Study of Gas Turbine Ingress using Computational Fluid

Study of Gas Turbine Ingress using Computational Fluid
Study of Gas Turbine Ingress using
Computational Fluid Dynamics
Le Wang
A thesis submitted for the degree of Doctor of Philosophy
University of Bath
Department of Mechanical Engineering
May 2013
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Abstract
The ingestion of hot mainstream gas into the wheel-space between the rotor and stator
discs is one of the most important internal cooling problems for gas turbine designers.
To solve this problem, engineers design a rim seal at the periphery of wheel-space and
direct a sealing flow from the internal cooling system to prevent ingress. The main
aim of this thesis is to build a simple computational model to predict the sealing
effectiveness of externally-induced ingress for engine designers. The axisymmetric
model represents a gas turbine wheel-space and provides useful information related to
the fluid dynamics and heat transfer in the wheel-space. At the same time, this model
saves much computation time and cost for engine designers who currently use
complex and time-consuming 3D models.
The computational model in this thesis is called the prescribed ingestion model.
Steady simulations are carried out using the commercial CFD code, ANSYS CFX
with meshes built using ICEM CFD. Boundary conditions are applied at the ingress
inlet of the model using experimental measurements and a mass-based averaging
procedure. Computational parameters such as rotational Reynolds number,
non-dimensional sealing flow rate and thermal conditions on the rotor are selected to
investigate the fluid dynamics and heat transfer at typical experimental rig operating
conditions. Different rim seal geometries are investigated and results are compared
with experimental data.
In addition to the prescribed ingestion model, two typical axisymmetric rotor-stator
system models without ingress are established. The aim of these rotor-stator models is
to investigate the fluid dynamics and heat transfer of the wheel-space in the situation
without ingress. The effects of geometry and turbulence model also are studied in
these simulations. Most results from these simulations are in good agreement with
experimental data from the literature, which enhances confidence in the prescribed
ingestion model.
1
For the prescribed ingestion model, the axial-clearance seal (the simplest rim-seal
geometry) is first simulated for externally-induced ingress. The sealing effectiveness
(on both the stator and rotor), fluid dynamics (in terms of swirl ratio and velocity
profiles) and heat transfer (in terms of Nusselt number) are investigated and are
shown to be in reasonable agreement with the experimental results from a rig at the
University of Bath. In these computations, the mass-weighted average boundary
condition is tested with the momentum-weighted average boundary conditions.
Different layouts of ingress inlet and egress outlet are also tested and the optimal one
is applied to other seal geometries. For heat transfer simulations, different thermal
wall boundary conditions are investigated to understand the effect of these conditions
on the distribution of Nusselt number on the rotor.
In addition to the axial-clearance seal, three other seals are presented in this thesis: a
radial-clearance seal, a double axial-clearance seal, and a radial-axial-clearance
combination seal. In accordance with the axial-clearance seal, the sealing
effectiveness and fluid dynamics in the wheel-space are investigated for these seals
and compared with experimental data. The performance of these four seal geometries
is ranked.
It is suggested that the prescribed ingestion model is a compact, relatively
straight-forward tool for engine designers. It allows the designer insight into the fluid
dynamics and heat transfer of rim seals, and supports the experimental data collected
at the University of Bath.
2
Acknowledgements
I would like to thank my supervisors, Prof. G.D. Lock and Dr. M. Wilson, for their
continued suggestion and guidance. Prof. J.M. Owen is also thanked for his advice. Dr.
C.M. Sangan and Dr. O.J. Pountney are acknowledged for their eagerness to offer
experimental results. Finally, Dr. K. Zhou is thanked for his assistance at the
preliminary stage of my study.
3
Contents
Abstract ..................................................................................................................... 1
Acknowledgements ................................................................................................... 3
Contents .................................................................................................................... 4
List of Figures ........................................................................................................... 6
List of Tables ........................................................................................................... 12
Nomenclature .......................................................................................................... 13
1.
2.
3.
4.
Introduction ...................................................................................................... 16
1.1.
A brief history of the jet engine .............................................................. 16
1.2.
Gas turbine ............................................................................................ 18
1.3.
Internal cooling ...................................................................................... 20
1.4.
Ingress ................................................................................................... 22
1.5.
Thesis aim and objectives ...................................................................... 23
1.6.
Thesis overview ..................................................................................... 24
1.7.
Publications ........................................................................................... 25
Literature review .............................................................................................. 26
2.1.
Rotor-stator systems .............................................................................. 26
2.2.
Ingress ................................................................................................... 34
2.3.
Previous research at University of Bath.................................................. 46
2.4.
Chapter summary................................................................................... 49
Computational method and 3D Computations ................................................... 50
3.1.
Turbulence model .................................................................................. 50
3.2.
Heat transfer .......................................................................................... 53
3.3.
Other computational settings and parameters ......................................... 55
3.4.
3D Computations for the ‘thin seal’ model ............................................. 56
3.5.
Chapter summary................................................................................... 61
Axisymmetric rotor-stator models ..................................................................... 62
4
5.
6.
7.
4.1.
Fluid dynamics for the axisymmetric rotor-stator model ........................ 63
4.2.
Heat transfer for the axisymmetric rotor-stator model ............................ 69
4.3.
Chapter summary................................................................................... 78
Prescribed ingestion model: Axial-clearance seal .............................................. 79
5.1.
Mass-weighted average assumption for ingestion................................... 80
5.2.
The effect of layout of ingress inlet and egress outlet ............................. 87
5.3.
Fluid dynamics in the wheel-space ......................................................... 91
5.4.
Distribution of sealing effectiveness in the wheel-space ......................... 96
5.5.
Heat transfer in the wheel-space............................................................100
5.6.
Chapter summary..................................................................................105
Prescribed ingestion model: other seal geometries ...........................................106
6.1.
Radial-clearance seal ............................................................................108
6.2.
Double axial-clearance seal................................................................... 115
6.3.
Radial-axial-clearance seal....................................................................123
6.4.
Sealing performance of all rim seal geometries .....................................127
6.5.
Chapter summary..................................................................................128
Conclusions and future work ...........................................................................129
7.1.
The axisymmetric rotor-stator models ...................................................129
7.2.
The prescribed ingestion models ...........................................................130
7.3.
Future work ..........................................................................................132
References..............................................................................................................133
Appendix................................................................................................................139
5
List of Figures
Figure 1-1 A simple model of Hero’s engine [1]................................................ 16
Figure 1-2 Ohain’s hydrogen-fuelled turbojet engine [3] ................................... 17
Figure 1-3 Frank Whittle’s patent [1] ................................................................ 17
Figure 1-4 Simple gas turbine system [4] .......................................................... 18
Figure 1-5 Variation of pressure, temperature and velocity in a turbojet [2]....... 19
Figure 1-6 Internal cooling system, including cooling paths [2] ........................ 20
Figure 1-7 Film cooling for turbine blades [2]................................................... 21
Figure 1-8 Generic rotor-stator turbine stage and double clearance-seal inset [6-7]
................................................................................................................. 22
Figure 2-1 Generic rotor-stator configuration [8] .............................................. 26
Figure 2-2 Batchelor-type flow in a rotor-stator system [9] ............................... 27
Figure 2-3 Flow regimes for a closed rotor-stator system [11] ........................... 28
Figure 2-4 Radial and tangential velocity profiles in a rotor-stator wheel-space [8]
................................................................................................................. 29
Figure 2-5 Measured and computed Nusselt numbers, Re   1.25  10 6 [8] .... 29
Figure 2-6 Computational (right) and experimental (left) Nusselt number contours,
Re   0.8  10 6 [17]................................................................................. 31
Figure 2-7 Computed streamlines superimposed onto experimental heat transfer
results, Re   0.8  10 6 , T  0.38 [17]................................................. 31
Figure 2-8 Effect of stator heat transfer on the distribution of Nu Re0.8 [19] .. 33
Figure 2-9 Variation of C w, min with Re w [25-27]........................................... 36
Figure 2-10 Variation of C w, min with 2 Gc Pmax1/ 2 [25-27] .............................. 36
Figure 2-11 Variations of Cw,min with C p ,max [30] .......................................... 37
6
Figure 2-12 Instantaneous velocity contours in the disk cavity [32] .................. 39
Figure 2-13 CFD velocity vectors in axial-radial plane of seal region [32] ........ 40
Figure 2-14 Comparison of local sealing effectiveness at the stator [33] ........... 41
Figure 2-15 Ingestion Mixing Efficiency [37] ................................................... 43
Figure 2-16 Steady state and time-averaged unsteady buffer cavity effectiveness
[44] ........................................................................................................... 45
Figure 2-17 Velocity vectors in the gap [45]...................................................... 45
Figure 2-18 Orifice ring [49-52] ....................................................................... 47
Figure 2-19 Comparison between theoretical effectiveness curves and
experimental data for axial-clearance seal with EI ingress (the solid lines are
theoretical curves) [51] ............................................................................. 48
Figure 3-1 (a) Schematic diagram of 3D thin-seal model (b) Computational mesh
[49] ........................................................................................................... 57
Figure 3-2 Computed circumferential distributions of C p ................................ 59
Figure 3-3 Streamlines with effectiveness in the r   plane at z / s  0.5 ..... 60
Figure 3-4 Variation of computed effectiveness with  o ................................. 61
Figure 4-1 The Bath Rig Model ........................................................................ 62
Figure 4-2 The Chen Rig Model ....................................................................... 63
Figure 4-3 Computed velocity profiles from Chen and Bath Rig Model compared
with measured data, T  0.081 ............................................................... 65
Figure 4-4 Computed and measured velocity profiles for the Bath Rig Model,
T  0.081 ................................................................................................ 67
Figure 4-5 Computed velocity profiles with different T for the Bath Rig Model
................................................................................................................. 68
Figure 4-6 The streamlines in whole cavity for two high sealing flow rate cases 69
Figure 4-7 Comparison between definitions for Nu , T  0.081 .................... 70
Figure 4-8 The swirl ratio at middle plane between the rotor and the stator,
7
T  0.081 ................................................................................................ 71
Figure 4-9 Radial distribution of Nu Re0.8 for different T ........................... 72
Figure 4-10 Radial distribution of temperature on the rotor surface for the Bath
Rig Model................................................................................................. 73
Figure 4-11 The effect of thermal condition at rotor surface on the radial
distribution of Nu Re0.8 .......................................................................... 74
Figure 4-12 Radial distribution of temperature on the rotor surface for the Chen
Rig Model................................................................................................. 75
Figure 4-13 The effect of geometry on the radial distribution of Nu Re0.8 ....... 76
Figure 4-14 The effect of turbulence model on the radial distribution of
Nu Re0.8 .................................................................................................. 77
Figure 5-1 (a) The experimental rig in University of Bath [51] (b) The prescribed
ingestion model with axial-clearance seal and mesh grid ........................... 80
Figure 5-2 Experimental data for axial-clearance seal with EI ingress [51]........ 81
Figure 5-3 Swirl ratio distribution for axial-clearance seal with Mass-weighted
and Momentum-weighted average assumptions, z / s =0.25 (symbols denote
the experimental data [60]) ....................................................................... 83
Figure
5-4 Secondary flow
streamlines
for
Momentum-weighted
and
Mass-weighted average at T  0.114 ..................................................... 84
Figure 5-5 The effect of  o on swirl ratio distribution, z / s =0.25 (symbols
denote the experimental data [60]) ............................................................ 86
Figure 5-6 Different layouts of ingress inlet and egress outlet ........................... 87
Figure 5-7 The effect of layout on swirl ratio distribution, z / s =0.25 (closed
symbols denote the experimental data [60] and open symbols denote the
experimental data [8]) ............................................................................... 89
Figure 5-8 The swirl contours for three layouts at T  0.242 ......................... 90
Figure 5-9 Comparison of swirl distributions for the prescribed ingestion model
8
and the Bath rig rotor-stator model with no ingestion, z / s =0.25 ............. 91
Figure 5-10 Comparison of swirl ratio for the prescribed ingestion model and
Chen et al. [8] at r / b =0.7 ....................................................................... 92
Figure 5-11 Comparison of swirl distribution for different rotational speed for the
prescribed ingestion model at similar T ................................................. 93
Figure 5-12 Secondary flow streamlines and swirl contours for the prescribed
ingestion model with axial-clearance seal.................................................. 93
Figure 5-13 Velocity distributions for the prescribed ingestion model with
axial-clearance seal ................................................................................... 95
Figure 5-14 Computed variation of effectiveness with C w ,o for axial-clearance
seal ........................................................................................................... 96
Figure 5-15 The computed variation of effectiveness with
o
for
axial-clearance seal compared with experimental data [51] ....................... 97
Figure 5-16 Radial distribution of effectiveness on the stator for the
axial-clearance seal compared with experimental data [60] ....................... 98
Figure 5-17 Radial distribution of effectiveness on the rotor for the
axial-clearance seal compared with experimental data [61] ....................... 99
Figure 5-18 Comparison of radial distribution of  c and  ad on the rotor
(symbols denote the experimental data [61]) ............................................100
Figure 5-19 The computed Tad compared with experimental data [61]...........102
Figure 5-20 The radial variation of Nu Re 
0.8
compared with experimental data
[55] ..........................................................................................................102
Figure 5-21 The radial variation of non-dimensional core temperature compared
with experimental data [55]......................................................................103
Figure 5-22 The computed radial variation of Nu Re 
0.8
including stator heat
transfer ....................................................................................................104
Figure 6-1 The experimental rigs [60] and computational models for (a)
9
Radial-clearance
seal
(b)
Double
axial-clearance
seal
(c)
Radial-axial-clearance seal .......................................................................107
Figure 6-2 Experimental data for radial-clearance seal with EI ingress [54] .....108
Figure 6-3 Swirl ratio distribution for radial-clearance seal, z / s =0.25 (symbols
denote the experimental data [60]) ...........................................................109
Figure 6-4 Swirl ratio distribution for radial-clearance and axial-clearance seal,
z / s =0.25 ................................................................................................ 110
Figure 6-5 Comparison of swirl distribution for different rotational speed for the
radial-clearance seal at similar T ........................................................... 111
Figure 6-6 The computed variation of effectiveness with  o for radial-clearance
seal compare with axial-clearance seal (open symbols denote the
experimental data [54]) ............................................................................ 112
Figure 6-7 The computed streamlines for both seal geometries, T  0.073 .... 113
Figure 6-8 The radial distribution of effectiveness on the stator for the
radial-clearance and axial-clearance seals (symbols denote the experimental
data [60]) ................................................................................................. 113
Figure 6-9 The radial distribution of effectiveness on the rotor surface for the
radial-clearance and axial-clearance seals................................................. 114
Figure 6-10 (a) Typical high-pressure gas turbine stage of a Rolls-Royce jet
engine; (b) detail of rim seal [6] ............................................................... 115
Figure 6-11 Experimental data for double axial-clearance seal with EI ingress [54]
................................................................................................................ 116
Figure 6-12 Swirl ratio distribution for double axial-clearance seal, z / s =0.25
(symbols denote the experimental data [60]) ............................................ 117
Figure 6-13 Swirl contour and flow streamlines in outer wheel-space for the
double axial-clearance, T  0.223 ......................................................... 118
Figure 6-14 Swirl ratio distribution for double and single axial-clearance seal,
z / s =0.25 ................................................................................................ 118
10
Figure 6-15 The computed variation of effectiveness with  o for the double
axial-clearance seal for (a) the outer sampling point and (b) the inner
sampling point (symbols denote the experimental data [54]) ....................120
Figure 6-16 Velocity vectors and sealing effectiveness around the inner seal
region for the double axial-clearance seal, T  0.019 ............................121
Figure 6-17 The radial distribution of effectiveness on stator for the double
axial-clearance and single axial-clearance seals (symbols denote the
experimental data [60]) ............................................................................122
Figure 6-18 Experimental data for double radial-axial-clearance seal with EI
ingress [60] ..............................................................................................123
Figure 6-19 Swirl ratio distribution for the radial-axial-clearance seal, z / s =0.25
(symbols denote the experimental data [60]) ............................................124
Figure 6-20 The computed variation of effectiveness with  o for the
radial-axial-clearance seal for outer sampling point (symbols denote the
experimental data [60]) ............................................................................125
Figure 6-21 The radial distribution of effectiveness on stator for the
radial-axial-clearance seal and the single radial-clearance seal (symbols
denote the experimental data [60]) ...........................................................126
Figure 6-22 The computed variation of effectiveness with  o for all rim seal
geometries (The open symbols denote the experimental data [60], the closed
symbols denote the computed effectiveness and the line is theoretical curves
[60]).........................................................................................................127
11
List of Tables
Table 3-1 The Wilcox k   model constants ................................................. 52
Table 3-2 Computational parameters for 3D computations ................................ 57
Table
5-1
Computational
parameters
for
Mass-weighted
and
Momentum-weighted average assumptions ............................................... 82
Table 6-1 Computational parameters for the radial-clearance seal ....................109
Table 6-2 Computational parameters for the double axial-clearance seal .......... 116
Table 6-3 Computational parameters for the radial-axial-clearance seal ...........124
12
Nomenclature
A Area
a Radius of sealing flow or superposed flow inlet
b Radius of seal
c Concentration
c p Specific heat capacity

C p Pressure coefficient ( ( p  p ) /(1 / 2  2 b 2 ))
.
Cw Non-dimensional flow rate ( m/ b)
C w,i Values of Cw for ingress
.
Cw, o Non-dimensional sealing flow rate ( mo /  b)
C w ,min Minimum value of Cw, o to prevent ingress
G Gap ratio (  s / b )
Gc Seal-clearance ratio (  sc / b )
h Local convective heat transfer coefficient
k Thermal conductivity
.
m Mass flow rate
Nu Nusselt number
p Static pressure
_
p Average static pressure along one vane pitch
Pr Prandtl number
q Rotor wall heat flux
r,  , z Radial, circumferential and axial coordinates
R Recovery factor
13
Re Rotational Reynolds number ( b 2 /  )
Re w Mainstream flow axial Reynolds number ( Wb /  )
s Axial space between rotor and stator
sc Seal clearance
T Static temperature
T1 Static temperature at sealing flow inlet
To ,1 Total temperature at sealing flow inlet
Tref Reference temperature
Trotor Fixed temperature on rotor
Tw Static temperature on rotor
Tw, ad Adiabatic disc temperature on rotor
Vr ,V ,Vz Radial, tangential and axial components of velocity
W Axial velocity in annulus
x Non-dimensional radial location ( r / b)
 Swirl ratio ( V / r )
__
 in Average swirl ratio at sealing flow inlet
 Sealing effectiveness
 c Concentration effectiveness
 c Adiabatic effectiveness for rotor
 Dynamic viscosity
T Turbulent flow parameter ( Cw ,o Re0.8 )
  Non-dimensional core temperature
 Density
14
 Non-dimensional sealing parameter ( C w / 2Gc Re  )
 i Value of  when C w  C w ,i
 o Value of  when C w  C w ,o
 min Value of  when C w  C w, min
 Angular velocity of rotating disc
Turbulence Model Constants
C , C 1 , C 2 ,  k ,   k   model constants
 ,  ,  ' ,  k ,   k   model constants
Subscripts
a Annulus
e Egress
EI Externally-induced ingress
i Ingress
in Initial
o Superposed flow or sealing flow
1,2 Locations in wheel-space and annulus, respectively
 Value in core at z / s  0.5
15
1. Introduction
1.1. A brief history of the jet engine
According to Newton’s third law of motion, the jet engine, one kind of reaction
engine, forces a fluid in a certain direction in order to produce a reaction that drives
the engine in the opposite direction. In modern industry, the jet engine plays a vital
role in many engineering fields. Lock [1] and Rolls-Royce [2] provide an overview of
the development of the jet engine.
Around the first century AD a simple practical example of jet engine, Hero’s engine
(Figure 1-1), was invented in Greece. Although it perhaps was used as a toy, it still
was an important milestone for the birth of jet engine. With the development of
human civilization, important progress for the jet engine happened in the early 20th
century. In 1922, Maxime Gillaume put forward his idea of an axial jet engine in his
patent [2]. In the 1930’s Hans von Ohain, in Germany, and Sir Frank Whittle, in
England, independently brought the idea to practice with the birth of turbojet.
Figure 1-1 A simple model of Hero’s engine [1]
Hans von Ohain patented his turbojet with both axial and centrifugal compression
when he studied for his doctorate at the University of Gottingen in 1934 [3]. His
16
design attracted the interest of an aircraft manufacturer, Heinkel. In 1937 their first
joint engine used hydrogen as the fuel and consisted of a radial compressor and radial
turbine (Figure 1-2). Two years later, Hans von Ohain designed his HeS3 engine,
which powered the He 178 just before the Second World War. The He 178 conducted
the first turbojet flight in the world. After the war, Hans von Ohain immigrated to
America and worked for Wright-Patterson Air Force Base. For the next 30 years he
contributed to the development of jet-powered aircraft in the US [1].
Figure 1-2 Ohain’s hydrogen-fuelled turbojet engine [3]
Figure 1-3 Frank Whittle’s patent [1]
In England Frank Whittle patented the first practical proposal for the jet engine which
he called “Improvements relating to the propulsion of aircraft and other vehicles” [1].
17
This patent presented a turbojet engine with an axial compressor, powered by an axial
turbine (Figure 1-3). In 1935 Whittle began to build the first prototype engine with
this concept. One year later he ran the world’s first bench test using a jet engine with
liquid fuel. After the fully successful experiments finished in 1940, the government
took note on Whittle’s research and the Whittle engine was used to power a Gloster
E28/39 experimental aircraft. In 1944, Rolls-Royce produced an improved Whittle
engine to power the Gloster Meteor 1 twin-engined fighter [1]. After the Second
World War, Whittle was proclaimed the “father of the jet engine”.
Hans von Ohain and Frank Whittle were not the only people who promoted the
research of the jet engine. At the same time, many other pioneers also made great
efforts for the development of this engine. For example Rene Lorn, a French engineer,
patented a ramjet in 1913 [1] and A.A. Griffth published an analysis of an axial
turbine in 1926 [2]. Owing to the effort of these pioneers, the jet engine has played a
vital role in modern industry. Many kinds of jet engine have applied to power civil
and military aircraft, ship, electricity generator and oil pumping.
1.2. Gas turbine
Figure 1-4 Simple gas turbine system [4]
In modern industry most jet engines are gas turbines, extracting energy from
18
combustion gases.
The three main parts of a gas turbine are an upstream compressor,
a downstream turbine and a combustion chamber in the middle (Figure 1-4). The
inflow air is pressurised in the compressor and is heated with injected fuel in the
combustion chamber. After the combustion process, the mixed gas is expanded
through the turbine and finally exits from a nozzle to produce thrust. The compressor
is driven by the turbine through a connecting shaft. The working cycle of gas turbine
is called Brayton cycle. The ideal cycle is described as three processes: isentropic
compression, constant pressure combustion and isentropic expansion. A typical
working cycle of a turbojet engine is shown in Figure 1-5. According to the figure,
pressure significantly increases in the compressor with a small drop in the combustion
chamber (in the ideal situation, pressure stays constant). Finally, the pressure reduces
in the turbine as the gas expands.
Normally the pressure rise in the compressor is
larger than the pressure drop in the turbine. Therefore, at the end of working cycle,
there is surplus pressure to produce the thrust of engine.
Figure 1-5 Variation of pressure, temperature and velocity in a turbojet [2]
Using a non-isentropic Brayton cycle, Saravanamuttoo et al. [5] show that the specific
work output of the gas turbine engine is dependent on both pressure ratio of
compressor (PR) and turbine entry temperature (TET). Hence, engine designers aim
to maximise these two parameters to gain the most powerful gas turbine. In the 1940s
19
the pressure ratio was about 5 and the turbine entry temperature was just 1050 K.
Nowadays the Rolls-Royce Trent 900 has a pressure ratio of 42 and the TET rises to
around 1800 K at take-off [2]. The high TET gives rise to a cooling problem for the
engine designer. Although metallurgical technology has developed substantially, it
cannot fully satisfy the requirements and demands for TET. The melting point of cast
alloys used for turbine blades is around 1550 K, which is much lower than the modern
TET. Therefore most engine designers require internal cooling technology to protect
turbine components in the high-temperature working environment.
1.3. Internal cooling
Figure 1-6 Internal cooling system, including cooling paths [2]
In the gas turbine, some of the compressed air does not enter the combustion chamber
20
instead it is used for cooling turbine components and sealing. The pressure drop in the
combustion chamber creates a pressure difference between the compressor and
turbine which drives the cool air flow into the turbine. In modern gas turbine engine
about 20% of the compressed air is applied to internal cooling system. However,
surplus compressed air used as coolant would lead to lower engine efficiency. For this
reason, an effective cooling system is vital for keeping a high efficiency in the gas
turbine engine.
In the internal cooling system, coolant flow is directed not only to the turbine nozzle
guide vanes and blades, but also to the turbine cavities between the stator and rotor. A
typical internal cooling system is shown in Figure 1-6. In the modern engine
multiple-feed, multiple-pass and extensive film cooling (Figure 1-7) is applied to the
first-stage vanes and blades which are exposed to the highest working temperature.
The coolant flow passes through internal passages and cools the blades from inside.
The flow exits from the blades through many tiny surface holes, creating a protective
film to cool the exterior of blades.
Figure 1-7 Film cooling for turbine blades [2]
21
1.4. Ingress
Figure 1-8 Generic rotor-stator turbine stage and double clearance-seal inset [6-7]
Figure 1-8 shows a typical high-pressure gas turbine rim seal, which is used to
prevent or reduce the amount of hot mainstream gas from the annulus that is ingested
into the wheel-space between the rotor and the stator. Sealing air, supplied from the
compressor, is fed into the wheel-space and the air can be used to control the amount
of ingested gas (referred as ingress). Too little sealing air can cause overheating and
fatigue and reduce operating life of the discs, however too much can reduce the
engine efficiency.
According to theoretical studies [6-7], there are two kinds of ingress;
externally-induced (EI) and rotationally-induced (RI) ingress. Externally-induced (EI)
ingress occurs when the external pressure distribution is non-axisymmetric, which is
created by the flow past the stationary vanes and rotating blades in the turbine annulus.
Ingress and egress occur through some parts of the seal clearance where the external
pressure in the mainstream is higher and lower respectively than that in the
22
wheel-space. On the other hand, even when the external distribution of pressure is
axisymmetric, rotationally-induced (RI) ingress can still occur. The rotating fluid in
the wheel-space creates a radial gradient of pressure, so that the pressure inside the
wheel-space can drop below that outside, which leads to ingress of external fluid
through the rim seal into the wheel-space along the stator surface. Meanwhile, the
‘disc-pumping effect’ causes egress near the rotor.
At the University of Bath, experiments, theoretical models and Computational Fluid
Dynamics (CFD) jointly contribute to the understanding of the fluid dynamics and
heat transfer associated with ingress and optimal seal performance.
1.5. Thesis aim and objectives
The main aim of this PhD thesis is to establish a simple computational model to
predict the sealing effectiveness of externally-induced ingress for engine designers.
This model also provides useful information about the fluid dynamics and heat
transfer in the wheel-space. The 2D model is a great simplification to the complex,
and costly, 3D unsteady CFD codes run by gas-turbine companies such as Siemens.
The engine designers need a simple and cost-effective design tool to rapidly attest
engine seal components.
To accomplish this aim, three key objectives were completed in this thesis:
1. Two typical axisymmetric rotor-stator system models without ingress were
established, in order to understand the fluid dynamics and heat transfer of the
wheel-space in the situation without ingress. The effects of geometry and
turbulence model were also studied. The axisymmetric rotor-stator model was
validated against experimental data from the literature.
2. The axial-clearance seal is firstly considered for a prescribed ingestion model.
A mass-weighted average boundary condition is applied to this model and the
23
optimal layout of ingress inlet and egress outlet was selected through
computations. The sealing effectiveness (on the stator and rotor), fluid
dynamics and heat transfer were investigated and were shown to be in
reasonable agreement with the experimental results from the test rig at the
University of Bath.
3. Three other seals are also presented in this thesis: the radial-clearance seal,
double axial-clearance seal and radial-axial-clearance combination seal. In
accordance with the axial-clearance seal, the sealing effectiveness and fluid
dynamics in the wheel-space were investigated for these seals and compared
with experimental data. Finally, the performances of these four sealing
geometries were ranked.
1.6. Thesis overview
Chapter 1 gives an introduction to the historical development of jet engine and gas
turbine and discusses the internal cooling problem in the gas turbine engine. A simple
introduction to ingress, the main issue in this thesis, is presented.
Chapter 2 presents a literature review, discussing the previous and current research on
rotor-stator systems and ingress.
Chapter 3 presents the computational method used in this thesis and introduces the
turbulence model and energy equation selected in the CFD code. Some results from
3D steady simulation are also shown in this chapter.
Chapter 4 presents the simulation for two typical axisymmetric rotor-stator system
models without ingress. The fluid dynamics and heat transfer of the wheel-space
without ingress as well as the effects of geometry and turbulence model are discussed
in these computations. Most results show good agreement with experimental data
from the literature.
Chapter 5 presents the prescribed ingestion model applied to the axial-clearance seal.
24
The mass-weighted average boundary condition and the layout of ingress inlet and
egress outlet are considered in this chapter. The sealing effectiveness (on the stator
and rotor) as well as the fluid dynamics in the wheel-space and heat transfer is
investigated. Reasonable agreement with the experimental results from the rig in the
University of Bath is demonstrated.
Chapter
6
presents
results
associated
with three
other
seal geometries
(radial-clearance seal, double axial-clearance seal and radial-axial-clearance
combination seal). The sealing effectiveness and fluid dynamics within the
wheel-space are investigated and the four seal geometries are ranked in terms of
performance.
Chapter 7 presents the main conclusions of this thesis and some possible future work.
1.7. Publications
Wang, L. and Wilson, M., 2012, Computations of Flow and Heat Transfer in a
Rotor-Stator System with Externally-Induced Ingestion. International Journal of Gas
Turbine, Propulsion and Power Systems, 4 (1), pp. 10-18.
This is included as Appendix.
25
2. Literature review
This chapter firstly provides an introduction to the fundamental fluid dynamics and
heat transfer for rotor-stator systems. After that, previous studies for ingress through
gas turbine rim seals are presented. The literature review includes experimental and
computational studies for understanding the ingress phenomenon. Lastly, theoretical
research (the orifice model) and experiments carried out on the University of Bath gas
turbine test rig are introduced.
2.1. Rotor-stator systems
Figure 2-1 Generic rotor-stator configuration [8]
As described in Chapter 1, a rotor-stator system in a gas turbine involves a disc
rotating next to a stationary casing, termed the rotor and stator, forming a cavity
known as a wheel-space. The system is defined as the rotor of diameter, b , rotating
at an axial distance s from the stator, as shown as Figure 2-1. This figure also shows
26
a superposed flow in entry near the axis of the system; in an engine, this is the cooling
air used to remove heat from the turbine rotor disc. Batchelor [9] proposed an initial
model for the flow between rotating and stationary discs (Figure 2-2). The model
suggested that there is a rotating fluid core between the two discs with an angular
velocity of magnitude between zero and  (the angular velocity of rotor). The
model also implied that two separate boundary layers would exist in the system. The
boundary layer on the rotor is similar to that on a free rotating disc; the stator
boundary involves radial inflow of fluid and an efflux from the boundary layer to the
core. In this type of flow, Owen and Rogers [10] showed that two non-dimensional
parameters, core swirl ratio and the turbulent flow parameter, are important to the
flow structure in the wheel-space. The core swirl ratio is defined as the ratio of the
tangential velocity component ( V / r ) inside the rotating core to the angular
velocity of the rotor at same radius. The turbulent flow parameter, T , combines the
rotational Reynolds number ( Re   b 2 / ) and the non-dimensional superposed

flow rate ( C w  m/ b ).
T  C w Re  0.8
(2-1)
Figure 2-2 Batchelor-type flow in a rotor-stator system [9]
27
Figure 2-3 Flow regimes for a closed rotor-stator system [11]
In 1960, Daily and Nece [11] carried out experiments for a closed rotor-stator system

( m  0 ) and proposed flow regimes in the wheel-space dependent on the rotational
Reynolds number and the axial gap ratio, G  s / b , as shown in Figure 2-3:
Regime I:
Laminar flow, small clearance with merged rotor-stator boundary layers
Regime II: Laminar flow, large clearance with separate rotor-stator boundary layers
Regime III: Turbulent flow, small clearance with merged rotor-stator boundary layers
Regime IV: Turbulent flow, large clearance with separate rotor-stator boundary
layers
Chen et al. [8] carried out experiments for a rotor-stator system and presented
measurements of velocity and Nusselt number. In the experiments, LDA
measurements were made for radial and tangential velocities, and fluxmeters were
used to measure the heat transfer on the heated rotor. The velocity profiles for no
superposed flow, shown in Figure 2-4, illustrated that the flow structure was in
accordance with Batchelor flow, with a radial outflow on the rotor ( z / s  0 ), a radial
inflow on the stator ( z / s  1 ) and with an inviscid rotating core between the two
boundary layers. The experiments with superposed flow found that the (un-swirled)
28
superposed flow reduces the core swirl ratio and also reduces the radially inward flow
on the stator. Computations carried out by Wilson et al. [12] gave similar results for
flow structure and velocity.
Figure 2-4 Radial and tangential velocity profiles in a rotor-stator wheel-space [8]
Figure 2-5 Measured and computed Nusselt numbers, Re   1.25  10
6
[8]
〇 uncorrected measurements; □corrected measurements; — computations
Furthermore, the results shown in Figure 2-5 demonstrated that Nusselt numbers
increase with increasing flow rate ( C w  2530 ~ 9680 , T  0.034 ~ 0.128 ) at a
given rotational speed. The corresponding computations agreed best with
29
measurements corrected to take heat transfer due to radiation into consideration, as
shown in Figure 2-5.
Do Soghe et al. [13-14] developed improved correlations for the core swirl ratio and
improved a correlation for the rotor disc pumped mass flow rate in order to improve a
one-dimensional rotor-stator modelling approach.
Pelle and Harmand [15-16] made a series of heat transfer experiments for a
rotor-stator system with an opened air-gap. They found that heat transfer depends on
the rotational Reynolds number ( Re  1.29  10 5 ~ 6.45  10 5 ) and the dimensionless
spacing between the rotor and the stator [15]. They also added a central jet flow inlet
to the experimental system in order to investigate the effect of the jet on heat transfer
[16]. In the region of the inlet, the influence of the jet was significant and hence the
local heat transfer rate increased considerably. At high radius, the heat transfer
distribution was similar to the result without a jet.
Lewis et al. [17] carried out CFD simulations for a rotor-stator system with pre-swirl
nozzles. They computed the radial and circumferential variation of Nusselt number
and compared with experimental results. Based on the radial distributions of Nu on
the rotor, the computed results illustrated viscous and inertial regimes for different
values of turbulent flow parameter T . It was suggested that the parameter Nu Re0.8
was a satisfactory correlating parameter for heat transfer in the viscous regime. For
the inertial regime, this parameter did not collapse either the computed or measured
results. The computed circumferential variation of Nu , which was consistent with
the experiments, revealed high heat transfer rates around the receiver holes, as shown
in Figure 2-6. The computed streamlines are shown in Figure 2-7. Combined with
measured heat transfer results, these illustrate that the flow from the nozzle can either
exit through the receiver hole or continue to a higher radius and recirculate into the
system and mix with the core flow.
30
Figure 2-6 Computational (right) and experimental (left) Nusselt number contours,
Re   0.8  10 6 [17]
(a) viscous regime T  0.13 (b) inertial regime T  0.24
Figure 2-7 Computed streamlines superimposed onto experimental heat transfer results,
Re   0.8  10 6 , T  0.38 [17]
31
Poncet and Schiestel [18] presented two different rotor-stator systems in their
computational study of heat transfer. The geometry of these two systems was the same
as for published experiments. The first rotor-stator system was enclosed by a heated
shroud, and an axial inlet flow was applied. The numerical results agreed with the
experimental data and the authors found that a recirculation zone controlled the heat
transfer ( Re   1.56  10 5 , T  0.19 ~ 0.61 ). The second rotor-stator system
consisted of a heated stator and a radially inward flow. The results from this model
also had good agreement with the published experimental data, and the agreement
was better than in the former case. The authors suggested that the inward radial flow
in the second system, which did not impinge on any wall, might be the cause for this
better agreement.
Javiya et al. [19] carried out CFD simulations for the pre-swirl rotor-stator system as
studied by Lewis et al. [17] in order to test the effects of turbulence model, near wall
modelling and the CFD code used on computed flow structures and heat transfer.
Although most turbulence models showed reasonably good agreement with
experiment, none of the models produced full details of the flow structure near the
pre-swirl jets, due to the limitation of the models in complex flows. The computations
gave good predictions of the heat transfer on the rotating disc at high pre-swirl flow
rates. At the lowest flow rate, the heat transfer was over-predicted. The authors
believed that sensitivity to heat transfer on the stator was one factor causing this
over-prediction. In order to study the issue of stator heat transfer, the authors carried
out computations with the stator at the same temperature as the unheated rotor rather
than using an adiabatic boundary condition. The results, shown in Figure 2-8, showed
that the magnitude of Nu reduced slightly when the stator heat transfer taken into
account, though the effect was small. The arrows in figure show the radial locations of
the pre-swirl inlets on the stator and the outlet holes on the rotor.
32
Figure 2-8 Effect of stator heat transfer on the distribution of Nu Re0.8 [19]
Evans et al. [20] compared computational results with published experiments for a
rotor-stator system using Fluent, in order to test the effects of turbulence model and
mesh density on the heat transfer results. The authors applied three turbulence models,
k   , k   and k   SST, and used two different mesh densities for different
flow conditions. The k   SST model with a fine mesh agreed best with the
experimental data for both the swirl velocity and the heat transfer coefficients.
However, regardless of the turbulence model, poor agreement with experiments for
heat transfer coefficients was obtained at low cooling flow rates and high rotational
speed ( Re   1.0  10 6 ). The authors gave a possible explanation that relatively large
ingestion at low flow rates could influence the heat transfer in the rotor-stator system.
The authors recommended that future CFD simulations should apply the k   SST
model, and that Fluent could be used with confidence when the rotational Reynolds
number is below 8 105 .
33
2.2. Ingress
Due to the importance of ingress, there are a large number of investigations about this
problem, including both experimental and computational studies. Among many
experimental techniques, concentration measurements are widely used in ingress
studies. These use a convenient tracer gas, such as CO2 , to characterize the sealing
effectiveness (  ). Solid surfaces become impermeable barriers and the boundary
conditions are known. Theoretical models often neglect the effect of diffusion. In
practice, diffusion can lead to non-zero ingress, which means the tracer gas used for
concentration measurements can pass through the rim seal by diffusion. Therefore, at
large values of sealing effectiveness, where ingress is relatively small, a theoretical
model, compared with concentration measurements, may underestimate the ingress
and consequently overestimate the effectiveness [6]. Computational studies have also
become an indispensable component of ingress research. Over the past decade,
computational fluid dynamics (CFD) has been used to compute pressure distributions,
sealing effectiveness and other important ingress parameters.
Bayley and Owen [21] used a simple rotor-stator rig with an axial-clearance rim seal
and without an external annulus to carry out ingress experiments. From the results,
they showed that increasing the sealing flow rate can increase the relative pressure in
the wheel-space, subsequently, reducing the ingested flow. They found that the
minimum value of non-dimensional sealing flow rate needed to prevent ingress,
Cw,min depends strongly on the seal clearance ratio, Gc , and the rotational Reynolds
number, Re , but is little affected by the rotor-stator clearance s . The following
empirical relationship was established:
Cw,min  0.61Gc Re
(2-2)
34
As their experiments were carried out without external flow, this empirical equation
applies only for rotationally-induced (RI) ingress according to the definition above. In
the following years, Phadke and Owen [22] applied flow visualization, pressure and
concentration measurements to determine Cw,min in a rig without external flow for
different seal geometries. They found that radial-clearance seals were more effective
than axial-clearance ones.
Graber et al. [23] used concentration measurement for several rim seal geometries
with no circumferential variation of the external pressure. They plotted the measured
values of sealing effectiveness versus t , where t  T / 4 . Through the
experiments, Graber et al. obtained the effects of seal-clearance ratio ( Gc ) and Re
on variation of  with t , and found no effects of external swirl on  .
Abe et al. [24] used a turbine rig in experiments with vanes in the external annulus
upstream of the rim seal in order to show that external flows in the annulus can also
ingress. After tests of several rim-seal geometries, the authors identified three factors
that affected ingress: the ratio of the velocities of the sealing air and the flow in the
annulus; the rim-seal clearance; the shape of the rim-seal.
In 1988, Phadke and Owen [25-27], through many experiments using an experimental
rig with an external annulus, measured the variation of C w, min with the axial
Reynolds number in annulus ( Re w  Wb /  ) as shown in Figure 2-9. According to
the figure, when Re w = 0, Cw,min is proportional to Re ; when the value of Re w is
large, Cw,min is hardly affected by Re and increases with the increasing Re w .
Phadke and Owen correlated results for different seal geometries with the following
empirical relationship for externally-induced (EI) ingress.
35
1/ 2
Cw,min  2 KGc Pmax
(2-3)
where
1
Pmax  C p ,max Re w2
2
(2-4)
Figure 2-9 Variation of C w, min with Re w [25-27]
Figure 2-10 Variation of C w, min with 2 Gc Pmax
1/ 2
[25-27]
36
C p ,max is a non-dimensional pressure difference in the external annulus. K is an
empirical constant and the data as shown in Figure 2-10 were correlated with
K  0.6 . Hamabe and Ishida [28] obtained a similar empirical relationship from
measurements in a turbine rig fitted with upstream vanes but not downstream blades.
The first published experimental data for a turbine rig with both vanes and blades
were presented by Green and Turner [29]. For low sealing flow rates, they obtained
lower ingestion than the case when vanes only were used.
Figure 2-11 Variations of Cw,min with C p ,max [30]
Bohn and Wolff [30] also carried out experiments for a rig with both vanes and blades.
They designed four different seal geometries to determine the value of Cw,min . As
shown in Figure 2-11, they also obtained a linear variation of Cw,min with C p ,max1/ 2 ,
which is same result as Phadke and Owen [25-27]. However, they found a different
37
K value for different seal geometries, which is not consistent with K  0.6 as
observed by Phadke and Owen.
Bohn and Wolff suggested that K  0.6 provides a
conservative estimation of Cw,min .
The research group at Arizona State University and its cooperative research institutes
[31-35] contributed greatly to the investigation of ingress. Roy et al. [31] described
experimental measurements for a single stage axial-flow turbine with two vane-blade
configurations. The main difference between the configurations was the inlet vane
turning angle. The measurements suggested that the instantaneous pressure field is
pivotal to ingestion. This 3D and unsteady field is influenced by the mainstream flow
rate, rotor speed, and sealing flow rate.
Roy et al. [32] carried on the experiments for a turbine with an axially overlapping
radial seal. Time-resolved velocity maps in the wheel-space were obtained by the PIV
technique, as shown in Figure 2-12. According to the figure, when the sealing flow
rate is low, the non-periodic red region with high tangential velocity represents the
ingested air from the mainstream. The explanation for the non-periodic variation is
that the relative positions of the blades and vanes do not remain the same azimuthally.
On the other hand, the result for high sealing flow rate in Figure 2-12 (b) indicates
that the tangential velocity is low throughout the wheel-space, which means that no
ingress occurs in this case, and unsteady large-scale structures which lead to large
velocity fluctuations have appeared. In short, this experimental measurement
demonstrated that the ingestion flow carried high tangential velocity fluid from the
mainstream to the wheel-space and the egress flow brought low tangential velocity
fluid from the wheel-space to the mainstream.
38
(a)
(b)
Figure 2-12 Instantaneous velocity contours in the disk cavity [32]
(a) Cw,o  1574 (b) Cw,o  8656
39
Figure 2-13 CFD velocity vectors in axial-radial plane of seal region [32]
Roy et al. [32] also described an unsteady, three-dimensional CFD model of a
single-stage axial turbine having similar geometry with their experimental rig
including vanes, blades and an axially overlapping radial clearance rim seal. The
computational sector model had one blade and one vane along with the rim seal and
wheel-space. The computations were carried out using Fluent Version 6.2. The
velocity vectors in the axial-radial plane (Figure 2-13) indicated that a recirculation
cell was formed downstream of the vane platform. A second recirculation cell exists
simultaneously at the rotor side of the rim seal. Furthermore, the radial, axial, and
tangential velocity contours revealed that some rapid changes in direction and
magnitude occur in some gap regions. The velocity contours also demonstrated that
when ingress occurs, both the axial velocity and tangential velocity are greater than
when egress occurs, which is consistent with their measurements.
Zhou et al. [33] continued the experiments and computations for three wheel-space
configurations with different aspect ratios (Config.1 having the maximum value and
Config.3 is the minimum). At low sealing rate, they also identified the regions of
ingress and egress around the rim seal through PIV images of instantaneous velocity.
Another essential result shown in Figure 2-14 is that ingested air from the external
annulus into the wheel-space decreased, and consequently the sealing effectiveness
40
increased, as the wheel-space aspect ratio became smaller. For computations, the
simulation for a 14.4° sector model under-predicted ingested hot air into the
wheel-space compared with measurements. One possible reason presented by authors
is that the sector model can not predict the circumferentially rotating low-pressure
regions which are able to augment ingestion.
Figure 2-14 Comparison of local sealing effectiveness at the stator [33]
Recently, Dunn et al. [34] reported an intensive computational study for two meshes
with different solver parameters. Although both solutions had strength and weakness,
both showed generally good agreement with the experimental results.
Gentilhomme et al. [35] conducted both pressure and concentration measurements for
a single stage turbine. The pressure measurements revealed that the ingested highly
swirling mainstream gas can increase radial pressure gradients in the wheel-space at
low sealing flow rate. The authors also carried out CFD studies for ingress and found
that the asymmetrical pressure created by the Nozzle Guide Vanes (NGVs) was only
slightly affected by the existence of rotor blades. However, the pressure asymmetry
due to the rotation is very significantly influenced by the NGVs.
41
Lewis and Wilson [36] conducted a computational study in a simplified model of a
gas-turbine rotor-stator wheel-space with an axial clearance rim seal, with
non-axisymmetric flow conditions created by a stator vane in an external mainstream.
They used the commercial code CFX Version 10 to investigate the effects of geometry
(different axial space between the vane trailing edge and the seal) and boundary
condition assumptions on results. The rotational Reynolds number used was 2.5 106 ,
which is typical of values used in experiments. The other non-dimensional parameters
used were of similar values to conditions in engines. Sensitivity to mesh size was
tested over a wide range by using different grid sizes. Through this computational
study, the fluid dynamics results illustrated that the circumferential variation of
pressure coefficient, C p , decreases with increasing distance downstream from the
vane trailing edge. The sealing effectiveness was found to be approximately constant
near the stator. Near the rotor, the effectiveness reduced slightly as radius increased.
The dimensionless temperature on both the stator and the rotor showed that the fluid
in the wheel-space was heated above the temperature of the external mainstream.
Mirzamoghadam et al. [37-38] reported 3D CFD computations for a full stage HP
turbine disk cavity. Based on these computational results, they found that the
asymmetrical annulus pressure can give rise to ingestion even at relatively high
sealing flow rate. They also demonstrated that the stator wake influences ingress more
than the rotor blade bow wave. In addition, Mirzamoghadam et al. [37] defined the
ingestion mixing efficiency using temperature data. The definition is given by
ing  (Tr  Tc ) /(Th  Tc )
(2-5)
42
Figure 2-15 Ingestion Mixing Efficiency [37]
Here Tc , Th and Tr are coolant inlet temperature, annulus temperature and local
temperature at radius r respectively. With this definition, efficiency equal to zero at
a given radius implies that no ingress occurs. As shown in Figure 2-15, the ingestion
mixing efficiency reduces, which also means that the sealing effectiveness increases,
as the sealing flow rate increases. A frictional heating correlation, which is essential
for the calculation of heat transfer in the wheel-space, was developed by
Mirzamoghadam and Xiao [39].
The combined experimental and computational study of Cao et al. [40] showed that
ingress is an incompressible flow phenomenon and that ingress can make the rotating
flow in the wheel-space unstable. Although the authors mentioned that a ‘segmental
domain’ model used in CFD may be unable to capture these instabilities, their
computations for a 90° segmental model still showed good agreement with those for a
full 360° domain. Nevertheless, Jakoby et al. [41] pointed out that their steady
calculation with a simplified sector model had less good agreement with
43
measurements than a 360° unsteady calculation at low sealing flow rate. Recently,
Rabs et al. [42] indicated that a full 360° model provides almost no improvement
when compared to sector models, if no large scale rotating structures occur. The use
of sector models was recommended due to the huge savings in computational cost.
The numerical simulations of Wang et al. [43] focus on the effect of the rim seal
region geometry on ingress. Close- and wide-spaced turbine stages with an
axial-clearance seal were tested and it was noted that the peak-to-trough pressure
variation, a driving factor for ingestion, for the wide-spaced stage is much less than
that for the close-spaced stage. For time-averaged calculations, both close- and
wide-spaced stages produce approximate ingestion characteristics, however, the
characteristics for the close-spaced configuration were significantly changed with
time, which is consistent with the high variation in the gas path pressure field.
Laskowski et al. [44] compared steady and unsteady simulations of ingress.
According to contours of effectiveness in the wheel-space and rim seal region (Figure
2-16), the steady results show no ingestion for three different circumferential
locations, however ingestion is present at all three locations in the time-averaged
unsteady result. The authors also compared effectiveness based on concentration and
temperature for the stationary blade and rotating blade cases. If the rotor blade was
stationary, these two definitions of effectiveness give similar results. In the rotating
blade case, the effectiveness based on temperature gave a lower value in the
wheel-space than that based on concentration. The authors pointed out that windage
(frictional heating), which increases the temperature in wheel-space and consequently
reduces the effectiveness, is the main reason for the difference between the two kinds
of effectiveness.
44
(a) Steady state CFD
(b) Time-averaged Unsteady CFD
Figure 2-16 Steady state and time-averaged unsteady buffer cavity effectiveness [44]
(a) simplified turbine rim seal model (b) full 1.5 stage turbine model
Figure 2-17 Velocity vectors in the gap [45]
Rabs et al. [45] carried out computations for a simplified turbine rim seal model
without vanes or blades and a full 1.5 stage turbine model in order to verify that
45
Kelvin-Helmholtz vortices could occur in the rim seal region. Both models showed
the existence of Kelvin-Helmholtz vortices and occurrence of ingress as shown in
Figure 2-17. The authors indicated that the Kelvin-Helmholtz vortices obtained by the
full 1.5 stage turbine model are weakened by the interaction of the vanes and the
blades, which was not included in the simplified turbine seal model.
O’Mahoney et al. [46] presented steady Large-Eddy Simulations (LES) results for a
turbine rim seal ingestion compared with published experimental data and an
unsteady RANS simulation. The results demonstrated that LES predicts more
ingestion through the rim seal than the unsteady RANS simulation, and accordingly
gives a closer agreement with experimental measurements of sealing effectiveness.
The CFD simulation of Julien et al. [49] produced large scale flow structures for no
purge flow and low purge flow rates, and illustrated that increasing the sealing flow
rate can reduce the circumferential pressure variations in the wheel-space hence
improve the sealing effectiveness.
Teuber et al. [48] carried out URANS computations to investigate the fluid mechanics
in a 3D model of a turbine stage. The computed swirl ratios in the wheel-space have
good agreement with measured values. The authors indicted that the minimum sealing
flow required preventing ingestion increases as the annulus Mach number increases.
2.3. Previous research at University of Bath
The research group at the University of Bath has devoted efforts to theoretical,
experimental and computational studies on the subject of ingress.
46
Figure 2-18 Orifice ring [49-52]
Owen et al. [6-7, 49-50] developed orifice models for the ingress problem. The orifice
equations are based on an ‘orifice ring’, as shown in Figure 2-18. According to the
orifice model, egress and ingress simultaneously cross different parts of the orifice
ring through elemental areas, the sum of which is equal to the clearance area of the
seal. Egress flows into the external annulus through a stream tube from the
wheel-space. Conversely, ingress starts in the annulus and ends in the wheel-space.
The main ‘orifice assumptions’ for inviscid flow are that rV is constant and
(r2  r1 ) / r1  1 ( r1 and r2 are radius of locations in wheel-space and annulus, as
shown in Figure 2-18). Meanwhile, it is assumed that the axial and tangential
gradients of velocity are much smaller than the radial. Lastly, although the equations
are derived for inviscid flow, discharge coefficients, Cd are introduced to account
for losses. Through the theoretical model, the equations for effectiveness and for
non-dimensional flow parameter for ingress  i ( C w,i / 2Gc Re  ) are obtained.
For EI ingress:
o


2 / 3
 min, EI [1   c (1   )2 / 3 ]3/ 2
(2-6)
47
 i , EI
1 

2 / 3
 min, EI [1   c (1   )2 / 3 ]3/ 2
(2-7)
For RI ingress:
o


1/ 2
 min, RI [1  (1   ) ][1   c 2 (1   )]1/ 2
(2-8)
 i , RI
1 

1/ 2
 min, RI [1  (1   ) ][1   c 2 (1   )]1/ 2
(2-9)
Where  c , the ratio of the discharge coefficients, is an empirical constant.
Figure 2-19 Comparison between theoretical effectiveness curves and experimental data for
axial-clearance seal with EI ingress (the solid lines are theoretical curves) [51]
Sangan et al. [51-52] carried out experiments on rigs with axial and radial clearance
48
rim seals for both EI and RI ingress in order to measure the sealing effectiveness and
hence deduce  i . Figure 2-19 shows a comparison between the experimental data
and the theoretical variation of effectiveness (at r / b  0.958 ) according to the above
equations (for EI ingress) for the axial-clearance seal. The fit between the equations
and the measured variation of  with  o was optimized using a statistical model
featuring the maximum likelihood estimates described by Zhou et al. [51]. The figure
shows that the agreement between the optimum theoretical curves and the
experimental data is very good. In 2012, Sangan et al. [54] extended experiments to
double clearance seals and theoretical curves also agreed very well with the
experimental data.
Pountney et al. [53] carried out heat transfer experiments on the test rig.
Thermochromic Liquid Crystal (TLC) was used to measure the temperature on the
rotor. Hence, the adiabatic effectiveness and the Nusselt number on rotor were
obtained to determine the effect of ingestion on the rotor. CFD studies [54] have also
been conducted at the University of Bath in order to compare results with the
theoretical model.
2.4. Chapter summary
This literature review has identified past and current research relevant to ingress in
rotor-stator systems; considerable experimental and theoretical research have been
supported by computational fluid dynamics. However, 3D CFD models are complex,
costly and not always suitable for the engine designer. The designer needs a simple,
rapid computational tool to link the experimental data and theoretical models for
design purposes. 2D simplified CFD model in this thesis satisfies this requirement.
49
3. Computational method and 3D Computations
The commercial code ANSYS-CFX Version 11.0 was used for the computations at the
beginning of the study. This was upgraded to Version 13.0 after 18 months. This
chapter gives a brief introduction for the turbulence model and heat transfer
calculations in this code. This information is based on the release notes from the
software provider. For all computations, if no other description is given, the
normalized convergence residuals levels for mass, momentum and turbulence were
1107 and 1106 for heat transfer. All meshes were generated using ANSYS
ICEM.
Some computed results from 3D steady computations are also presented in this
chapter, as a preliminary study for ingress. These results include pressure in the
annulus, secondary flow streamlines and sealing effectiveness.
3.1. Turbulence model
Due to the good compromise between numerical effort and computational accuracy,
two-equation turbulence models are widely used in fundamental flow computations.
For this kind of turbulence model, turbulent viscosity is modelled using turbulent
velocity and turbulent length scale. Both the velocity and length scale are found by
solving separate transport equations. The equations shown below are based on the
help files from ANSYS-CFX Version 13.0.
In the k -epsilon ( k   ) two-equation turbulence model, the turbulent velocity is
computed from the turbulent kinetic energy ( k ) and the turbulent length scale is
estimated from the turbulent kinetic energy ( k ) and the turbulence eddy dissipation
(  ). Hence, these two new variables are introduced into the system of equations. The
continuity equation and the momentum equations are shown below:
50



( U j )  0
t x j
(3-1)
U j
U i
U

p


( U iU j )  

 eff ( i 
)  SM
t
x j
x i x j
x j
xi
[
]
(3-2)
In these equations, eff is the effective viscosity accounting for turbulence, so that:
eff    t
(3-3)
The term t is the turbulent viscosity. In k   model this is found from:
 t  C 
k2

(3-4)
In this equation, C is a constant and the values of k and  are obtained by
differential transport equations for the turbulence kinetic energy and the turbulence
eddy dissipation.
k-equation:
 k
 ( k )



( U j k ) 
(  t )
 Pk    Pkb
t
x j
x j
 k x j
[
]
(3-5)
[
]
(3-6)
 -equation:
 (  )


 


( U j  ) 
(  t )
 (C 1 Pk  C 2   C 1 Pb )
t
x j
x j
  x j
k
Here C 1 , C 2 ,  k and   are constants. Pkb and P b represent the influence of
the buoyancy forces. Pk is the turbulence production due to viscous forces.
The k   model requires the complex non-linear damping functions. Therefore, the
performance of the near wall treatment for low-Reynolds number computations is
51
unsatisfactory. In order to modify this disadvantage, Wilcox [57] developed the
k   model which assumes that the turbulence viscosity is linked to the turbulence
kinetic energy ( k ) and turbulent frequency (  ). The relationship is shown below:
t  
k

(3-7)
Similar to the k   model, the k   model solves two transport equations for
turbulent kinetic energy and turbulent frequency.
k-equation:
 k
 ( k )



( U j k ) 
(  t )
 Pk   ' k  Pkb
t
x j
x j
 k x j
[
]
(3-8)
 -equation:
 
 (  )




( U j  ) 
(  t )
  Pk   2  Pb
t
x j
x j
  x j
k
[
]
(3-9)
In these equations, the model constants are shown in Table 3.1.


'
k

5/9
0.075
0.09
2
2
Table 3-1 The Wilcox k   model constants
The main disadvantage of the Wilcox k   model is it has strong sensitivity to
free-stream conditions. For example, the different value of  at the inlet can lead to
great variation in the results. In order to solve this problem, a modified k   model
was developed by Menter [58]. The new model blends the k   model near the
wall region and the k   model in the outer region. At the same time, the shear
stress transport (SST) formulation combines two parts of the model and, hence, the
new model is called the SST k   model. The SST k   model gives highly
accurate predictions of the onset and the amount of flow separation under adverse
pressure gradient. The turbulence viscosity in this model is modified by:
52
t  
 1k
max( 1 , SF2 )
(3-10)
The two transport equations are transformed to:
k-equation:
 k
 ( k )



( U j k ) 
(  t )
 Pk   ' k  Pkb
t
x j
x j
 k 3 x j
[
]
(3-11)
 -equation:
 (  )


( U j  ) 
t
x j
 

1 k 

(  t )
 (1  F1 )2 
  3 Pk   3  2  Pb
x j
  3 x j
  2 x j x j
k
[
]
(3-12)
Here F1 and F2 are blending functions. F1 is a function of the wall distance, which
is equal to one near the surface and zero outside the boundary layer. F2 restricts the
limiter to the wall boundary. These blending functions are critical to the SST k  
model and their formulations are based on the distance to the nearest wall and on the
flow variables. In equation (3-10), S is an invariant measure of the strain rate.
In short, the SST k   model is more suitable for high accuracy boundary layer
simulations. If no other description is given, the SST k   model is adopted for all
computations in this thesis.
3.2. Heat transfer
Heat transfer models are used to compute the temperature throughout the flow. The
effects of conduction, convection, turbulent mixing and viscous work are considered
in the heat transfer model. In this thesis, the total energy model in ANSYS-CFX is
adopted for all computations. This model includes the transport of enthalpy and
53
kinetic energy effects. Therefore, the total energy model has better performance than
other heat transfer models when kinetic energy effect is not neglected. The equations
for this heat transfer model also come from the help files from ANSYS-CFX Version
13.0. The total energy equation is shown below:
 ( htot ) p

   ( Uhtot )    ( T )    (U   )  U  S M  S E
t
t
(3-13)
Here S E is the energy source and htot is the total enthalpy, which linked to the
static enthalpy h(T , p) by:
1
htot  h  U 2
2
(3-14)
The term   (U   ) represents the work due to viscous stresses and is called the
viscous work term. The term U  S M represents the work due to external momentum
sources and is neglected.
The heat flux at the wall can be modelled using the thermal law-of-the-wall function
of Kader [59]. The wall heat flux is calculated using the relationship shown below:
qw 
c p u *
T
(Tw  T f )
(3-15)
Here Tw is the temperature at the wall, T f is the near-wall fluid temperature and
c p is the fluid heat capacity. According to equation 3-15, if the wall temperature is
given as boundary condition, then the wall heat flux can be computed. The
non-dimensional temperature ( T  ) is modelled by blending the viscous sub-layer and
logarithmic law of the wall.
T   Pr y *e (  )  [2.12 ln( y * )  (3.85 Pr1/ 3  1.3) 2  2.12 ln(Pr)]e ( 1/  )
(3-16)
54
Here Pr is the fluid Prandtl number and  is given by:

0.01(Pr y * ) 4
1  5 Pr 3 y *
(3-17)
The Nusselt number ( Nu ) is the dimensionless heat transfer and the general definition
is shown below. At a boundary within a fluid, this number represents the ratio of
convective to conductive heat transfer across the boundary. The specific definition for
Nusselt number in rotor-stator systems is discussed in the literatures. In the next
chapter, two definitions are given and compared.
Nu 
hr
k
(3-18)
3.3. Other computational settings and parameters
For all computations in this thesis, the ideal gas is used for fluid properties and
consequently density is computed using the ideal gas law. A high resolution setting is
applied for the advection scheme and an average ambient (atmospheric) pressure
condition is applied at the outlet boundary. In order to compute the sealing
effectiveness, the concentration is introduced into computations as an additional
variable. This additional variable (  ) is solved by the transport equation in
ANSYS-CFX Version 13.0:

 (  )
   ( U )    (( D  t ) )  S 
t
Sct
(3-19)
Here, D , the kinematic diffusivity, is 1.6  10 5 m 2 / s for this additional variable
(concentration).
The definition of concentration effectiveness  c is used:
55
c 
c  ca
co  c a
(3-20)
Here the subscripts a and o refer to the air in the annulus and sealing flow at inlet
to the system respectively.
In the computations, three computational parameters are used to present the sealing

flow. The first parameter is the non-dimensional sealing flow rate C w ,o (= mo / b ).
The non-dimensional sealing parameter  o ( C w ,o / 2Gc Re  ) is the second
parameter. These two parameters are mainly used for the computation of sealing
effectiveness. The last parameter is the turbulent flow parameter: T ( C w,o Re 
0.8
),
which governs the fluid structure and heat transfer in the wheel-space.
3.4. 3D Computations for the ‘thin seal’ model
Early in this investigation 3D computations were carried out as a preliminary study
for ingress problem. The 3D ‘thin seal’ model used here is a version of the model
developed and tested by Owen et al. [49, 56]. A schematic diagram and computational
mesh of the 3D model, illustrated in Figure 3-1, shows a rotor-stator wheel-space with
an outer radius b = 0.195m, an axial-clearance rim seal and the generic vane used in
the Bath experimental rig. The ‘thin seal’ means the radial dimension of the seal is
made as thin as permitted by meshing consideration. This ‘thin seal’ approximation
can help prevent the formation of a vortex inside the seal clearance, which would
inhibit the ingested flow into the wheel-space. The 3D model is an 11.25° sector
model with approximately 1.7 million cells, incorporating one vane pitch. The outer
annulus represents the mainstream gas path through the turbine stage. The system has
two inlets: the sealing air inlet at the inner radius of the wheel-space and the external
mainstream inlet upstream of the vane.
The model has been run at a rotational Reynolds number Re = 7.8  10 5 and at
56
three non-dimensional sealing flow rates Cw, o . The detailed computational
parameters are shown in Table 3-2. In addition to the momentum and energy
equations, a further transport equation was solved for conservation of a
non-interacting scalar, which allowed a tracer to be introduced at the mainstream inlet
in order to calculate the amount of ingress and hence sealing effectiveness.
(a)
(b)
Figure 3-1 (a) Schematic diagram of 3D thin-seal model (b) Computational mesh [49]
Re 
Re w
Gc
7.8  10 5
4.3  10 5
0.01


mo / ma
C w ,o
o
2%
2.8  10 3
0.061
4%
5.6  10 3
0.122
12%
16.8  10 3
0.366
Table 3-2 Computational parameters for 3D computations
57
The pressure difference in the annulus is the principal driving mechanism for
externally-induced ingress. The pressure coefficients ( C p ) in the annulus is computed
at two locations: on the stator hub, half way between the vane trailing edge and the
stator-side of the seal (location A); and on the annulus wall radially outward of the
axial centre of the seal clearance (Location B). These two locations are illustrated in
Fig 3-1 (a). The definition of C p is shown here:
_
p p
Cp 
1 / 2  2 b 2
(3-21)
_
Here p is the average static pressure along one vane pitch. Figure 3-2 show the
computed circumferential distribution of C p at two locations for three different
values of  o . The figures display that the maximum value and the magnitude of the
variation form peak to trough are reduced by increasing  o , the sealing flow rate.
The magnitude of the variation at Location B is smaller than that at Location A.
However, the circumferential locations of the maximum and minimum values are
almost the same at Location A and B. These results show that the two locations give a
qualitatively similar pressure variation contributing to ingestion. The sealing flow can
decrease the magnitude of the pressure variation and consequently reduce the ingress.
58
(a) Location A
(b) Location B
Figure 3-2 Computed circumferential distributions of C p
Figure 3-3 shows the streamlines with effectiveness in the r   plane at z / s  0.5
(axial centre plane of the seal clearance). When  o is small (0.061), the annulus
flow is seen to enter the wheel-space through the seal clearance. Due to the mixing
between the ingested flow and the sealing flow, the effectiveness in that ingested
region is around 0.25. Increasing the sealing flow to  o =0.122, the wheel-space is
almost sealed.
59
 o =0.061
 o =0.122
Figure 3-3 Streamlines with effectiveness in the r   plane at z / s  0.5
The computed variation of effectiveness in the wheel-space ( r / b  0.958 ) with  o
is shown in Figure 3-4. In the figure, the theoretical curve [51] was fitted to the
experimental data using the statistical technique of Zhou et al. [53]. The figure shows
that although the computed effectiveness increases as  o increases, the computed
values over-predict the experimental data. This result indicates the 3D ‘thin seal’
60
model would under-predict the ingress level. Some unsteady flow behaviours maybe
contribute to this under-predict.
Figure 3-4 Variation of computed effectiveness with  o
3.5. Chapter summary
In this chapter, a brief introduction to the turbulence model and methods of heat
transfer calculation in ANSYS-CFX is given. Computational results from 3D steady
computations are presented using a “thin seal” model. This model provided a
qualitative description of ingress but under-predicted the levels. Moreover, this 3D
thin-seal model was computational expensive with about 72 hours for each
computation (using a single 2.8GHz processor). A simpler, more rapid model called
“prescribed ingestion” will be presented in this thesis. Rotor-stator system models
without ingress are studied in Chapter 4. Subsequently, Chapter 5 and 6 give detailed
information from the prescribed ingestion model.
61
4. Axisymmetric rotor-stator models
The axisymmetric rotor-stator model represents the wheel-space between the rotor
and stator discs. In this chapter, the computational results from 2D rotor-stator models
with no ingress will be compared with the published experimental data in Chen et al.
[8]. For fluid dynamics, the velocity profiles in the wheel-space are computed and the
effects of boundary conditions are presented. For heat transfer, the Nusselt number on
the rotor is calculated, and the influence of thermal boundary conditions and the
turbulence model are investigated. Results for two different configurations are also
compared in order to study the effect of wheel-space geometry on the fluid dynamics
and heat transfer. Generally, the computational results show good agreement with
experimental data, validating the axisymmetric CFX rotor-stator model for prediction
of the fluid dynamic and heat transfer in the wheel-space.
Figure 4-1 The Bath Rig Model
The geometries for the axisymmetric rotor-stator wheel-space models used in this
chapter are shown in Figures 4-1 and 4-2. The first one, Figure 4-1, is called the Bath
Rig Model, based on the experimental test rig used for ingress experiments at the
62
University of Bath. This model has a radial inlet for supposed (sealing) flow and
sloping surfaces near the inlet at a  r / b  0.61 . The geometry of the second model,
Figure 4-2, is identical to that of the experimental rotor-stator rig used by Chen et al.
[8]. Hence, this model is called the Chen Rig Model. An axial sealing flow inlet is
located at the axis of rotation. The Bath Rig Model contains around 16000 mesh cells
and the Chen Rig Model around 77000 cells. All computations in this chapter are
carried out at Re  1.25  106 for four different values of sealing flow rate that are
the same as those in Chen et al. [8].
Figure 4-2 The Chen Rig Model
4.1. Fluid dynamics for the axisymmetric rotor-stator model
To understand the fluid dynamics in the wheel-space, velocity profiles are presented
for the Bath Rig Model and Chen Rig Model. Figure 4-3 shows computed velocity
63
distributions for both the Chen Rig and the Bath Rig Models compared with the
experimental data of Chen et al. [8] for T = 0.081 (no results for the Bath Rig Model
are shown at x  0.6 as this is inward of the location of the inlet for the Bath testing
rig geometry). The measured distributions of non-dimensional radial and
circumferential velocities reported by Chen et al. [8] at the four radial locations,
shown in Figure 4-2 0.6≤ x  r / b ≤0.85, are also presented. The abscissa in the figure
represents the non-dimensional axial location, where the stator is at z / s  0 and
z / s  1 is the rotor wall.
Generally, both sets computed results show reasonably good agreement with the
experimental data and with each other, even though the geometry of the two
wheel-spaces is different. The results for radial velocity show the typical rotor-stator
flow behaviour, with flow radially outward on the rotor ( z / s  1 ), radially inward on
the stator ( z / s  0 ) and almost no radial flow in the middle of wheel-space. For
radial velocity distribution at x  0.7 , the computed result from Chen Rig Model has
more similarity with the experimental data than Bath Rig Model. This illustrates that
the flow at low radius in the Bath Rig Model is influenced by the details of the
wheel-space geometry near the inlet. The difference between two models reduces with
increasing non-dimensional radius x . At low radius ( x  0.6 ), the computed
velocities tend to underestimate the inflow on the stator; consequently, the outflow on
the rotor is overestimated. The difference also reduces with increasing x . These
results illustrate that the flow in the source region is strongly influenced by inlet
conditions. For the non-dimensional circumferential velocity (swirl ratio), there is
very little effect of geometry and both models give good agreement with the
experimental data. There is a core of nearly constant swirl ratio fluid between the
separate boundary layer on the rotor and stator at each radial location and the core
swirl ratio increases as x increases.
64
Figure 4-3 Computed velocity profiles from Chen and Bath Rig Model compared with measured
data, T  0.081
65
__
The computations in Figure 4-3 use a zero-average inlet swirl ratio (  in  0 ) and an
adiabatic rotor wall as boundary conditions. Two further computations were carried
out in order to investigate the influence of boundary conditions on the velocity
profiles for the Bath Rig Model. The first computation uses a non-zero average inlet
__
swirl ratio (  in  0.25 from the literature [56]) and an adiabatic rotor wall. In the
second computation, as the ideal gas law is used to compute density, a fixed rotor
temperature equal to 355K ( Trotor  355K ) was used to study the influence of thermal
condition on the fluid dynamics. A zero-average inlet swirl ratio was also applied in
this computation.
The computed distributions for the radial and circumferential (tangential) components
of velocity obtained for Cw,o  6100 at the three different non-dimensional radial
locations ( x =0.7, 0.8 and 0.85) are shown in Figure 4-4. The experimental data of
Chen et al. [8] are also included. For radial velocity, the differences between the
computed and measured values mainly appear at low radius ( x =0.7), which illustrates
that the flow at low radius is influenced by the swirl ratio at inlet. Other than in the
inlet region, there is not much difference between all three computed results,
especially at high radial locations. For circumferential velocity, the computation with
non-zero inlet swirl ratio gives a higher value for the core rotation than in the
experiment (in the experiment of Chen et al. [8], there was no swirl at inlet), and the
two zero-swirl cases give a closer result, though slightly under predicting the
experimental data. This shows that the inlet swirl increases the swirl in the
wheel-space. The thermal condition on the rotor surface has negligible effect on either
radial or circumferential velocity distributions.
66
Figure 4-4 Computed and measured velocity profiles for the Bath Rig Model, T  0.081
67
For consistency with the experiment and for convenience for heat transfer
__
computations, the third boundary condition (  in  0 , Trotor  355K ) is used
subsequently, and the effect of sealing flow rate on velocity distributions is
investigated. The turbulent flow parameter, T = Cw, o Re0.8 , is used to represent the
sealing flow rate. Four sealing flow rates are selected with T varying from 0.034 to
0.128. Figure 4-5 shows the computed radial and circumferential velocity
distributions at x =0.8 for the four values of T . The magnitude of the outward
radial velocity near the rotor increases and the inward radial velocity near the stator
decreases as T
increases. For non-dimensional circumferential velocity, the
magnitude of V / r in the core falls with increasing T , illustrating that the higher
flow rates of zero-swirl sealing flow reduces the core rotation.
Figure 4-5 Computed velocity profiles with different T for the Bath Rig Model
68
The computed secondary flow streamlines for the two highest T cases, shown in
Figure 4-6, further illustrate the typical rotor-stator flow behaviour as discussed for
Figure 4-4 and 4-5. The streamlines contours illustrate that a secondary flow
recirculation occurs at low radius near the rotor, due to the sloping geometry for the
Bath Rig Model in that area, which further explains the differences between computed
and measured radial velocity distribution at low radius in Figure 4-4. This
recirculation region becomes larger with increasing T .
T  0.081
T  0.128
Figure 4-6 The streamlines in whole cavity for two high sealing flow rate cases
4.2. Heat transfer for the axisymmetric rotor-stator model
To investigate the heat transfer on the rotor, the Nusselt number, the ratio of
convective to conductive heat transfer normal to the boundary, is calculated. Owen
and Rogers [10] showed that
Nu
is proportional to Re0.8 for turbulent
boundary-layer flow in rotor-stator systems; consequently the parameter Nu Re0.8 is
independent of Re . Lewis et al. [17] also mention that Nu Re0.8 is a correlating
parameter in rotor-stator systems. Therefore, this parameter is adopted in this thesis.
69
The definition of Nusselt number in Lewis et al. was given by:
Tw,ad
V2,
2
2
V , 2
r
 To ,1 
R
(1 
) (eq.4-1)
2c p
2c p
r
Nu 
qr
(eq.4-2)
k (Tw  Tw ,ad )
Where V , is the circumferential velocity in the core, c p is the specific heat at
constant pressure and k is the thermal conductivity of air. Chen et al. [8] used a
different definition for Nu , as shown below.
2
Tref
r
 T1  R
2c p
Nu 
2
qr
k (Tw  Tref )
(4-3)
(4-4)
Figure 4-7 Comparison between definitions for Nu , T  0.081
70
V ,
0.4
r
0.3
0.2
0.1
0
0.6
0.7
0.8
0.9
1
x
Figure 4-8 The swirl ratio at middle plane between the rotor and the stator, T  0.081
The main difference between the definitions is that Lewis et al. [17] introduces the
effect of the core swirl ratio into the definition. Figure 4-7 shows the comparison
between results using the two definitions of Nu for the radial variation of Nu Re0.8
for the Bath Rig Model when the turbulent flow parameter is equal to 0.081. The two
definitions give similar results and there is good agreement with the measurements of
Chen et al.. At high radius, the definition used by Chen et al. gives a slightly higher
value than that used by Lewis et al. The swirl ratio ( V , / r ) at the mid-plane
between the rotor and the stator ( z / s  0.5 ) is the determining factor for the
difference. The computed variation of swirl ratio is shown in Figure 4-8. At low
radius, the difference between the two definitions of Nu is small due to the
relatively small value of V , / r . As radius increases, V , / r increases and the
difference is visible in Figure 4-7. The definition used by Chen et al. will be adopted
here for consistency with the Chen et al. experimental data.
The effect of T on the radial distribution of Nu Re0.8 is shown in Figure 4-9. The
measurements made by Chen et al. for x >0.6 in their rig are also shown. Both the
experimental data and the computed results indicate that Nu Re0.8 increases as T
increases. The agreement between computations and measurements is poor at low
values of T . This is mainly due to low levels of computed turbulence in the
71
computations
using
SST
k 
turbulence
model
at
these
conditions
( Re  1.25  106 ). However, the agreement at high T is satisfactory. Some
simulations are carried out for trying to improve the agreement at low T condition
in this and next sections.
0.8
Figure 4-9 Radial distribution of Nu Re
for different T
In the above computations, the rotor surface is set to a uniform constant temperature
(355K), which is not the same as in the experiments. As shown in Figure 4-10, a part
of measured temperatures from Chen et al. [8] were fitted using a 4th degree
polynomial for the smallest and largest T cases, and the effect of the using these
fitted temperature conditions was investigated. Figure 4-11 illustrates the results for
both cases. The results show almost no difference at high T . There is a slight
improvement at low T , but the agreement with experiment remains poor. It is
concluded from Figure 4-11 that the temperature at the rotor surface weakly affects
the level of Nu Re0.8 , but that there is no significant effect on the distribution.
72
Figure 4-10 Radial distribution of temperature on the rotor surface for the Bath Rig Model
73
Figure 4-11 The effect of thermal condition at rotor surface on the radial distribution of
Nu Re0.8
74
Figure 4-12 Radial distribution of temperature on the rotor surface for the Chen Rig Model
The effect of geometry on the heat transfer in the system was studied by compare
previous results with the Chen Rig Model for T = 0.034 and 0.081. The fit to the
measured temperature distribution was applied for consistency with the experimental
data. The wheel-space for the Chen Rig Model is large and hence the more measured
temperature points are available and have been used. Therefore, a different function,
sum of sine, is applied, as shown in Figure 4-12.
75
Figure 4-13 The effect of geometry on the radial distribution of Nu Re0.8
Computed radial distributions of Nu Re0.8 for the Chen and Bath Rig Models are
shown in Figure 4-13. In general, the effect of geometry is small, especially for the
high T case. At high T , the comparison is better between the Chen Rig Model
result and the experimental data. The computed results for the Bath Rig Model show
an effect at the inlet region. For lower T case, there still is poor prediction of the
76
measurements at larger values of x  r / b for the Chen Rig Model.
0.8
Figure 4-14 The effect of turbulence model on the radial distribution of Nu Re
As discussed previously, these poor results for low T are likely to be due mainly to
the turbulence model. Further computations using the Chen Rig Model with different
turbulence models are shown in Figure 4-14. In these computations, results using the
k   turbulence model are compared with those of the SST k   turbulence
77
model. The k   model produces much higher values of Nu Re0.8 , over predicting
the experimental data at both low and high T due to the wall function near-wall
treatment. These results suggest that these two turbulence models cannot predict
turbulence accurately for low value of T , though the SST k   turbulence model
shows relatively better performance due to the low Reynolds number resolved
boundary layer near-wall treatment. The low Reynolds number treatment needs very
fine meshes ( y  ~1). The y  values for the models used in this thesis are typically 1
to 1.5 for the SST k   turbulence model while the value used by Chen et al. is less
than 0.5. Therefore the computed results for low T shown here are worse than that
of Chen et al., shown in Figure 2-5. Models with very fine mesh increases
computation time, which may be not suitable for engine design.
4.3. Chapter summary
The geometry difference between the Bath and Chen Rig Model influences the axial
distribution of radial velocity at low radius. No effect of geometry is found on the
distribution of circumferential velocity. For heat transfer, the thermal condition on the
rotor and the geometry has little influence on the radial distribution of Nusselt number.
Furthermore, the SST k   turbulence model provides reasonable results for the
heat transfer at high T . However, the computational results are not good at low T ,
which is mainly due to low levels of computed turbulence in the selected turbulence
model and moderately fine mesh. Most results in this chapter show that the simple 2D
axial-symmetry rotor-stator model is validated and can quantitatively predict most
fluid dynamic and heat transfer features in the wheel-space. At the same time, the size
of model reduces markedly compared with 3D models and, consequently, the
computing time reduces to 12 hours for each computation.
78
5. Prescribed ingestion model: Axial-clearance seal
This chapter will present the prescribed ingestion model with the simplest seal
geometry, the axial-clearance seal. The prescribed ingestion model geometry is based
on the experimental rig at the University of Bath (Figure 5-1 (a)) and is shown in
Figure 5-1 (b). The computational model includes the inner seal at low radius and the
outer wheel-space from the experimental rig. Sealing flow enters the outer
wheel-space through the inner seal. An ingress inlet and an egress outlet are located at
the outer shroud of wheel-space as shown. This model contains around 45000 mesh
cells and the SST k   turbulence model is used. In this chapter, different boundary
assumptions for the ingress flow will be discussed. Figure 5-1 (b) shows the ingress
inlet at the centre of the outer shroud with the outflow boundary is adjacent to the
rotor. This arrangement was found to give the best performance. Detailed results of
the computed fluid dynamics in the wheel-space are presented using this arrangement,
and the computed sealing effectiveness compared with experimental results. Heat
transfer computations have also been carried out using this prescribed ingestion model
for the axial-clearance seal.
(a)
79
(b)
Figure 5-1 (a) The experimental rig in University of Bath [51] (b) The prescribed ingestion model
with axial-clearance seal and mesh grid
5.1. Mass-weighted average assumption for ingestion
Figure 5-2 shows measurement for a 2-mm ( s c ) axial-clearance seal with
externally-induced (EI) ingress from experiments were carried out at the University of
Bath. The experiments [55] reveal that the sealing effectiveness on the stator is
virtually invariant with radius. The data in Figure 5-2 is based on the measurements
collected at r / b =0.958. As the non-dimensional sealing flow is increased from 0 to
 min, EI , the sealing effectiveness increases from 0 to 1. Both sealing effectiveness (  )
and non-dimensional flow parameter for ingress (  i, EI ) are displayed in this figure.
The symbols denote experimental measurements and the lines are theoretical curves
fitted to the experimental points using the statistical technique of Zhou et al. [53].
80
These experimental data are for the design condition. For consistency, most of the
computations for the prescribed ingested model are also based on experiments at the
design condition and are carried out for one of two rotational Reynolds numbers:
Re  = 5.32  10 5 and 8.17  10 5 .
According to Figure 5-1 (b), the main requirement for the computational model is the
ingested flow rate and its associated (inlet) boundary conditions. The value of the
ingested flow rate can be deduced from the experimental data shown in Figure 5-2.
For EI ingress, the flow ingested from the mainstream flow in the annulus would enter
the wheel-space through the rim seal with a relatively high value of swirl ratio. The
prescribed ingestion model boundary condition assumes some mixing of the ingested
flow prior to entering the wheel-space. Two possible assumptions are discussed here.
The first is a mass-weighted average assumption for which the swirl ratio of the
ingested flow at the ingress inlet boundary is given by:
Figure 5-2 Experimental data for axial-clearance seal with EI ingress [51]

Mass-weighted average:  i ,mass 

mi  ann  mo  o


(5-1)
mi  mo
81
 ann is the swirl ratio in the annulus and  o is the swirl ratio of the sealing flow at
the sealing flow inlet. An additional assumption is a momentum-weighted average.

Momentum-weighted average:  i,mom 

mi Vr ,i  ann  mo Vr ,o  o

(5-2)

mi Vr ,i  mo Vr ,o
Here Vr ,i is the radial velocity of is ingested flow at ingress inlet and Vr , o is the
radial velocity of sealing flow at sealing flow inlet. These two velocities are
calculated as:

V r ,i

mi
mo

, Vr ,o 
2bsi
2ro s o
(5-3)
Where s i and s o are the axial clearance of ingress inlet and sealing flow inlet
respectively. ro is the radius of the axial clearance at the sealing flow inlet.
The value used for  ann is obtained from the 3D computations with annulus
described in Chapter 3. As  o is small in comparison with  ann ,  o was assumed
initially to be zero. After comparisons for two weighting assumptions, the effect of the
value of  o will be discussed.
Re 
8.17  10 5
T


mo
mi
 i,mass
 i,mom
0.063
0.01176
0.00971
0.892
0.740
0.114
0.02128
0.00669
0.470
0.158
0.242
0.04516
0.00165
0.069
0.002
Table 5-1 Computational parameters for Mass-weighted and Momentum-weighted average
assumptions
Three sealing flow rates were chosen to compare the mass-weighted and
momentum-weighted averaging assumptions.
The parameters used for the
82
computations are shown in Table 5-1. Note that the turbulent flow parameter T is
directly linked to  o : T  2Gc  o Re 
0.2
.
Figure 5-3 Swirl ratio distribution for axial-clearance seal with Mass-weighted and
Momentum-weighted average assumptions, z / s =0.25 (symbols denote the experimental data
[60])
Figure 5-3 shows computed swirl ratio distributions at z / s =0.25 using the
mass-weighted and momentum-weighted average assumptions.
Experimental
measurements [60] also are shown in the figure. The figure shows that the swirl ratio
in the wheel-space reduces as the sealing flow rate increases. In general, the
computations have qualitatively captured the trends measured during the experiments.
At both high and low sealing flow ( T  0.063 and T  0.242 ), the computations
agree well at all radii. Moreover, the mass-weighted average assumption gives results
closer to the experimental data than the momentum-weighting assumption.
At T  0.114 , the momentum-weighted assumption gives  i =0.158, which is
much smaller than the experimental data near r / b =1. The secondary flow
83
streamlines for this case are shown in Figure 5-4. Unusual circulations occur near the
rim seal region for the Momentum-weighted assumption. These unwanted circulations
give rise to a different trend of swirl ratio to experiment at high radius. In comparison,
the mass-weighted assumption gives reasonable  i when compared with the
measurement and a reasonable flow structure.
Figure 5-4 Secondary flow streamlines for Momentum-weighted and Mass-weighted average at
T  0.114
At high sealing flow rate ( T  0.242 ), the difference between the mass- or
momentum-weighted average assumptions is very small and can be ignored. When
the sealing flow is high and consequently the ingested flow is very small, the
influence of ingress on the swirl ratio in wheel-space becomes negligible.
In short, according to the figure, the mass-weighted average assumption gives good
agreement with experiment and provides a more realistic estimate for the inlet swirl
ratio for the ingested flow than the momentum-weighted average assumption.
Therefore, the mass-weighted average assumption will be adopted in the prescribed
ingestion model in this thesis.
84
The effect of value of  o on the swirl ratio distribution in wheel-space is shown in
Figure 5-5. The value of  o was obtained by computations involving the inner
wheel-space inboard of the inner seal in the experimental rig, as shown in Figure 5-1
(a).
Figure 5-5 illustrates that there is little effect of  o on the swirl ratio distribution in
the wheel-space. Slight differences exit at low radius for the computations at each of
the three sealing flow rates. Note that  o is small in comparison with  ann and has
a minimum influence on the final value of  i according to the definition of
mass-weighted average assumption. For convenience, the remaining computations for
the prescribed ingestion model adopt  o equal to zero, which means that the sealing
flow has no swirl at inlet.
The mass-weighted average assumption is applied not only to the swirl ratio of the
ingested flow, but also to the mixed concentration of ingested flow.
The
mass-weighted average concentration is similar to that for the swirl ratio and given
by:

ci,mass 

mi ca  mo co


(5-4)
mi  mo
Here c a and
co are the concentration in the annulus and in the sealing flow at
inlet respectively. The solution for the concentration as a passive scalar allows
comparisons to be made with measurements of CO2 tracer concentration made in
experiments. For the computations, c a  0 and co  1 .
85
Figure 5-5 The effect of  o on swirl ratio distribution, z / s =0.25 (symbols denote the
experimental data [60])
86
5.2. The effect of layout of ingress inlet and egress outlet
Figure 5-6 Different layouts of ingress inlet and egress outlet
In the preliminary studies of the prescribed ingestion model, the ingress inlet and
egress outlet were both located about the mid-plane of the model on the outer shroud,
in order to simulate this real location at the rim seal. These computations, however,
resulted in the ingested flow leaving through the egress outlet directly (short-circuit
flow). Hence, the inlet and outlet region were separated in order to study the influence
of ingress on the flow in the wheel-space. Three different possible arrangements of
the inlet and outlet are discussed here referred to as Layout A, Layout B and Layout C
as illustrated in Figure 5-6. For all layouts, at the top wheel-space, half of the outer
shroud is treated as stationary ( z / s =0~0.5) and half is treated as rotating
( z / s =0.5~1.0).
Figure 5-7 shows the computed swirl ratio distribution at z / s =0.25 for the three
layouts for Re  = 8.17  10 5 . In general, there is little difference between the results
for these three layouts, except at high radius. At T  0.063 (Figure 5-7 (a)), the
ingested inlet for Layout B ( z / s =1/3) is closest to the location z/s=0.25, where
measurement are available. Layout B results in an over-prediction of the measured
swirl near to r/b=1. In this diagram, the data with no ingestion from Chen et al. [8] at
87
a similar T ( 0.081) are included. Both computations and experiments give
reasonable swirl ratio level compared with Chen et al. data although the value of T
is slightly different. The results from the Bath rig are higher than the Chen et al. data
due to the lower T used. For T  0.114 (Figure 5-7 (b)) both the ingested flow
rate and its prescribed swirl level reduce, so that the over-prediction of measured swirl
for Layout B is less severe.
(a)
88
(b)
(c)
Figure 5-7 The effect of layout on swirl ratio distribution, z / s =0.25 (closed symbols denote the
experimental data [60] and open symbols denote the experimental data [8])
89
The greatest difference between results for the three layouts occurs at the highest T .
In this case, the ingested flow rate and its associated swirl level is small and has little
influence on the computed swirl distribution. The different location of the egress
outlet becomes the main factor causing the differences between the results. Figure 5-8
shows the swirl contours for the three layouts at T  0.242 . For Layout A, the outlet
is on the rotor side and the rotating shroud separates the inlet and outlet. According to
the contours, the rotating shroud introduces high swirl and this consequently
influences the swirl ratio near the stator. In the contours for Layout C, the high swirl
produced by rotating shroud does not influence the ingested flow due to the outlet at
the mid-plane. This layout, therefore, gives the lowest swirl. For Layout B, there still
is a part of rotating shroud between the inlet and outlet and this gives rise to an
intermediate level of swirl. Layout A gives the most accurate swirl ratio for most
cases compared with the measurements, although slightly over-predicting the swirl
ratio at the very high T case. Hence, Layout A was chosen for the prescribed
ingestion model.
Figure 5-8 The swirl contours for three layouts at T  0.242
90
5.3. Fluid dynamics in the wheel-space
In this section, the fluid dynamics in the wheel-space for the prescribed ingestion
model is discussed. Figure 5-9 shows the comparison between swirl distributions for
the prescribed ingestion model and the Bath rig rotor-stator model (with no ingress)
for three different values of T . The open symbols represent the  i,mass at the
ingress inlet for the prescribed ingestion model. The figure illustrates that the zero
swirl sealing flow reduces the swirl ratio in wheel-space. At each value of T , the
prescribed ingestion model gives rise to higher swirl in the wheel-space, due to the
swirl ratio associated with the ingested flow. The influence of ingress on swirl ratio at
high values of non-dimensional radius ( r / b ) decreases as T increases as the
amount of ingestion also reduces.
Figure 5-9 Comparison of swirl distributions for the prescribed ingestion model and the Bath rig
rotor-stator model with no ingestion, z / s =0.25
91
Figure 5-10 shows the comparison of swirl ratio for the prescribed ingestion model
and Chen et al. [8] at r / b =0.7. According to the value of T , the Chen et al. data
should be between the two lines predicted by the prescribed ingestion model.
However, both results from the prescribed ingestion model are higher than the result
from Chen et al. The narrow gap of the prescribed ingestion model as shown in Figure
5-1 (b) results in a high swirl ratio at the inlet of the outer wheel-space, and
consequently leads to the feature shown in this figure.
Figure 5-11 shows the swirl distribution at different Re  with similar values of T
for the prescribed ingestion model. The two results are very close although the
rotational speed is different. This illustrates that Re  has no significant effect on the
distribution of swirl ratio and that T is the dominant factor governing this
distribution.
Figure 5-10 Comparison of swirl ratio for the prescribed ingestion model and Chen et al. [8] at
r / b =0.7
92
Figure 5-11 Comparison of swirl distribution for different rotational speed for the prescribed
ingestion model at similar T
Figure 5-12 Secondary flow streamlines and swirl contours for the prescribed ingestion model
with axial-clearance seal
93
Figure 5-12 shows secondary flow streamlines and swirl contours in the wheel-space
for the prescribed ingestion model. According to the streamlines, at low radius the
sealing flow enters towards the rotor. At the top of the wheel-space some of ingested
flow migrates directly to the outlet and the rest is drawn towards the stator. A core of
rotating fluid exists between the stator and rotor. The angled rotor surface at low
radius causes a secondary flow circulation and this increases in size as the sealing
flow rate ( T ) increases.
Detailed velocity profiles for the T  0.114 case are shown in Figure 5-13.
Tangential velocity is almost invariant with z in the rotating core at the three radial
locations shown, and the value of the swirl ratio increases with radius. The peak value
of radial velocity near the rotor decreases with radius and the radial velocity is close
to zero between stator and rotor boundary layers. These features illustrate that the
ingestion has only a slight effect on the rotor-stator flow structure in the wheel-space.
94
(a)
(b)
Figure 5-13 Velocity distributions for the prescribed ingestion model with axial-clearance seal
95
5.4. Distribution of sealing effectiveness in the wheel-space
Figure 5-14 Computed variation of effectiveness with C w ,o for axial-clearance seal
The non-dimensional sealing flow rate ( C w ,o ) and non-dimensional sealing parameter
(  o ) are two common parameters used to represent the sealing flow in computations
and experiments. The variation of computed sealing effectiveness (at the monitor
location on the stator at r/b=0.958 as illustrated in the inset diagram) with C w ,o at
two rotational speeds is shown in Figure 5-14. The sealing effectiveness increases
with increasing C w ,o , as the sealing flow reduces ingestion from the annulus. It is
clear that the gradient of the  c curve with C w ,o is different at the two rotational
speeds. According to the figure, at the same C w ,o , higher effectiveness is obtained at
the lower rotational speed. In other words, a larger C w ,o is required to maintain the
same effectiveness as Re  increases.
96
Figure 5-15 The computed variation of effectiveness with  o for axial-clearance seal compared
with experimental data [51]
The results in Figure 5-14 are re-plotted using the non-dimensional sealing flow
parameter  o in Figure 5-15. In this figure, the closed symbols denote the computed
results, while experimental measurements [51] are shown as open symbols and the
theoretical curve fit for the measured effectiveness is also shown. Both the
experimental and computed results illustrate that the effect of Re  on sealing
effectiveness vanishes when plotted in this figure.  min , the minimum value of  o
required to prevent ingress, is independent of rotational speed. The computed results
have the same qualitative trend as the experimental data (and theoretical fit), however
the effectiveness is over-predicted. The computed value of  min , the minimum flow
rate to prevent ingress, agrees reasonably well with the experimental data.
Figure 5-16 shows the computed radial distribution of effectiveness on the stator.
Experimental data [60] are included for comparison. The open symbols represent the
C i , mass at the ingress inlet. The experimental data suggest that the ingress flow mixes
fully at the rim seal region, so that consequently the concentration (representing
97
effectiveness) of the fluid in the boundary layer on the stator varies little with radius.
The computed results have a similar trend to the experiments, and accord qualitatively
with the results of 3D computations such as those of Rabs et al. [42]. The radial
variation in the computed results is slightly greater than in the experiments, indicating
some further mixing exists in the stator boundary layer for the computations.
Furthermore, as in Figure 5-15, the computations over-predict the measured values of
effectiveness. The migration of some of the flow from the prescribed ingestion inlet
directly to the outlet at the outer radius of wheel-space (as shown in Figure 5-12)
contributes to this over-prediction.
Figure 5-16 Radial distribution of effectiveness on the stator for the axial-clearance seal compared
with experimental data [60]
The computed radial distribution of effectiveness on the rotor is shown in Figure 5-17
and is compared with the measured adiabatic effectiveness for the rotor [61].
Compared with the results for the stator, higher values of sealing effectiveness occur
on the rotor, since the sealing flow provides thermal protection. In general, the
computations qualitatively predict the trends observed in the experimental data.
Furthermore, the computations over-predict the measured effectiveness on the stator
98
and this fluid enters the boundary layer on the rotor by entrainment through the core
region. The computed result also over-predicts the effectiveness for the lower value of
T shown. At the higher value of T , the computed rotor effectiveness agrees well
with the measurements, although for this case both computations and experiments
show that the rotor is well protected from the effect of ingestion.
Figure 5-17 Radial distribution of effectiveness on the rotor for the axial-clearance seal compared
with experimental data [61]
The adiabatic effectiveness is obtained by the heat transfer computations in the next
section. The definition of the adiabatic effectiveness is given by:
 ad 
Tad  Ta
*
Tad  Ta
Here Tad
*
(5-5)
is the value of Tad when there is no ingress and Ta is the temperature of
the air in the annulus ( 14.5 C ). Figure 5-18 compares the radial distribution of  c
and  ad on the rotor at a similar sealing flow rate (  o ). The figure indicates that
both definitions of effectiveness provide almost identical distributions on the rotor at
similar sealing flow rates. However, the computed adiabatic effectiveness still
99
over-predicts the measurement.
Figure 5-18 Comparison of radial distribution of  c and  ad on the rotor (symbols denote the
experimental data [61])
5.5. Heat transfer in the wheel-space
Heat transfer computations also were carried out using the prescribed ingestion model
for the axial-clearance seal. As discussed in the previous chapter, the temperature on
the rotor surface slightly influences the Nusselt number and an accurate surface
temperature distribution is difficult to obtain. Hence, for convenience, the heat
transfer computations apply to a uniform surface temperature on the rotor. The
temperature of the sealing flow is 57.5  C , which is same with the heat transfer
experiments in University of Bath. In order to produce the heat flux on the rotor
surface, a cool uniform surface temperature ( 20  C ) was adopted. At the same time,
an adiabatic stator wall is used in these computations. The air temperature in the
annulus is 14.5 C for the experiments and computations. For the first computations,
this temperature was used as the temperature of ingested flow. However, this
100
arrangement did not provide good agreement with experimental results. It is
demonstrated that not only the swirl ratio but also the temperature is mixed when the
ingested flow enters the wheel-space. Therefore, the mass-weighted average
assumption also is adopted for the temperature:

Ti 

mi Ta  mo To


(5-6)
mi  mo
Here Ta and To are the air temperature in the annulus ( 14.5 C ) and the
temperature of the sealing flow ( 57.5  C ) respectively.
In Chapter 4, two different definitions of Nusselt number were used, based on two
temperatures: Tw, ad or Tref . However, these definitions are deduced for the
rotor-stator system without ingress and they cannot consider the influence of ingress
on temperature in the wheel-space. Using these definitions unreasonable values of
Nu were obtained in the computations. Therefore, the heat transfer computation in
this chapter uses a simpler definition for Nusselt number:
Nu 
qr
k (Ts  Tad )
(5-7)
Here q is the heat flux to the rotor, Ts is the surface temperature and Tad is the
adiabatic surface temperature. Tad is gained by separate computations with an
adiabatic rotor wall at the same fluid conditions (sealing flow rate and ingested flow
rate). Figure 5-19 shows the computed and experimental measurements of adiabatic
surface temperature. The experimental data [61] were obtained by the thermochromic
liquid crystal (TLC) data based on the solution of the 1D Fourier equations for
convective heat transfer. The computed adiabatic surface temperatures result directly
from ANSYS CFX. The adiabatic computations provide reasonable values of Tad
and produce similar trends to the experiments. The computed Tad is marginally
higher than the experimental data.
101
Figure 5-19 The computed Tad compared with experimental data [61]
Figure 5-20 The radial variation of Nu Re 
0.8
compared with experimental data [55]
102
In accordance with previous results for Nusselt number in Chapter 4, Figure 5-20
shows the computed variation of Nu Re 
0.8
in comparison with the experimental
data [55]. The experimental uncertainties are calculated by the method discussed in
the literature [55]. Both the computations and the experimental data show that
Nu Re 
0.8
is almost invariant with the radius on the rotor, except in the region near
the inlet and outlet. The computed results over-predict the experimental data, but
capture qualitatively the main features of the experimental data. The main reason for
the differences is the over-prediction of adiabatic surface temperature in Figure 5-19.
As mentioned in Chapter 3, the radiation heat transfer is not included in the heat
transfer model in the computations. Therefore, the effect of radiation heat transfer
could be one reason of this over-prediction. Figure 5-20 also shows that Nu increases
as T , or sealing flow, increases and as ingested flow decreases. When ingress exists,
the high swirl brought by ingested flow can increase the swirl ratio in the core and
consequently reduce the Nusselt number.
Figure 5-21 The radial variation of non-dimensional core temperature compared with experimental
data [55]
103
The core temperature is an important feature for the heat transfer to the rotor. Figure
5-21 shows the radial variation of non-dimensional core temperature (   ), which is
defined by:
 
T  Tin
To  Tin
(5-8)
Here T is the air temperature at an axial distance of z/s=0.3 from the stator; this
location is considered to be in the fluid core outside the boundary layer. Tin is the
initial temperature of the air in a transient experiment. In the computation, the
temperature of the rotor ( 20  C ) is used as Tin . Figure 5-21 shows that for both the
computations and the experimental data [55], when ingress occurs and the cold
ingested air reduced the core temperature at high radius. The computed core
temperatures are higher than the experimental data. It should be noted that the core
temperatures are also influenced by the heat transfer to the stator. The thermal
conditions on the stator for the computations and the experiments are quite different.
Despite this,   has been reasonably predicted by the computations.
Figure 5-22 The computed radial variation of Nu Re 
0.8
including stator heat transfer
104
Generally, the influence of heat transfer to the stator on the rotor Nusselt number is
thought to be very small [19]. However, in order to study the effect of stator heat
transfer, computations have been conducted with the stator at the same temperature as
the rotor ( 20  C ). Figure 5-22 shows the effect of stator heat transfer on the radial
variation of Nu Re 
0.8
on the rotor. According to the figure, the stator heat transfer
can reduce Nu , but the effect is minor. This is in accordance with 3D results
presented by Javiya et al. [19].
5.6. Chapter summary
In summary, the prescribed ingestion model applied to the axial-clearance seal gives
reasonable results for fluid dynamics, sealing effectiveness and heat transfer in
comparison with the experimental data. The radial variation of effectiveness on the
stator from this 2D model is similar to published 3D simulations [42]. The agreement
between computed and measured heat transfer is fair, and these heat transfer tests
have not previously been studied computationally. The 2D model has the significant
advantage of reduced complexity and computational costs, with each computation
approximately 10 hours. In the next chapter, this prescribed ingestion model is applied
to other seal geometries.
105
6. Prescribed ingestion model: other seal geometries
Following development of the prescribed ingestion model for the axial-clearance seal,
this chapter presents prescribed ingestion model results for three other seal geometries:
a radial-clearance seal, a double axial-clearance seal and a radial-axial-clearance seal.
The experimental geometries and computational models for these three seals are
shown in Figure 6-1. As with the axial-clearance seal, the mass-weighted average
assumption is used for ingress boundary conditions and the position of the ingress
inlet and egress outlet also are as shown in the figure for the three models. The egress
outlet is located at the rotor side of the axial overlap piece for the radial-clearance and
radial-axial-clearance seals. These models contain around 40000 mesh cells. The fluid
dynamics in the wheel-space and sealing effectiveness are studied for each seal and
the seal performance of all geometries is compared. The computations were carried
out at two rotational Reynolds numbers ( Re  ), which are 5.32  10 5 and 8.17  10 5 .
(a)
106
(b)
(c)
Figure 6-1 The experimental rigs [60] and computational models for (a) Radial-clearance seal (b)
Double axial-clearance seal (c) Radial-axial-clearance seal
107
6.1. Radial-clearance seal
The radial-clearance seal (Figure 6-1 (a)) is a generic seal geometry, with an axial
overlap piece on the rotating disc compared with the axial-clearance seal. The
literature [51] shows this seal geometry has better performance than the axial
clearance seal. The egress outlet is positioned at the base of the axial overlap piece at
the rotor surface. The boundary surface of the axial overlap rotates with rotor. The
computational parameters for the radial-clearance seal are shown in Table 6-1. The
value of  i is deduced using the experimental data for the radial-clearance seal [54],
shown in Figure 6-2. The computations at the higher Re  were carried out for
comparison with measured values of swirl ratio. The lower Re  computations were
carried out to compare measured and computed distributions of sealing effectiveness.
Figure 6-2 Experimental data for radial-clearance seal with EI ingress [54]
108
Re 
8.17  10 5
5.32  10 5
C w ,o
o
T
i
966
0.0188
0.018
0.0328
1932
0.0376
0.036
0.0233
3918
0.0763
0.073
0.0075
1030
0.0308
0.027
0.0266
1598
0.0478
0.042
0.0187
2444
0.0731
0.064
0.0085
Table 6-1 Computational parameters for the radial-clearance seal
Figure 6-3 shows the swirl ratio distribution at z / s =0.25 in the wheel-space for the
radial-clearance seal. Closed symbols denote the experimental data [60]. The open
square symbols shown at r / b =1 denote the ingress swirl ratio (  i,mass ) boundary
condition calculated using the mass-weighted average assumption. The computed
swirl is in reasonably good agreement with the experimental data, again showing that
the mass-weighted average assumption provides a reasonable estimate for the swirl
ratio for the ingested flow entering the wheel-space.
Figure 6-3 Swirl ratio distribution for radial-clearance seal, z / s =0.25 (symbols denote the
experimental data [60])
109
Figure 6-4 Swirl ratio distribution for radial-clearance and axial-clearance seal, z / s =0.25
Figure 6-4 shows swirl ratio distributions (at z / s =0.25) for the radial-clearance and
axial-clearance seals at the three values of T , together with computed results for
zero sealing flow ( T  0 ). Experimental results from Chen et al. [8] are shown as
open symbols in this figure. Generally, at the same sealing flow rate ( T ), the swirl
ratio is higher at high radius for the axial-clearance seal than for the radial-clearance
seal, since a greater amount of ingested flow with higher swirl at inlet occurs for the
axial-clearance seal. The difference between the results for the two seals reduces as
sealing flow rate increases and the effects of ingress weaken. For T  0.073 , the
swirl distribution is almost the same for the two seals and is close to the experimental
results of Chen et al. for a similar value of T (=0.081). For the radial-clearance seal,
the edge of the rotating axial overlap ( z / s =0.265) is close to the z / s =0.25 location
and there is a rapid increase in swirl ratio at high radius near r / b =1 for each T . At
low radius, there is little difference between the results for the two seals. Therefore, it
can be concluded that the flow structure in the wheel-space at relatively low radius is
governed mainly by T and the seal geometry only influences the flow in the outer
110
region of wheel-space.
Figure 6-5 Comparison of swirl distribution for different rotational speed for the radial-clearance
seal at similar T
Similar to the axial-clearance seal, Figure 6-5 shows the swirl distribution at different
Re  for broadly similar values of T for the radial-clearance seal. This result
illustrates again that Re  has no significant effect on the distribution of swirl ratio
and that T is the dominant factor for the flow structure in the wheel-space.
The sealing effectiveness is the main measure of the performance for each rim-seal
geometry. In Chapter 5, it was shown proved that the variation of sealing effectiveness
with  o is independent of Re  . Hence, in this chapter, the variation of sealing
effectiveness with  o is investigated for other seal geometries. Figure 6-6 shows the
computed and measured variation of sealing effectiveness with  o for the
radial-clearance seal. Computed results for the axial-clearance seal are also included.
In the figure, the open symbols denote the experimental data for the radial-clearance
seal [54], the closed symbols denote the computed effectiveness (black:
radial-clearance seal, grey: axial-clearance seal) and the line [54] is the orifice model
theoretical curve fitted to the experimental data. For the radial-clearance seal, the
111
computed effectiveness shows better agreement with the experimental data and the
theoretical curve than that for the axial-clearance seal (in Figure 5-15), where some of
the ingested flow migrated directly to the outlet in axial-clearance seal model. For the
radial-clearance seal, all of the ingested flow enters the boundary layer on the stator
due to the location of the outlet in the prescribed ingestion model. Hence, the ingested
flow can fully influence the computed effectiveness in the boundary layer on the
stator and consequently better agreement with the measurements is obtained for the
radial-clearance seal. The computed secondary flow streamlines for both seal
geometries at the same sealing flow rate are show in Figure 6-7. It is clear that almost
no difference exists at low radius and differences only emerge at high radius (near the
seal region). The different flow paths of the ingested fluid are also shown by the
streamlines. At the same sealing flow rate (  o ), the boundary condition setting of the
ingress inlet for the radial-clearance seal gives higher sealing effectiveness than that
for the axial-clearance seal due to the better performance of the radial-clearance seal.
This leads to the higher effectiveness for the radial-clearance seal in Figure 6-6 at the
same value of  o .
Figure 6-6 The computed variation of effectiveness with  o for radial-clearance seal compare
with axial-clearance seal (open symbols denote the experimental data [54])
112
Figure 6-7 The computed streamlines for both seal geometries, T  0.073
Figure 6-8 The radial distribution of effectiveness on the stator for the radial-clearance and
axial-clearance seals (symbols denote the experimental data [60])
113
Figure 6-8 shows the radial distribution of sealing effectiveness on the stator for both
radial- and axial-clearance seal geometries at the same value of T , together with the
experimental data for the radial-clearance seal [60]. The open square symbols shown
at r / b =1 denote the ingress concentration ( C i , mass ) boundary condition calculated
using the mass-weighted average assumption for the radial-clearance seal. Similar to
the variation of sealing effectiveness with  o , the computed results for the
radial-clearance seal show reasonably good agreement with the experimental data.
The computed results also show that the effectiveness is almost invariant with radius.
For the corresponding axial-clearance seal results, there is lower sealing effectiveness
as noted previously and the variation with radius is greater than for the
radial-clearance seal. For the radial-clearance seal, mixing is confined to a region very
close to the inlet, as illustrated in the streamlines (Figure 6-7).
Figure 6-9 The radial distribution of effectiveness on the rotor surface for the radial-clearance and
axial-clearance seals
Due to absence of experimental data for the rotor, Figure 6-9 shows only the
computed radial distribution of sealing effectiveness on the rotor for both radial- and
114
axial-clearance seal geometries at the same value of T . The vertical dashed lines
illustrate the overlap region for the radial-clearance seal. Compared with the
effectiveness on the stator, smaller differences exist on rotor between the two seal
geometries. For the radial-clearance seal, the step change in effectiveness values
shown at high radius are due to the axial overlap surfaces of the seal.
6.2. Double axial-clearance seal
Figure 6-10 (a) Typical high-pressure gas turbine stage of a Rolls-Royce jet engine; (b) detail of
rim seal [6]
Double-clearance rim-seals are used in typical turbine stages of engines, as illustrated
in Figure 6-10. This section and the next section evaluate the prescribed ingestion
method for double-clearance seal geometries. The double axial-clearance, which
features axial-clearances for both outer and inner seals (Figure 6-1 (b)), is presented in
this section. The wheel-space is separated into an outer and an inner wheel-space by
the inner axial-clearance seal. The mass-weighted average assumption is applied for
boundary conditions as before and the location of the egress outlet is the same as for
115
the single axial-clearance seal, shown in Figure 6-1 (b). The computed results for the
double axial-clearance are compared with those for the single axial-clearance seal.
The computational parameters for this seal geometry are shown in Table 6-2. The
value of  i is deduced from the experimental data for the double axial-clearance
seal [54], shown in Figure 6-11. The computations at the higher rotational speed are
carried out for compare with measurements of swirl ratio and the lower rotational
speed for comparison with measured radial variations of sealing effectiveness.
Figure 6-11 Experimental data for double axial-clearance seal with EI ingress [54]
Re 
8.17  10 5
5.32  10 5
C w ,o
o
T
i
3060
0.0596
0.057
0.0606
5934
0.1156
0.111
0.0375
11969
0.2332
0.223
0.0048
737
0.0221
0.019
0.0779
2018
0.0604
0.053
0.0597
2993
0.0895
0.079
0.0481
Table 6-2 Computational parameters for the double axial-clearance seal
116
Figure 6-12 Swirl ratio distribution for double axial-clearance seal, z / s =0.25 (symbols denote
the experimental data [60])
Figure 6-12 shows the swirl ratio distribution at z / s =0.25 in the wheel-space for the
double axial-clearance seal. The closed symbols denote the experimental data [60].
The open square symbols at r / b =1 denote the ingress swirl ratio (  i,mass ) used as the
boundary condition calculated with the mass-weighted average assumption. Generally,
the computed results have reasonable agreement with the experimental data in both
the outer and inner wheel-space. At the highest value of T (=0.223), the computed
swirl ratio is higher than the measurements in the outer wheel-space. This was also
true for the single axial-clearance seal (Figure 5-7 (c)), and the reason for the
over-prediction is the same. The rotating boundary between the ingress inlet and
egress outlet influences the swirl ratio of the ingested flow around the ingress inlet
region, and this influence continues for the ingested flow in the wheel-space. The
swirl ratio contours and secondary flow streamlines for the outer wheel-space for
T  0.223 are shown in Figure 6-13 with a fine scale. The figure illustrates the
effect of the rotating shroud on the swirl ratio in the outer wheel-space. For the single
117
seal, the effect is extended over the full wheel-space, but the effect is greater in the
confined outer wheel-space for the double axial-clearance seal.
Figure 6-13 Swirl contour and flow streamlines in outer wheel-space for the double
axial-clearance, T  0.223
Figure 6-14 Swirl ratio distribution for double and single axial-clearance seal, z / s =0.25
118
Figure 6-14 shows a comparison of the distribution of swirl ratio for the single
axial-seal and the double axial-clearance seal at a similar sealing flow rate. Generally,
the difference between the seal geometries is small at low and high radius. A
reduction in swirl ratio occurs for the double axial-clearance seal due to the inner seal
insert. The flow structure is mainly controlled by T .
Two sampling points for sealing effectiveness are used for the double axial-clearance
seal. One is in the outer wheel-space at r / b =0.958 and the second is in the inner
wheel-space at r / b =0.85. The definitions of sealing effectiveness at the two
sampling points are same as that for single seals, as shown in Chapter 3.
c 
c  ca
co  c a
(6-1)
The effectiveness is collected at r / b =0.958 for single seals. For consistency, the
outer sampling point ( r / b =0.958) is used for the comparison of the outer seal with
that of the single seals and the inner sampling point ( r / b =0.85) is used for
comparison between different double seals.
Figure 6-15 (a) and (b) show the computed and measured variation of sealing
effectiveness with  o for the outer and inner sampling points for the double
axial-clearance seal. In the figures, the open symbols denote the experimental data
[54]; the closed symbols denote the computed effectiveness and the lines are the
theoretical curves [54] for this seal geometry. For the outer sampling point, the
computed sealing effectiveness has good agreement with the experimental data and
the theoretical curve. There is a slight over-prediction of effectiveness at lower sealing
flow rates for the computations. However, for the inner sampling point, the
computations over-predict the effectiveness. Both computations and measurements
show that the effectiveness is higher at the inner than at the outer sampling point at
same value of  o .
119
(a)
(b)
Figure 6-15 The computed variation of effectiveness with  o for the double axial-clearance seal
for (a) the outer sampling point and (b) the inner sampling point (symbols denote the experimental
data [54])
120
Figure 6-16 Velocity vectors and sealing effectiveness around the inner seal region for the double
axial-clearance seal, T  0.019
The over-prediction of effectiveness at the inner sampling point is due to blocking of
the flow at the inner seal region. Velocity vectors around the inner seal region for the
double axial-clearance seal, shown in Figure 6-16, illustrate the secondary flow
structure. At the base of the inner seal clearance, most of the inward flow is prevented
from entering the inner wheel-space by the strong sealing flow and a recirculation in
the seal clearance (the black line in Figure 6-16). Although ingestion in the inner
wheel-space is under-predicted, the outer wheel-space is the more important region of
interest for engine designers, and, the prescribed ingestion model for the
double-clearance seal gives reasonable prediction of effectiveness in the outer
wheel-space.
121
Figure 6-17 The radial distribution of effectiveness on stator for the double axial-clearance and
single axial-clearance seals (symbols denote the experimental data [60])
Figure 6-17 shows the radial distribution of sealing effectiveness on the stator for the
double and single axial-clearance seals at similar conditions. The experimental data
for the double axial-clearance seal [60] are also shown. The open square symbols
shown at r / b =1 denote the ingress concentration ( C i , mass ) boundary condition
calculated using the mass-weighted average assumption for the double axial-clearance
seal. For the double axial-clearance seal, both computations and experiment show a
significant increase in sealing effectiveness across the inner seal clearance. The
computations again over-predict the effectiveness. In the outer wheel-space
( r / b >0.9), the computed effectiveness has a reasonable level compared with the
experimental data. For similar conditions, both seal geometries give the similar
effectiveness level in outer wheel-space, which means that the performance of the
outer seal for the double axial-clearance seal is close to that of the single
axial-clearance seal. These results suggest that a better estimate of C i , mass may be
needed for the prediction of effectiveness in the outer seal region for this
122
configuration.
6.3. Radial-axial-clearance seal
The radial-axial-clearance seal has a radial-clearance outer seal and an axial-clearance
inner seal (Figure 6-1 (c)). The mass-weighted average assumption is used and the
location of egress outlet is same as for the single radial-clearance seal, see Figure 6-1
(c). The computational parameters for this seal geometry are shown in Table 6-3. The
value of  i is deduced from experimental data for the radial-axial-clearance seal
[60], shown in Figure 6-18. The computations at the higher value of Re  are carried
out for comparison with measured swirl ratios. The computations at the lower values
of Re  are carried out for comparison with measured radial variations of sealing
effectiveness.
Figure 6-18 Experimental data for double radial-axial-clearance seal with EI ingress [60]
123
Re 
8.17  10 5
5.32  10 5
C w ,o
o
T
i
2147
0.0418
0.04
0.0394
3435
0.0669
0.064
0.0244
4294
0.0836
0.08
0.015
1011
0.0303
0.028
0.0481
1602
0.0479
0.042
0.0369
2480
0.0742
0.065
0.02
Table 6-3 Computational parameters for the radial-axial-clearance seal
Figure 6-19 Swirl ratio distribution for the radial-axial-clearance seal, z / s =0.25 (symbols
denote the experimental data [60])
Figure 6-19 shows the swirl ratio distribution at z / s =0.25 in wheel-space for the
radial-axial-clearance seal. The closed symbols denote the experimental data [60] and
the open square symbols at r / b =1 denote the mass-weighted average ingress swirl
124
ratio (  i,mass ) boundary condition. One computed result for the single radial-clearance
seal at similar T is also shown for comparison. In the inner wheel-space, the
computations under-predict the swirl ratio. In the outer wheel-space, the computations
mostly agree well with the measurements although there is over-prediction at the
lowest value of T . Similar to the comparison between double and single
axial-clearance seals, there is little difference between the results for the
radial-axial-clearance seal and the single radial-clearance seal, except in the region of
the inner seal. In this region the radial-axial-clearance seal gives rise to a lower swirl
ratio due to the additional sealing effect of the stationary inner seal insert.
Figure 6-20 The computed variation of effectiveness with  o for the radial-axial-clearance seal
for outer sampling point (symbols denote the experimental data [60])
Figure 6-20 shows the computed and experimental variation of sealing effectiveness
with  o for the outer sampling points for radial-axial-clearance seal. The open
symbols denote the experimental data [60], the closed symbols denote the computed
effectiveness and the line is theoretical fit [60] for this seal geometry. The
computations show very good agreement with the trend of the experimental results
125
and the theoretical fit. For the inner sampling point, the computations over-predict
sealing effectiveness for the reasons discussed previously for other double-clearance
seals. The results from inner sampling point for this seal geometry are therefore not
shown here.
Figure 6-21 The radial distribution of effectiveness on stator for the radial-axial-clearance seal and
the single radial-clearance seal (symbols denote the experimental data [60])
Figure 6-21 shows the radial distribution of sealing effectiveness on the stator for the
radial-axial-clearance seal, and also the single radial-clearance seal for similar
conditions. The experimental data for the radial-axial-clearance seal [60] are also
shown. The open square symbols shown at r / b =1 denote the ingress concentration
( C i , mass ) boundary condition calculated using the mass-weighted average assumption
for the radial-axial-clearance seal. For the radial-axial-clearance seal, the
computations again over-predict effectiveness in the inner wheel-space but are in
reasonable agreement with the experimental data in the outer wheel-space. The
measured sealing effectiveness decreases with increasing radius in the outer
wheel-space, suggesting that the flow is not fully mixed in this region. Due to the
126
location of the outlet near the rotor in the prescribed ingestion model, mixing is
inhibited and the computed effectiveness distribution is more flat. Compared with the
single radial-clearance seal at similar conditions, there is a reduction in effectiveness
in the outer wheel-space for the radial-axial-clearance seal. For this geometry, most of
the ingested flow is contained in the outer wheel-space with the inner wheel-space
being well-sealed.
6.4. Sealing performance of all rim seal geometries
Figure 6-22 The computed variation of effectiveness with  o for all rim seal geometries (The
open symbols denote the experimental data [60], the closed symbols denote the computed
effectiveness and the line is theoretical curves [60])
In the previous and current chapters, four rim seal geometries have been studied using
prescribed ingestion models. In this section, the sealing performance of these
geometries is compared. Figure 6-22 shows the computed and measured variation of
sealing effectiveness with  o for all of the rim seal geometries. For the two
127
double-clearance rim-seals, the sealing effectiveness at the outer sampling point is
used for comparison. The computations for the single axial-clearance seal over-predict
the effectiveness, whereas the other three geometries have reasonable agreement with
the experimental data (and theoretical curve fits). Generally, the two radial-clearance
seals show better sealing performance than the two axial-clearance seals at the same
sealing flow rate. The single radial-clearance has better performance than the
radial-axial-clearance seal, and the two axial-clearance seals have almost the same
sealing performance. Although the computations over-predict sealing effectiveness in
the inner wheel-space for the two double clearance seals, the improvement in
effectiveness at low radius, due to the inner seal, is still distinct. In other words, the
inner seal acts to protect the inner wheel-space.
6.5. Chapter summary
The axisymmetric model has limitation in terms of predicting ingress for double
clearance rim seal. However the prescribed ingestion model with all seal geometries
provides reasonable results for fluid dynamics and sealing effectiveness in
comparison with the experimental results. Much less computing time is needed for the
prescribed ingestion model compared with the 3D model. Hence, the model may be
regarded as a simple, quick and convenient computational tool for the engine designer.
When experimental information is not available, the distribution and effect on flow
and heat transfer of ingestion in the wheel-space could be investigated by imposing
hypothetical ingress conditions for a model involving any seal geometry.
128
7. Conclusions and future work
A new axisymmetric model for ingress research, the prescribed ingestion model, is
presented in this thesis. This model includes only the wheel-space between the stator
and the rotor and deduces the flow rate of ingestion from experimental data and
theoretical curves [51, 54 and 60]. The model is a fast computational tool compared
with more complex 3D models. The main conclusions will be summarized here and
some possible future work also proposed.
7.1. The axisymmetric rotor-stator models
Before the prescribed ingestion model, two traditional axisymmetric rotor-stator
models are studied for fluid dynamics and heat transfer in the wheel-space without
ingress. Thereby, the axisymmetric model with ANSYS CFX was validated. The two
axisymmetric rotor-stator models are the Bath Rig Model and Chen Rig Model
respectively, as discussed in Chapter 4.
In terms of fluid dynamics, the differences between the Bath and Chen Rig Models
influence the axial distribution of radial velocity at inlet to the wheel-space. Both
geometries illustrate typical rotor-stator flow behaviour, with flow radially outward on
the rotor, radially inward on the stator, and almost no radial flow in the middle of
wheel-space. The magnitude of the outward radial velocity near the rotor increases
and the inward radial velocity near the stator decreases with T . The swirl ratio
(non-dimensional circumferential velocity) in the core region between the rotor and
stator is invariant with z but increases as radius increases. At a constant radius, the
swirl reduces with increasing T . This illustrates that the sealing flow can reduce the
swirl ratio in the wheel-space. It is also shown that the thermal condition on the wall
(rotor) has almost no influence on the velocity distribution in the wheel-space; even
with the ideal gas law is used in these computations.
129
For heat transfer, the two geometries also have no distinct differences in terms of the
distribution of Nusselt number, except near the inlet region. The computations
indicate that Nu Re0.8 increases as T increases. Furthermore, the temperature
distribution at the rotor surface slightly affects the value of Nu Re0.8 , but does not
affect the distribution. The SST k   turbulence model provides more reasonable
heat transfer results at high T compared with the k   model. However, the
computations under-predict the Nusselt number at low T , which is mainly due to the
low levels of computed turbulence in the selected turbulence model and moderately
fine meshes.
7.2. The prescribed ingestion models
The prescribed ingestion model, using four rim seal geometries, is presented in
Chapters 5 and 6. The four geometries are the axial-clearance seal, radial-clearance
seal, double axial-clearance seal and radial-axial-clearance seal respectively. At first,
the mass-weighted average assumption was tested for the axial-clearance seal and it
provided results which compared favourably with the experimental data [51, 60].
Three different layouts of ingress inlet and egress outlet were used. The best results
were obtained with the ingress inlet positioned at the centre of shroud for all
geometries. The outlet was positioned at rotor side of shroud for two the
axial-clearance seals. For the radial ones, the outlet is at the rotor wall and the bottom
of the axial overlap.
The computations for all rim seal geometries show that the ingested flow increases the
swirl ratio in the wheel-space and the magnitude of increase is weakened as the
sealing flow increases. At the same T , the geometry only influences the distribution
of swirl ratio at high radius (near rim seal region) and the fluid structure at low radius
is dominated by T . Due to the inserted inner seal, the double clearance seals have a
lower swirl ratio than the single clearance seals near the inner seal region with same
T condition. The computed streamlines show the basic fluid structure in the
130
wheel-space with the sealing flow entering the boundary layer on the rotor at low
radius; a part of ingested flow flows through the outlet directly and the remainder
enters the stator boundary layer at the periphery of the wheel-space. A core of inviscid
rotating fluid exists between the stator and rotor.
The variation of sealing effectiveness with  o at r/b=0.958 and the radial
distribution of sealing effectiveness on the stator are presented for all rim seal
geometries. Presenting the variation of sealing effectiveness with  o eliminates the
effect of Re  . For all geometries, the sealing effectiveness increases as  o
increases, though the sealing performance of each seal is unlike. The two
radial-clearance seals have a higher effectiveness, and consequently better sealing
performance, than the two axial-clearance seals at the same  o . The single
radial-clearance has the best performance among all geometries at this radius.
However, the double clearance seals provide an improvement in terms of
effectiveness at low radius. The radial distributions on the stator show that if the fluid
is fully mixed near the rim seal region, the effectiveness of the fluid in the boundary
layer on the stator is almost invariant with radius. The small radial variation in the
computations at high radius indicates that the flow is not fully mixed near rim seal
region in the computations.
Heat transfer computations were only carried out for the axial-clearance seal. The
values of Nu Re 
0.8
are shown to be almost invariant with radius on rotor, except in
the regions near the inlet and outlet. The Nusselt number increases as T increases
and as ingested flow decreases. The ingested flow increases the swirl ratio in the
wheel-space and consequently reduces the Nusselt number. The computed Nu are in
fair agreement with measurements, and these heat transfer experiments have not
previously been studied computationally.
The prescribed ingestion model is potentially a useful tool to the engine designer.
When experimental information is not available, the distribution and effect on flow
and heat transfer of ingestion in the wheel-space could be investigated by imposing
hypothetical ingress conditions for a model involving any seal geometry.
131
7.3. Future work
Although the prescribed ingestion model has provided reasonable results, it still has
limitations and can be improved. Firstly, this prescribed ingestion model could
combine with a theoretical study in order to determine more accurate boundary
conditions for the ingested flow. As discussed above, the axisymmetric model blocks
the ingested flow entering the inner wheel-space for double clearance seals. A
separate prescribed ingestion models for the inner wheel-space might solve this
problem. Furthermore, finer meshes could be applied for heat transfer computation in
order to improve the results at low T and heat transfer computations could be
expanded to all rim seal geometries. The effect of radiation heat transfer can be
considered for heat transfer computation in order to get better agreement with
experimental data. The prescribed ingestion model could apply to engine geometries
and engine conditions, and could be translated into a practical engine tool by
engineers at Gas Turbine companies.
Work discussed in Chapters 4 and 5 were published (see Appendix). Further papers
based on the prescribed ingestion model for other seal geometries (Chapter 6) are to
be published.
132
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138
Appendix
International Journal of Gas Turbine, Propulsion and
Power Systems
Computations of Flow and Heat Transfer in a Rotor-Stator System with
Externally-Induced Ingestion
139
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