CORESPTR as derived & displayed in worksheet

CORESPTL insertion loss

= ZERo (i.e.

ZERo silencer effect)

TL out figures to be entered by user (BYO =

Bring Your

Own)

 the model for the sound power level radiated by duct (or casing) walls referred to as Lw out is selected as shown in the table below: model 2081 HAN ASH source

[AV1]

[AV2]

[AV3] [AV4] (*)

* the correction factor to account for gradually decreasing values of the sound power level inside the duct as the distance from the sound source increases only accounts the sound attenuation Δ (dB/m) due to internal ductwork losses which is computed as Di/L

5.3: How to use SILDIS

Operating conditions / security level / safety

See corresponding § in the chapter General considerations

For safety reasons, some cells of the original file provided to the user (as mentioned in the table below) for which input data are foreseen to be entered by the user are pre-filled with the value “1/0”, among the yellow cells for which the color orange is used (*).

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Worksheet

[in COALA]

[in CODAP]

[in-out COPPA]

Cells

E13, J37, W38

W23

X53, X54 (**)

* something like that

** attention has to be paid to the fact that the considered sheet is not included in the worksheets listed below

Worksheets

Regarding the COmputation of Break-Out Noise, the software SILDIS is configurated in order to allow the user to access to various worksheets being linked as shown in fig. 5.21 (the overview of the worksheets being shown in table below).

Fig. 5.2

Worksheet

[in-out CORED IN->OUT]

Suitable for mountings

Rectangular duct

Input data

for duct: dimensions (for some models: longitudinal sound attenuation as well)

Results

indicators of performance (acoustics)

[in-out COCID IN->OUT

[in-out COBON]

Circular duct

Rectangular duct or silencer casing

Circular duct or silencer for duct: dimensions (for some models: longitudinal sound attenuation as well) for duct or silencer casing: dimensions

(for some models: longitudinal sound casing

Input data, alerts and results: the key points

attenuation as well)

The best use of the software requires the knowledge of some key points in relation with: indicators of performance (acoustics) indicators of performance (acoustics) o the input data

See corresponding § in the chapter General considerations o some alerts in case of input data involving a warning of the user o the place where (and the way) some results are presented

Those key points are reviewed worksheet per worksheet hereafter: the cells will be referred to thanks to their EXCEL’s coordinates

(column / line) in the following part of the present user’s manual.

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Worksheet [in-out COBON]

o

Input data :

Item

Cell for input

Foreseen action Comment

Perimeter of the cross section of the silencer (m)

Area of the cross section of the silencer (m2)

R20

R22

Input a positive real

Input a positive real

Model for TL out

Model of silencer

R27

R33

Select a model (in the proposed list)

Select a model (in the proposed list)

Model for Lw out

Finite elements method (0/1)

?

R38

R40

Select a model (in the proposed list)

Input 0 to answer “no”; input 1 to answer “yes”

The recourse to finite elements method makes sense in case of ducts with a big length or in case of silencers o

Main displays of the results :

Tables of results

sound power level radiated out of the duct (casing) section of interest: see lines 42 to 46 (columns AA to AN)

sound power level downstream of considered section of duct (silencer) + sound power level radiated out of the

duct (casing) section of interest: see lines 48 to 52 (columns AA to AN)

Note:

Tables of results already displayed in other worksheets, being input data for the present work sheet

sound power level in the exit plane of the duct (casing) section of interest: see lines 18 to 22 (columns AA to AN)

sound transmission loss of the duct wall (casing): see lines 25 to 29 (columns AA to AN)

insertion loss of the silencer: see lines 31 to 34 (columns AA to AN)

(longitudinal) sound attenuation: see lines 36 to 39 (columns AA to AN)

5.4: Examples of computation with SILDIS

Example 5.4.1 circular duct wall (spiral-seam pipe)

Envisaged application

It is wished to compute the sound power level radiated out of a circular duct walls (spiral-seam pipe) for room conditions: temperature

17°C [1], pressure 1E5 Pa [2]. The duct is made of steel [3], for which the natural effective critical frequency is considered [4] with a thickness 0.65 mm [5], with a diameter D=250mm [6]. The length of the duct is 1 m [7]. The flow rate is 1400 m3/h [8]. The sound velocity in steel is accounted as 5100 m/s. Regarding models of computation: the procedures basing the model referred to as 2 081 are selected [9] except for the high frequency [10].

Note: the unsilenced sound power spectrum is as shown in the table below [11].

F(Hz) 63 125 250 500 1000 2000 4000 8000

Lw0 (dB ref 1pW)

73.6 61.6 49.5 44.0 38.3 33.8 35.5 30.5

Note: the sound power level radiated out of a circular duct walls is displayed in 2 worksheets of SILDIS: in worksheet [in-out COCID

IN->OUT] and in worksheet [in-out COBON]

Input data

The input data required for the computation are listed hereafter in reference with the above data (see placemarks).

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The input cells will be referred to thanks to their EXCEL’s coordinates (column / line) in the following part of the present user’s manual.

Worksheet [in COALA]

Item

Temperature

Pressure

Reference g)

Model of effective critical frequency

Thickness

Cell for input

D6

D7

W31

Y31

W37

W38

Reference acoustic power spectrum

D65 to

K65

Worksheet [in-out COCID IN->OUT]

Item

Diameter D

Cell for input

AH49

AH51

AH53

Length L

Mass flow rate

Model of cut-off frequency fco model of annular expansion frequency fRokt

AH64

R108 model of HF limitation model for Rdif

R113

R149

Foreseen action

Input a real number

Input a real positive number

Select a reference

(material in the proposed list)

Select 1 or 2 in the proposed list

Select a model (in the proposed list)

Input a real positive number

Input numbers

Foreseen action

Input a positive real

Input a positive real

Input a positive real

Select a model (in the proposed list)

Select a model (in the proposed list)

Select a model (in the proposed list)

Select a model (in the proposed list)

Input

17

100000

STEEL

1

NAT

0.00065

73.6; 61.6; 49.5; 44.0;

38.3; 33.8; 35.5; 30.5

Input

0.25

1

=1400/3600*AH58

-

NAT

MOI

2

See placemark / comment

[1]

[2]

[3]

[4]

[5]

[11]

See placemark

[6]

[7]

[8]

-

[9]

[9]

-

Only if one wishes to use the sound power level transmitted by the walls of a circular duct wall is displayed in worksheet [in-out

COCID IN->OUT]

Item

Cell for input

Foreseen action Input See placemark

model R158

Select a model (in the proposed list)

[9]

Worksheet [in-out COBON]

Item

Cell for input

Perimeter of the cross section of the silencer (m)

R20

Area of the cross section of the silencer (m2)

R22

Foreseen action

Input a positive real

Input a positive real

Input

0.7853

0.049

See placemark

[6]

[6]

Model for TL out

Model of silencer

Model for Lw out

Finite elements method (0/1)

?

R27

R33

R38

R40

Select a model (in the proposed list)

Select a model (in the proposed list)

Select a model (in the proposed list)

Input 0 to answer “no”; input 1 to answer “yes”

COCID

ZER

2081

0

No silencing effect accounted

[9]

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Screenshots of the worksheets (for the example of computation)

Screenshot of worksheet [in-out COALA]

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Screenshot of worksheet [in-out COCID IN->OUT]

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Screenshot of worksheet [in-out COBON]

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Appendix to Section 5: list of symbols

General

Cf. corresponding § in Section 1,2,3 and 4

Lw0: sound power level without soundproofing equipment (dB ref. 1pW) i.e. in the entrance plane of the duct (casing) section of interest

Lw1: sound power level with soundproofing equipment (dB ref. 1pW) i.e. in the exit plane of the duct (casing) section of interest

Casing

TL out: sound transmission loss of the duct wall (casing) (dB)

Lw out: sound power level radiated by duct (casing) walls (dB ref. 1pW)

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Section 6: computation of bends

(MODULE 6 of the software)

6.1: Introduction

Terms and definitions

For the needs of the present user’s manual, the following terms and definition apply:

No particular term or definition (cf. section 1, section 2, cf. section 3, cf. section 4, cf. section 5, cf. section 6)

Mountings and geometry

The geometry used for the computation of bends is as follows:

inlet cross section

rectangular circular rectangular

outlet cross section

rectangular circular circular

6.2: Scientific and technical background

The prediction of acoustic performances of bends with SILDIS is founded on a scientific and technical background in relation with: o analytical models for taking into account the properties of materials and various physical phenomena useful on the occasion of the computation o measurement results for feeding some of those models and for allowing the necessary improvement (through correction factors) of the correlation between some calculations and on site observations

The obtained results are not comparable with standardized measurement due to the lack of such documents.

6.2.1Thermodynamics and fluid dynamics:

Steps of the computation

Step [a]

All computations have been gathered in this single step for the sake of simplicity. See corresponding § in Section 1

6.2.2 Acoustics:

Bloc diagram

on fig 6.1 below

Fig. 6.1

Note 1: the service conditions dependence has been omitted for the sake of simplicity. See: report [PhRxx-015x]

Note 2: the main steps (the steps involving a physical modeling) being referred to from [AW] to [AY] have been taken into account for the bloc-diagram above (some of the parameters of the above bloc diagram are not independent); the frequency dependence has been omitted for the sake of simplicity

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Steps of the computation

Step [AW]

This step aims at calculating the insertion loss without self noise of bends o

Bibliography (references) :

[AW1]

-

[AW2]

[AW3]

[AW4] o

Comments :

 when used, the cut off frequency for the first higher mode fco is computed depending on the speed of sound c, the

Mach number in the airways M, and the geometry of the duct, according to various models as shown in the table below: model

HAN

MUN source [AW1] [AW2]

 when used, the model of 90° bend (type) is selected among various models as shown in the table below: model source comment

SH-ED

[AW3]

SHarp-

EDged

Step [AX]

This step aims at calculating the self noise of bends o

Bibliography (references) :

[AX1]

-

[AX2]

SH-ED+TV

[AW3]

SHarp-

Edged withTurning

Vanes

BE-RA

[AW3] with BEnd-

RAdius

[AX3]

[AX4] o

Comments :

 the self noise is computed according to various models as shown in the table below: model source

HAN

[AX1]

2081

[AX3]

SMA

[AX4]

Step [AY]

This step aims at calculating the insertion loss of the bend including its self noise. o

Bibliography (references) :

[AY1]

-

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Comments :

The sound power level downstream of the bend including self noise (Lw1 in dB ref 1E-12W) is basically computed at frequency steps of 1/1 octave (in reference to a reference acoustic power spectrum Lw0 ref 1E-12W).

Lw1 = 10 * log [10^ (0.1 * (Lw0 – Di’)) + 10^ (0.1 * Lw)]

Lw being the self noise (acoustic power of flow noise in dB ref 1E-12W)

The insertion loss taking into account the self noise (Di in dB) is basically computed at frequency steps of 1/1 octave (in reference to a reference acoustic power spectrum Lw0 ref 1E-12W).

Di = Lw0 – Lw1

In case of rectangular ducts, the obtained results are comparable with the standardized measurement: see NF EN ISO 7235

Acoustics - Laboratory measurement procedures for ducted silencers and air terminal units- Insertion loss, flow noise and total pressure loss (2004).

6.3: How to use SILDIS

Operating conditions / security level / safety

See corresponding § in the chapter General considerations

For safety reasons, some cells of the original file provided to the user (as mentioned in the table below) for which input data are foreseen to be entered by the user are pre-filled with the value “1/0”, among the yellow cells for which the color orange is used (*).

Worksheet

[in COALA]

Cells

E13, J37, W38

* something like that

Worksheets

** attention has to be paid to the fact that the considered sheet is not included in the worksheets listed below

Regarding the COmputation of BENDs, the software SILDIS is configurated in order to allow the user to access to various worksheets being linked as shown in fig. 6.2 (the overview of the worksheets being shown in table below).

Fig. 6.2

Note: temperature and pressure conditions as well as reference spectrum one should enter in worksheet in COALA

Worksheet Suitable for mountings Input data Results

[in COALA]

all for sets, for reference spectrum --

[in-out COBEND]

COmputation of BENDs

Input data, alerts and results: the key points

for bend: dimensions, flow rate

The best use of the software requires the knowledge of some key points in relation with: indicators of performance (acoustics) o the input data

See corresponding § in the chapter General considerations o some alerts in case of input data involving a warning of the user o the place where (and the way) some results are presented

Those key points are reviewed worksheet per worksheet hereafter: the cells will be referred to thanks to their EXCEL’s coordinates

(column / line) in the following part of the present user’s manual.

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Worksheet [in-out COBEND]

o

Input data :

Item

Cell for input

I5

Foreseen action Comment

mass flow rate Qm (kg/s) model of cut-off frequency fco model of 90° bend (type) adimensional bend radius model of self noise

N5

S5

X5

AC5

Input a real

Select a model (in the proposed list)

Select a model (in the proposed list)

Input a positive real

Select a model (in the proposed list)

Only in case of rectangular inlet cross section & rectangular outlet cross section

Item

Cell for input

H23

Foreseen action

biggest dimension a1 (m) smallest dimension b1 (m biggest dimension a2 (m) smallest dimension b2 (m)

H24

P23

P24

Input a positive real

Input a positive real

Input a positive real

Input a positive real

Comment

Only in case of circular cross section

Item

diameter D (m)

Cell for input

P47

Foreseen action

Input a positive real

Comment

Only in case of rectangular inlet cross section & circular outlet cross section

Item

Cell for input

Foreseen action

biggest dimension a1 (m) smallest dimension b1 (m)

H23

H24

Input a positive real

Input a positive real

Comment

diameter D (m) o

Main displays of the results :

P47 Input a positive real

Tables of results in case of rectangular inlet cross section & rectangular outlet cross section

insertion loss without self noise Di’: see lines 21 to 24 (columns S to AD)

self noise Lw: see lines 26 to 30 (columns S to AD)

sound power level downstream of bend: see lines 32 to 36 (columns S to AD)

insertion loss with self noise Di: see lines 38 to 41 (columns S to AD)

Tables of results in case of circular cross section

insertion loss without self noise Di’: see lines 44 to 47 (columns S to AD)

self noise Lw: see lines 49 to 53 (columns S to AD)

sound power level downstream of bend: see lines 55 to 59 (columns S to AD)

insertion loss with self noise Di: see lines 61 to 64 (columns S to AD)

Tables of results in case of rectangular inlet cross section & circular outlet cross section

insertion loss without self noise Di’: see lines 67 to 70 (columns S to AD)

self noise Lw: see lines 72 to 76 (columns S to AD)

sound power level downstream of bend: see lines 78 to 82 (columns S to AD)

insertion loss with self noise Di: see lines 84 to 87 (columns S to AD)

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6.4: Examples of computation with SILDIS

Example 6.4.1 circular bend

Envisaged application

It is wished to compute the acoustic performance of a circular bend for room conditions: temperature 17°C [1], pressure 1E5 Pa [2].

The sound power spectrum upstream of bend is as shown in the table below [3].

F(Hz)

Lw0 (dB ref 1pW)

63

73.3

125

60.6

250

45.0

500

41.1

1000

37.0

2000

34.7

4000

37.4

8000

32.5

The flow rate is 1400 m3/h [4]. Model of cut-off frequency fco not accounting flow speed is selected [5]. Bend radius is considered

[6], adimensional bending ratio being 0.15 [7]. Regarding models of computation: the procedures basing the model referred to as 2081 are selected [8]. The duct is with a diameter D=250mm [9].

Input data

The input data required for the computation are listed hereafter in reference with the above data (see placemarks).

The input cells will be referred to thanks to their EXCEL’s coordinates (column / line) in the following part of the present user’s manual.

Screenshots of the worksheets (for the example of computation)

Worksheet [in COALA]

Item

Temperature

Cell for input

D6

Foreseen action

Pressure D7

Input a real number

Input a real positive number

Reference acoustic power spectrum

D65 to

K65

Input numbers

Input

17

100000

73.3 ; 60.6 ; 45.0 ; 41.1 ;

37.0 ; 34.7 ; 37.4 ; 32.5

Worksheet [in-out COBEND]

o

Input data :

Item

Cell for input

I5 mass flow rate Qm (kg/s) model of cut-off frequency fco

N5 model of 90° bend (type) adimensional bend radius model of self noise

S5

X5

AC5

Foreseen action

Input a real

Select a model (in the proposed list)

Select a model (in the proposed list)

Input a positive real

Select a model (in the proposed list)

Input

=1400/3600*I10

HAN

BE-RA

0.15

2081

Only in case of circular cross section

Item

diameter D (m)

Cell for input

P47

Foreseen action

Input a positive real

Input

0.25

See placemark / comment

[1]

[2]

[3]

See placemark / comment

[4]

[5]

[6]

[7]

[8]

See placemark / comment

[9]

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Screenshots of the worksheets (for the example of computation)

Screenshot of worksheet [in-out COALA]

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Screenshot of worksheet [in-out COBEND]

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Appendix to Section 6: list of symbols

General

Cf. corresponding § in Section 1,2,3,4,5

Bend

Lw0: sound power level without soundproofing equipment (dB ref. 1pW) i.e. in the entrance plane of the bend

Lw1: sound power level with soundproofing equipment (dB ref. 1pW) i.e. in the exit plane of the bend

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Section 7: computation of nozzle reflection

(MODULE 7 of the software)

7.1: Introduction

Terms and definitions

For the needs of the present user’s manual, the following terms and definition apply:

No particular term or definition

Mountings and geometry

The geometry used for the computation of bends is as follows: rectangular or circular

7.2: Scientific and technical background

The prediction of acoustic performances of bends with SILDIS is founded on a scientific and technical background in relation with: o analytical models for taking into account the properties of materials and various physical phenomena useful on the occasion of the computation o measurement results for feeding some of those models and for allowing the necessary improvement (through correction factors) of the correlation between some calculations and on site observations

The obtained results are not comparable with standardized measurement due to the lack of such documents.

7.2.1Thermodynamics and fluid dynamics:

Steps of the computation

Step [a]

All computations have been gathered in this single step for the sake of simplicity. See corresponding § in Section 1

7.2.2 Acoustics:

Bloc diagram

on fig 7.1 below

Fig. 7.1

Note 1: the service conditions dependence has been omitted for the sake of simplicity. See: report [PhRxx-015x]

Note 2: the main steps (the steps involving a physical modeling) being referred to from [AW] to [AY] have been taken into account for the bloc-diagram above (some of the parameters of the above bloc diagram are not independent); the frequency dependence has been omitted for the sake of simplicity

Steps of the computation

Step [AZ]

This step aims at calculating the insertion loss without self noise o

Bibliography (references) :

[AZ1]

[AZ2]

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Comments :

 the insertion loss is computed according to various models as shown in the table below: model

2081

ISO source [AZ1] [AZ2]

Step [AAA]

This step aims at calculating the self noise o

Bibliography (references) :

No particular bibliography applicable o

Comments :

 the self noise is assumed to be negligible:

Step [AAB]

This step aims at calculating the insertion loss including self noise. o

Bibliography (references) :

[AAB1]

o

Comments :

The sound power level including self noise (Lw1 in dB ref 1E-12W) is basically computed at frequency steps of 1/1 octave

(in reference to a reference acoustic power spectrum Lw0 ref 1E-12W).

Lw1 = 10 * log [10^ (0.1 * (Lw0 – Di’)) + 10^ (0.1 * Lw)]

Lw being the self noise (acoustic power of flow noise in dB ref 1E-12W)

The insertion loss taking into account the self noise (Di in dB) is basically computed at frequency steps of 1/1 octave (in reference to a reference acoustic power spectrum Lw0 ref 1E-12W).

Di = Lw0 – Lw1

In case of rectangular ducts, the obtained results are comparable with the standardized measurement: see NF EN ISO 7235

Acoustics - Laboratory measurement procedures for ducted silencers and air terminal units- Insertion loss, flow noise and total pressure loss (2004).

7.3: How to use SILDIS

Operating conditions / security level / safety

See corresponding § in the chapter General considerations

For safety reasons, some cells of the original file provided to the user (as mentioned in the table below) for which input data are foreseen to be entered by the user are pre-filled with the value “1/0”, among the yellow cells for which the color orange is used (*).

Worksheet

[in COALA]

Cells

E13, J37, W38

* something like that

Worksheets

** attention has to be paid to the fact that the considered sheet is not included in the worksheets listed below

Regarding the COmputation of NOZzle reflections, the software SILDIS is configurated in order to allow the user to access to various worksheets being linked as shown in fig. 7.2 (the overview of the worksheets being shown in table below).

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Fig. 7.2

Note: temperature and pressure conditions as well as reference spectrum one should enter in worksheet in COALA

Worksheet Suitable for mountings Input data Results

[in COALA]

all for sets, for reference spectrum

COmputation of NOZzle

[in-out CONOZ]

reflection

Input data, alerts and results: the key points

dimensions

The best use of the software requires the knowledge of some key points in relation with:

-- indicators of performance (acoustics) o the input data

See corresponding § in the chapter General considerations o some alerts in case of input data involving a warning of the user o the place where (and the way) some results are presented

Those key points are reviewed worksheet per worksheet hereafter: the cells will be referred to thanks to their EXCEL’s coordinates

(column / line) in the following part of the present user’s manual.

Worksheet [in-out CONOZ]

o

Input data :

Item

Cell for input

I5

Foreseen action Comment

mass flow rate Qm (kg/s) model of cut-off frequency fco model of reflection loss

Solid angle factor

P5

V5

P7

Input a real

Select a model (in the proposed list)

Select a model (in the proposed list)

Input a positive real

Only in case of rectangular cross section

Item

Cell for input

Foreseen action Comment

biggest dimension a (m) smallest dimension b (m

P23

P24

Only in case of circular cross section

Item

Cell for input

Input a positive real

Input a positive real

Foreseen action Comment

diameter D (m) o

Main displays of the results :

P47 Input a positive real

Tables of results in case of rectangular inlet cross section & rectangular outlet cross section

insertion loss without self noise Di’: see lines 21 to 24 (columns S to AD)

self noise Lw: see lines 26 to 30 (columns S to AD)

sound power level downtream: see lines 32 to 36 (columns S to AD)

insertion loss with self noise Di: see lines 38 to 41 (columns S to AD)

Tables of results in case of circular cross section

insertion loss without self noise Di’: see lines 44 to 47 (columns S to AD)

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self noise Lw: see lines 49 to 53 (columns S to AD)

sound power level downstream: see lines 55 to 59 (columns S to AD)

insertion loss with self noise Di: see lines 61 to 64 (columns S to AD)

7.4: Examples of computation with SILDIS

Example 7.4.1 circular mouth

Envisaged application

It is wished to compute the reflection loss of a circular mouth for room conditions: temperature 14.1°C [1], pressure 1E5 Pa [2] with the methodology corresponding to the so called model 2081 [3]. The considered solid angle factor is 2 [4]. The considered diameter of the mouth is 0.2 m [5].

Input data

The input data required for the computation are listed hereafter in reference with the above data (see placemarks).

The input cells will be referred to thanks to their EXCEL’s coordinates (column / line) in the following part of the present user’s manual.

Screenshots of the worksheets (for the example of computation)

Worksheet [in COALA]

Item

Temperature

Cell for input

D6

Pressure D7

Foreseen action

Input a real number

Input a real positive number

Worksheet [in-out CONOZ]

o

Input data :

Item

Cell for input

mass flow rate Qm

(kg/s) model of cut-off frequency fco model of reflection loss

Solid angle factor

I5

P5

V5

P7

Foreseen action

Input a real

Select a model (in the proposed list)

Select a model (in the proposed list)

Input a positive real

Only in case of circular cross section

Item

diameter D (m)

Cell for input

P47

Foreseen action

Input a positive real

Input

14.1

100000

Input

-

-

2081

2

Input

0.2

See placemark / comment

[1]

[2]

See placemark / comment

[3]

[4]

See placemark / comment

[5]

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Screenshots of the worksheets (for the example of computation)

Screenshot of worksheet [in-out COALA]

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Screenshot of worksheet [in-out CONOZ]

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Appendix to Section 7: list of symbols

General

Cf. corresponding § in Section 1,2,3,4,5, 6

Mouth

Lw0: sound power level without soundproofing equipment (dB ref. 1pW) i.e. in the entrance plane of the bend

Lw1: sound power level with soundproofing equipment (dB ref. 1pW) i.e. in the exit plane of the bend

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Section 8: computation of sound impact of a duct system

(MODULE 8 of the software)

8.1: Introduction

Terms and definitions

For the needs of the present user’s manual, the following terms and definition apply:

No particular term or definition (cf. section 1, section 2, cf. section 3, cf. section 4, cf. section 5, cf. section 6)

Mountings and geometry

The geometry used for the computation of impact of a duct system is as follows (for each component):

inlet cross section

rectangular circular rectangular

outlet cross section

rectangular circular circular

8.2: Scientific and technical background

The prediction of sound impact of a duct system with SILDIS is founded on a scientific and technical background in relation with: o analytical models for taking into account the properties of materials and various physical phenomena useful on the occasion of the computation o measurement results for feeding some of those models and for allowing the necessary improvement (through correction factors) of the correlation between some calculations and on site observations

The obtained results are not comparable with standardized measurement due to the lack of such documents.

8.2.1Thermodynamics and fluid dynamics:

Steps of the computation

Step [a]

All computations have been gathered in this single step for the sake of simplicity. See corresponding § in Section 1

8.2.2 Acoustics regarding the longitudinal noise propagation i.e. for the computation of the sound power

level downstream of the duct system:

Bloc diagram

on fig IDS.1 below (this bloc diagram is used within a waterfall computation for all the components of the system, referred to as C1 to C10)

Fig. IDS.1

Lw1calc

Note 1: the service conditions dependence has been omitted for the sake of simplicity. See: report [PhRxx-015x]

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Note 2: the main steps (the steps involving a physical modeling) being referred to from [BAA] to [BAC] have been taken into account for the bloc-diagram above (some of the parameters of the above bloc diagram are not independent); the frequency dependence has been omitted for the sake of simplicity

Steps of the computation

Step [BAA]

This step aims at calculating the sound power level downstream of the components (resp. downstream the full duct system) as well as insertion loss of each component including its self noise. o

Bibliography (references) :

[BAA1]

o

Comments :

The sound power level downstream of the component including self noise (Lw1 in dB ref 1E-12W) is basically computed at frequency steps of 1/1 octave (in reference to a reference acoustic power spectrum Lw0 ref 1E-12W).

Lw1 = 10 * log [10^ (0.1 * (Lw0 – Di’)) + 10^ (0.1 * Lw)]

Lw being the self noise (acoustic power of flow noise in dB ref 1E-12W)

The insertion loss taking into account the self noise (Di in dB) is basically computed at frequency steps of 1/1 octave (in reference to a reference acoustic power spectrum Lw0 ref 1E-12W).

Di = Lw0 – Lw1

In case of rectangular ducts, the obtained results are comparable with the standardized measurement: see NF EN ISO 7235

Acoustics - Laboratory measurement procedures for ducted silencers and air terminal units- Insertion loss, flow noise and total pressure loss (2004).

Step [BAB]

This step aims at calculating the sound pressure level downstream at the specified distance of the duct system o

Bibliography (references) :

[BAB1]

o

Comments :

The sound pressure level downstream of the full duct system at a specified distance (Lp1calc in dB ref 120µPa) is basically computed at frequency steps of 1/1 octave as

Lp1calc = Lw1calc + ( Lp1calc - Lw1calc - DI) + DI

8.2.3 Acoustics regarding the transverse noise propagation i.e. for the computation of the sound power

level transmitted by the walls of the duct system:

Bloc diagram

on fig IDS.2 below (the components of the system are referred to as C1 to C10)

Lwoutcalc

Fig. IDS.2

Note 1: the service conditions dependence has been omitted for the sake of simplicity. See: report [PhRxx-015x]

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Note 2: the main steps (the steps involving a physical modeling) being referred to from [AAB] to [AAB] have been taken into account for the bloc-diagram above (some of the parameters of the above bloc diagram are not independent); the frequency dependence has been omitted for the sake of simplicity

Steps of the computation

Step [BAC]

This step aims at calculating the sound pressure level at a specified distance of the duct system o

Bibliography (references) :

[BAC1]

o

Comments :

The sound pressure level downstream of the full duct system at a specified distance (Lpoutcalc in dB ref 120µPa) is basically computed at frequency steps of 1/1 octave as

Lpoutcalc = Lwoutcalc + ( Lpoutcalc - Lwoutcalc)

8.3: How to use SILDIS

Operating conditions / security level / safety

See corresponding § in the chapter General considerations

For safety reasons, some cells of the original file provided to the user (as mentioned in the table below) for which input data are foreseen to be entered by the user are pre-filled with the value “1/0”, among the yellow cells for which the color orange is used (*).

Worksheet

[in COALA]

Cells

E13, J37, W38

* something like that

** attention has to be paid to the fact that the considered sheet is not included in the worksheets listed below

Worksheets regarding the longitudinal noise propagation i.e. for the computation of the sound power level downstream of the duct system

Regarding the computation of the Impact of a Duct System, the software SILDIS is configurated in order to allow the user to access to various worksheets being linked as shown in fig. IDS.3 (the overview of the worksheets being shown in table below).

Fig. IDS.3

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Note: temperature and pressure conditions as well as reference spectrum one should enter in worksheet in COALA

Worksheet

[in COALA]

[in CODIS]

Suitable for mountings

all all

Input data

for sets, for reference spectrum particular conditions for the design of the silencer

Results

--

--

[in-out CODIS1]

[in-out CODIS2

[in-out CORESPTL]

[in-out CORESPTR]

[in-out COSTDU]

R, R’’, C1, C2

Q, C0

RPTR, RPTR’’

RPTL, RPTL’’ all condition of propagation (of sound) for duct: dimensions, flow rate indicators of performance (acoustics

& Aerodynamics)

[in-out COBEND]

all for bend: dimensions, flow rate

[in-out CONOZ]

all

Input data, alerts and results: the key points

for duct: dimensions

The best use of the software requires the knowledge of some key points in relation with: indicators of performance (acoustics indicators of performance (acoustics) o the input data

See corresponding § in the chapter General considerations o some alerts in case of input data involving a warning of the user o the place where (and the way) some results are presented

Those key points are reviewed worksheet per worksheet hereafter: the cells will be referred to thanks to their EXCEL’s coordinates

(column / line) in the following part of the present user’s manual.

Worksheet [in-out IDS] page 1

o

Input data :

Item

Cell for input

Foreseen action Comment

Noise source

Configuration

GSA (*) type

L3

L5

L7

Input a string

Input a string

Input a string

* GSA = General Silencing Arrangement. Cf. appendix

GSAC-EX

Component

Matrix

C25 to C34

D25 to

D34

Input a string

Select a model (in the proposed list)

Lw1ref (dB ref. 1pW) E88 to O88 Input a real

If no input in N88 (resp. O88), displayed value is computed from 1/1 octave bends input data

Directivity index (dB)

Lp1calc-Lw1calc-DI (dB)

Lp1ref (dB ref. 1pW)

E95 to

M95

N97

E107 to

O107

Comments

In case of use of models BYO17 to BYO19 only

C113 to

C122

Item

Insertion loss without flow noise (dB)

Cell for input

E135 to

M137

Input a real

Input a real

Input a real

Input a string

Foreseen action

Input a real

If no input in N107 (resp. O107), displayed value is computed from 1/1 octave bends input data

Comment

Bring Your Own input data

Flow noise (dB)

E142 to

M144

Input a real Bring Your Own input data o

Main displays of the results :

Tables of results for components

sound power level downstream of components Lw1: see lines 50 to 62 (columns B to O)

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insertion loss with self noise Di: see lines 64 to 76 (columns B to O)

Tables of results for full duct system

sound power level downstream of duct system Lw1calc: see lines 78 to 82 (columns B to O)

sound pressure level downstream of duct system Lp1calc at a specified distance: see lines 97 to 101 (columns B to O)

Worksheets regarding the transverse noise propagation i.e. for the computation of the sound power level transmitted by the walls of the duct system

Regarding the computation of IMPACT, the software SILDIS is configurated in order to allow the user to access to various worksheets being linked as shown in fig. IDS.4 (the overview of the worksheets being shown in table below).

Fig. IDS.4

Note: temperature and pressure conditions as well as reference spectrum one should enter in worksheet in COALA

Worksheet Suitable for mountings Input data Results

[in COALA]

all for sets, for reference spectrum -- for dimensions, for models of

[in COBON]

all computation

Input data, alerts and results: the key points

The best use of the software requires the knowledge of some key points in relation with:

-- o the input data

See corresponding § in the chapter General considerations o some alerts in case of input data involving a warning of the user o the place where (and the way) some results are presented

Those key points are reviewed worksheet per worksheet hereafter: the cells will be referred to thanks to their EXCEL’s coordinates

(column / line) in the following part of the present user’s manual.

Worksheet [in-out IDS] page 1

o

Input data :

Item

Sound power level radiated by components walls

Lwoutref (dB ref. 1pW)

Lpoutcalc - Lwoutcalc (dB)

Cell for input

U17 to

AC26

U38 to

AE38

U45 to

U54

Foreseen action

Enter a real

Input a real

Input a real

Comment

If no input in AD38 (resp. AE38), displayed value is computed from 1/1 octave bends input data

Lpoutref (dB ref. 20μPa)

Comments

U88 to

AE88

T113 to

T122

Input a real

Input a string

If no input in AD88 (resp. AE88), displayed value is computed from 1/1 octave bends input data o

Main displays of the results :

Tables of results for components

sound pressure level at a specified distance Lpoutcalc: see lines 56 to 68 (columns S to AE)

Tables of results for full duct system

sound power level radiated by components walls Lwoutcalc: see lines 28 to 32 (columns S to AE)

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8.4: Examples of computation with SILDIS

Example 8.4.1 cylindrical attenuator without core + bend + (straight) duct , the acoustic performance of each component being predetermined

Envisaged application

It is wished to compute for room (temperature 17°C [1], pressure 1E5 Pa [2]) the acoustic performance of a duct system made of:

-

a cylindrical attenuator without core

The insertion loss without flow noise Di’ is as shown in the table below [3].

F(Hz)

Di’(dB )

63

2

125

4

250

8

The flow noise Lw is assumed to be negligible [4].

500

16

1000

31

2000

22

4000

12

8000

11

Note: the performance of this silencer may have been simulated with SILDIS. If so, performance would be displayed in worksheet referred to as [in-out CODIS2]

-

a bend

The insertion loss without flow noise Di’ is as shown in the table below [5].

F(Hz)

Di’(dB )

63

0

125

0

250

0

The flow noise Lw is as shown in the table below [6]

500

1

1000

2

2000

3

4000

3

8000

3

F(Hz)

Lw (dB ref.1pW )

63

26.9

125

23.0

250

18.1

500

12.5

1000

6.5

2000

-0.1

4000

-7.0

8000

-14.4

Note: the performance of this bend may have been simulated with SILDIS. If so, performance would be displayed in worksheet referred to as [in-out COBEND]

-

a (straight) duct

The insertion loss without flow noise Di’ is as shown in the table below [7].

F(Hz)

Di’(dB )

63

0.1

125

0.1

250

0.2

The flow noise Lw is assumed to be negligible [8].

500

0.2

1000

0.3

2000

0.3

4000

0.3

8000

0.3

Note: the performance of this duct may have been simulated with SILDIS. If so, performance would be displayed in worksheet referred to as [in-out COBEND]

The sound power spectrum upstream of the duct system is as shown in the table below [9].

F(Hz) 63 125 250 500 1000 2000 4000 8000

Lw0 (dB ref 1pW)

64.7 51.1 38.6 31.5 26.1 20.4 22.9 24.9

The acoustic performance of each component is predetermined and referred to as BYO17 [10], BYO18 [11], BYO19 [12]

Input data

The input data required for the computation are listed hereafter in reference with the above data (see placemarks).

The input cells will be referred to thanks to their EXCEL’s coordinates (column / line) in the following part of the present user’s manual.

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Worksheet [in COALA]

Item

Temperature

Pressure

Cell for input

D6

D7

Reference acoustic power spectrum

Item

Noise source

Configuration

GSA (*) type

D65 to

K65

Worksheet [in-out IDS] page 1

Cell for input

L3

L5

L7

Component C25 to C27

Foreseen action

Input a real number

Input a real positive number

Input numbers

Foreseen action

Input a string

Input a string

Input a string

Input a string

Input

17

100000

64.7 ; 51.1 ; 38.6 ; 31.5

26.1 ; 20.4 ; 22.9 ; 24.9

Input

-

-

- cylindrical attenuator without core resp. bend resp. (straight) duct

See placemark / comment

[1]

[2]

[9]

See placemark / comment

Matrix

Insertion loss without flow noise (dB)

D25 to

D27

E135 to

M137

E142 to

M144

Select a model (in the proposed list)

Lw1ref (dB ref. 1pW)

Directivity index (dB)

Lp1calc-Lw1calc-DI (dB)

Lp1ref (dB ref. 1pW)

Comments

E88 to O88

E95 to

M95

N97

E107 to

O107

C113 to

C122

In case of use of models BYO17 to BYO19 only

Item

Cell for input

Input a real

Input a real

Input a real

Input a real

Input a string

Foreseen action

Flow noise (dB)

Input a real

Input a real

BYO17 resp. BYO18 resp. BYO19

-

-

-

-

-

Input

2 ; 4 ; 8 ; 16 ; 31 ; 22 ; 12 ;

11 resp. 0 ; 0 ; 0 ; 1 ; 2 ; 3

; 3 ;3 resp.0.1 ; 0.1 ; 0.2 ;

0.2 ; 0.3 ; 0.3 ; 0.3 ; 0.3

-200 ; -200 ; -200 ; -200 ; -

200 ; -200 ; -200 ; -200 resp. 26.9 ; 23.0 ; 18.1 ;

12.5 ; 6.5 ; -0.1 ; -7.0 ; -

14.4 resp. -200 ; -200 ; -

200 ; -200 ; -200 ; -200 ; -

200 ; -200

[10],[11],[12] if not predetermined, but computed with SILDIS, the selection should have been CODIS2 resp.

COBEND resp. COSTDU

See placemark / comment

[3] resp. [5] resp. [7]

[4] resp. [6] resp. [8]

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Screenshots of the worksheets (for the example of computation)

Worksheet [in COALA]

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Worksheet [in-out IDS] page 1

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Appendix to Section 8: list of symbols

General

Cf. corresponding § in Section 1,2,3,4

Duct system

Lp1calc: sound pressure level with soundproofing equipment downstream of the duct system (dB ref. 1pW) i.e. at a specified distance from the exit plane of the duct system: calculated with SILDIS

Lp1ref: sound pressure level with soundproofing equipment downstream of the duct system (dB ref. 1pW) i.e. at a specified distance from the exit plane of the duct system: reference = target, imposed limit, etc…

Lw0: sound power level without soundproofing equipment (dB ref. 1pW) i.e. in the entrance plane of the component

Lw1: sound power level with soundproofing equipment (dB ref. 1pW) i.e. in the exit plane of the component

Lw1calc: sound power level with soundproofing equipment downstream of the duct system (dB ref. 1pW) i.e. in the exit plane of the duct system: calculated with SILDIS

Lw1ref: sound power level with soundproofing equipment downstream of the duct system (dB ref. 1pW) i.e. in the exit plane of the duct system: reference = target, imposed limit, etc…

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Section 9: computation of sound decay in enclosed spaces

(MODULE 9 of the software)

9.1: Introduction

Terms and definitions

For the needs of the present user’s manual, the following terms and definition apply (cf. NF EN ISO 3382-2):

Reverberation time (T): duration necessary for the average acoustic volumetric energy in a room to decrease by 60 dB after noise off.

Reverberation time can be computed by using a dynamic range below 60 dB, and then extrapolating to the time corresponding to a 60 dB decay. It is then noted accordingly. Thus, if T is derived from the first instant where the decay curve reaches 5 dB and 25 dB below initial level, it is noted T20. If decay values from 5 dB to 35 dB below the initial level are used, it is noted T30.

Geometry

In case of a rectangular (shoebox shaped) room, the geometry is as follows (this is not the only geometry for which simulation can be performed): fig.9.1

9.2: Scientific and technical background

The prediction of sound decay in a room with SILDIS is founded on a scientific and technical background in relation with: o analytical models for taking into account the various physical phenomena useful on the occasion of the computation o measurement results for feeding some of those models and for allowing the necessary improvement (through correction factors) of the correlation between some calculations and on site observations

As far as reverberation time is concerned, the obtained results are comparable with the standardized measurement: see NF EN ISO

3382-2 Acoustics - Measurement of room acoustics parameters- Part 2: reverberation time in ordinary rooms.

9.2.1Thermodynamics and fluid dynamics:

Steps of the computation

Step [a]

All computations have been gathered in this single step for the sake of simplicity. See corresponding § in Section 1

9.2.2 Acoustics:

Bloc diagram :

The computation scheme of sound decay in a room is according the bloc-diagram below (cf. fig. 9.2):

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Note 1: the service conditions dependence has been omitted for the sake of simplicity.

Note 2: the main steps (the steps involving a physical modeling) being referred to from [BAD] to [BAI] have been taken into account for the bloc-diagram above (some of the parameters of the above bloc diagram are not independent); the frequency dependence has been omitted for the sake of simplicity

Note 3: depending on the model selected for the step [BAH], steps [BAE], [BAF], [BAG] may not be part of the computation scheme

Note 4: depending on the model selected for the step [BAI], step [BAH] may not be a separate part of the computation scheme (when the used approach is based on explicit reverberation time allowing a direct calculation of reverberation time)

Steps of the computation

Step [a]

Cf. section 1

Steps [N], [O]

Cf. section 2

Step [BAD]

This step aims at calculating the walls, floor & ceiling absorption area o

Bibliography (references) :

[BAD1]

[BAD2] o

Comments :

 the absorption coefficients alpha of walls, floor and ceiling are accounted as shown in the table below: model NAT MOD source [BAD1] [BAD2]

Comment

NATural (i.e. as entered as

Sabine’s coefficients)

MODified absorption coefficients in order to limit them to

100 %):

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fig.9.2

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Step [BAE]

This step aims at accounting atmospheric absorption o

Bibliography (references) :

[BAE1]

o

Comments :

 the atmospheric absorption area is computed using an attenuation coefficient of sound power in air accounted for climatic conditions as shown in the table below:

Temperature (°C) Humidity ratio (%)

10

30-50

50-70

70-90

30-50

20 50-70

70-90

Step [BAF]

This step aims at accounting objects (fitting) absorption area o

Bibliography (references) :

[BAF1]

-

[BAF2]

-

Step [BAG]

This step aims at accounting the scattering coefficient of walls, floor & ceiling o

Bibliography (references) :

[BAG1]

-

[BAG2]

-

[BAG3]

-

[BAG4]

-

Step [BAH]

This step aims at calculating the sound decay in the room (after noise off) o

Bibliography (references) :

[BAH1]

-

[BAH2]

-

[BAH3]

-

[BAH4]

-

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Step [BAI]

This step aims at calculating the reverberation time of the room o

Bibliography (references) :

[BAI1]

-

-

[BAI2]

-

[BAI3]

-

[BAI4]

[BAI5]

-

[BAI6]

-

[BAI7]

-

[BAI8]

-

[BAI9]

-

[BAI10]

-

[BAI11]

-

[BAI12]

-

-

[BAI13]

-

[BAI14]

-

[BAI15]

-

[BAI16]

-

[BAI17]

- o

Comments when accounting (natural) Sabine’s coefficients):

 the reverberation time T is computed according to various general models as shown in the table below (with the exception of model SAK, all models are implemented in considering - in parallel - on the one hand: original formulas and on the other hand modified formulas to account solid angles)

Model SAB

Source [BAI1]

Applicable even for non- rectangular room

Non-diffuse sound fields accounted (*)

Scattering accounted

Explicit formula for T

Comment yes no no yes

(**)

* as per [BAI6], when one suppose a diffuse acoustic field, this means that the dimensions of enclosed space are similar and that absorption is distributed in the whole space; the existence of diffusing objects is moderating those limitations.

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Comments when accounting modified absorption coefficients in order to limit them to 100 %:

 the reverberation time T is computed according to various general models as shown in the table below (with the exception of model SAK, all models are implemented in considering - in parallel - on the one hand: original formulas and on the other hand modified formulas to account solid angles)

Model SAB EYR MIL KUT

Source [BAI1] [BAI1] [BAI1]

CRE

[BAI2] equation 2-

31

[BAI2][BAI3][BAI4]][BAI5]

Applicable even for non- rectangular room

Non-diffuse sound fields accounted (*)

Scattering accounted

Explicit formula for T yes no no yes yes no no yes yes no no yes yes no no yes yes no (**)(***) no (**)(***) no (**)(***) no yes no yes no

Comment - - - - yes yes yes

Correction for inhomogeneit y accounting differences in absorption coefficient of elementary surfaces αk

(k=1to N)

Correction for inhomogeneit y accounting differences in absorption coefficient of opposite walls αxj,

αyj ,αzj

(j=1 to 2)

Correction for inhomogeneit y accounting differences in absorption coefficient of opposite walls couples

αx, αy, αx

Model FIT

[BAI1]

NEU

[BAI6] to

[BAI9]

[BAI10

ARA

[BAI10] [BAI10] Source

Applicable even for non- rectangular room

Non-diffuse sound fields accounted (*)

Scattering accounted

Explicit formula for T

Comment no no no yes

- no no no yes

- no no no yes

(****) no no no yes

(****) no no no yes

(****)

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Model

[BAI11] to

[BAI12]

ISO

[BAI11] to

[BAI12]

[BAI11] to

[BAI12]

NIJ

[BAI13]

SAK

[BAI14] to

[BAI16]

HOD

[BAI17] Source

Applicable even for non- rectangular room

Non-diffuse sound fields accounted (*)

Scattering accounted

Explicit formula for T

Comment no yes yes yes if appropriate model used

- no yes yes yes if appropriate model used

- no yes yes no if appropriate model used

- yes no no yes

- no yes yes no

- no no no yes

-

* as per [BAI11], when one suppose a diffuse acoustic field, this means that the dimensions of enclosed space are similar and that absorption is distributed in the whole space; the existence of diffusing objects is moderating those limitations.

** for the model KUT only, the relative variance of the path length distribution γ

2

(depending on room dimensions ratio) is accounted according to various models as shown in the table below:

Model ZER PAR TOT

Source -

[BAI3] equation 13

[BAI3] equation 12

Comment

γ

2

=ZERo

PARtial

(power series approximatio n)

TOTal (exact formula)

*** for the model KUT only, the inhomogeneity (non-uniform placement) of sound absorption is accounted according to various models as shown in the table below:

Model ZER PAR1 PAR2 TOT

Source -

[BAI3] equation 27

[BAI2] equation 2-

80

[BAI3] equation 25

PARtial ( power series

Comment

ZERo consideration approximatio n & not accounting

Σρi2Si2)

not accounting

Σρi2Si2)

TOTal (exact formula)

**** for the model ARA only, un-cleared variations occur for modelling when accounting solid angles

The obtained results are comparable with standardized measurement: cf. NF EN ISO 3382-2 Acoustics - Measurement of room acoustics parameters- Part 2: reverberation time in ordinary rooms.

9.3: How to use SILDIS

Operating conditions / security level / safety

See corresponding § in the chapter General considerations

For safety reasons, some cells of the original file provided to the user (as mentioned in the table below) for which input da ta are foreseen to be entered by the user are pre-filled with the value “1/0”, among the yellow cells for which the color orange is used (*).

Worksheet

[in COALA]

[in-out COPPA]

Cells

E13, J37

X53, X54

* something like that

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Worksheets

Regarding the COmputation of SOund Decay, the software SILDIS is configurated in order to allow the user to access to 1 worksheet referred to as “in-out COSOD” being possibly linked as shown in fig. 9.3 to worksheets considered in previous sections of this User’s

Manuel (the overview of the worksheets being shown in table below).

Fig. 9.3

Worksheet Suitable for mountings Input data Results

[in COALA]

[in COPPA]

all all material parameters limit angle of computation absorption coefficient, areas of

[in-out COSOD]

all absorbing surfaces, models accounted

Input data, alerts and results: the key points

The best use of the software requires the knowledge of some key points in relation with:

-- absorption coefficient reverberation time o the input data

See corresponding § in the chapter General considerations

As far as porous media, series cloths and series perforated protections are concerned, specific data bases (libraries) ( will ) allow the design to be made with in-built engineering data (constants) referred to as “Usual” in the worksheets of the software.

Warning: some properties of the presently referenced materials still not have been checked by reliable sources.

See also report

[PhRXX-015] Collection of soundproofing constructions systems: a companion to “User’s manual for the software SILDIS”

data base (library) for porous media

 contents of the library: 21 possible references of material layers

data base (library) for series cloths

 contents of the library: 21 possible references of material layers

Note: the cloth referenced RESISTAIR can be used (with an appropriate value for the flow resistance) for the simulation of losses of a thin plate (for example at normal incidence: due to the conditions of mounting)

data base (library) for series perforated protections

 contents of the library: 21 possible references of material layers o some alerts in case of input data involving a warning of the user o the place where (and the way) some results are presented

Those key points are reviewed worksheet per worksheet hereafter: the cells will be referred to thanks to their EXCEL’s coordinates

(column / line) in the following part of the present user’s manual.

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Worksheet [in-out COSOD]

o

Input data :

Item

Cell for input

Foreseen action Comment

Language

Date

Project

Title

Temperature

Length L (m)

Width B (m)

Height H (m) xs ys zs hs

Room form variance γ

2

Objet fraction ψ

Sound poser level reference spectrum (dB ref.1 pW)

Sound attenuation in air coefficient

Area of elementary surfaces

Absorption coefficient

Scattering coefficient δ

Equivalent absorption area of objects associated with surfaces

C1

H1

B3

B4

I5

D7

D8

D9

I12

I13

I14

I16

E19

E21

E24 to

M24

E29 to

M29

E35 to E39

& E45 to

E49 [resp.

E62 to E66

&, E72 to

E76 ; E89 to E93 &

E99 to

E103]

E35 to

M39 &

E45 to

M49 [resp.

E62 to

M66 &,

E72 to

M76 ; E89 to M93 &

E99 to

M103]

E42 to

M42 &

E52 to

M52 [resp.

E69 to

M69 &,

E79 to

M79 ; E96 to M96 &

E106 to

M106]

E55 to

M55 [resp.

E82 to

M82 ;

E109 to

M109] for English input E, for

French input F

Modification of the displayed date

Input a string

Input a string

Input a real number

Input a real number

Input a real number

Input a real number

Input a real number

Input a real number

Input a real number

Input a real number

Input a real number

Input a real number

Input a real number

Input a real number

Input a real number

Input a real number

Input a real number

Input a real number

Room dimension according x-axis

Room dimension according y-axis

Room dimension according z-axis

Solid angle calculation point coordinate according x-axis

Solid angle calculation point coordinate according y-axis

Solid angle calculation point coordinate according z-axis

Source height

For model KUT only

For model ISO only

In 1E-3 Neper per meter

Sabine's coefficient for partitions couples x, y & z

Equivalent absorption area of objects present in central area

E115 to

M115

Input a real number

Consideration of model

For NO input 0, for YES If NO is entered, Sabine’s coefficient will be used for

MOD for limitation to 100 % K128 input 1 the simulation of absorption coefficients

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(0/1)

Variance model

Inhomogeneity model

Modified formula (0/1) atmospheric attenuation in each direction (0/1)

C132

C134

G132

K134

Select a model

Select a model

For NO input 0, for YES input 1

For general model KUT only

For general model KUT only

For general model NIJ only

For general model ARA only

Elementary time period Δt

(s) for calculation of T

T evaluation range start (dB)

T evaluation range end (dB)

Item

O132

O133

O134

Cell for input

Input a real number

Input a real number

≤ 0

Input a real number

< 0

For general models ISO & SAK only

For general models ISO & SAK only

For general models ISO & SAK only o

Comments :

 data of the second table (below) are taken into account only for the calculations using solid angles

Foreseen action Comment

y mini, y maxi, z mini, z maxi

R35 to U39

& R45 to

U49

Input a real number

Coordinates of elementary surfaces in x planes i.e. in planes x= 0 & x=L x mini, x maxi, z mini, z maxi

R62 to

U66 &,

R72 to U76

R89 to U93 x mini, x maxi, y mini, y maxi

& R99 to

U103 o

Main displays of the results :

Input a real number

Input a real number

Coordinates of elementary surfaces in y planes i.e. in planes y= 0 & y=B

Coordinates of elementary surfaces in z planes i.e. in planes z= 0 & z=H

Tables of results

reverberation time considering absorption coefficients as entered, potentially above 100% : see lines 117 to 126

not considering atmospheric attenuation, not considering objects see lines 119 to 121 : not accounting solid

angles (columns A to O), accounting solid angles (columns R to AB)

considering atmospheric attenuation, not considering objects see lines 124 to 127 : not accounting solid

angles (columns A to O), accounting solid angles (columns R to AB)

reverberation time considering eventually modified absorption coefficients : see lines 136 to 208

not considering atmospheric attenuation, not considering objects see lines 136 to 156 : not accounting solid

angles (columns A to O), accounting solid angles (columns R to AB)

considering atmospheric attenuation, not considering objects see lines 161 to 181: not accounting solid

angles (columns A to O), accounting solid angles (columns R to AB)

considering atmospheric attenuation, considering objects see lines 186 to 206 : not accounting solid angles

(columns A to O), accounting solid angles (columns R to AB)

9.4: Examples of computation with SILDIS

Example 9.4.1 room with discrepancies in dimensions & with non-homogene distribution of absorbing areas

Envisaged application

It is wished to compute for a temperature 14.8°C [1] the reverberation time of an empty room with dimensions L=20 m [2], B=10m

[3], H=5m [4], when neglecting atmospheric absorption [5], with absorption coefficients as follows: short walls 0.10 [6], long walls

0.20 [7], floor & ceiling 0.40 [8] and with a scattering coefficient of 0.20 [9] for all surfaces. For models ISO and SAK, , elementary time period Δt (s) to be considered is 0.005 s [10], T30 to be considered [11].

Input data

The input data required for the computation are listed hereafter in reference with the above data (see placemarks).

The input cells will be referred to thanks to their EXCEL’s coordinates (column / line) in the following part of the present user’s manual.

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Worksheet [in-out COSOD]

Item

Cell for input

Temperature

Length L (m)

Width B (m)

Height H (m)

Sound attenuation in air coefficient

Area of elementary surfaces

Absorption coefficient

Absorption coefficient

Absorption coefficient

Scattering coefficient δ

I5

D7

D8

D9

E29 to

M29

E35 to E39

& E45 to

E49 [resp.

E62 to E66

&, E72 to

E76 ; E89 to E93 &

E99 to

E103]

E35 to

M39 &

E45 to

M49

E62 to

M66 &,

E72 to

M76

E89 to

M93 &

E99 to

M103

E42 to

M42 &

E52 to

M52 [resp.

E69 to

M69 &,

E79 to

M79 ; E96 to M96 &

E106 to

M106]

Foreseen action

Input a real number

Input a real number

Input a real number

Input a real number

Input a real number

Input a real number

Input a real number

Input a real number

Input a real number

Input a real number

Input

14.8

20

10

5

0

10

0.10

0.20

0.40

0.20

See placemark / comment

[1]

[2]

[3]

[4]

[5]

-

[6]

[7]

[8]

[9]

Elementary time period Δt

(s) for calculation of T

T evaluation range start (dB)

T evaluation range end (dB)

O132

O133

O134

Input a real number

Input a real number

≤ 0

Input a real number

< 0

0.005

-5

-35

[10]

[11]

[11]

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Screenshots of the worksheets (for the example of computation)

Worksheet [in-out COSOD]

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Appendix to Section 9: list of symbols

General

Cf. corresponding § in Sections 1 & 2

Sound decay

A obj, x (m2) : equivalent absorption area of objects associated with surfaces for x=0 and x=L

A obj, y (m2) : equivalent absorption area of objects associated with surfaces for y=0 and y=B

A obj, z (m2) : equivalent absorption area of objects associated with surfaces for z=0 and z=H

N: number of elementary absorbing surfaces considered (for walls, floor & ceiling)

T: reverberation time (s)

T20: reverberation time derived from the first instant where the decay curve reaches 5 dB and 25 dB below initial level (s)

T30: reverberation time derived from the first instant where the decay curve reaches 5 dB and 35 dB below initial level (s)

αx: average absorption coefficient of the couple of opposite walls in direction x

αy: average absorption coefficient of the couple of opposite walls in direction y

αz: average absorption coefficient of the couple of opposite walls in direction z

αx1 (resp. αx2): average absorption coefficient of 1 among the couple of opposite walls in direction x

αy1 (resp. αy2): average absorption coefficient of 1 among the couple of opposite walls in direction y

αz1 (resp. αz2): average absorption coefficient of 1 among the couple of opposite walls in direction z

αk: absorption coefficient of an elementary wall, floor or ceiling surface considered among N

δ x=0 [resp. δ x=L] : scattering coefficient of surface x=0 [resp. x=L]

δ y=0 [resp. δ y=B] : scattering coefficient of surface y=0 [resp. y=B]

δ z=0 [resp. δ z=H] : scattering coefficient of surface z=0 [resp. z=H]

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