/smash/get/diva2:479537/FULLTEXT01.pdf

/smash/get/diva2:479537/FULLTEXT01.pdf
WAKE MEASUREMENTS BEHIND
AN ARRAY OF
TWO MODEL WIND TURBINES
Jan Bartl
Master of Science Thesis
KTH School of Industrial Engineering and Management
Energy Technology EGI-2011-127 MSC EKV 866
Division of Heat and Power Technology
SE-100 44 STOCKHOLM
Master of Science Thesis EGI 2011:127 MSC
EKV866
Wake Measurements Behind
An Array Of
Two Model Wind Turbines
Jan Bartl
Approved
Examiner
Supervisor
Oct-31-2011
Damian Vogt
Miroslav Petrov
Commissioner
Contact person
ABSTRACT
During the last decades the exploitation of energy from the wind has become one of the most promising
renewable energy technologies. The main strive in today’s development of wind turbines is to increase
the efficiency of the turbine and to build bigger rotors that are able to extract more power out of the
wind.
When it comes to the planning and designing of a wind park, also the aerodynamic interactions between
the single turbines must be taken into account. The flow in the wake of the first row turbines is
characterized by a significant deficit in wind velocity and by increased levels of turbulence.
Consequently, the downstream turbines in a wind farm cannot extract as much power from the wind
anymore. Furthermore, the additional turbulence in the wake could be a reason for increased material
fatigue through flow-induced vibrations at the downstream rotor.
The main focus of this experimental study is to investigate the local velocity deficit and the turbulence
intensities in the wake behind an array of two model wind turbines. For two different turbine separation
distances, the wake is scanned at three different downstream positions. The experiments are performed
at the wind tunnel (1.9m x 2.7m cross section) at NTNU Trondheim using two model wind turbines with
a rotor diameter of 0.9m. A hot wire probe is used to scan the wake behind the model turbines in defined
positions.
Moving axially downstream the velocity deficit in the wake gradually recovers and the turbulence
intensity levels slowly decrease. Furthermore, a gentle expansion of the wake can be observed. The wake
profiles measured in close distances behind the rotor are characterized by evident asymmetries. Further
downstream in the wake turbulent diffusion mechanisms cause a more uniform and more symmetrical
flow field. Moreover, the turbulence intensity behind the second wind turbine is found to be significantly
higher than behind one unobstructed turbine. Also, considerably higher velocity deficits are found in the
near wake behind the second turbine compared to the wake behind one unobstructed turbine. However,
the velocity profile at five rotor diameters downstream in the wake behind the second turbine is already
very similar to the velocity distribution behind the first turbine. Furthermore, the velocity field and
turbulence intensity distribution in the wake behind the second turbine is more symmetrical and more
uniform than behind the first turbine.
I
AFFIDAVIT
I hereby declare that I wrote thesis on my own without any assistance from a third party. I
confirm that no sources have been used other than those clearly marked as other sources.
This thesis has not been received by any examination board, neither in this nor in a similar
form.
Trondheim, October 31st, 2011
II
ACKNOWLEDGEMENTS
The present thesis has been performed at Norges Teknisk-Naturvitenskapelige Universitet
(NTNU) in Trondheim. It will be submitted for the degree Diplom-Ingenieur at
Technische Universität München (TUM) as well as for the degree Civilingenjör at Kungliga
Tekniska Högskolan (KTH) in Stockholm.
Many people have been involved in supervising this thesis, who I would like to express my
gratitude to:
First of all, I would like to thank Professor Lars Sætran at the Department of Energy and
Process Engineering at NTNU for giving me the opportunity to work on this thesis. Thank
you for many fruitful discussions and for always being available when help was needed.
My biggest thanks goes to Fabio Pierella with whom I spent numerous hours in the wind
tunnel throughout this project. Thank you for teaching me all the experimental
procedures, for your creative ways of solving problems but above all for a fun time in and
outside of the wind tunnel laboratory.
Also, I would like to thank Pål Egil Eriksen at the Department of Energy and Process
Engineering at NTNU whose self-written data conversion programs I used for the
evaluation of the hot wire signals.
At TUM I would like to thank Professor Rudolf Schilling at the Chair of Fluid Mechanics
for supervising and accrediting this thesis from distance.
Special thanks to Matthias Faust who helped in organizing with words and deeds before
the thesis even started.
Many thanks to Andreas Rosenberger for taking over the supervision at TUM. Thank you
for proofreading and your helpful comments.
At KTH I would like to thank Damian Vogt of the Department for Heat and Power
Technology for officially examining this thesis.
Many thanks to Miroslav Petrov for supervising the project at KTH and for organizing all
the paper work involved with this thesis.
Special thanks to Jens Fridh for imparting the contact to Miro and for teaching me how to
work experimentally during my time at KTH. During this thesis I could profit in many
ways from what I have learned back then.
Finally, I would like to thank my friends Andreas Hövelmann and Michael Tiefenbrunn for
proofreading. Thank you for your helpful comments and corrections.
III
IV
Table of Contents
TABLE OF CONTENTS
ABSTRACT....................................................................................................................................... I
AFFIDAVIT ..................................................................................................................................... II
ACKNOWLEDGEMENTS .......................................................................................................... III
TABLE OF CONTENTS ................................................................................................................ V
LIST OF FIGURES ...................................................................................................................... VII
LIST OF TABLES ........................................................................................................................... X
NOMENCLATURE ...................................................................................................................... XI
1
BACKGROUND ...................................................................................................................... 1
1.1
WIND POWER ..................................................................................................................... 1
1.2
WIND TURBINE AERODYNAMICS ...................................................................................... 2
1.2.1 Energy Extraction from the Wind ................................................................................. 3
1.2.2 Blade Aerodynamics ..................................................................................................... 7
1.2.3 Wake Aerodynamics ...................................................................................................... 8
1.3
WIND FARM ARRANGEMENT........................................................................................... 13
1.4
MOTIVATION ................................................................................................................... 16
2
OBJECTIVES ........................................................................................................................ 17
3
METHODOLOGY................................................................................................................. 19
4
EXPERIMENTAL SETUP ................................................................................................... 21
4.1
TEST RIG .......................................................................................................................... 21
4.1.1 Closed-Return Wind Tunnel ........................................................................................ 21
4.1.2 Model Wind Turbines .................................................................................................. 22
4.1.3 Turbine Blades ............................................................................................................ 24
4.1.4 Traverse Mechanism ................................................................................................... 25
4.2
INSTRUMENTS .................................................................................................................. 26
4.2.1 Barometer ................................................................................................................... 26
4.2.2 Inlet nozzle .................................................................................................................. 26
4.2.3 Reference Pitot tube .................................................................................................... 27
4.2.4 Thermocouple ............................................................................................................. 27
4.2.5 Traverse Pitot tube ...................................................................................................... 28
4.2.6 Hot wire probe ............................................................................................................ 28
4.2.7 RPM sensor ................................................................................................................. 30
4.2.8 Torque transducer ....................................................................................................... 30
4.2.9 Force balance ............................................................................................................. 31
4.3
INSTRUMENT CALIBRATIONS ........................................................................................... 32
4.3.1 Pressure transducer calibration ................................................................................. 32
4.3.2 Hot wire calibration .................................................................................................... 33
4.3.3 Torque sensor calibration ........................................................................................... 33
4.3.4 Force balance calibration ........................................................................................... 34
4.4
CONTROL SYSTEM ........................................................................................................... 35
V
Table of Contents
5
MEASUREMENT CAMPAIGN & DATA EVALUATION .............................................. 37
5.1
MEASUREMENT CAMPAIGN ............................................................................................. 37
5.2
DATA EVALUATION ......................................................................................................... 42
5.2.1 Evaluation of Power and Thrust Curves ..................................................................... 42
5.2.2 Evaluation of Wake Velocity Field.............................................................................. 43
5.2.2.1
5.2.2.2
5.3
6
Velocity Deficit .................................................................................................................................. 43
Turbulence Intensity ........................................................................................................................... 44
MEASUREMENT UNCERTAINTY ....................................................................................... 45
RESULTS & DISCUSSION .................................................................................................. 47
6.1
INLET FLOW FIELD .......................................................................................................... 47
6.2
TURBINE ARRANGEMENT (A): SINGLE TURBINE MEASUREMENTS ................................ 49
6.2.1 Turbine Performance Curves ...................................................................................... 50
6.2.1.1
6.2.1.2
First Turbine Performance .................................................................................................................. 50
Second Turbine Performance ............................................................................................................. 51
6.2.2 Downstream Flow Field.............................................................................................. 53
6.3
TURBINE ARRANGEMENT (B): TURBINE DISTANCE X/D=3 ............................................. 56
6.3.1 Turbine Performance Curves ...................................................................................... 57
6.3.2 Downstream Flow Field.............................................................................................. 59
6.3.2.1
6.3.2.2
Horizontal Line Wake Measurements ................................................................................................ 59
Full Area Wake Measurements........................................................................................................... 61
6.4
TURBINE ARRANGEMENT (C): TURBINE DISTANCE X/D=5 ............................................. 66
6.4.1 Turbine Performance Curves ...................................................................................... 67
6.4.2 Downstream Flow Field.............................................................................................. 68
6.4.2.1
6.4.2.2
Horizontal Line Wake Measurements ................................................................................................ 68
Full Area Wake Measurements........................................................................................................... 70
6.5
COMPARISON OF TURBINE ARRANGEMENTS (A), (B) AND (C) ....................................... 73
6.5.1 Turbine Performance Curves ...................................................................................... 74
6.5.2 Downstream Flow Field.............................................................................................. 75
6.5.2.1
6.5.2.2
6.5.2.3
1D Wake ............................................................................................................................................. 75
3D Wake ............................................................................................................................................. 80
5D Wake ............................................................................................................................................. 84
6.6
VARIATIONS IN TIP SPEED RATIO.................................................................................... 86
6.6.1 Turbine Performance Curves ...................................................................................... 87
6.6.2 Downstream Flow Field.............................................................................................. 90
7
CONCLUSIONS & FUTURE WORK................................................................................. 99
7.1
7.2
CONCLUSIONS.................................................................................................................. 99
FUTURE WORK ............................................................................................................... 104
REFERENCES ............................................................................................................................. 107
APPENDIX: COMPARISON OF PERFORMANCE CURVES ............................................. 113
VI
List of Figures
LIST OF FIGURES
Fig. 1.1:
Imaginary wind tube around a wind turbine rotor showing a decrease in wind velocity
and a distinct pressure drop over the rotor ...................................................................... 3
Fig. 1.2:
Typical CP- and CT– curves of a modern wind turbine ................................................ 5
Fig. 1.3:
Stream lines around wind turbine blades at different angles of attack .......................... 7
Fig. 1.4:
Velocity triangle on a wind turbine blade ........................................................................ 9
Fig. 1.5:
Formation of the tip vortex ............................................................................................. 10
Fig. 1.6:
Cylindrical shear layer in the wake of the rotor induced by tip vortices ....................... 11
Fig. 1.7:
Turbulent mixing process in the wake behind a wind turbine rotor .............................12
Fig. 1.8:
Wind turbine wake effects in the Danish offshore wind farm “Horns Rev 1” [20] .......13
Fig. 1.9:
CFD simulation of the propagation of wind turbine wake in a wind farm arrangement
[21] .....................................................................................................................................14
Fig. 4.1:
Wind tunnel at the Fluid Engineering laboratory at NTNU [27] ...................................21
Fig. 4.2:
The two model wind turbines set up in the wind tunnel of NTNU ............................... 22
Fig. 4.3:
Experimental setup and reference orientation .............................................................. 23
Fig. 4.4:
View on blade in (a) streamwise and (b) circumferential projection [29] ................... 24
Fig. 4.5:
Scaled blade profile NREL S826 14% thickness [30] .................................................... 25
Fig. 4.6:
Automatic traverse system installed in NTNU’s wind tunnel ....................................... 25
Fig. 4.7:
Schematic sketch of the inlet contraction ...................................................................... 26
Fig. 4.8:
Parallel probe setup ......................................................................................................... 28
Fig. 4.9:
Hot wire probe ................................................................................................................. 29
Fig. 4.10:
CTA circuit containing a Wheatstone bridge ................................................................. 29
Fig. 4.11:
Cross section of the hub of the second turbine [27] .......................................................31
Fig. 4.12:
Calibration curve of a pressure transducer .................................................................... 32
Fig. 4.13:
Calibration curve for the hot wire probe signal ............................................................. 33
Fig. 5.1:
Location of measurement points for the Horizontal Line Wake measurements ......... 39
Fig. 5.2:
Location of measurement points for the Full Area Wake measurements .................... 40
Fig. 5.3:
Data acquisition and evaluation for CP and CT curves ................................................... 42
Fig. 5.4:
Velocity signal in a turbulent flow .................................................................................. 44
Fig. 6.1:
Mean velocity (Um) and turbulence intensity (u’/Um) at the wind tunnel inlet ........... 47
Fig. 6.2:
Velocity deficit (Um/U∞) and turbulence intensity (u’/Um) at the wind tunnel inlet ... 48
Fig. 6.3:
Experimental setup and axial probe measurement stations for turbine arrangement
(A): the single turbine measurements ............................................................................ 49
Fig. 6.4:
Performance curves of the first turbine (Tu1) at different inflow wind speeds: (a)
power coefficient CP and (b) thrust coefficient CT ......................................................... 50
Fig. 6.5:
Performance curves of the unobstructed second turbine (Tu2) at different inflow wind
speeds: (a) power coefficient CP and (b) thrust coefficient CT ....................................... 51
Fig. 6.6:
Velocity deficit (Um/U∞) and turbulence intensity (u’/Um) in the wake 1D, 3D and 5D
downstream of the unobstructed turbine....................................................................... 53
VII
List of Figures
Fig. 6.7:
Experimental setup and axial measurement stations for turbine arrangement (B) .... 56
Fig. 6.8:
CP curve of the second turbine (red) operating 3D downstream of the first turbine: (a)
reference velocity U∞=11.5 m/s (b) reference velocity Uref,3D=7.8 m/s ......................... 57
Fig. 6.9:
Velocity deficit (Um/U∞) and turbulence intensity (u’/Um) in the wake 1D, 3D and 5D
downstream of the second turbine operating 3D downstream of the first turbine ..... 59
Fig. 6.10:
Velocity deficit (Um/U∞) and turbulence intensity (u’/Um) in the wake 1D downstream
of the second turbine operating 3D downstream of the first turbine ........................... 62
Fig. 6.11:
Velocity deficit (Um/U∞) and turbulence intensity (u’/Um) in the wake 3D downstream
of the second turbine operating 3D downstream of the first turbine ........................... 62
Fig. 6.12:
Velocity deficit (Um/U∞) and turbulence intensity (u’/Um) in the wake 5D downstream
of the second turbine operating 3D downstream of the first turbine ........................... 62
Fig. 6.13:
Experimental setup and axial measurement stations for turbine arrangement (C) .... 66
Fig. 6.14:
CP curve of the second turbine operating 5D downstream of the first turbine: (a)
reference velocity U∞=11.5 m/s (b) reference velocity Uref,5D=8.1 m/s .......................... 67
Fig. 6.15:
Velocity deficit (Um/U∞) and turbulence intensity (u’/Um) in the wake 1D, 3D
downstream of the second turbine operating 5D downstream of the first turbine ..... 68
Fig. 6.16:
Velocity deficit (Um/U∞) and turbulence intensity (u’/Um) in the wake 1D downstream
of the second turbine operating 5D downstream of the first turbine ........................... 70
Fig. 6.17:
Velocity deficit (Um/U∞) and turbulence intensity (u’/Um) in the wake 3D downstream
of the second turbine operating 5D downstream of the first turbine ........................... 70
Fig. 6.18:
Comparison of the performance curves and the wakes 1D and 3D downstream of the
second turbine, when the turbine is (A) unobstructed, (B) operating 3D downstream
of the first turbine and (C) operating 5D downstream of the first turbine .................. 73
Fig. 6.19:
CP curve of the second turbine operating (A) unobstructed, (B) 3D and (C) 5D
downstream of the first turbine: (a) reference velocity U∞=11.5 m/s (b) reference
velocity Uref,3D=7.8 m/s and Uref,5D=8.1 m/s .................................................................... 74
Fig. 6.20:
Velocity deficit (Um/U∞) and turbulence intensity (u’/Um) in the wake 1D downstream
of the second turbine operating (A) unobstructed, (B) 3D and (C) 5D downstream of
the first turbine ................................................................................................................ 75
Fig. 6.21:
Velocity deficit (Um/U∞) and turbulence intensity (u’/Um) in the wake 1D downstream
of the second turbine operating 3D downstream of the first turbine (B) ..................... 78
Fig. 6.22:
Velocity deficit (Um/U∞) and turbulence intensity (u’/Um) in the wake 1D downstream
of the second turbine operating 5D downstream of the first turbine (C) ..................... 78
Fig. 6.23:
Velocity deficit (Um/U∞) and turbulence intensity (u’/Um) in the wake 3D downstream
of the second turbine operating (A) unobstructed, (B) 3D and (C) 5D downstream of
the first turbine ................................................................................................................ 80
Fig. 6.24:
Velocity deficit (Um/U∞) and turbulence intensity (u’/Um) in the wake 3D downstream
of the second turbine operating 3D downstream of the first turbine (B) ..................... 82
VIII
List of Figures
Fig. 6.25:
Velocity deficit (Um/U∞) and turbulence intensity (u’/Um) in the wake 3D downstream
of the second turbine operating 5D downstream of the first turbine (C) ..................... 82
Fig. 6.26:
Velocity deficit (Um/U∞) and turbulence intensity (u’/Um) in the wake 5D downstream
of the second turbine operating (A) unobstructed and (B) 3D downstream of the first
turbine .............................................................................................................................. 84
Fig. 6.27:
Experimental setup and axial probe measurement station for the investigation of the
effect of turbine tip speed ratio variations ..................................................................... 86
Fig. 6.28:
CP curves of the second turbine operating in the wake 3D downstream for varying tip
speed ratios of the first turbine: (a) reference velocity U∞=11.5 m/s (b) Uref,opt=7.8
m/s, Uref,low=8.4 m/s and Uref,high=9.0 m/s ...................................................................... 88
Fig. 6.29:
Combined power output (CP,Tu1 + CP,Tu2) of both turbines operated in 3D distance for
the nine investigated test cases ....................................................................................... 89
Fig. 6.30:
Velocity deficit (Um/U∞) and turbulence intensity (u’/Um) in the wake 3D downstream
of the second turbine for the TSR Cases 1, 2 and 3 .........................................................91
Fig. 6.31:
Velocity deficit (Um/U∞) and turbulence intensity (u’/Um) in the wake 3D downstream
of the second turbine for the TSR Cases 4, 5 and 6 ........................................................91
Fig. 6.32:
Velocity deficit (Um/U∞) and turbulence intensity (u’/Um) in the wake 3D downstream
of the second turbine for the TSR Cases 7, 8 and 9 ........................................................91
Fig. 6.33:
Velocity deficit (Um/U∞) and turbulence intensity (u’/Um) in the wake 3D downstream
of the second turbine for the TSR Cases 1, 4 and 7 ........................................................ 92
Fig. 6.34:
Velocity deficit (Um/U∞) and turbulence intensity (u’/Um) in the wake 3D downstream
of the second turbine for the TSR Cases 2, 5 and 8 ....................................................... 92
Fig. 6.35:
Velocity deficit (Um/U∞) and turbulence intensity (u’/Um) in the wake 3D downstream
of the second turbine for the TSR Cases 3, 6 and 9 ....................................................... 92
Fig. 6.36:
Comparison of the minimum velocity deficit (Um/U∞)min and the maximum turbulence
intensity (u’/Um)max in the 3D wake for the nine different test cases ........................... 96
Fig A.1:
CP and CT curves of second turbine operating unobstructed at five different inflow
wind speeds ..................................................................................................................... 113
Fig A.2:
Reynolds number effect on model turbine performance characteristics [28] ............ 114
IX
List of Tables
LIST OF TABLES
Table 4.1:
Dimensions of the experimental setup ........................................................................... 23
Table 5.1:
Measurement campaign .................................................................................................. 38
Table 6.1:
Investigated test cases with different tip speed ratios of the turbines ......................... 87
X
Nomenclature
NOMENCLATURE
Latin Symbols
A
Area
[m2]
c
Cord length
[mm]
C
Coefficient
[-]
D
Rotor Diameter
[mm]
F
Force
[N]
p
Pressure
[Pa]
r
Radius
[mm]
R
Rotor radius
[mm]
Re
Reynolds number
[-]
T
Torque
[Nm]
U
Absolute velocity
[m/s]
V
Relative velocity
[m/s]
x
x-coordinate
[mm]
y
y-coordinate
[mm]
z
z-coordinate
[mm]
Pitch angle
[°]
Yaw angle
[°]
Density
[kg/m3]
Tip speed ratio
[-]
Circumferential component
[-]
Kinematic viscosity
[m²/s]
Rotational Speed
[1/s]
Greek Symbols
Subscripts
avg
Average
ax
Axial reference
hub
Hub
m
Mean
XI
Nomenclature
max
Maximum
min
Minimum
rot
Axial measurement station in the plane of the rotor
P
Power
stat
Static
T
Thrust
tip
Tip
tot
Total
Tu1
first (upstream) model wind turbine
Tu2
second (downstream) model wind turbine
Abbreviations
ACD
Actuator Disc Method
AD
Anno Domini
BC
Before Christ
CFD
Computational Fluid Dynamics
CTA
Constant Temperature Anemometry
EEA
European Environment Agency
GWEC
Global Wind Energy Council
HAWT
Horizontal Axis Wind Turbine
KTH
Kungliga Tekniska Högskolan
NTNU
Norges Teknisk-Naturvitenskapelige Universitet
LDA
Laser Doppler Anemometry
LES
Large Eddy Simulation
PS
Pressure Side
RPM
Revolutions per Minute
SS
Suction Side
TE
Trailing Edge
TI
Turbulence Intensity
TSR
Tip Speed Ratio
Tu1
First (upstream) model wind turbine
Tu2
Second (downstream) model wind turbine
TUM
Technische Universität München
XII
XIII
XIV
Background
1
BACKGROUND
1.1 Wind Power
The exploitation of wind energy and its conversion to useful energy is one of the oldest
methods in energy transformation. The earliest known utilization of wind power was in
sailing boats, which used the aerodynamic drag and lift forces. Around 1700 BC a wind
powered system was used to irrigate agricultural fields in ancient Mesopotamia [1]. Almost
two millenniums later, about 500-900 AD, the first windmills were developed in old
Persia. In early developments of windmills the kinetic energy in the wind was converted
into mechanical energy, which was at that time primarily used for grinding grain and
pumping water [2].
The first windmills designed for electric power production were developed in the late 19th
century in more or less at the same time in the United States, Scotland and Denmark. In
the beginning of the 20th century fossil fuelled developments began to dominate the power
production all over the world, relegating wind power devices a rather insignificant role in
small-scale applications. The renewed interest in wind power for electric power
production arose in the late 1960s as the first signs of fossil fuel resources being finite
emerged. Wind as a primary energy resource was eventually considered to have a
significant potential for electrical power production [3]. The first countries to seize the
potential of wind power and setting up commercial wind turbines were Denmark,
Germany and the United States.
In the late 1990s a new awareness of a sustainable management of energy resources
evolved, stimulating a renewed interest in renewable energy sources. This could be
ascribed to substantial drawbacks of both fossil fuelled power plants and nuclear power
plants regarding their sustainability. From both sides of the Atlantic one could hear
politicians speak of a “global clean-energy revolution” [4], in which the exploitation of
wind power could play an essential role. From a global point of view wind power is one of
the most promising renewable energy sources as wind is available everywhere on the
planet and at some places even features a considerable energy density.
In the end of each calendar year the Global Wind Energy Council (GWEC) publishes a
report on the state of the global wind energy market. The latest report for 2010 shows the
enormous significance of today’s wind industry. Although the annual growth rate
1
Background
decreased for the first time, the globally installed wind power capacity increased by 24.1%
and in the end of 2010 stands at 197.0 GW. [5]
In terms of capacity China with 44.7 GW installed wind power took over the lead from the
United States, which currently have 40.2 GW installed. Within Europe the biggest
capacities are set up in Germany and Spain, making up a total of 27.2 GW respectively
20.7 GW in the end of 2010 [5]. Norway’s share is considerably smaller as it has lower
energy needs and is almost completely supplied by hydropower. Norway’s installed wind
power comprises a total installed power of 0.4 GW in the end of 2009 [6]. However,
Norway could play an important role in the future energy supply in Europe having a large
potential for onshore and offshore wind power in its coastal regions at the Atlantic Ocean
[7]. As Norway already is the largest hydropower producer in Europe there are
considerations that the Norwegian hydropower plants could act as a balance for the
growing amount of intermittent wind power entering the electrical grid. Therefore, experts
consider Norway to become the “battery” for renewable energy within Europe [8].
According to the European Environment Agency (EEA) wind power can play a key role in
achieving Europe’s future energy targets. For the year 2030 the EEA predicts an
economically competitive potential of 30400 TWh for Europe, of which 27000 TWh would
be produced by onshore wind farms and 3400 TWh by offshore wind farms [9]. As the
installation and maintenance of onshore wind power is much cheaper and economically
more competitive, the main focus is directed on the exploitation of onshore potentials
until 2030 [9].
1.2 Wind Turbine Aerodynamics
In the following section it is tried to give an elementary overview of the most important
aerodynamic concepts concerning a wind turbine. Starting with the rotating wind turbine
as an energy extraction device, it is thereafter looked into the basics of wind turbine blade
aerodynamics. Finally, the basic aerodynamic conditions that prevail in a wind turbine
wake are presented. However, wind turbine aerodynamics is a very complex field, of which
many aspects are not yet completely investigated.
2
Background
1.2.1 Energy Extraction from the Wind
Any kind of fluid contains energy, which can exist in different forms: potential energy,
thermodynamic pressure, kinetic energy and thermal energy [10]. When looking into basic
wind turbine aerodynamics only the kinetic energy and the pressure energy contained in
the wind are relevant. Temperature and potential effects in a wind flow can be neglected.
As a wind turbine by definition extracts kinetic energy from the wind, the wind passing
through the wind turbine rotor has to slow down.
Assuming a boundary between the mass of air passing through the rotor and the
unaffected flow a circular stream tube can be imagined as depicted in Fig. 1.1. For air flows
below
, density changes in the air can be neglected. Under normal ambient
conditions, an air flow, which is slower than
, can be regarded as an
incompressible flow. According to the continuity equation the mass flow rate along the
stream tube must be constant.
(1.1)
Consequently, the cross sectional area of the stream tube must become wider as the wind
is slowed down by the rotor. However, the wind velocity does not suddenly change over
the rotor, it decreases continuously. Starting in a certain distance in front of the rotor
plane, the kinetic energy in the wind is transformed to pressure energy as the blockage of
the rotor affects the flow upstream of the rotor.
Fig. 1.1:
Imaginary wind tube around a wind turbine rotor showing a decrease in wind
velocity and a distinct pressure drop over the rotor
The static pressure built up upstream of the rotor, on the other hand, is reduced in one
distinctive step as shown in Fig. 1.1. The air exiting from the rotor is at a static pressure
3
Background
level below the atmospheric pressure. As the velocity in the imaginary wind tube continues
to decrease downstream of the rotor the static pressure rises again and reaches the
atmospheric pressure level
at a certain distance downstream of the rotor [11].
The energy extracted from the wind is partly converted into mechanical energy on the
rotor shaft, whereas the other part is dissipated by the generated turbulence in the
downstream flow field [11]. When quantifying the power extracted by wind turbine usually
a simplified model, called the “Actuator Disc Concept”, is used. The turbine rotor is
reduced to a simple actuator disc, which induces a velocity variation to the free-stream
flow.
and the air mass flow ̇
Combining the kinetic energy
, the power
contained in the imaginary wind tube can be quantified as follows.
(1.2)
As the density of the air
power
is almost constant for a normal range of wind velocities, the
grows proportionally with the cube of the wind velocity
obvious that the power available in the imaginary wind tube
square of the rotor diameter
. Moreover, it is
increases with the
.
One of the most important parameters for wind turbines is the non-dimensional power
coefficient
, which is defined as the actually extracted power on the rotor axle divided by
the maximum power contained in the wind tube.
(1.3)
Applying the momentum theory, the German aerodynamicist Albert Betz [12] found in
1920 that the maximum power extractable from the wind in an imaginary wind tube
amounts
(1.4)
This is called the Betz Limit and until today no wind turbine has been designed surpassing
this limit. The complete derivation of the Betz Limit can be found in many text books
dealing with wind turbine aerodynamics, such as [3] or [11].
4
Background
Another important parameter used to describe the performance of a wind turbine is the
thrust coefficient
, which is often used to describe the load onto the turbine blades and
the structural design of the turbine tower. It is defined as the total axial thrust force
onto the rotor divided by a dynamic reference force from the wind onto the rotor area.
(1.5)
In theory the power coefficient
can be increased by increasing rotational speed of the
turbine, by increasing the number of rotor blades or by increasing the lift by either
pitching the blades or increasing chord length [11].
The rotational speed
of the turbine is often represented by a non-dimensional
parameter called tip speed ratio , which is defined as the speed of the rotor tip divided by
the approaching wind speed
.
(1.6)
The non-dimensional parameters
and
of a wind turbine vary with the incident wind
speed as well as the rotational speed of the turbine, which are included in the tip speed
ratio
. This makes it possible to express the performance of a wind turbine in
characteristic curves. Typical performance curves for power and thrust of a modern wind
turbine are shown in Fig. 1.2.
Fig. 1.2:
Typical CP- and CT– curves of a modern wind turbine
5
Background
The power coefficient
features a distinct maximum at a certain tip speed ratio , for
which ideal flow conditions predominate in every section of the turbine blade profile. This
point is usually the design operating point of the wind turbine. Modern wind turbines
usually reach a maximum
value of around 0.45 to 0.50 [13], which is significantly
below the Betz limit. Firstly, no blade design is aerodynamically perfect so that there are
always losses due to drag. There always will be aerodynamic losses at the blade tips and
blade roots for any blade design [11]. Additionally, friction losses in the bearings and
gearbox have to be taken into account. At lower than design tip speed ratios a negative
angle of attack at the inner section of the blade (close to the blade root) causes stall. This is
often referred to as the “stall region”, in which considerable power losses occur [14]. At
higher than design tip speed ratios highly positive angles of attack cause a considerable
amount of drag on the blades, which is responsible for a significant decrease in the power
coefficient with increasing tip speed ratios [11]. In this region, the flow separates from the
blade profiles. When the turbine does not extract any more energy from the wind, the
value consequently goes down to zero again. The inner part of the rotor aerodynamically
acts as a propeller, which actually adds energy to the fluid. Only the outer part of the rotor
performs as a turbine and still extracts energy from the wind flow. When the amount of
energy added to the flow and extracted from the flow are in balance, this is called the “runaway” point of the wind turbine. In case the wind turbine would not be connected to an
electrical generator, the turbine would rotate at the tip speed ratio
The thrust coefficient
at the run-away point.
of a wind turbine is of great importance for the construction of
the rotor support and the structural design of the turbine tower [11]. It continuously grows
with increasing tip speed ratio. The blockage effect of the rotor rises with increasing
rotational speeds and thus causes higher thrust forces onto the turbine. In the transition
from the stall region to the optimum tip speed often a slight buckling of the curve can be
observed as the blades are not operated in stalled conditions any more.
6
Background
1.2.2 Blade Aerodynamics
The blades of a wind turbine are designed with the goal to extract as much energy from the
wind as possible. Dependent on the wind speed at the turbine site and a variable or
constant rotational speed operation of the turbine, a specific blade design is developed.
Most turbine blades are designed according to the blade element method wherein the
blades are cut into infinitesimally small span-wise blade elements. On every blade
elements the two-dimensional cross section is adjusted so that the angle of attack and the
aerodynamic forces are optimized.
During the operation of a wind turbine many situations occur where the flow locally does
not hit the blades at the designed angle of attack. This can be caused by the highly
stochastic wind field hitting the rotor as well as too slow or too high rotational speeds of
the rotor, which can lead to stall at a certain section of the blade. The development of stall
at a span-wise blade element is depicted in Fig. 1.3.
Fig. 1.3:
Stream lines around wind turbine blades at different angles of attack
Fig. 1.3 (a) shows a wind turbine blade profile hit by the incoming relative flow at the
design angle of attack. The flow adheres and follows the blade profile perfectly. When the
relative angle of attack is increased as shown in Fig. 1.3 (b) it is still possible that the flow
7
Background
adheres and follows the profile. Exceeding the critical angle of attack, a certain limit
dependent on the blade profile itself, however, the flow cannot follow the blades contour
anymore and highly turbulent recirculation zones appear near the blade surface as shown
in Fig 1.3 (c). So-called stalled conditions are dominant in this section of the blade
resulting in substantial aerodynamic losses.
The span-wise position on the blade, the operating conditions of the turbine and the
composition of the incoming wind to the rotor have a considerable influence on the flow
exiting from the turbine rotor. The flow behind the turbine rotor is called wake and it is
characterized by very turbulent flow. The flow field in the wake behind the rotor is
influenced by a number of aerodynamic effects.
1.2.3 Wake Aerodynamics
The aerodynamic conditions prevailing in the wake of a wind turbine have been one of the
main topics of research since the beginning of wind turbine research. As mentioned above
stall is an essential phenomenon during the operation of a wind turbine, which together
with non-uniform transient inflow defines the general aerodynamic conditions prevailing
in the wake of a wind turbine. Although a modern rotor of a horizontal axis wind turbine
only consists of three rotating blades, many aerodynamic effects combine to a very
complex flow field in the wake. In a comprehensive literature study about wind turbine
wakes from 2003, Vermeer et al. conclude that “some of the most basic aerodynamic
mechanisms governing the power output are not yet fully understood” [10].
The main features of the turbine wake are a considerable velocity deficit and increased
turbulence levels. The velocity deficit yields a significantly lower power extraction of the
downstream wind turbines in a wind farm arrangement. The increased turbulence levels
in the wake can involve bigger fatigue loads on the downstream turbines [14].
The aerodynamic structures of the flow field in the wake of a wind turbine rotor depend on
many different parameters. The aerodynamics of the incoming flow, the aerodynamic
design of the blade as well as the rotational speed of the rotor itself have an influence on
which sections of the blades stall occurs or not. However, there are some basic
aerodynamic phenomena, which are predominant in almost every wind turbine rotor.
8
Background
One of the most important aerodynamic phenomena is the rotation of the flow field in the
wake of a wind turbine rotor. The velocity triangles in front of (Index 1) and behind
(Index 2) a cross section of a wind turbine blade are sketched in Fig. 1.4.
Fig. 1.4:
Velocity triangle on a wind turbine blade
Under idealized conditions there is a purely axial inflow (1)
to the wind
turbine rotor. In the flow field downstream of the rotor (2), however, the absolute flow
velocity features a velocity component in circumferential direction
creating a rotation
of the flow in the wake behind the rotor. As it can be seen in Fig 1.4, the circumferential
component
causes the wake to counter-rotate in respect to the direction of rotation of
the turbine rotor
. Manwell et al. rationalize that the “flow behind the rotor rotates in
the opposite direction to the rotor, in reaction to the torque exerted by the flow on the
rotor” [3].
However, also a number of other aerodynamic phenomena have to be taken into account
when investigating the turbulent structures in the wake. Another dominating
phenomenon is the formation of the tip vortex, which leads to a shear layer that separates
the highly turbulent flow in the rotor wake from the surrounding ambient flow. Wind
turbine blades have a profile that creates aerodynamic lift similar to the profile of an
airplane wing. The air around a blade profile is accelerated that a pressure side (PS) and a
9
Background
suction side (SS) are established. The pressure difference between the PS and the SS
generates the aerodynamic lift and thereby sets the blades into rotation.
On the tip of the blade a three-dimensional secondary flow establishes. In order to
decrease the pressure difference between the high pressure air on the pressure side flows
around the blade tip to the lower pressure on the suction side as shown in Fig. 1.5. This
secondary flow around the tip mixes with the main flow around the blade, which creates a
vortex behind the blade tip.
Fig. 1.5:
Formation of the tip vortex
A similar observation can be made at the wingtips of airplanes where the tip vortex
phenomenon considerably reduces the effective area of the wing that creates lift. The tip
vortex is characterized by high velocities and low pressures and induces additional
aerodynamic losses. This can be attributed to the fact that the effective angle of attack is
reduced in regions close to the tip as some air is sucked sideways through the pressure
gradient at the tip [15].
On most wind turbine blade designs there is also a sharp edge near the root of the blade.
Also around the root edge a secondary flow establishes due to the pressure gradient
between the blade’s pressure and suction side. When mixing with the main flow the root
vortex is generated in the same way as described above. However, the aerodynamic losses
caused by the root vortex are assumed to be considerably lower than those by the tip
vortex as the relative velocities are significantly lower near the root [16].
10
Background
The tip vortices shed by the turbine blades move further downstream in helical spirals. As
the speed of the blade tips
speed
usually is much higher than the incoming wind
, the distance between the tip vortex spirals is very low. Therefore, the vortex
system can be approximated as a very turbulent cylindrical shear layer [17]. A schematic
sketch of the tip vortices forming a cylindrical shear layer is presented in Fig. 1.6.
Fig. 1.6:
Cylindrical shear layer in the wake of the rotor induced by tip vortices
The low velocity turbulent flow in the wake is separated from the surrounding faster
moving laminar flow by this shear layer. Moreover, the considerably weaker root vortices
create a turbulent swirl in the region around the rotor axis, which is however of
significantly weaker intensity.
It has been shown that the aerodynamics in the wake behind a wind turbine rotor is
characterized by a complex vortex system, which is influenced by a number of different
phenomena: the structures in the incoming wind flow, the swirl generated by the rotation
of the blades, the root vortices and the shear layer created by the tip vortices. Additionally,
the geometry of the wind turbine tower and nacelle affect the turbulent structures
prevailing in the wake.
11
Background
The distinct tip and root vortices destabilize when moving downstream. The small-scale
turbulence of the vortices brakes down into large-scale turbulence due to turbulent mixing
processes [18]. Fig. 1.7 shows a model of the turbulent mixing process in the wake behind
the rotor and the corresponding velocity profiles.
Fig. 1.7:
Turbulent mixing process in the wake behind a wind turbine rotor
Moving further downstream, the cylindrical shear layer expands due to turbulent
diffusion. The turbulence in the shear layer mixes the slow moving fluid in the wake with
high velocity fluid surrounding it. Thus, momentum is transported into the wake, which
results in a wake expansion but reduction in velocity deficit [19]. The mean velocity
gradually recovers and the velocity profiles smoothen when moving downstream in the
wake as shown in Fig. 1.7. At a certain downstream distance the shear layer reaches the
center of the wakes indicating the end of the “near wake” region. After a “transition
region” the wake is completely developed, which is thus called the “far wake region” [17].
The root vortices and tip vortices are predominant in the near wake regions. The number
of blades, adherent or stalled flow and three-dimensional flow have a large influence on
the flow in this region [10]. In the far wake region, however, the focus is no longer on the
flow phenomena around the rotor blades. The single turbulence generating phenomena
have mixed into a general turbulence distribution, which dominates the flow [18]. When
modeling an entire wind farm, far wake simulation is the main focus [10].
When defining the downstream distance x/D, where the near wake ends, different values
can be found in the literature. Vermeer et al. [10] as well as Sanderse [19] define the near
wake to be over at around x/D=1, whereas Gómez-Elivra et al. [17] claim that the near
wake ends somewhere between x/D= 2-5 rotor diameters.
12
Background
1.3 Wind Farm Arrangement
During the last decades strong efforts have been made to increase the efficiency of wind
turbines in order to extract as much energy as possible from the wind. The research
focused on optimizing the single components of a turbine. Gearless wind turbines were
introduced and another main focus was the aerodynamic optimization of the turbine
blades.
When it comes to optimizing a whole wind farm as one single power production device,
also the aerodynamic interactions between the single turbines of the wind farm have to be
taken into account. As the first row wind turbines extract a considerable amount of the
kinetic energy in the wind there is much less energy left for the turbines in the following
rows. The distance between the single turbines, the arrangement pattern and the amount
of power extracted from the wind by the single turbines are some of the most important
parameters when designing a wind farm.
Fig. 1.8:
Wind turbine wake effects in the Danish offshore wind farm “Horns Rev 1” [20]
Fig. 1.8 shows the turbulent flow field in the Danish offshore wind farm “Horns Rev 1”. At
the time the picture was taken the air in the rotor plane of the turbines was very humid.
The rotating wind turbine blades locally induced condensation of the humid air making it
possible to see the turbulent flow structures in the wake of the wind turbines [20]. It can
13
Background
be clearly seen that the turbulent flow in the wake of the first row turbines hits and
interacts with the following turbine rows.
There are two main effects of wake interaction in a wind farm arrangement. Obviously, the
velocity deficit in the wake of the first turbine yields a significantly lower power extraction
of the following downstream wind turbines. Furthermore, the increased turbulence levels
in the wake of the first row turbines cause higher fatigue loads for the downstream
turbines [10].
In order to investigate the aerodynamic properties prevailing in a wind turbine wake CFD
computer simulations and wind tunnel experiments on model wind turbines are nowadays
performed. Full scale measurements on wind turbine wakes are by far too expensive or
simply not possible.
In a CFD simulation Ivanell et al. [21] investigated the propagation of the wake through an
array of two wind turbines. In this Large Eddy Simulation (LES) study the Actuator Disc
Method (ACD) was used for modelling the wind turbines. Applying the 3D solver
“EllipSys3D” and multi block finite volume grid, the first turbine was impinged with a pregenerated turbulence. Fig. 1.9 shows a 2D plot of the velocity deficit in the wake
propagating through three turbine rows at a zero degree inflow angle.
Fig. 1.9:
CFD simulation of the propagation of wind turbine wake in a wind farm
arrangement [21]
From this simulation Ivanell et al. [21] conclude that turbulent inflow to the first row
turbines leads to a complex but realistic flow structure in the wake. They state, however,
that this study does not give any correlation between the turbulence intensity of the inflow
and the level of production yet. In order to be able to find a correlation further
investigations would have to be made including real wind farm measurement data for
verification.
14
Background
When designing a wind farm an economic compromise for the separation distance of the
single wind turbines has to be found. On the one hand space in a wind farm is not
unlimited; on the other hand the losses in energy extraction due to wake interactions are
quite considerable. In modern wind farms, such as the Horns Rev 1 from 2002, the single
wind turbines are set up with a separation distance of around 7 rotor diameters (7D) [22].
In a recent study, however, Barber et al. [23] recommend that the spacing between the
single turbines should be increased to 12-15D in order to optimize the overall power
output. According to Barthelmie et al. [24] the average power losses that can be ascribed
to wind turbine wakes range in the order of 10-20% compared to a wind farm of
unobstructed turbines.
The effect of increased fatigue loads on the downstream turbine due to turbulent flow in
the wake was measured to be 80% in a real wind farm in Vindeby, Denmark [19]. As a
consequence the blades of the downstream turbines are predicted to have a considerably
shorter lifetime. Nevertheless, the difference in fatigue loads on turbines operating in the
wakes of multiple upstream turbines was found to be small [19].
In fact the arrangement of the single turbines in a wind farm in order to maximize the
overall power output is a very complex problem. In a study from 2007 Marmidis et al. [25]
applied the mathematical “Monte Carlo” method to simulate the maximum energy
production versus the minimum installation costs of different placement patterns of the
turbines in a wind farm.
When optimizing a wind farm with respect to the overall maximum power output, not only
the separation distance and the placement pattern, but also the operation points of the
single turbines are of importance. By extracting a lower amount of energy from wind by
the upstream wind turbine more kinetic wind energy is left for the downstream turbine.
This reduction in the so-called axial induction factor can be achieved by controlling the
blade pitch angle or the tip speed ratio of the upstream turbine. An investigation by
Johnson and Thomas [26] has shown that an operation of the first turbine slightly below
its maximum power point considerably increases the power output of the downstream
turbine and thereby increases the overall output of the two turbine setup. This implies that
the total power output of wind farm might be enhanced by actively controlling pitch angle,
yaw angle and tip speed ratio of the single wind turbines.
15
Background
1.4 Motivation
One of the main goals in modern wind farm design is to reduce the interaction between
the single wind turbines. However, the disposable space for a wind farm is not unlimited,
which results unavoidably in interactions of the wind turbine wakes for certain wind
directions. In a wind farm the wakes of the first row turbines cause a non-uniform flow
field, which hits the second row turbines.
The wake of a horizontal-axis wind turbine can be characterized by turbulent flow
structures in rotational motion. A substantial velocity deficit and high turbulence
intensities are the main features in the wake of a wind turbine. The velocity deficit is equal
to a loss of kinetic energy in the wake, which constitutes a loss of power available for the
downstream turbines. Increased turbulence levels may affect the dynamic loads onto the
rotor blades of the downwind turbines. Furthermore, it could be possible that the swirling
motion exiting from a wind turbine rotor could excite an eigenfrequency of the blades of
the downstream turbine and thereby cause material fatigue.
Investigating the influence of the wake of the upstream turbine onto the performance and
dynamic behavior of the downstream turbine the next logical step is to examine the wake
behind the downstream turbine. A number of numerical models have been and are being
developed, which require comprehensive experimental data for validation. Wind tunnel
simulations under controlled conditions are a powerful means to achieve this.
Moreover, this experimental study of the wake behind an array of two model wind
turbines shall contribute to a comprehensive understanding of the turbulent flow
structures in wind turbine wakes, which could be helpful in the planning and design of
future wind farms.
16
Objectives
2 OBJECTIVES
The main focus of performing the measurements in the wind tunnel laboratory at NTNU is
to get a picture of the flow conditions, i.e. the local velocity deficit and the turbulence
intensities, in the wake behind an array of two model wind turbines. This study shall help
to get an extensive knowledge of the complex flow field in wind turbine wakes and act as
an experimental database for the validation of numerical models. It is desirable that this
experimental study can contribute to yield data that can be used in the design of future
wind farms.
The objectives of the present work are the experimental investigation of
•
the influence of the wake of the first turbine onto performance of the downstream
turbine at different turbine separation distances
•
the axial development of the local velocity deficit and turbulence intensities in the
wake downstream of the second turbine
•
the axial development of the dimensions of the wake
•
the influence on the velocity deficit and turbulence intensities when the distance
between the first and second turbines is increased
•
the effect of different tip speed ratio combinations of the first and second turbine
onto the flow field in the wake behind the second turbine
17
Objectives
18
Methodology
3 METHODOLOGY
This experimental investigation is performed in the wind tunnel at NTNU’s Department of
Energy and Process Technology. The closed-return wind tunnel is equipped with one force
balance, which makes it possible to measure the thrust force onto one of the two model
wind turbines.
Two fully operational three-bladed model wind turbines with a rotor diameter of about
are available. Both turbines are equipped with torque sensors on their rotor
shafts and optical RPM-sensors inside the hub casing. It is thereby possible to measure the
power the turbine extracts from the wind directly.
Inside the wind tunnel there is a three-axis traverse system installed, which can be
controlled by a LabVIEW computer program. This traverse system allows scanning the
flow field in the wake of the wind turbine arrangement automatically. To do this, a parallel
setup of a Pitot tube and a hot wire probe is used. The hot wire signal is calibrated against
the signal acquired from the parallel Pitot tube, which itself is calibrated against a manual
Lambrecht manometer. The hot wire probe is connected to a Constant Temperature
Anemometry (CTA) circuit. The output signal yields a velocity signal with very high
frequency resolution, which then can be recalculated into a mean velocity and turbulence
intensity.
A National Instruments BNC-2110 data acquisition board and an in-house designed
LabVIEW routine are used to record the acquired data on the computer.
For the post-processing of the recorded data an in-house programmed FORTRAN routine
temperature-corrects the data acquired from the hot wire and converts it to mean velocity
and turbulence intensity values. Finally, meaningful plots are created using the software
MATLAB for the evaluation of the measured flow parameters.
19
Methodology
20
Experimental Setup
4 EXPERIMENTAL SETUP
4.1 Test Rig
4.1.1 Closed-Return Wind Tunnel
This experimental study is performed in the large wind tunnel at the Department of
Energy and Process Technology at NTNU. The driving fan has a maximum power of
, which makes it possible to generate wind speeds up to
in the
test section of the wind tunnel. The air flow enters the test section through an inlet
contraction, which is equipped with static pressure holes at the circumferences of two
defined cross sections. In chapter 4.2.3 it is explained how these pressure holes are used to
calculate the inlet speed of the wind tunnel.
Fig. 4.1:
Wind tunnel at the Fluid Engineering laboratory at NTNU [27]
As shown in Fig. 4.1 the airflow then enters the
tunnel. It has a cross section of
long test section of the wind
height and
width. The roof of the
tunnel is adjusted so that a zero static pressure gradient is present in flow direction over
the entire test section [14]. After passing through the driving fan, the air flows back to the
inlet contraction in a closed loop tunnel above the test section.
21
Experimental Setup
4.1.2 Model Wind Turbines
In NTNU’s wind tunnel laboratory two fully operational model wind turbines are
available. Both model wind turbines were originally designed as prototypes for tidal
turbines by the Norwegian company Hammerfest Strøm AS. The turbines are now
equipped with new wind-optimized blades, which are described in chapter 4.1.3 in detail.
Fig. 4.2 shows a picture of the first experimental setup with both model wind turbines
established in NTNU’s wind tunnel.
Fig. 4.2:
The two model wind turbines set up in the wind tunnel of NTNU
The first model wind turbine (Tu1) is mounted on a 6-component force balance, which is
located underneath the test section of the wind tunnel. The force balance makes it possible
to measure the thrust force onto the turbine and is more thoroughly described in chapter
4.2.9. The second model wind turbine (Tu2) is fixed on the wind tunnel floor through a
wooden plate. The rotors of both model turbines are driven by a 0.37 kW AC electric
motor produced by Siemens [28]. The motor is located at the level of the wind tunnel floor
and drives the rotor axis through a belt, which runs inside the turbine mast for the first
turbine respectively behind the turbine mast for the second turbine. The rotational speed
both turbine rotors is controlled by a Siemens Micromaster 440 frequency inverter from
22
Experimental Setup
outside of the wind tunnel. The motors can be impinged with a wide range of rotational
speeds and similarly work as generators when the turbine rotors are subject to an external
wind load. The inverters are connected to a standard electrical heater, which acts as an
electrical load for the excess power produced by the turbine rotors in this case.
Fig. 4.3 shows a sketch of the basic experimental setup in the wind tunnel. The separation
distance
between the two model turbines can be varied. The dashed red lines refer to
the axial downstream measurement locations where the aerodynamic probes are traversed
in order to record the flow field in the wake of the turbines. An overview of the most
important dimensions is presented in Table 4.1.
Fig. 4.3:
Experimental setup and reference orientation
Rotor diameter Tu1
D1
940 mm
Rotor diameter Tu2
D2
900 mm
Hub diameter Tu1
dhub1
130 mm
Hub diameter Tu1
dhub2
90 mm
Hub height Tu1
hhub1
950 mm
Hub height Tu2
hhub2
950 mm
Separation distance between the turbines
x/D1
3 resp. 5
Wind tunnel height
h
1900 mm
Wind tunnel width
w
2700 mm
Wind tunnel length
l
12000 mm
Table 4.1:
Dimensions of the experimental setup
In comparison to a real wind turbine, the rotor dimension of the model turbines are in the
scale of about
. With a hub diameter of
respectively
the dimensions of the nacelle are much bigger in respect to the rotor diameter than in a
real turbine. This has to be taken into account when analyzing and comparing the
structure of the wake behind the turbine.
23
Experimental Setup
The first model wind turbine, which is mounted on the force balance, is additionally
supported by four wooden blocks in order to achieve the same hub height as the second
turbine. Both turbines are positioned centrally in the wind tunnel having an equal distance
to both wind tunnel side walls. Paying to the fact that both turbines are equipped with the
exactly same blades but the hub diameter of the first turbine is slightly bigger, the rotor
diameter of the first turbine exceeds that of the second turbine insignificantly.
4.1.3 Turbine Blades
As mentioned above both model wind turbines are equipped with the same blades.
Standard NREL airfoils of the type S826 with a 14% thickness are used. The chord length
distribution and the twist of the rotor blade are designed according to a standard blade
element momentum method [29].
Fig. 4.4 shows a view onto the model blade in streamwise and circumferential projection.
Fig. 4.4:
View on blade in (a) chordwise view and (b) leading edge view [29]
The profile, which features a separation ramp at the back, is designed for a Reynolds
number of
to give maximum lift [29]. According to Krogstad and Lund
the blade geometry can be characterized by a “gentle separation due to trailing edge
ramp”, a “rapid transition on suction side due to small radius of curvature”, a “low
sensitivity to surface roughness” and a “strong separation on lower side at negative angle
of attack” [29]. A cross section of the NREL S826 profile is shown in Fig. 4.5. Further
information on the profile can be found in the document [30].
24
Experimental Setup
Fig. 4.5:
Scaled blade profile NREL S826 14% thickness [30]
A comprehensive investigation of the blade geometry mounted on the Department’s
second model wind turbine (Tu2) was performed by Karlsen [16] as well as Krogstad and
Lund [29] applying experimental and computational methods.
4.1.4 Traverse Mechanism
The test section at NTNU’s wind tunnel is equipped with an automatic computercontrolled traverse mechanism as sketched in Fig. 4.6. The traverse system is fixed on rails
right underneath the roof of the wind tunnel. It is possible to bring the traverse
mechanism into the right streamwise position by moving it manually on the rails.
Fig. 4.6:
Automatic traverse system installed in NTNU’s wind tunnel
With an aerodynamic probe connected to it, the traverse system allows automatic flow
measurements at almost any position in the wind tunnel. The position of the probe can be
controlled by a computer in all three dimensions using in-house designed LabVIEW
software.
25
Experimental Setup
4.2 Instruments
4.2.1 Barometer
The ambient pressure is acquired through a mercury barometer produced by Lambrecht.
It is manually read from a mercury column in the unit [mm Hg]. If needed, the pressure
can be recalculated into [Pa] using the formula
[
]
[
]
(4.1)
4.2.2 Inlet nozzle
Before the air flow enters the test section of the wind tunnel, it passes through an inlet
contraction, which is simultaneously used as a nozzle that measures the inlet velocity. In
this contraction there are pressure holes around the entire circumference at two defined
axial stations as schematically shown in Fig. 4.7. By measuring the pressures
these defined circumferences and knowing the areas
the velocity
and
and
at
, it is possible to calculate
at the outlet of the contraction. This velocity is equal to the inlet velocity to
the test section
of the wind tunnel.
Fig. 4.7:
Schematic sketch of the inlet contraction
Applying the continuity equation the inlet velocity can be calculated from
√
(
26
)
(4.2)
Experimental Setup
In the present wind tunnel the area ratio square is
(4.3)
4.2.3 Reference Pitot tube
In order to be able to double check the velocity at the wind tunnel inlet a Pitot tube is
installed at a height of about
above the wind tunnel floor and a distance of about
from the right wind tunnel wall.
It is possible to calculate the velocity
from the pressure difference given by the
Pitot tube.
(4.4)
√
In contrast to the inlet speed acquired at the inlet contraction
, the velocity
is only acquired in one defined position at the wind tunnel inlet.
4.2.4 Thermocouple
For acquiring the temperature in the wind tunnel a thermocouple is placed at the right
wind tunnel wall. The voltage from the thermocouple is converted into a signal on a
National Instruments NI 9211 thermocouple board and sent to the computer. The
temperature in the wind tunnel is used to calculate the air density and for the temperature
correction of the hot wire signal during the post-processing of the acquired data.
27
Experimental Setup
4.2.5 Traverse Pitot tube
The flow field in the wake behind the model turbines is traversed using another Pitot
probe and a hot wire probe in a parallel setup as depicted in Fig. 4.8.
Fig. 4.8:
The velocity
Parallel probe setup
is again calculated from the pressure difference of the total and the
static pressure measured with the Pitot tube.
(4.5)
√
The hotwire probe has a much higher frequency response than a Pitot tube and therefore
is much more appropriate for measurements in turbulent flow. The Pitot tube fixed right
next to the hot wire probe is however essential for the calibration of the hot wire probe. It
also can be used to double-check the velocity values acquired by the hot wire probe.
4.2.6 Hot wire probe
The main instrument for acquiring the velocity field in the wake behind the model
turbines is a hot wire probe connected to a constant temperature anemometry (CTA)
circuit. The probe head of a hot wire probe consists of a very thin tungsten wire in the
range of
in diameter connected to two prongs [31]. The resistance of the wire changes
28
Experimental Setup
with the wire Temperature
, which itself is a function of the flow velocity
because of
the convective heat transfer ̇ from the wire.
Hot wire anemometry is an appropriate technique to measure velocity fluctuations in
turbulent flow. Hot wires feature a high time resolution, which makes it possible to record
fluctuations up to several hundred
[32]. For all measurements performed in the scope
of this project a non-commercial in-house prepared single-wire probe is applied. A
frequency response test performed according to Jørgensen [32] yielded a system
bandwidth of
. A basic sketch of a hot wire probe is presented in Fig. 4.9.
Fig. 4.9:
Hot wire probe
The hot wire probe is connected to a CTA circuit, which contains a Wheatstone bridge as
depicted in Fig. 4.10. Therein, the probe is connected to one arm of the bridge and
supplied with electrical current at exactly the same rate as heat is lost to the surrounding
flow [32]. The variable resistor
defines the operating resistance and the operating
temperature of the hot wire. The bridge is balanced by a servo amplifier , which keeps the
wire resistance
constant. Thus, also the wire temperature remains constant
independently of heat transfer rate to the surrounding fluid.
Fig. 4.10:
CTA circuit containing a Wheatstone bridge
29
Experimental Setup
If the bridge is in balance there is no voltage difference
over the bridge. In case of an
increase in flow velocity the wire resistance decreases. Thus, there will be a voltage
difference at the input of the current regulating amplifier
, which then increases the
current supplied to the hot wire. Accordingly, the wire resistance
increases until the
Wheatstone bridge is balanced again. Therefore, the bridge voltage
is dependent on the
convective heat transfer to the surrounding fluid [31].
A comprehensive and very useful practical guide for hot wire anemometry is written by
Jørgensen [32].
4.2.7 RPM sensor
Moreover, the two model wind turbines are equipped with optical RPM sensors inside the
hub casing. A metal disc with a small gap in one position is fixed to the rotor axis inside
the casing. When the gap is passing the optical sensor, it gives a signal.
Fig. 4.11 shows the position of the optical rpm sensor inside the hub casing of the second
turbine.
4.2.8 Torque transducer
Both model wind turbines are equipped with torque transducers connected to the rotor
shaft. The location of the torque sensor inside the second model wind turbine (Tu2) is
shown in Fig. 4.11.
30
Experimental Setup
Fig. 4.11: Cross section of the hub of the second turbine [27]
A torque transducer of the type T20W N/2 Nm sold by HBM is installed. After being
calibrated, the torque transducers make it possible to obtain the torque by the wind onto
the turbine rotor.
4.2.9 Force balance
The wind tunnel at NTNU is equipped with a six-component force balance produced by
Carl Schenck AG, which makes it possible to acquire the thrust force from the wind onto
the turbine mounted on it. However, just one turbine can be fixed on the balance. During
this measurement campaign the force balance is installed underneath the wind tunnel
near the wind tunnel inlet. Therefore, the first model wind turbine was installed on it. It is
possible to rotate the force balance 360°, which can be useful for wake measurements in
yawed conditions.
31
Experimental Setup
4.3 Instrument calibrations
4.3.1 Pressure transducer calibration
Before starting with the actual velocity measurements the three pressure transducers
connected to Inlet Contraction pressure holes, the Reference Pitot tube and the Traverse
Pitot tube have to be calibrated. The pressure transducers convert a pressure difference
[Pa] into an electrical signal [Volt].
For the calibration procedure the pressure transducers are connected in parallel to a
manual Lambrecht manometer. Thereafter, the wind tunnel speed is increased in defined
steps yielding an increase in the alcohol column of the Lambrecht manometer and an
electrical signal from the pressure transducer.
Fig. 4.12 shows an example of a calibration curve for one of the pressure transducers.
Fig. 4.12: Calibration curve of a pressure transducer
Knowing the density of the methylated alcohol, the alcohol column at the Lambrecht
manometer can be recalculated into a pressure difference in [Pa]. Plotting the pressure
difference in [Pa] versus the electrical signal in [Volt] a linear dependency can be derived.
By fitting a straight line to the measured values the calibration coefficient
can be found.
32
in [Pa/Volt]
Experimental Setup
4.3.2 Hot wire calibration
As explained in chapter 4.2.6 the electrical signal at the output of the CTA circuit is the
bridge voltage
[Volt]. This signal is calibrated versus the velocity
[m/s] acquired
from the Traverse Pitot tube, which is positioned right next to the hot wire probe
(Fig. 4.8). As shown in an exemplary calibration curve in Fig. 4.13 the dependency of the
velocity on the hot wire voltage is not linear.
Fig. 4.13: Calibration curve for the hot wire probe signal
A higher grad polynomial fit must be applied in order to create a calibration curve. For this
project a fourth grade polynomial fit function is applied yielding five calibration
coefficients.
4.3.3 Torque sensor calibration
Moreover, the torque sensors connected to the turbine shafts have to be calibrated. This is
done by blocking the rear part of the rotor shaft and creating a defined torque on the
frontal part of the shaft. Step by step defined weights are put onto a hanging device, which
is connected to a rotor blade in a certain distance. The torque sensor is subjected to
defined values of torque in [Nm] simultaneously yielding an electrical signal in [Volt]. A
linear dependency between the torque [Nm] and the signal [Volt] is found yielding one
calibration coefficient
in [Nm/Volt].
33
Experimental Setup
4.3.4 Force balance calibration
One of the two model turbines is mounted on the six-component force balance making it
possible to acquire the thrust force onto the rotor. In the scope of this project all
experiments are performed with a rotor yaw angle of zero degrees. Thus, only one
component of the force balance in axial direction, the R6 component, has to be calibrated.
Similar to the torque sensor calibration, defined weights are successively put onto a
hanging device creating defined force values [N] onto the R6 force transducer. Also for the
force balance a linear dependency between the force [N] and the electrical signal [Volt]
from the force transducer is found. One calibration coefficient
linear regression.
34
in [N/Volt] is derived by a
Experimental Setup
4.4 Control System
The signals of the pressure transducers, the CTA circuit, the torque sensors and the force
balance are first amplified and then digitalized by a National Instruments BNC-2110 data
acquisition board. An in-house designed LabVIEW interface is used to control the
acquired values. The LabVIEW routine features a window for real time signal monitoring
as well as acquisition window, which makes it possible to log the acquired data into ASCIIformatted file text files.
By controlling the sampling frequency and the number of samples attained per
measurement point it is possible to set the sampling time. For thrust force and torque
measurements
with a sampling frequency of
are taken resulting in
of sampling time per measurement point. The mean averages of the measured
thrust forces and torques are taken over the sampling time of
. For Pitot tube
and Inlet contraction measurements the same settings are sufficient.
When sampling the signal from the hot wire probe, however, a much higher sampling
frequency must be used as it is desired to record a high frequency signal of a turbulent
flow. Hence, a sampling frequency of
sampling time of
and
yielding a
is used for hot wire measurements. The time series of all the
single measurement points must be recorded in order to be able to reconstruct the signal
with all its turbulent fluctuations properly. The mean average of the velocity and
turbulence properties can thereafter be derived from the recorded time series samples
over a time span of
.
35
Experimental Setup
36
Measurement Campaign
5 MEASUREMENT CAMPAIGN & DATA EVALUATION
5.1 Measurement Campaign
Within the scope of this project a number of test runs on the described experimental setup
comprising the two model turbines in the wind tunnel are performed. An overview of all
measurements and experimental setups is presented in Table 5.1.
In a first step the flow field at the wind tunnel inlet is scanned using the hot wire probe in
exactly the same cross sectional area, in which later full area wake measurements are
performed. This is done to show that there is a rather uniform laminar inflow with low
turbulence intensities to the first wind turbine. As the flow field is expected to be quite
uniform, this first traverse matrix only contains 117 measuring points.
Thereafter,
and
curves are recorded independently for both model turbines
separately. Therefore, the first and then the second turbine are installed on the force
balance. This is done for a number of different wind tunnel inlet speeds. In addition to the
speed
at the inlet contraction, the torque
at the rotor shaft and the thrust force
from the wind onto the rotor are logged for varying rotational speeds
of the turbines.
This is done to ensure that the wind turbines have regular operating characteristics and to
work out the maximum power point of the turbines.
Although the focus of this investigation is on the wake behind an array of two model
turbines, a number of wake measurements behind one model turbine are performed,
which is referred to as Arrangement (A). This is done in order to generate some data for
comparison with the wake behind two turbines. Measurements of the velocity field in the
wake of one turbine have already been carried out by Adaramola and Krogstad [33].
Additional data for more axial measurement stations and for turbulence intensity are
needed, so that a number of new wake measurements are performed.
The flow field in the wake is scanned in a horizontal line at hub height (
)
behind one model wind turbine (Tu2) at three axial stations 1D, 3D and 5D downstream of
the turbine rotor. For each measurement station the flow field is sampled in 27 measuring
points, from
to
. A sketch of the measurement grid for those
Horizontal Line Wake measurements is presented in Fig. 5.1. The black frame in the
sketch represents the wind tunnel boundaries.
37
Measurement Campaign
Type and location of
Resultant
Method /
Measurement
measurement
parameters
Instruments
points
1. Empty wind tunnel
Area traverse of the wind tunnel inlet
HW CTA
117
2. Arrangement (A): One turbine in the wind tunnel
CP and CT curves of the unobstructed first
RPM sensor,
model turbine (Tu1)at three different inlet
Torque sensor,
wind speeds
Balance
CP and CT curves of the unobstructed
RPM sensor,
second model turbine (Tu2)at five
Torque sensor,
different inlet wind speeds
Balance
Line Wake at 1D, 3D & 5D downstream of
HW CTA
an unobstructed turbine (Tu2)
20 - 25
20 - 25
27 per wake
3. Arrangement (B): Two turbines separated x/D=3 rotor diameters
CP curve of the second turbine operating in
RPM sensor,
the wake of the first turbine (x/D=3)
Torque sensor
Line Wake at 1D, 3D and 5D downstream
of the second turbine
Full Area Wake at 1D, 3D and 5D
downstream of the second turbine
20 - 25
HW CTA
27 per wake
HW CTA
425 per wake
4. Arrangement (C): Two turbines separated x/D=5 rotor diameters
CP curve of the second turbine operating in
RPM sensor,
the wake of the first turbine (x/D=5)
Torque sensor
Line Wake at 1D and 3D downstream of
the second turbine
Full Area Wake at 1D and 3D downstream
of the second turbine
20 - 25
HW CTA
27 per wake
HW CTA
425 per wake
5. Tip speed ratio variations: Two turbines separated x/D= 3 rotor diameters
CP curves of the second turbine for a low
RPM sensor,
TSR (λ=3), the optimum TSR (λ=5,5) and
Torque sensor
a high TSR (λ=9) of the first turbine
20 - 25
Line Wake at 3D downstream of the
second turbine for 9 different TSR
HW CTA
combinations
Table 5.1:
Measurement campaign
38
27 per wake
Measurement Campaign
In a second experimental setup, Arrangement (B), both model wind turbines are installed
in the wind tunnel with a separation distance of
rotor diameters between the
turbines. The first turbine (Tu1) is mounted to the force balance and the second turbine
(Tu2) to the wind tunnel floor. In this setup the power coefficient
of the second turbine
operating in the wake of the first is recorded for varying tip speed ratios . However, it is
not possible to measure the thrust coefficient
force balance. Having acquired the
ratio
of the second turbine as it is not fixed to a
curves both turbines are operated at a tip speed
at their maximum power point for this experimental setup.
The wake behind the array of two turbines is thereafter traversed in a horizontal line at
three axial stations 1D, 3D and 5D downstream of the second turbine rotor. The flow field
is scanned in 27 points in same measurement locations as before ( Fig. 5.1). This line
traverse yields values for the mean velocity deficit
and the turbulence intensities
in the locations of the measuring points.
Fig. 5.1:
Location of measurement points for the Horizontal Line Wake measurements
Furthermore, full area wake measurements are carried out at the same axial stations 1D,
3D and 5D downstream of the second turbine. For each axial measurement station, the
flow field is scanned in a rectangular cross section from
and
to
to
respectively to the center of the rotor hub. The hot
wire probe is traversed in steps of
in vertical and horizontal direction
39
Measurement Campaign
resulting in a measurement grid of 425 measuring point per axial station. The
measurement grid used for the full area wake measurements is depicted in Fig. 5.2.
In a third experimental setup, Arrangement (C), the distance between the turbines is
increased to
rotor diameters. Firstly, a new
curve of the second turbine
operating in the wake 5D downstream of the first is recorded. Again, horizontal line wake
and full area wake measurement are performed in the axial locations 1D and 3D
downstream of the second turbine on the measurement grids shown in Fig. 5.1
respectively Fig. 5.2. Due to length limitations of the wind tunnel, it is not possible to
measure the wake 5D downstream of the second turbine in this experimental setup.
Fig. 5.2:
Location of measurement points for the Full Area Wake measurements
In a final test series of this project the influence of variations in the tip speed ratio
of
both turbines on the flow field in the wake is analyzed. For this investigation the
separation distance between the two turbines is reduced to
rotor diameters
again.
Three
curves of the second turbine are recorded for three different operating points of
the first turbine. The first curve is again logged for the optimum operation point of the
first turbine (
Thereafter,
(
), which has been done in the second experimental setup already.
curves for a low rotational speed (
) and a high rotational speed
) are recorded. Adaramola and Krogstad [14] extensively studied the effect on the
power output of the second turbine when the first turbine is operated at different tip speed
40
Measurement Campaign
ratios. However, the first turbine was equipped with a different set of blades during their
experiments.
Finally, the velocity deficit and the turbulence intensities in the wake are measured in a
horizontal line 3D downstream of the second turbine for nine different combinations of tip
speed ratios of the two turbines. At first, the tip speed ratio of the first turbine is kept
constant while the tip speed ratio of the second turbine is varied to three different
operating points. Similarly, three different tip speed ratios of the first turbine are set while
the rotational speed of the second turbine is kept constant. Consequently, nine horizontal
line wake measurements are performed as shown in Table 6.1.
41
Measurement Campaign
5.2 Data Evaluation
5.2.1 Evaluation of Power and Thrust Curves
As previously mentioned, wind turbine performance curves are usually depicted as
functions of the power coefficient
and the thrust coefficient
ratio . In order to record these curves, the rotational speed
force
over the rotor tip speed
, the torque
onto the rotor are sampled at different inflow velocities
and the thrust
as schematically
shown in Fig. 5.3.
Fig. 5.3:
Data acquisition and evaluation for CP and CT curves
As previously shown in equation (1.6), the tip speed ratio
is defined as the rotor tip speed
divided by the approaching wind speed.
(5.1)
The power coefficient
is calculated as the ratio of the power gained from the wind
turbine and the power available from the kinetic energy from the wind through the rotor
area as previously shown in equation (1.3). As the power onto the wind turbine shaft is
defined as
, the power coefficient can be directly calculated from equation (5.2).
(5.2)
The thrust coefficient
is defined as the total axial thrust force
onto the rotor divided
by a dynamic reference force from the wind onto the rotor area as previously shown in
equation (1.5).
(5.3)
42
Measurement Campaign
5.2.2 Evaluation of Wake Velocity Field
The flow field in the wake behind the array of the two model wind turbines is traversed
with a parallel setup of a Pitot tube and a hot wire probe. The Pitot tube is only used for
the calibration of the hot wire circuit and to double check the acquired data from the hot
wire signal. Sampling the time series of the hot wire exposed to highly turbulent flow in
the turbine wake, a signal of high frequency is recorded. The signal is evaluated regarding
the mean velocity deficit
⁄
[-] and the turbulence intensity
⁄
[%] in the wake.
For temperature correction and statistical evaluation of the hot wire signal, in-house
designed FORTRAN routines are used. The results are plotted using the evaluation
software MATLAB.
5.2.2.1
Velocity Deficit
Hot wire measurements are very temperature-sensitive as the bridge voltage
dependent on the fluid velocity and temperature. A temperature change of
is
yields a
velocity error of approximately 2% [31]. During longer hot wire measurements the fluid
temperature is observed to rise between 5 and 8 K. Therefore, a temperature correction is
essential.
The bridge voltage
at the output of the CTA is temperature corrected according to
(
For a discrete number of
)
(5.4)
measuring samples the mean velocity
is averaged as
follows:
∑
(5.5)
The velocity deficit is defined as the ratio of mean velocity
and freestream velocity
(5.6)
The velocity deficit
is a non-dimensional parameter [-].
43
:
Measurement Campaign
5.2.2.2 Turbulence Intensity
In chapter 1.2.3 it is explained how the rotor of a wind turbine induces turbulences to the
flow in the wake. Turbulent flow is characterized as a three-dimensional, non-stationary
flow and strongly rotational flow [34]. The sequence of the measured flow parameters is
seemingly influenced by random. Therefore, it must be described statistically. Fig. 5.4
shows an example of a velocity signal acquire from an aerodynamic measurement in a
turbulent flow.
Fig. 5.4:
The actual velocity
velocity
Velocity signal in a turbulent flow
at a certain point of time can be split up into two parts, the mean
and the velocity fluctuation
in that specific point of time:
(5.7)
The turbulent fluctuation
is defined as the standard deviation from the mean. With
being the deviation of one certain measuring point from the mean, the
standard deviation can be calculated.
√ ∑
(5.9)
The turbulence intensity is defined as the ratio of the standard deviation
velocity
and the mean
.
(5.10)
Typically, the turbulence intensity
is given in percentages [%].
44
Measurement Campaign
5.3 Measurement Uncertainty
If the flow parameters of an air flow during an experiment change, it is possible that the
measurements performed with a hot wire probe are distorted. Apart from the flow
conditions, there are several effects in the chain of instruments that can influence the
accuracy of the hot wire signal. That includes the hot wire probe, the anemometer circuit
and the data acquisition board. Additionally, inaccuracies in the instruments used for
calibration have to be taken into account.
The most important source of errors in hot wire measurements are temperature variations
in the flow. According to Jørgensen, a change in temperature of
can evoke an error in
measured velocity of about 2% [32]. The voltage signals of all hot wire measurements
performed in the scope of this project are temperature corrected according to equation
(5.4). Also, variations of the flow pressure, which are directly influenced by the ambient
pressure, can influence the heat transfer at the hot wire. As the pressure difference from
the calibration procedure to the actual measurement is usually small, the influence of
pressure variations is usually neglected. Furthermore, the humidity of the air has an
influence on the heat transfer at the hot wire. However, Jørgensen evaluates this influence
to be very small and thereby negligible [32].
The measurement chain begins at the hot wire probe. A misalignment of the probe head is
a possible source of error. However, this influence can normally be neglected, if the probe
head is aligned in the same way during the calibration procedure and the experiment
itself. The hot wire voltage is balanced by a CTA circuit in the anemometer. Drift, noise
and the frequency response of the anemometer can pose a possible source of error. Also
these influences are estimated to be of minor importance as commercial anemometers
feature low drift, low noise and good frequency characteristics when justified in the right
way. Dependent on the resolution of the data acquisition board, the conversion of the
signal from analog to digital can be a possible source of error. For sufficiently high
resolutions, the influence of the data acquisition board onto the overall measurement
uncertainly is estimated to be very low [32].
A major source of uncertainty in hot wire measurements, however, is assumed to stem
from the probe calibration process. The hot wire signal is calibrated against a Pitot tube as
a reference. The Pitot signal acquired through a pressure transducer is calibrated against a
manual manometer. In this procedure, the flow velocity is calculated from a manual
45
Measurement Campaign
reading of the alcohol column on the manometer. Each of these steps can contain
inaccuracies and therefore must be regarded as a significant source of uncertainty.
As presented in chapter 4.3.2 the dependency of the flow velocity
on the hot wire voltage
is not linear. A higher grade polynomial curve is fitted to the single calibration points,
which involves certain curve fitting errors. This curve fitting process can be a significant
source of uncertainties [32].
To sum up, it can be concluded that the major influences on the uncertainty of a hot wire
measurement can be ascribed to inaccuracies during the instrument calibration process,
the curve fitting errors during the hot wire calibration and temperature variations in the
flow (if not corrected).
46
Results & Discussion
6 RESULTS & DISCUSSION
6.1 Inlet Flow Field
Initially, the flow field at the wind tunnel inlet is scanned in the same cross sectional area
of the subsequent full area wake measurements. The hot wire probe is traversed applying
the automatic traverse, which is positioned on rails right underneath the wind tunnel roof.
No turbines are installed in the wind tunnel during this inlet traverse, which means there
is no blockage effect due to downstream wind turbines. The wind tunnel fan is driven at
, which yields an average inflow wind speed of about
when the
wind tunnel is empty. If the model wind turbines were installed in the wind tunnel, the
blockage due to the wind turbines would causes an increase in average inflow wind
velocity up to around
.
The inlet is traversed at 117 measuring points in an area from
and
to
with respect to the center of the later
installed turbine rotor. Fig. 6.1 shows the results for the mean velocity
turbulence intensity
[m/s] and the
[%] at the wind tunnel inlet.
u’/Um [%]
Um [m/s]
Fig. 6.1:
to
Mean velocity (Um) and turbulence intensity (u’/Um) at the wind tunnel inlet
The velocity distribution in the inlet flow field is quite uniform except for locally slower
velocities near the wind tunnel roof and a slight speed-up near the right wind tunnel
endwall. Mean velocities between
and
near the upper wind tunnel endwall
near the right endwall are measured. The region of slightly higher
wind speeds is outside the rotor area and therefore not a main concern. The slower wind
47
Results & Discussion
velocities near the wind tunnel roof, however, have a significant influence on the inflow to
the rotor. The slower wind speeds in this region can be ascribed to a blockage effect of the
traverse system, which is installed on rails right underneath the wind tunnel roof. The
blockage causes a local increase in static pressure and therefore a decrease in flow velocity.
As the wind tunnel roof is located only
rotor diameters above the wind turbine
center, this phenomenon was also previously discovered by Adaramola and Krogstad [14].
The blockage effect of the traverse system can also be seen in the full area mapping of the
wake development behind the model turbines.
Although the turbulence intensities seem to be vary a little as plotted in Fig. 6.1, they are
actually quite uniformly distributed and at a very low turbulence level. The turbulence
intensities at the inlet of the wind tunnel range between
and
. Although these values are slightly higher than a maximum freestream
turbulence intensity of
measured by Adaramola and Krogstad [33] in the
same wind tunnel, they still can be considered as a very low turbulence levels.
In Fig. 6.2 exactly the same data as plotted in Fig 6.1 is presented. However, in Fig. 6.2 the
same scale for the colour coding as for the full area wake plots is used. The uniformity in
mean velocity (depicted as velocity deficit
here) and turbulence intensity becomes
even more obvious in these plots. Likewise, the slower velocities near the wind tunnel roof
can be observed.
u’/Um [%]
Um/U∞ [-]
Fig. 6.2:
Velocity deficit (Um/U∞) and turbulence intensity (u’/Um) at the wind tunnel inlet
It can be concluded, that, except for a local slow-down in mean velocity near the wind
tunnel roof, the inflow to the first wind turbine is quite uniform and has very low
turbulence intensities.
48
Results & Discussion
6.2 Turbine Arrangement (A): Single Turbine Measurements
The experimental investigation of the wake behind one single turbine is not a main focus
in the scope of this work. A comprehensive study of the turbine performance and the wake
behind one single turbine was already conducted by Adaramola and Krogstad [28], [33] at
NTNU’s wind tunnel laboratory. However, their studies were not performed under exactly
the same boundary conditions. Therefore, some basic performance and wake
measurements are performed again in order to create data for comparison to the wake
behind an array of two wind turbines. The experimental setup and the axial stations for
the hot wire probe measurements are sketched in Fig. 6.3.
Fig. 6.3:
Experimental setup and axial probe measurement stations for turbine arrangement
(A): the single turbine measurements
At first,
and
curves for the first model wind turbine (Tu1) are recorded at different
inflow wind speeds. Thereafter, the second turbine (Tu2) is set up alone in the wind
tunnel. After some
and
curves are recorded for the second turbine at a number of
different inlet wind speeds, wake measurements are performed in a horizontal line in 1D,
3D and 5D downstream of the turbine rotor.
49
Results & Discussion
6.2.1 Turbine Performance Curves
6.2.1.1
First Turbine Performance
The power coefficient and the thrust coefficient of the first turbine (Tu1) are presented in
Fig. 6.4. The curves are recorded for three different inflow wind speeds,
and
,
, which are close to the design inflow wind speed of the
blades.
Fig. 6.4:
Performance curves of the first turbine (Tu1) at different inflow wind speeds:
(a) power coefficient CP and (b) thrust coefficient CT
Analyzing the power coefficient it becomes obvious that the curves for
are almost identical. A slight bump at
respectively at
for
for the
and
curve
can be identified. As these bumps are not very
distinct, they have not been further investigated. The run-away point of the power curve
for
is at about
and hence slightly below the run-away point of the curves
for higher inflow velocities. Also the maximum power point at
is slightly lower
for the
are more or less
curve. As the shape for
and
identical, it can be claimed that a Reynolds-independent curve is reached at
. Therefore,
has been chosen as the design inflow velocity
for all succeeding experiments. The maximum power point can be identified for about
and amounts a maximum power of about
The thrust coefficients
.
for the three different inlet speeds are nearly congruent. The
thrust continuously increases with growing tip speed ratios
of
. Between
and
reaching a maximum value
a steeper increase in thrust can be observed. In
50
Results & Discussion
this region a transition from stalled conditions to optimal operating conditions takes
place, which also can be observed in the
curve.
6.2.1.2 Second Turbine Performance
The power coefficient and the thrust coefficient measured for the unobstructed second
turbine (Tu2) are presented in Fig. 6.5. Power and thrust curves for the second turbine
were already recorded by Karlsen [16], Loland [35] as well as Adaramola and Krogstad
[28] for the same turbine. A comparison between Adaramola and Krogstad’s results and
the re-recorded performance curves recorded at five different inlet wind speeds is
presented in the Appendix. The curves are recorded for five different inflow wind speeds,
of which three curves for
,
and
are shown in
Fig. 6.5.
Fig. 6.5:
Performance curves of the unobstructed second turbine (Tu2) at different inflow
wind speeds: (a) power coefficient CP and (b) thrust coefficient CT
Above
inlet speed the power and thrust curves are fully developed and
therefore smoothly shaped. However, the maximum power point of the
curve still is slightly below the
turbine at design inflow speed
tip speed ratio of
curve. The power curve for the second
has its maximum power point
. The run-away point can be found at
at a
.
The thrust curves for the three different inlet speeds are almost congruent. Insignificant
deviations can be found at high tip speed ratios between
and
Reynolds number does not have hardly any influence on the thrust curves.
51
. The
Results & Discussion
The power curve at design inflow speed
matches very good with the curves
found by Karlsen [16], Loland [35] as well as Adaramola and Krogstad [28] for the same
turbine. However, Adaramola and Krogstad found a Reynolds-independent curve already
(see Appendix).
at a little lower wind tunnel inflow speed
Furthermore, the thrust curves are in good agreement with the results found previously by
Adaramola and Krogstad. The thrust curves as shown in Fig. 6.5, however, reach slightly
higher thrust values of about
than Adaramola and Krogstad’s curve, which
features a maximum thrust of approximately
(see Appendix).
According to the Betz theory [12], the thrust coefficient is below one for full size wind
turbines. As the model wind turbines are installed in a closed wind tunnel, the blockage of
the wind tunnel endwalls causes an increased local velocity in front of the rotor, resulting
in a higher thrust force onto the rotor [35].
52
Results & Discussion
6.2.2 Downstream Flow Field
In Fig. 6.6 the mean velocity deficit
[-] and the turbulence intensity
[%] are
shown for three axial downstream positions. Horizontal line wake measurements in hub
height are presented for the axial measurement stations 1D, 3D and 5D downstream of the
unobstructed second turbine (Tu2). At a wind tunnel inflow speed of
second turbine is run at a tip speed ratio of
point at
Fig. 6.6:
, the
corresponding to its maximum power
.
Velocity deficit (Um/U∞) and turbulence intensity (u’/Um) in the wake 1D, 3D and 5D
downstream of the unobstructed turbine
Velocity deficit
Analyzing the axial development of the velocity deficit in the wake behind one single
turbine, it can be observed that the velocity deficit recovers moving downstream. At 1D
downstream a minimum mean velocity of
(corresponds to
measured. At 3D downstream the minimum velocity amounts
corresponds to a velocity deficit of
to
respectively
) is
, which
. At 5D the mean velocity has recovered
.
Wake dimensions
Furthermore, it can be observed that the wake becomes broader moving downstream due
to turbulent diffusion from the surrounding flow. The 1D wake is characterized by strong
velocity gradients behind the rotor tips at
53
and
and the wake width
Results & Discussion
amounts approximately
rotor radii. The velocity gradients of the 3D and 5D
wake are significantly weaker yielding a smoother velocity profile and a slightly broader
wake. The 5D wake features a wake width of approximately
rotor radii.
Wake asymmetries
Focusing on the center of the wake, it can be observed that the 1D wake is characterized by
a very asymmetrical velocity field with high variations in mean velocity deficit. Moving
further downstream, the wake profile becomes more symmetrical and the variations
gradually even out. The near wake at 1D is dominated by distinct single root and tip
vortices, whereas these single vortices mix to a more uniform structure due to turbulent
diffusion when moving downstream. The asymmetries in the horizontally measured
velocity profile can be traced back to the influence of the wake of the wind turbine tower.
The flow exiting from the rotor is in a swirling motion that is counter-rotating to the rotor
as explained in chapter 1.2.3. This rotating flow in the rotor wake is hitting the tower at a
certain angle and moving into the lower-pressure region in the tower wake yielding an
asymmetrical velocity distribution [23]. These asymmetries are dominating the shape of
the velocity and turbulence intensity profile in the 1D wake. This idea is confirmed by
results found by Nygard [36], who performed a comprehensive study about the deflection
of the tower wake due to wake rotation on the first wind turbine (Tu1) at NTNU’s wind
tunnel laboratory.
Turbulence intensities
The turbulence intensity gradually goes back moving downstream in the wake. For the 1D
wake a maximum turbulence intensity of
a maximum of
could be found, which reduces to
in the 5D wake.
Likewise to the velocity profiles, it can be observed that the turbulence profiles in the wake
become broader moving downstream. Due to turbulent diffusion from the surrounding
flow, the circular turbulent shear layer slowly increases in diameter.
The 1D wake is characterized by three distinct peaks with very high turbulences levels. It
can be observed that peaks in the turbulence intensity profile occur at positions with high
54
Results & Discussion
velocity gradients in the velocity profile. The peaks at
and
can clearly be
ascribed to the tip vortices, whereas the peak in the center is assumed to occur due to a
combination of the root vortices and turbulent structures behind the turbine nacelle.
Moving downstream, these peaks in turbulence intensity gradually reduce. The turbulent
peak, which can be ascribed to the root vortices, goes back at a higher rate than the tip
vortex peaks. The profiles become more even and smoother due to diffusion processes
moving downstream from the rotor. Distinct maxima in the tip vortex region at
and
still can be found in the 5D wake. The maximum in the wake center induced
by the root vortices cannot be found in the 5D wake profile anymore.
Distinct asymmetries are also evident in the turbulence intensity profiles, especially in the
1D profile. Again, the tower wake influence transported by the swirling motion in the wake
is assumed to be the reason for these asymmetries.
Classification of results
In the past, Adaramola and Krogstad performed a number of wake measurements using a
Pitot tube [33] respectively a LDA system [37] on the same experimental setup.
Furthermore, some velocity profiles in the wake behind the single model wind turbine
(Tu2) were recorded by Loland [35] using a Pitot tube.
The velocity deficit profile measured at 1D downstream matches almost exactly with the
Pitot measurement performed in [33]. A very good agreement can also be found with the
1D profile measured in [35], although the curve is slightly above the newly measured
profile. A different reference velocity
is assumed to be the reason for this displacement.
Moreover, the velocity profiles measured at 4D and 7D in [35] fit well into the axial
development of the wake as measured in the present project.
The shape of turbulence intensity profile measured at 3D downstream gives good
agreement with the turbulence profile measured in [37]. Notice that Adaramola and
Krogstad refer the standard deviation
to the inflow velocity
whereas in this work the turbulence intensity is defined as
in their paper [37],
.
Evident asymmetries in velocity profiles are, among others, also found by Barber et al.
[23] and Smith [38].
55
Results & Discussion
6.3 Turbine Arrangement (B): Turbine distance x/D=3
The main focus in this project is the investigation of the development of the wake behind
an array of two model wind turbines. In a first experimental setup, the second model
turbine is installed
rotor diameters downstream of the first model turbine. The
experimental setup and the axial stations for the hot wire probe measurements are
sketched in Fig. 6.7.
Fig. 6.7:
Experimental setup and axial measurement stations for turbine arrangement (B)
The first model turbine is mounted on the force balance, whereas the second turbine is
fixed to the wind tunnel floor. The first wind turbine is operated at a tip speed ratio of
about
output
, which corresponds to the optimal operating point at a maximum power
. A power curve of the second turbine operating in the wake of the
first turbine is recorded yielding the optimal operating point for the second turbine. As the
second turbine is not mounted to the force balance, no thrust curve is acquired in this
setup. At three axial measurement stations 1D, 3D and 5D downstream of the second
model turbine, wake measurements are performed. The velocity deficit and the turbulence
intensity are measured in a horizontal line at hub height at the three measurement
stations, followed by full area wake measurements at the exact same downstream
positions.
56
Results & Discussion
6.3.1 Turbine Performance Curves
A comparison of the
curve of the second turbine operating unobstructed and in the
wake 3D downstream of an upstream turbine is presented in Fig. 6.8. The upstream
turbine is operating at maximum
. The two graphs in Fig. 6.8 (a) and (b) actually show
the same data, but the data in the second picture is referred to a different reference
velocity.
(a)
Fig. 6.8:
(b)
CP curve of the second turbine (red) operating 3D downstream of the first turbine:
(a) reference velocity U∞=11.5 m/s (b) reference velocity Uref,3D=7.8 m/s
In Fig. 6.8 (a) both power curves are referred to the wind tunnel inflow velocity
be observed that the second turbine reaches a maximum power of
. It can
when
operating in the wake 3D downstream. This corresponds to about 31% of the power
extracted from the wind of the unobstructed turbine. Being exposed to a considerably
lower velocity in the wake of the first turbine, the run-away point goes back to a tip speed
ratio of
.
In order to compare the performance of the second turbine operating in the wake, the
power curve is referred to a lower reference velocity
as depicted in Fig. 6.8 (b).
When the second turbine is operated in the wake of the first turbine, it is subjected to a
completely different inflow field. This flow field can be characterized by a non-uniform
velocity distribution and very high, unevenly distributed turbulent flow structures.
Therefore, the power curve is stretched to the run-away tip speed ratio of the unobstructed
second turbine.
57
Results & Discussion
Although the power curve of the second turbine does not necessarily have to have the
same run-away tip speed ratio when operating in the wake, the reference velocity
is chosen here to simplify the comparison with the unobstructed setup.
It can be observed that the power curve matches almost perfectly with the curve of the
unobstructed turbine. It reaches a maximum
the maximum
, which is just slightly lower than
of the unobstructed turbine.
Comparing this power curve at a reference velocity of
to the power curve
of the second turbine operating unobstructed at an inlet speed of
as shown
in Fig. A.1 (Appendix), it can be seen that the power curve of the turbine operating in the
turbulent wake is fully developed. At a rather laminar inflow field of
,
however, the power curve features a distinct bump at design tip speed ratios. This can be
ascribed to a Reynolds number effect, which is described in detail in Appendix.
Thus, it can be concluded that the second wind turbine operating in a highly turbulent
flow in the wake of an upstream turbine has a fully developed power curve and reaches
similar efficiency as the unobstructed turbine.
58
Results & Discussion
6.3.2 Downstream Flow Field
6.3.2.1
Horizontal Line Wake Measurements
In Fig. 6.9 the axial development of the velocity deficit
intensity
[-] and the turbulence
[%] is shown for three axial positions. Horizontal line wake measurements
in hub height are presented for the axial measurement stations 1D, 3D and 5D
downstream of the second turbine operating 3D downstream of the first turbine. At a wind
tunnel inflow speed of
, both turbines are operated at their maximum
power point at
Fig. 6.9:
respectively
.
Velocity deficit (Um/U∞) and turbulence intensity (u’/Um) in the wake 1D, 3D and 5D
downstream of the second turbine operating 3D downstream of the first turbine
Velocity deficit
Similar to the wake behind a single turbine the velocity deficit in the wake behind an array
of two turbines recovers when moving downstream. At 1D downstream a minimum mean
velocity of
is measured, which corresponds to a velocity deficit of
. Moving to 3D downstream, the minimum mean velocity amounts
(
) and at 5D downstream the minimum velocity recovers to
(
.
Wake dimensions
Likewise to the wake behind the single turbine, the wake becomes broader moving
downstream. The 1D wake is nearly
rotor radii broad, whereas the 5D wake has a
59
Results & Discussion
wake width of almost
approximately
rotor radii. This corresponds to a growth rate of
in horizontal direction. Turbulent diffusion from the
surrounding flow causes this phenomenon, but also the influence of the wake of the first
turbine must be taken into account when judging the wake width. An in-depth
investigation of what phenomena can actually be ascribed to the first turbine wake is
found in chapter 6.5. The 1D wake features significantly stronger velocity gradients in the
turbulent shear layer than the 3D and 5D wake.
Wake asymmetries
The wake measurements in a horizontal line show obvious asymmetries at 1D
downstream. These can be explained by the influence of the tower wake being deflected by
the rotating motion in wake of the turbine rotor. The 1D wake is characterized by
significant variations in mean velocity in the center of the wake. Two distinct minima,
which be ascribed to the shear layer created by the tip vortex rotation, can be made out.
The 3D and 5D wake, however, are characterized by an almost symmetrical shape
featuring only one distinct minimum in mean velocity.
Turbulence intensities
Analyzing the axial development of the turbulence intensity profiles, an increase in width
can be observed moving axially downstream. The turbulent shear layer induced by the tip
vortices gradually diffuses into the surrounding flow.
The 1D profile features three distinct maxima that can be ascribed to the tip and root
vortices. The highly asymmetrical profile has a maximum turbulence intensity of
.
The profile in the wake 3D downstream of the second turbine is characterized by two
distinct peaks, which slightly moved towards the center of the wake. The peak in the
center of the wake disappeared completely. The profile has a maximum turbulence
intensity of
and can be characterized by much smoother and more
symmetrical shape than the 1D profile.
60
Results & Discussion
No more distinct vortex structures can be identified in the turbulence intensity profile 5D
downstream of the second turbine. The vortices have mixed into one single peak due to
turbulent diffusion processes. This fully developed turbulence profile has a maximum
intensity of
.
6.3.2.2 Full Area Wake Measurements
At the same three axial positions, the flow field is traversed in a rectangular including a
total of 425 measuring points. The mean velocity deficit
intensity
[-] and the turbulence
[%] are depicted in colour coded contour plots in Fig. 6.10, Fig. 6.11 and
Fig. 6.12 for the axial positions 1D, 3D respectively 5D downstream of the second turbine,
which is operating 3D downstream of the first turbine.
61
Results & Discussion
u’/Um [%]
Um/U∞ [-]
Fig. 6.10:
Velocity deficit (Um/U∞) and turbulence intensity (u’/Um) in the wake 1D
downstream of the second turbine operating 3D downstream of the first turbine
u’/Um [%]
Um/U∞ [-]
Fig. 6.11:
Velocity deficit (Um/U∞) and turbulence intensity (u’/Um) in the wake 3D
downstream of the second turbine operating 3D downstream of the first turbine
u’/Um [%]
Um/U∞ [-]
Fig. 6.12:
Velocity deficit (Um/U∞) and turbulence intensity (u’/Um) in the wake 5D
downstream of the second turbine operating 3D downstream of the first turbine
62
Results & Discussion
Velocity deficit
As observed in the horizontal line profiles, the 1D wake features strong velocity gradients
right outside the rotor swept area as shown in Fig 6.10. The highest velocity deficits of
about
can be found above the center of the rotor and right to the center in
the region near the blade tips. Further downstream the velocity deficit decreases visibly
and the highest deficits are located slightly underneath the center of the turbine rotor. The
minimum velocity found in the 3D wake amounts
features a minimum velocity of
, whereas the 5D wake
.
Wake dimensions
The 1D wake has a horizontal expansion from
direction it only grows until
to
, whereas in vertical
referring to the wake’s velocity profile.
The upper half of the wake is thus not entirely circular, which can be ascribed to a
blockage effect of the traverse system on the wind tunnel roof. The same phenomenon was
found by Adaramola and Krogstad, who claim that the vertical growth rate near the roof is
only about 85% of the growth rate in horizontal direction [33]. The blockage effect of the
traverse system is also found in the mapping of the wind tunnel inflow velocity as
described in chapter 6.1.
Moving further downstream, it can be observed that the wake expands in all directions. As
seen before, the horizontal expansion is much more distinct in comparison to the vertical
expansion. 5D downstream of the second turbine rotor, the wake is almost
rotor
radii broad. The velocity gradients become weaker when the wake is moving downstream.
Fluid of higher kinetic energy is slowly transported into the center of the wake due to
turbulent diffusion. Hence, the area of high velocity deficit shrinks moving downstream in
the wake.
It can be clearly observed that the center of the maximum velocity deficit is located slightly
underneath the center of the rotor in the 3D and 5D wake. A certain downshift of the
highest velocity deficit is also found in experiments featuring a simulated atmospheric
boundary layer by Talmon [39], [40]. Referring to a computational study by Crespo et al.
63
Results & Discussion
[41] validating Talmon’s results, Vermeer et al. conclude that “this downshift is mainly due
to the shear of the incoming flow and the presence of the ground” [10].
In the present experiments, however, there is no shear in the inlet flow field. Thus, it is
assumed that the blockage due to the traverse system near the wind tunnel roof is
responsible for this displacement. Furthermore, a lower-pressure region in the tower wake
could possibly cause a certain downshift in the wake. In order to assess the influence of the
traverse mechanism respectively the tower, a vertical traverse of the flow field using a
manual traverse mechanism is recommended.
Wake asymmetries
The center of the 1D wake is characterized by high velocity deficits behind the rotor swept
area. It can be observed that there are some centers of extra high velocity deficits in the
upper and right half of the velocity field, which are not evenly distributed around the
circumference. The flow field is not rotationally symmetric. It is assumed that these
asymmetries stem from the influence of the turbine tower. The flow exiting from the rotor
blades is rotating and hitting the turbine tower resulting in a non-uniform velocity
distribution in the center of the wake. Barber et al. [23] observed a similar phenomenon
while mapping the full area wake behind a single turbine. They assume that the rotating
flow in the rotor wake is hitting the tower at a certain angle and moving into the lowerpressure region in the tower wake yielding an asymmetrical velocity distribution [23].
These asymmetries are dominating the shape of the velocity and turbulence intensity
profile in the 1D wake. Moving further downstream, the profiles become more
symmetrical due to turbulent mixing processes.
Turbine tower influence
Analyzing the lower half of the velocity field, the influence of the turbine tower can be
clearly seen. The presence of the tower causes a bluff body wake characterized by an
additional velocity deficit. At the lower edge of the scanned velocity field it can be seen
that the wake around the turbine tower is slightly shifted towards the left hand side.
Looking in downstream direction, the turbine rotor is rotating counter-clockwise. Thus,
64
Results & Discussion
the flow in the wake is rotating in clockwise direction shifting the flow field around the
tower a little bit to the left.
The same phenomenon becomes even more obvious in the velocity distributions shown in
Fig. 6.11 and Fig. 6.12. In the 3D and 5D measurements, the flow around the tower is
shifted even more to the left hand side. These findings are in accordance with
investigations made by Nygard [36] on the first wind turbine. He states that “as the wake
propagates downstream, the tower wake is displaced due to the clockwise rotation of the
wake” [36].
Turbulence intensities
Investigating the turbulence intensity profile in the 1D wake as depicted in Fig. 6.10, it can
be observed that the highest turbulences are in a distinct ring behind the rotor blade tips.
This is obviously due to the very turbulent shear layer formed by the blade tip vortices.
Three independent cores of very high turbulence intensity levels above
can
be found. However, these cores are not distributed uniformly around the circumference.
The center of the wake can be characterized by a very non-uniform turbulence
distribution. Both cores of rather high and relatively low turbulence intensities coexist.
Slightly to the right of the rotor center a core of comparatively low turbulence of about
can be found.
In the 3D wake as shown in Fig. 6.11 only two cores of very high turbulences above
are found in the lower half of the flow field. The turbulence level in the
center of the wake is increased to about
. Likewise the velocity profiles, the
wake becomes broader and the gradients of turbulence intensity are reduced.
The turbulence intensity profile of the 5D wake as presented in Fig. 6.12 still is quite
asymmetrical. Only one core of very high turbulences can be found in the right half of the
flow field. Turbulent diffusion causes a further increase in the wake extensions and
smoother gradients in turbulence intensity.
65
Results & Discussion
6.4 Turbine Arrangement (C): Turbine distance x/D=5
In a second experimental setup, the separation distance between the two model turbines is
increased to
rotor diameters. As shown in Fig. 6.13, hot wire probe measurements
are performed 1D and 3D downstream of the second turbine. Due to a limited length of the
wind tunnel, wake measurements 5D downstream of the second turbine are unfortunately
not possible in this experimental setup.
Fig. 6.13:
Experimental setup and axial measurement stations for turbine arrangement (C)
Likewise in the initial setup, the first turbine is mounted on the force balance whereas the
second turbine is fixed to the wind tunnel floor. The first wind turbine is operated at the
same tip speed ratio of about
maximum power output
, corresponding to the optimal operating point at a
. As the separation distance is increased, a new
power curve of the second turbine operating in the wake 5D downstream is recorded
yielding the optimal operating point for the second turbine in this setup. With the second
turbine being operated at the optimal power point, the wake is recorded at two axial
stations 1D and 3D downstream of the second turbine. Wake measurements yielding the
velocity deficit and the turbulence intensity are again performed in a horizontal line at hub
height and a full area grid behind the turbines at the two axial measurement stations.
66
Results & Discussion
6.4.1 Turbine Performance Curves
Fig. 6.14 shows a comparison of the
curve of the second turbine operating unobstructed
and 5D downstream of the first turbine. The upstream turbine (Tu1) is operated at its
maximum power point at about
. The same data is presented in Fig 6.14 (a) and (b)
the only difference being a different reference velocity.
(a)
(b)
Fig. 6.14:
CP curve of the second turbine operating 5D downstream of the first turbine:
(a) reference velocity U∞=11.5 m/s (b) reference velocity Uref,5D=8.1 m/s
Both power curves are referred to the wind tunnel inflow velocity
in Fig. 6.14(a).
Operating 5D downstream of the first turbine, the second turbine reaches a maximum
power of
, which corresponds to about 33% of the power the unobstructed
turbine extracts from the wind.
For a better comparison, the
curve is referred to a lower reference velocity
as
presented in Fig. 6.8 (b). In the same way as before, the power curve is stretched to the
run-away tip speed ratio of the unobstructed second turbine. It can be observed that the
power curve matches almost perfectly with the curve of the unobstructed turbine. The
maximum power coefficient of
is just slightly lower than the maximum
of the
unobstructed turbine.
Again, it can be seen that the second wind turbine operating in a turbulent flow in the
wake of an upstream turbine has similar operating characteristics as the unobstructed
turbine.
67
Results & Discussion
6.4.2 Downstream Flow Field
6.4.2.1 Horizontal Line Wake Measurements
The velocity deficit
[-] and the turbulence intensity
[%] for the two axial
measurement stations 1D and 3D downstream of the second turbine operating 5D
downstream of the first turbine are presented in Fig. 6.15. Both model wind turbines are
operated at their maximum power point at
respectively
.
Fig. 6.15:
Velocity deficit (Um/U∞) and turbulence intensity (u’/Um) in the wake 1D, 3D
downstream of the second turbine operating 5D downstream of the first turbine
Velocity deficit
As observed before, the velocity deficit in the wake behind an array of two turbines
recovers when moving downstream. A minimum mean velocity of
corresponding to a velocity deficit of
is measured at 1D downstream.
Moving to 3D downstream, the minimum mean velocity recovers to
corresponding to a velocity deficit of
.
Wake dimensions
A broadening of the wake can also be observed in this setup when moving downstream.
The 1D wake is approximately
wake width of about
growth rate of about
rotor radii broad, whereas the 3D wake has a
rotor radii. Similar to the first setup, this corresponds to a
in horizontal direction.
68
Results & Discussion
Wake asymmetries
The velocity deficit profiles acquired from the horizontal line wake measurements are
almost symmetrical in this setup. The 1D profile features two distinct minima, of which
the right one is slightly lower. The 3D velocity profile is nearly symmetrical for this setup.
Obvious asymmetries can be observed in the turbulence intensity profiles, especially for
the 1D profile. The influence of the tower wake being deflected by the rotating motion in
wake of the turbine rotor and thereby deflecting turbulent structures, such as the root
vortices is assumed to cause these asymmetries.
Turbulence intensities
An increase in wake width can also be observed when analyzing the axial development of
the turbulence intensity profiles. The 1D profile is characterized by three distinct maxima,
which can be ascribed to the tip and root vortices. A maximum turbulence intensity of
can be found in the highly asymmetrical profile.
The turbulence intensity profile in the 3D wake features two distinct peaks, which moved
towards the center of the wake. The peak in the center of the wake disappeared completely
at 3D. The profile has a much smoother and more symmetrical shape than the 1D profile
and features a maximum turbulence intensity of
69
.
Results & Discussion
6.4.2.2 Full Area Wake Measurements
For the two axial positions 1D and 3D downstream of the second turbine, the flow field is
traversed in a rectangular measurement grid consisting of 425 measuring points. For the
second turbine operating 5D downstream of the first turbine, the mean velocity deficit
[-] and the turbulence intensity
[%] are presented in colour coded contour
plots in Fig. 6.16 and Fig. 6.17.
u’/Um [%]
Um/U∞ [-]
Fig. 6.16:
Velocity deficit (Um/U∞) and turbulence intensity (u’/Um) in the wake 1D
downstream of the second turbine operating 5D downstream of the first turbine
u’/Um [%]
Um/U∞ [-]
Fig. 6.17:
Velocity deficit (Um/U∞) and turbulence intensity (u’/Um) in the wake 3D
downstream of the second turbine operating 5D downstream of the first turbine
70
Results & Discussion
Velocity deficit
Analyzing the velocity deficit in the 1D wake as depicted in Fig 6.16, it can be observed that
the highest velocity deficit of about
can be found left underneath the center
of the rotor. Behind the nacelle and the center of the rotor and the velocity deficit is only
about
. Further downstream in the 3D wake, the velocity deficit decreases
to a minimum of
. The area of the highest velocity deficit is located a little
underneath the center of the rotor.
Wake dimensions
Discussing the wake velocity profile, the 1D wake has a horizontal expansion from
to
while in vertical direction it only extends about
. As
observed before, the blockage effect of the traverse system on the wind tunnel roof
prevents the wake from spreading in vertical direction at the same rate as in horizontal
direction. Moving downstream to 3D, the wake expands, especially in horizontal direction.
Much weaker velocity gradients can be found in the 3D wake. Fluid of higher kinetic
energy slowly diffuses towards the center of the wake. Thus, the area affected by a high
velocity deficit diminishes moving downstream in the wake.
In this case the vertical growth rate is only about 70% of the growth rate in horizontal
direction, which is even less as the 85% found by Adaramola and Krogstad [33]. The
minor velocity deficit near the wind tunnel roof due to the blockage effect of the traverse
system has already been observed in the mapping of the wind tunnel inflow velocity as
described in chapter 6.1.
Again, a certain downshift of the center of highest velocity deficit is found in the 3D wake.
As explained before, the blockage due to the traverse system is assumed to cause this
displacement.
Wake asymmetries
High velocity deficits are dominating the area behind the rotor swept area in the 1D wake.
In the center of the wake the areas of high velocity deficit are not evenly distributed
around the circumference. The highest velocity deficit is found left underneath the center
71
Results & Discussion
of the wake. As clarified before, these asymmetries are assumed to stem from the influence
of the turbine tower. Analyzing the 3D wake, the velocity distribution in center of the wake
becomes more symmetrical due to diffusion processes.
Turbine tower influence
The counter-clockwise rotating turbine rotor is inducing a clockwise rotation of the flow in
the wake behind the rotor. Due to the clockwise rotation of the wake, the flow is hitting the
tower at a certain angle, deflecting the flow field behind the tower a little bit to the left.
This phenomenon can be clearly seen at the lower edge of the velocity field in the 1D as
well as the 3D wake. Besides an asymmetrical wake width at the lower edge of the 1D and
3D wake, a clear deflection of the tower wake around
can be observed. As stated
before, this conclusion is in accordance with Nygard’s [36] findings.
Turbulence intensities
The turbulent shear layer, which is formed by the blade tip vortices, becomes visible in a
distinct ring of high turbulences of approximately
in the 1D wake as shown
in Fig. 6.16. Around six to seven cores very high turbulence intensities can be found
unevenly distributed around the circumference. In the center of the wake both cores of
rather high and relatively low turbulence intensities can be found resulting in a very nonuniform turbulence distribution. There is a core of comparatively low turbulence of about
on the right of the rotor center. A little left of the rotor center, however,
higher turbulence intensities of about
can be found.
The 3D wake as shown in Fig. 6.17 can be characterized by only three cores of high
turbulence intensities above
is increased to about
. The turbulence level in the center of the wake
. The regions of high and low turbulence intensity have
mixed into a more symmetrical wake. However, the wake is not yet fully developed at 3D,
as the center of the wake still features lower turbulence intensity levels as the ring
surrounding it. As observed in the velocity profiles, the gradients of the turbulence
intensity become weaker and the wake becomes broader 3D downstream of the second
turbine.
72
Results & Discussion
6.5 Comparison of Turbine Arrangements (A), (B) and (C)
In this chapter, the results attained from the different experimental setups, which have
been presented in the previous chapters, are compared and discussed. As shown in
Fig. 6.18 the performance curves and the wakes 1D and 3D downstream of the second
model wind turbine are compared, for three different experimental setups: (A) the
unobstructed second turbine, (B) the second turbine operating 3D downstream of the first
turbine and (C) the second turbine operating 5D downstream of the first turbine.
Fig. 6.18:
Comparison of the performance curves and the wakes 1D and 3D downstream of the
second turbine, when the turbine is (A) unobstructed, (B) operating 3D downstream of the first
turbine and (C) operating 5D downstream of the first turbine
The second model wind turbine has different performance characteristics when operating
unobstructed or in different separation distances
behind an upstream turbine. Thus,
the power curve acquired for the unobstructed second turbine and the second turbine
operating
respectively
rotor diameters downstream are different. The
first turbine is operated at its maximum power point of
ratio of
at a tip speed
for the turbine arrangements (B) and (C). Also, the second model wind
turbine is operated at its maximum power point, which is different for each turbine
arrangements (A), (B) and (C).
The 1D wake and the 3D wake of the turbine arrangements (A), (B) and (C) are discussed
comparing the wake profiles measured in a horizontal line in hub height. These analyzes
are complemented by a comparison of the full area wakes recorded for the turbine
arrangements (B) and (C).
As it is not possible to record the 5D wake for turbine arrangement (C) due to space
limitations, a comparison of the of the horizontal line wake measurements at 5D is only
made for arrangements (A) and (B).
73
Results & Discussion
6.5.1 Turbine Performance Curves
A comparison of the
curve of the second turbine operating (A) unobstructed as well as
(B) in the wake 3D and (C) 5D downstream of an upstream turbine is presented in
Fig. 6.19. The upstream turbine (Tu1) is operating at its maximum
Fig. 6.19 (a) shows the
tunnel inflow speed
in all three cases.
curves of all three turbine arrangements referred to the wind
whereas Fig. 6.19 (b) relates the three
curves to different
reference velocities.
(a)
Fig. 6.19:
(b)
CP curve of the second turbine operating (A) unobstructed, (B) 3D and (C) 5D
downstream of the first turbine:
(a) reference velocity U∞=11.5 m/s (b) reference velocity Uref,3D=7.8 m/s and Uref,5D=8.1 m/s
In Fig. 6.19 (a) all three power curves are referred to the wind tunnel inflow velocity
. In case the second turbine is operated in the wake 3D downstream, it has
a maximum power coefficient of
. That corresponds to about 31% of the
power extracted of the unobstructed turbine.
When operated in the wake 5D downstream, the second turbine reaches a maximum
power coefficient of
, which corresponds to about 33% of the power the
unobstructed turbine extracts from the wind. The kinetic energy in the flow in the wake
has consequently recovered from 3D to 5D, although the recovery rate is very small.
As the second turbine is subjected to a considerably lower kinetic energy when operating
wake 3D respectively 5D downstream, the performance curves of the turbine operating in
the wake are referred to lower reference velocity
respectively
as depicted in
Fig. 6.19 (b). As explained before, the reference velocities are chosen that the 3D and 5D
power curves are stretched to the run-away tip speed ratio of the unobstructed second
74
Results & Discussion
turbine. It can be observed, that the 3D and 5D power curves are fully developed and
match very well with the curve of the unobstructed turbine. The maximum
the stretched curves are just insignificantly lower than the maximum
values of
of the
unobstructed turbine.
As stated before, it can be seen that second wind turbine operating in a turbulent flow in
the wake of an upstream turbine has similar operating characteristics as the unobstructed
turbine. Regardless of the downstream distance, the power curves are fully developed and
reach a similar efficiency as the unobstructed turbine.
6.5.2 Downstream Flow Field
6.5.2.1
1D Wake
The velocity deficit
[-] and the turbulence intensity
[%] in the wake 1D
downstream of the second turbine are compared for the three different cases (A), (B) and
(C) in Fig. 6.20. The second model wind turbine is operated at its maximum power point,
which is different for each setup:
Fig. 6.20:
,
and
.
Velocity deficit (Um/U∞) and turbulence intensity (u’/Um) in the wake 1D
downstream of the second turbine operating (A) unobstructed, (B) 3D and (C) 5D downstream of
the first turbine
75
Results & Discussion
Velocity deficit
Comparing the velocity deficit of the three different configurations in the 1D wake, it can
be observed that the velocity deficit behind two turbines is considerably higher than
behind one unobstructed turbine. As the second turbine extracts additional kinetic energy
from the fluid, the highest velocity deficit is found for configuration (B). A minimum mean
velocity of
, corresponding to a velocity deficit of
, is found at
.
When operating 5D downstream of the first turbine (C) the minimum velocity deficit
increases to
as more kinetic energy is recovered between the two turbines.
In the unobstructed case (A), the minimum velocity deficit amounts
is significantly higher. Conversely, this means that the mean velocity
decreases between 11% and 13% of the inflow velocity
, which
additionally
when a second wind turbine is
set up 5D respectively 3D behind the first turbine.
Wake dimensions
Analyzing the velocity profiles in the 1D wake of the three different configurations, it can
be observed that all three profiles have approximately the same velocity deficit of
at
. The higher kinetic energy losses in the center of the wake for
configurations (B) and (C) can be attributed to the presence of a second energy extracting
turbine. Furthermore, it can be observed that the wake is significantly broader for
configurations (B) and (C). The unobstructed configuration (A) can be characterized by
sharp edges from
to
, whereas the 1D wakes for configurations (B)
and (C) feature a smoother shape outside the rotor swept area. The additional losses in
kinetic energy between
and
can be ascribed to the influence of the
wake of the first turbine (Tu1).
Wake asymmetries
Obvious asymmetries can be found in the 1D velocity deficit profile of the unobstructed
turbine (A). Three distinct unevenly distributed minima and significant variations in
velocity deficit can be observed in the center of the wake. Analyzing the velocity deficit
76
Results & Discussion
profiles of configuration (B) and (C) however, a much smoother and more symmetrical
shape can be found. The center of the 1D wake can be characterized by only two minima
and a local maximum at
.
In the unobstructed configuration (A) a rather laminar inflow is hitting the rotor. Due to
the rotating motion of the flow in the wake, the wake behind the turbine tower is deflected
and causes significant asymmetries. In case the second turbine is operating in the wake of
an upstream turbine however, it is subjected to a highly turbulent inflow. The increased
turbulence levels accelerate the mixing process in the wake, which leads to a smoother and
more symmetrical velocity distribution as found for cases (B) and (C).
Turbulence intensities
Comparing the turbulence intensity profiles in the 1D wake for the three different
configurations, a number of similarities stick out. All three turbulence profiles are
characterized by three distinct maxima, of which the ones at
can be ascribed to
the vortices shed at the blade tips. The central maximum is located at
and can
be attributed to the root vortices interacting with the flow around the nacelle.
Analyzing the center of the wake, however, an overall increase in turbulence intensity for
configurations (B) and (C) becomes apparent. Although the maxima feature similar
turbulence intensity levels as in the unobstructed configuration, the space between the
distinct vortex structures is characterized by higher turbulences. As the inflow to the rotor
is already very turbulent in the arrangements (B) and (C), the turbulence intensities seem
to add up in these regions.
As observed in the velocity profiles, the 1D turbulence intensity profiles are significantly
broader for the configurations (B) and (C). Turbulent structures, which stem from the first
turbine wake, are assumed to be responsible for this phenomenon.
The full area wake measurements of the 1D wake for the second wind turbine operating
(B) 3D respectively (C) 5D downstream of the first turbine are compared in Fig. 6.21 and
Fig. 6.22.
77
Results & Discussion
u’/Um [%]
Um/U∞ [-]
Fig. 6.21:
Velocity deficit (Um/U∞) and turbulence intensity (u’/Um) in the wake 1D
downstream of the second turbine operating 3D downstream of the first turbine (B)
u’/Um [%]
Um/U∞ [-]
Fig. 6.22:
Velocity deficit (Um/U∞) and turbulence intensity (u’/Um) in the wake 1D
downstream of the second turbine operating 5D downstream of the first turbine (C)
Inner wake
Comparing the velocity contour plots, very similar structures in the center of the wake are
noticeable. A region of lower velocity deficits of approximately
can be
found in the center of both wakes surrounded by some cores of higher velocity deficits
down to
. Remarkably, the locations of the cores of higher and lower velocity
deficits match quite well for the two different wake recordings. The high deficit core in the
left lower half of the rotor swept area as well as the tapering of the lower velocity core to
left upper half can be found in both velocity plots.
A similar picture is given by the turbulence intensity plots. Obviously, the cores of very
high turbulence intensities of more than
can be found in almost the same
78
Results & Discussion
locations for both turbine separation distances. The cores of high turbulence intensity can
be found in a ring behind the blade tips in the lower half and the right upper half of the
rotor swept area. For both configurations (B) and (C) a similarly shaped core of
comparatively low turbulence intensities is found in the center of the wake.
It is therefore assumed that the flow structures in the center of the wake (e.g. in the wake
behind the rotor swept area) are predominately governed by the rotational motion of the
second turbine rotor. The influence of the first turbine and the turbine separation distance
is insignificant in the center of the wake.
Outer wake
When comparing the dimensions of the 1D wake outside the rotor swept area, however,
the influence of the separation distance to the first wind turbine becomes evident. When
the turbine separation distance is increased to 5D as done in configuration (C), the wake is
visibly broader. This can be observed in the velocity deficit plots as well as the turbulence
intensity plots. Referring to the turbulence intensity plots, the 1D wake is about
rotor diameters broad for a turbine separation distance of 3D (B) whereas it
covers almost
rotor diameters for the 5D configuration (C). The radial
widening of the first turbine wake with increasing axial downstream distance is assumed
to be the cause for this phenomenon.
79
Results & Discussion
6.5.2.2 3D Wake
The results of the horizontal line measurements 3D downstream of the second turbine are
compared for the three different cases (A), (B) and (C) in Fig. 6.23. In the same way as
before, the second turbine is operated at its maximum power point.
Fig. 6.23:
Velocity deficit (Um/U∞) and turbulence intensity (u’/Um) in the wake 3D
downstream of the second turbine operating (A) unobstructed, (B) 3D and (C) 5D downstream of
the first turbine
Velocity deficit
Similar to the findings made for the 1D wake, the velocity deficit in the 3D wake behind
two turbines is found to be significantly higher than behind one unobstructed turbine.
This is because the additional extraction of kinetic energy from the wind by the second
turbine. The second turbine being located 3D downstream (B), a fully developed wake
profile with a minimum velocity deficit of about
is found. For the 5D
downstream configuration (C) the minimum velocity deficit amounts
. In
case the second turbine is operated unobstructed (A), the minimum velocity deficit
amounts only about
. Consequently, the presence of a second wind turbine
causes an additional decrease in mean velocity
wind tunnel inflow speed
.
80
between 9% and 10% referred to the
Results & Discussion
Wake dimensions
As noticed before for the 1D wake, also the 3D wake profiles have approximately the same
velocity deficit of
at
. Apart from the significantly higher velocity
deficit behind the rotor for configurations (B) and (C), also the 3D wake is noticeably
broader for these configurations. The presence of an upstream turbine is responsible for
smoother velocity gradients outside the rotor area in contrast to the sharp velocity
gradients of the unobstructed configuration (A). The additional losses in kinetic energy for
configurations (B) and (C) between
and
can therefore be ascribed
to a reduced inflow velocity that stems from the first turbine wake.
Wake asymmetries
The velocity profile in the 3D wake behind the single unobstructed turbine (A) can be
characterized by obvious asymmetries behind the rotor swept area. For turbine
arrangement (B) and especially for configuration (C) very smooth, almost symmetrical
velocity profiles are found. When the second turbine is operated in the wake of an
upstream turbine, the velocity profiles are fully developed at 3D downstream. Only one
distinct minimum close to
is observed for configurations (B) and (C). Being
subjected to a very turbulent inflow, the turbulent mixing processes in the wake behind
the second turbine are accelerated that a Gaussian shaped profile is already developed in
the 3D wake.
Turbulence intensities
Analyzing the turbulence intensity profiles of the different configurations in the 3D wake,
the turbulence levels for the turbine arrangements (B) and (C) are significantly increased
compared to the unobstructed configuration (A). Especially in the center behind the rotor
swept area, the turbulence intensities are approximately double as high as for the
unobstructed single turbine. As the inflow to the second rotor is already very turbulent in
configurations (B) and (C), additional turbulence is added by the second turbine rotor.
The 3D turbulence profile of the unobstructed turbine (A) still can be characterized by two
distinct peaks at
that stem from the tip vortices. An additional peak in the center
81
Results & Discussion
of the wake caused by the root vortices can be found. In configurations (B) and (C),
however, only two peaks are found at
. Due to the increased turbulence in
these setups, the more intense diffusion processes have transported the peaks towards the
center of the wake already at 3D downstream distance.
As observed in the 1D wake, the 3D turbulence intensity profiles for the configurations (B)
and (C) are significantly broader than for the unobstructed arrangement (A). The
turbulent shear layer in the wake of the first wind turbine mixes with the second turbine
wake and thereby broadens the area of increased turbulent levels.
The results attained from the full area wake measurements of the 3D wake for the second
wind turbine operating (B) 3D respectively (C) 5D downstream of the first turbine are
compared in Fig. 6.24 and Fig. 6.25.
u’/Um [%]
Um/U∞ [-]
Fig. 6.24:
Velocity deficit (Um/U∞) and turbulence intensity (u’/Um) in the wake 3D
downstream of the second turbine operating 3D downstream of the first turbine (B)
u’/Um [%]
Um/U∞ [-]
Fig. 6.25:
Velocity deficit (Um/U∞) and turbulence intensity (u’/Um) in the wake 3D
downstream of the second turbine operating 5D downstream of the first turbine (C)
82
Results & Discussion
Inner wake
Comparing the 3D velocity contour plots of configurations (B) and (C), similar circular
structures in the center of the wake are found. Although the center of the wake is slightly
deflected to the left side in configuration (B), the general picture in both configurations is
very similar. Both wakes are characterized by one single minimum and smooth velocity
gradients.
Also, the turbulence intensity plots of the two different configurations show a very similar
picture. Three cores of rather high turbulence intensity levels of more than
are found for both turbine arrangements. Remarkably, the cores are located in
approximately the same spots behind the rotor swept area for both configurations. The
center of the wake is characterized by comparatively low turbulence intensities between
and
.
Similarly to the 1D wake plots, the inner part of the 3D wake is predominately governed by
the second turbine rotor. Hardly any influence of the turbine separation distance is found
in the center of the wake.
Outer wake
As seen in the 1D wake, the influence of the separation distance to the first wind turbine
becomes evident when comparing the dimensions of the 3D wake outside the rotor swept
area. The dimensions of the 3D wake are visibly bigger, when the turbine separation
distance is increased to 5D as done in configuration (C). A comparison of the two velocity
deficit plots as well as the two turbulence intensity plots allows the same conclusion. In
turbine configuration (B) the 3D wake is about
it covers estimated
rotor diameters broad whereas
rotor diameters in configuration (C) when comparing the
turbulence intensity plots.
As the first turbine wake is growing in radial direction with increasing downstream
distance, these observations are assumed to be significantly influenced by the first turbine
wake.
83
Results & Discussion
6.5.2.3 5D Wake
The velocity deficit
[-] and the turbulence intensity
[%] in the wake 5D
downstream of the second turbine are compared for the turbine configurations (A) and (B)
in Fig. 6.26. For turbine arrangement (C) it is not possible to acquire any data for the 5D
wake due to a limited length of the wind tunnel. The second model wind turbine is
operated at its maximum power point for both configurations.
Fig. 6.26:
Velocity deficit (Um/U∞) and turbulence intensity (u’/Um) in the wake 5D
downstream of the second turbine operating (A) unobstructed and (B) 3D downstream of the first
turbine
Velocity deficit
Comparing the minimal velocity deficit of unobstructed second turbine (A) and the second
turbine as operating in the 3D wake (B), only a rather minor difference can be found. The
minimal velocity deficit of
for configuration (B) is only a slightly smaller
than for the unobstructed configuration (A), in which a minimum velocity deficit of
can be found. Still, the extraction of additional kinetic energy from the
wind of a second turbine is evident in the 5D wake. However, in the 5D wake the
difference in mean velocity
between the two configurations reduces down to only 3%
referred to the inflow speed
. This is significantly less than a difference of 13% and 9%
found in the 1D respectively the 3D wake. As the velocity distributions are very similar, it
be assumed that an imaginary third wind turbine set up
downstream of the
second turbine would be able to extract a similar amount of energy from the flow as the
second turbine.
84
Results & Discussion
Wake dimensions
Apart from the slightly higher velocity deficit behind the rotor in turbine configuration
(B), also the 5D wake is significantly broader in this configuration. The wake of the
upstream turbine causes the additional losses in kinetic energy for configuration (B)
between
and
. As observed for the 1D and 3D wake profiles, also
the different 5D wake profiles have a similar values of velocity deficit at
.
Wake asymmetries
The velocity profile of the unobstructed turbine (A) still features evident asymmetries 5D
behind the rotor swept area. The 5D wake profile for configuration (B), however, is almost
perfectly symmetrical. A symmetrical shaped profile is fully developed at 5D due to the
turbulent inflow accelerating the mixing processes in the wake.
Turbulence intensities
The turbulence intensity levels in turbine arrangement (B) are visibly increased in
comparison to the unobstructed configuration (A). A maximum turbulence intensity of
can be found for arrangement (B) compared to
in
arrangement (A). Especially in the center behind the rotor swept area, the turbulence
intensities are more than double as high as for the unobstructed turbine. Additional
turbulence is added by the second turbine rotor to the already very turbulent inflow in
configuration (B).
The 5D turbulence profile of the unobstructed turbine (A) is characterized by two distinct
peaks at
that stem from the tip vortices. In configuration (B), however, only one
peak in turbulence intensity is found in the center of the wake. Also the turbulence
intensity profile is fully developed. As observed in the 1D and 3D wake, the 5D turbulence
intensity profile for the configuration (B) is considerably broader as for the unobstructed
arrangement (A). The broader wake in arrangement (B) can be ascribed to the turbulent
shear layer in the wake of the first wind turbine mixing into the second turbine wake.
85
Results & Discussion
6.6 Variations in Tip Speed Ratio
In the final test series the influence of variations in the tip speed ratio
of both turbines
on the flow field in the wake is investigated. The separation distance between the two
turbines is fixed to
rotor diameters for this test series. Turbine performance
curves and wake profiles are recorded for different tip speed ratio combinations of the two
turbines. The experimental setup and the one probe measurement station are sketched in
Fig 6.27.
Fig. 6.27:
Experimental setup and axial probe measurement station for the investigation of the
effect of turbine tip speed ratio variations
Firstly, three
curves of the second turbine are recorded for three different operating
points of the first turbine. At the optimum operation point of the first turbine (
),
the power curve of the second turbine is acquired again. Thereafter, second turbine
curves for a low rotational speed (
) and a high rotational speed (
) of the first
turbine are recorded.
Finally, wake profiles are measured in a horizontal line at hub height 3D downstream of
the second turbine. Altogether, nine different tip speed ratio combinations of the two
turbines are investigated. At first, the tip speed ratio of the first turbine is kept constant
while the tip speed ratio of the second turbine is varied to three different operating points.
Thereafter, three different tip speed ratios of the first turbine are set while the rotational
speed of the second turbine is kept constant. That results in nine horizontal line wake
measurements as presented in Table 6.1. The nine wake measurements are from here on
referred to as “Case 1” to “Case 9”.
86
Results & Discussion
TSR first turbine
Case 1
optimal (
(Reference Case)
)
low (
1350 rpm
)
high (
1350 rpm
low (
low (
)
optimal (
low (
)
low (
)
high (
)
optimal (
)
1130 rpm
2150 rpm
high (
)
low (
)
500 rpm
2150 rpm
high (
Case 9
)
1500 rpm
high (
Case 8
)
500 rpm
750 rpm
Case 7
)
1020 rpm
750 rpm
Case 6
)
1500 rpm
750 rpm
Case 5
)
500 rpm
optimal (
Case 4
)*
1000 rpm
optimal (
Case 3
tip speed ratio
optimal (
1350 rpm
Case 2
*
)
TSR second turbine
)
high (
2150 rpm
)
1500 rpm
of the second turbine referred to the wind tunnel inflow speed
Table 6.1:
Investigated test cases with different tip speed ratios of the turbines
6.6.1 Turbine Performance Curves
The
curves of the second turbine operating in the wake 3D downstream of an upstream
turbine, which is operating a three different tip speed ratios, are compared in Fig. 6.28.
The curves presented in Fig. 6.28 (a) are referred to the wind tunnel inflow speed
. In
Fig. 6.28 (b) the power curves are referred to different reference velocities in order to
compare their shape to the
curve of the unobstructed turbine. For the first turbine
operating at its maximum power point at
turbine is depicted in red. The
ratio of
, the power curve of the second
curve of second turbine for a low first turbine tip speed
is presented in blue. The yellow curve represents the power curve for a
high first turbine tip speed ratio (
).
87
Results & Discussion
(a)
Fig. 6.28:
(b)
CP curves of the second turbine operating in the wake 3D downstream for varying tip
speed ratios of the first turbine:
(a) reference velocity U∞=11.5 m/s (b) Uref,opt=7.8 m/s, Uref,low=8.4 m/s and Uref,high=9.0 m/s
Comparing the power curves of the second turbine in Fig. 6.28 (a) it can be observed that
the second turbine has the lowest
when the first turbine is operated at its
maximum power point. As the first turbine extracts the maximum possible power from the
wind at
, only a small amount of kinetic energy is left in the wind so that
the second turbine reaches a maximum power coefficient of
corresponding to 31% of the power extracted from the unobstructed turbine. In case the
first turbine is operated at a lower or higher than optimum tip speed ratio, the amount of
kinetic energy left for the second turbine is significantly bigger. For a low tip speed ratio
of the first turbine only about
are extracted from the first
turbine. In this case the second wind turbine reaches a maximum power coefficient of
corresponding to 39% of power extracted in the unobstructed case.
Likewise, the first turbine has a power coefficient of
high tip speed ratio of
when driven at a
. For this setup the second wind turbine reaches a
maximum power coefficient of
corresponding to 41% of the power
extracted from the unobstructed second turbine.
The shapes of the different
curves at different reference velocities are compared in
Fig. 6.28 (b). Being stretched to the same run-away tip speed ratio of the unobstructed
case, the second turbine power curve is almost identical when the first turbine is operated
at a low tip speed ratio of
As observed before, the operational characteristics of
the second turbine operating in the wake of the first turbine at its optimum point are also
88
Results & Discussion
very similar to the unobstructed case. A slightly lower maximum efficiency of
is reached in this case. The shape of the second turbine power curve
when operated in the wake of the first turbine operated at a high tip speed ratio of
, however, differs visibly from the unobstructed case. A maximum efficiency of
is reached when being stretched to the run-away tip speed ratio of the
unobstructed case.
A comparison of the combined power coefficients of both turbines for the nine different
test cases is presented in Fig. 6.29. The black lower parts of the bars are the power
coefficients of the first turbine, which is
for the first three cases and
for cases 4-6 respectively
coefficients of the second turbine
for cases 7-9. The power
constitute the upper part of the bars, which are
coloured according to the power curves presented in Fig. 6.28.
Fig. 6.29:
Combined power output (CP,Tu1 + CP,Tu2) of both turbines operated in 3D distance for
the nine investigated test cases
It can be observed that the maximum combined power output is obtained for test case 1, in
which both turbines are operated at their maximum power point. Comparing cases 1,4 and
7, it can be seen that the part of the power extracted by the second turbine
significantly increases, when less energy is extracted by the first turbine in cases 4 and 7.
In this specific setup, the combined power in cases 4 and 7 does, however, by far not reach
the maximum extracted power of case 1.
Nevertheless, it should be noted that a variation in first turbine tip speed ratio from the
optimum can lead to an increased overall power output. A comprehensive study on the
wake interference effect on the performance of a downstream turbine was performed by
Adaramola and Krogstad [14] at NTNU’s wind tunnel. They investigated the effects of
89
Results & Discussion
variations in turbine separation distance
angle
and first turbine tip speed ratio
, first turbine yaw angle , first turbine pitch
on the total power output from both turbines.
They found a slight increase in total power output from both turbines, when the upstream
turbine was operated at a slightly higher tip speed ratio than the optimum design tip speed
ratio [14].
6.6.2 Downstream Flow Field
The velocity deficit
[-] and the turbulence intensity
[%] in the wake 3D
downstream of the second model wind turbine are recorded for nine different tip speed
ratio combinations of the two turbines.
Firstly, the wake profiles are compared for a constant TSR of the first turbine and varying
tip speed ratios of the second turbine. The 3D wake profiles for test cases 1, 2 and 3, in
which the first turbine is driven at the optimum TSR, are compared in Fig. 6.30.
Fig. 6.31 shows the graphs acquired for a low first turbine TSR (
) in the test
cases 4, 5 and 6. The wake profiles for test cases 7, 8 and 9, which represent a high first
turbine TSR (
) are presented in Fig 6.32.
Thereafter, the exactly same data for the nine test cases is presented again. However, the
single test cases are compared in a different order to each other as some properties of the
single profiles are thus more apparent. This time, the velocity deficits and turbulence
intensities in the 3D wake are compared again for varying tip speed ratios of the first
turbine and a constant TSR of the second turbine. In Fig. 6.33 the test cases 1, 4 and 7 are
compared. For the optimum TSR of the first turbine, the maximum power point of the
second turbine is found at
(case 1). When the first turbine is operated at low
TSR, the second turbine maximum power point is at
(case 4). For a high first
turbine TSR, the maximum power point of the second turbine is found at
(case
7). The wake profiles for the test cases 2, 5 and 8 are presented in Fig. 6.34. The first
turbine TSR is varied, while the second turbine is constantly operated at a low TSR.
Finally, Fig. 6.35 shows the wake profiles for test cases 3, 6 and 9, which represent a
varying first turbine TSR in combination with a high second turbine tip speed ratio.
90
Results & Discussion
Constant TSR of the first turbine, varying TSR of the second turbine
Fig. 6.30:
Velocity deficit (Um/U∞) and turbulence intensity (u’/Um) in the wake 3D
downstream of the second turbine for the TSR Cases 1, 2 and 3
Fig. 6.31:
Velocity deficit (Um/U∞) and turbulence intensity (u’/Um) in the wake 3D
downstream of the second turbine for the TSR Cases 4, 5 and 6
Fig. 6.32:
Velocity deficit (Um/U∞) and turbulence intensity (u’/Um) in the wake 3D
downstream of the second turbine for the TSR Cases 7, 8 and 9
91
Results & Discussion
Varying TSR of the first turbine, constant TSR of the second turbine
Fig. 6.33:
Velocity deficit (Um/U∞) and turbulence intensity (u’/Um) in the wake 3D
downstream of the second turbine for the TSR Cases 1, 4 and 7
Fig. 6.34:
Velocity deficit (Um/U∞) and turbulence intensity (u’/Um) in the wake 3D
downstream of the second turbine for the TSR Cases 2, 5 and 8
Fig. 6.35:
Velocity deficit (Um/U∞) and turbulence intensity (u’/Um) in the wake 3D
downstream of the second turbine for the TSR Cases 3, 6 and 9
92
Results & Discussion
Velocity deficit
Comparing the minimum velocity deficit of the nine investigated test cases, the same
trends can be observed in Fig. 6.30 to 6.32. When the first turbine tip speed ratio is kept
constant, the minimum velocity deficit in the 3D wake is very dependent on the second
turbine TSR. The highest velocity deficit can be found for a high tip speed ratio of the
second turbine (black curves) in Fig. 6.30, Fig. 6.31 and Fig. 6.32. A low second turbine
TSR is yielding the lowest velocity deficit in all comparisons. For a high first turbine TSR
as compared in Fig. 6.32 the velocity profiles of the second turbine driven at optimum TSR
(case 8) respectively high TSR (case 9) are almost identical.
When however the second turbine TSR is kept constant, an operation of the first turbine at
the optimum point causes the highest velocity deficits as shown in Fig. 6.33 to 6.35. In
these cases the maximum possible kinetic energy has been extracted by the first turbine
yielding higher velocity deficits behind the second turbine. In case the first turbine is
operated at high tip speed ratios, the lowest velocity deficit could be found.
A comparison of the velocity deficit values of all nine investigated test cases is presented in
Fig. 6.36 in the end of this chapter.
Freestream velocity
Analyzing the velocity profiles in a region outside of the rotor wake from approximately
to
, the blockage effect in the wind tunnel due to the different
rotational speeds of the second turbine rotor is apparent. The higher the second turbine
TSR, the higher is the blockage due to the rotor swept area. Consequently, the flow that
passes between the turbine rotor and the wind tunnel endwalls has a higher velocity when
there is an increased blockage due to the turbine rotors. In Fig. 6.30 to 6.32 a high second
turbine TSR (black curve) causes freestream velocities up to
freestream velocities for an optimum and low TSR are always slightly lower.
93
, whereas the
Results & Discussion
Wake dimensions
Investigating the dimensions of the wake profiles, the tip speed ratio of the second turbine
does not seem to have a significant influence. It is rather the influence of the first turbine
TSR, which defines the width of the wake behind the array of the two model turbines.
Referring to the velocity deficit profiles, the wake is about
rotor radii broad for a
low first wind turbine TSR (cases 4, 5 & 6). In case the first turbine is operated at optimum
TSR, the wake is about
width of approximately
rotor radii broad. For a high first turbine TSR a wake
rotor radii is found.
As the wake expands when moving downstream, the first turbine wake has grown a little
more than the second turbine wake at the axial measurement station 3D downstream of
the second turbine. Therefore, the second turbine rotational speed does not influence the
width of the wake.
Wake asymmetries
Focusing on the center of the wake from
to
, clear asymmetries are
apparent in some of the wake profiles. The most obvious asymmetries are found for low
tip speed ratios of the second turbine (cases 2 & 5). If second turbine is driven at high tip
speed ratios as in cases 3, 6 and 9, however, the velocity profiles are almost symmetrical.
As explained before, the asymmetries can be ascribed to an interference of the rotation of
the flow in the rotor wake and the wake of the turbine tower. The obvious asymmetries at
low rotational speeds of the second turbine are assumed to be stem from a strong rotation
in the rotor wake. The strength of the rotation of the flow in wake is dependent on the size
of the circumferential component
in the flow behind the rotor (see Fig. 1.4). When the
turbine is rotating at a higher tip speed ratio, the circumferential component
and thus
the strength of the wake rotation reduces. Therefore, higher symmetries are found at high
TSRs of the second turbine.
However, also the first turbine TSR seems to have a certain influence on the symmetry in
the wake velocity profile. All velocity profiles as plotted in Fig. 6.32 are almost perfectly
symmetrical, although the second turbine is operated at low, optimum and high TSR
(cases 7, 8 & 9). As the first turbine is driven at a high rotational speed in all three cases, it
94
Results & Discussion
causes increased turbulence levels in the incoming flow to the second turbine rotor. These
increased turbulence levels are assumed to intensify the turbulent mixing process in the
wake yielding more symmetrical profiles.
Turbulence intensities
Analyzing the turbulence intensity profiles of the nine investigated test cases, it can be
observed that all profiles can be characterized by two distinct peaks. These two peaks can
be ascribed to the vortices shed from the blade tips of the second turbine rotor.
The highest turbulence intensities can be found for a high tip speed ratio of the second
turbine (cases 3, 6 & 9), whereas the lowest turbulence intensities are measured for low
second turbine TSRs (cases 2, 5 & 8). A comparison of the maximum turbulence intensity
levels found in all nine investigated test cases is presented in Fig. 6.36 in the end of this
chapter.
In most cases the peaks are deflected from their original position
towards the
center of the wake. At higher second turbine tip speed ratios the turbulence intensity
profiles are more symmetrical than at low tip speed ratios. The highest asymmetry in a
turbulence intensity profile is found for case 5, in which both the first and the second
turbine are operated at low tip speed ratios. It is assumed that in this case there is a strong
rotation in the flow behind the second turbine rotor and that the mixing process in the
wake is weaker due to a reduced turbulence level in the incoming flow to the second rotor.
When the first turbine is operated at high tip speed ratios as in cases 7, 8 and 9, the
turbulence intensity profiles are all almost symmetrical. High turbulence levels in the
incoming flow are assumed to enhance the mixing process in these cases, in which high
symmetries are also found in the the velocity deficit profiles.
Analyzing the wake dimension with respect to the width of the turbulence intensity
profiles, the same conclusions as found for the velocity profiles can be made. The wake
width is mainly influenced by the tip speed ratio of the first turbine, whereas the second
turbine TSR does not have hardly any influence. High first turbine TSRs cause wider
wakes profiles as observed in Fig. 6.33 to 6.35.
95
Results & Discussion
Comparison of minimum velocity deficit and maximum turbulence intensity
In Fig. 6.36 the minimum velocity deficit
intensity
and the maximum turbulence
measured in the wake 3D downstream of the second turbine are
compared for the nine investigated test cases.
Fig. 6.36:
Comparison of the minimum velocity deficit (Um/U∞)min and the maximum
turbulence intensity (u’/Um)max in the 3D wake for the nine different test cases
Minimum velocity deficit
Comparing all nine investigated test cases, the highest velocity deficit can be found in
case 3, in which the first turbine is operated at its optimum tip speed ratio and the second
turbine at a high TSR. A proportion of only about
of the incident flow
velocity can be found in the minimum of the velocity profile. Remarkably, the minimum
velocity deficit is even higher as in case 1, in which both turbine are operated at optimum
TSR and the most kinetic energy is extracted from the wind (see Fig. 6.29). The lowest
value of velocity deficit is recorded for test case 8, in which the first turbine is operated at
high, the second at low TSR. The minimum velocity found in the profile for case 8
corresponds to a value of about
.
As observed before, the velocity deficit is always highest, when the second turbine is
driven at high TSR and the first turbine TSR is kept constant (cases 3, 6 & 9). For a
constant first turbine TSR, the lowest velocity deficit can always be found for a low second
turbine TSR (cases 2, 5 & 8). When however the first turbine TSR is varied and the second
turbine TSR is kept constant, the highest velocity deficits are acquired for an optimum
TSR of the first turbine (comparing cases 1, 4 & 7 respectively 2, 5 &8 respectively 3, 6 &
9). In these cases (cases 1, 2 & 3) the maximum possible kinetic energy has been extracted
96
Results & Discussion
by the first turbine causing higher velocity deficits behind the second turbine. For the tip
speed ratios set in these experiments, a low first turbine TSR yields higher velocity deficits
than a high first turbine TSR (comparing cases 4 , 5 & 6 to cases 7, 8 & 9).
Maximum turbulence intensity
The highest maximum in turbulence intensity of
is found in case 3,
in which the first turbine is operated at optimum TSR and the second turbine at high TSR.
In general, a high second turbine TSR causes high maximum turbulence levels of more
than
(cases 3, 6 & 9). The lowest maximum in the turbulence intensity profiles of
is recorded for test case 8, in which the first turbine is operated at
high TSR and the second at low TSR. It can be observed that a low second turbine TSR
yields comparatively low maximum turbulence intensities (cases 2, 5 & 8). The tip vortices
shed from the second turbine rotor are assumingly not as strong for higher second turbine
rotational speeds.
The maximum turbulence intensities in the 3D wake behind the second turbine seem to be
primarily influenced by the second turbine rotational speed. The influence of the first
turbine TSR is small. Surprisingly, a high first turbine TSR as set in cases 7, 8 & 9 yields
lower maximum turbulence intensities as for a low (cases 4, 5 & 6) or an optimum first
turbine TSR (cases 1, 2 & 3).
Noteworthy, the maximum turbulence intensities are seemingly coupled to the minimum
values of velocity deficit. High maximum turbulence intensity is observed in cases with
high minimum velocity deficit and the other way round.
97
Results & Discussion
98
Conclusions
7 CONCLUSIONS & FUTURE WORK
7.1 Conclusions
Turbine Performance
Analyzing the performance curves of a single turbine acquired at different wind tunnel
inlet speeds, a smooth shape of the curves can be observed at wind speeds higher than
. At slower wind speeds laminar separation effects in certain sections of the
blades cause abnormal bumps in the power and thrust curves. For the design inflow speed
of approximately
coefficient of
the first model wind turbine reaches a maximum power
. In case the second model wind turbine is operated
unobstructed, a maximum power coefficient of
is measured. Since both
turbines are equipped with exactly the same set of blades, the small difference in hub
diameter seems to have a significant effect on the performance curves. At the maximum
investigated tip speed ratio of about
respectively
, maximum thrust coefficients of
are recorded for the two turbines. The fact
that these values are higher than one can be subscribed to a blockage effect by the wind
tunnel endwalls.
In case the second turbine is operated in the wake of an upstream turbine, different
maximum power points are found. For a turbine separation distance of
second turbine reaches a maximum power coefficient of
the
. That
corresponds to about 31% of the power extracted of the unobstructed turbine. When
operated in the wake 5D downstream, the second turbine has a maximum power
coefficient of
, which corresponds to about 33% of the power the
unobstructed turbine extracts from the wind. Comparing the shapes of the power curves at
proportioned reference velocities, it can be observed that the second turbine operating in
the wake has very similar operating characteristics as the unobstructed turbine. For both
investigated downstream distances, the power curves are fully developed and reach a
similar efficiency as the unobstructed turbine.
99
Conclusions
Axial development of the wake velocity deficit
Evaluating the axial development of the velocity deficit in the wake, similar conclusions
can be drawn for all investigated turbine arrangements. Moving downstream in the wake
behind one single turbine or an array of two turbines, the velocity deficit recovers with
increasing downstream distance. Comparing the velocity deficit in the wake of the three
investigated configurations, it can be observed that the velocity deficit behind an array of
two turbines is considerably higher than behind one unobstructed turbine. The highest
velocity deficit is found for a small turbine separation distance of
, as the second
turbine extracts additional kinetic energy from the fluid. In case the separation distance
between the turbines is increase to
, the minimum velocity deficit increases
slightly. More kinetic energy is recovered between the two turbines. The additional
decrease in minimum mean velocity in the 1D wake ranges between 11% and 13%, if a
second turbine is set up 5D respectively 3D downstream of the first turbine. Furthermore,
it can be observed that the velocity profile at 5D behind the second turbine is already very
similar to the velocity distribution behind the first turbine. It can therefore be assumed
that an imaginary third wind turbine set up
downstream of the second turbine
would be able to extract a similar amount of energy from the flow as the second turbine.
Furthermore, a gentle broadening of the wake can be observed for all configurations when
moving axially downstream. As the turbulent flow in the wake gradually diffuses into the
uniform flow outside the wake, the wake slowly grows in dimensions. For wake
measurements behind two turbines a horizontal growth rate of approximately
is calculated. Moreover, it has been observed that the vertical growth rate
is only about 70% of the growth rate in horizontal direction, which can be ascribed to a
blockage effect of the wind tunnel roof and the automatic traverse system located there.
Axial development of the wake turbulence intensity
Moving downstream in the wake, the turbulence intensities gradually decrease for all
investigated turbine configurations. The further downstream the velocity field is scanned,
the broader the turbulence intensity profiles become. The turbulent wake slowly diffuses
into the surrounding flow. Moreover, the turbulence intensity profiles become visibly
100
Conclusions
smoother further downstream in the wake due to turbulent diffusion processes in the
center of the wake. The distinct vortices blur into one complex turbulent structure, which
is characterized by a more uniform turbulence intensity profile.
Comparing the turbulence intensity levels of the three different turbine configurations (A),
(B) and (C), significantly increased turbulence levels can be observed for the cases
featuring an upstream turbine. Especially for downstream distances 3D and 5D more than
double as high turbulence intensities are measured in the center of the wake than for the
unobstructed case. Since the inflow to the second rotor operated in the wake of an
upstream turbine is already very turbulent, the turbulence intensity levels seem to add up
due to the additional turbulence generated by the second turbine rotor.
The turbulent inflow to the rotor is also assumed to be responsible for the stronger mixing
process in the wake behind an array of two turbines. Three distinct peaks can be found in
the turbulence intensity profiles in the 1D wake for the unobstructed and both obstructed
turbine arrangements. The left and right peak can be attributed to the vortices shed from
the blade tips whereas the central peak stems from turbulence generated by the blade
roots and the turbine nacelle. The 5D wake behind the array of two turbines is
characterized by only one peak, whereas two peaks in turbulence intensity are measured in
the unobstructed configuration.
Wake asymmetries and turbine tower influence
Especially the near wake is characterized by a very asymmetrical flow field with high
variations in mean velocity and turbulence intensity, when investigating the wake in the
region behind the rotor swept area. Moving further downstream, the wake profile becomes
more symmetrical and these variations gradually even out. The evident asymmetries in the
near wake velocity and turbulence profiles are assumed to stem from the influence of the
turbine tower. The rotating flow exiting the rotor is hitting the tower at a certain angle
yielding an asymmetrical velocity distribution in the wake behind the turbine.
Furthermore, the presence of the tower causes an additional velocity deficit in the lower
half of the scanned flow field. Due to the clockwise rotation of the rotor wake, the wake
behind the turbine tower is visibly deflected to the left.
101
Conclusions
Influence of the first turbine resp. the second turbine on the wake profiles
Comparing the wake measurements at different turbine separations distances, it is
possible to evaluate the influence of the first turbine respectively the second turbine wake.
It can be observed that the flow structures in the wake directly behind the rotor swept area
are governed by the rotational motion of the second turbine rotor. The influence of the
turbine separation distance is found to be insignificant to the basic flow structures in this
part of the wake.
Comparing the dimensions of the wake profiles, the influence of the first turbine wake is
evident. At all downstream distances the dimensions of the wake are visibly bigger, when
the turbine separation distance is increased. As the first turbine wake is growing in radial
direction with increasing downstream distance, the outer dimensions are assumed to be
predominately influenced by the first turbine wake.
Tip speed ratio variations
When the tip speed ratio of the first wind turbine is set to a higher or lower value than at
its maximum power point, a significant increase in the maximum power point of the
second turbine performance curve can be observed. More kinetic energy is left in the flow,
in case the first wind turbine is not operated at its design tip speed ratio. With the settings
of the investigated test cases in the scope of this project, a speed-up or slow-down of the
first turbine, however, does not yield an increase in the total power output of both
turbines.
It can be concluded that the minimum velocity deficit in the wake behind the two turbines
is very dependent on the tip speed ratio of the second turbine. The highest velocity deficit
is found for a high second turbine rotational speed. Conversely, a low second turbine tip
speed ratio yields comparatively low velocity deficits. For constant second turbine tip
speed ratios, however, an operation of the first turbine at the optimum power point causes
the highest velocity deficits. In this case, the maximum possible kinetic energy is extracted
by the first turbine.
102
Conclusions
Evaluating the dimensions of the wake profiles, the tip speed ratio of the second turbine
does not seem to have a significant influence. It is rather the influence of the first turbine
tip speed ratio, which defines the width of the wake behind the array of the two turbines.
The most obvious asymmetries are found for low tip speed ratios of the second turbine. In
case the second turbine is driven at high rotational speeds, the velocity profiles in the wake
are almost symmetrical. The obvious asymmetries at low rotational speeds of the second
turbine are assumed to originate from a strong rotation in the rotor wake interacting with
the turbine tower. Nevertheless, also high tip speed ratios of the first turbine increase the
symmetry in the wake velocity profile. It is assumed that high first turbine rotational
speeds cause increased turbulence levels in the incoming flow to the second turbine rotor,
which intensify the turbulent mixing process in the wake.
The maximum turbulence intensities in the wake behind the second turbine are majorly
influenced by the second turbine rotational speed. The highest turbulence intensities can
be found for a high tip speed ratio of the second turbine, whereas the lowest turbulence
intensities are measured for low second turbine rotational speeds. The influence of the
first turbine tip speed ratio is found to be small.
103
Future work
7.2 Future work
Analyzing the results of the measurements performed during this project, a number of
answers could be found but simultaneously even more questions popped up. A major topic
of discussion in this paper is the evident asymmetries found in the velocity deficit and
turbulence intensity profiles. Although the influence of the turbine tower is assumed to
cause these asymmetries, a further investigation of this phenomenon could possibly help
to associate the peaks in the wake profiles to interactions of the air flow with solid
structures. A number of questions emerge: At which angles is the turbine wake hitting the
tower? At which rotational speed is the wake rotating? Why are there unevenly distributed
centers of high turbulence intensity and high velocity deficit in the near wake?
A vorticity analysis in the near wake could be a first step to find some answers to those
questions. Therefore, velocity measurements in more than one dimension would have to
be performed. Multi-wire CTA measurements or Pitot tube measurements with a five-hole
probe could be convenient experimental techniques.
Evaluating the full area wake profiles, it is observed that the center of the maximum
velocity deficit is located slightly underneath the center of the rotor in the 3D and 5D
wake. A blockage effect due to the traverse system underneath the wind tunnel roof is
assumed to be responsible for this displacement. Also, a lower-pressure region in the
tower wake is suspected to cause a certain downshift in the wake. In order to assess the
influence governing this phenomenon, it is recommended to perform a vertical traverse of
the flow field using a simple manual traverse mechanism.
In the present experimental setup there are numerous possibilities of parameter
variations. So far, both turbines are operated at their maximum power point at one pitch
angle and one yaw angle. Two different turbine separation distances are investigated. In
these cases, wake measurements at up to three downstream distances are performed.
Moreover, the tip speed ratios of the two turbines are varied to three defined operating
points. In the resulting nine test cases, however, the turbines are set up in only one
separation distance. So far, only the 3D wake is investigated, but especially the 1D wake is
assumed to give further knowledge about the dependency of asymmetries in the wake of
the tip speed ratios of the two turbines. Additionally, a variation of the tip speed ratios
104
Future work
while the turbine separation distance is increased is assumed to yield some interesting
results. Furthermore, full area wake measurements at different tip speed ratio
combinations could clarify some flow phenomena in the wake.
Besides the turbine separation distance and the tip speed ratios, there are a number of
other parameters that could be varied in the present experimental setup. A variation of the
blade pitch angles of the first and/or second model wind turbine is expected to have a
significant influence onto the flow structures in the wake behind the second turbine. In
addition, a variation in yaw angle of the first and/or second model wind turbine would
yield some relevant information about the development of the velocities and turbulences
in the wake under yawed conditions.
In order evaluate an optimum turbine separation distance in a wind farm, the axial
separation distance should be further increased. Also, a number of wake measurements
further downstream in the wake would be favorable to estimate an appropriate turbine
separation distance. For wake measurements up to 10-12D downstream and the present
model size, the wind tunnel at NTNU’s laboratory is not long enough. An implementation
of the current test case into a CFD model could be a convenient tool to obtain some results
at more downstream distances.
All the data acquired from the experiments performed in the wind could be useful as input
data for an extensive CFD study of the same experimental setup. If a comparison of the
computational and the experimental results yielded a sufficiently good correspondence,
the CFD routines could represent a powerful tool to predict the aerodynamic behavior of
wind turbines in a wind farm arrangement.
105
106
References
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112
Appendix
APPENDIX: COMPARISON OF PERFORMANCE CURVES
Three power and thrust curves of the unobstructed second turbine at three different wind
tunnel inlet speeds are presented in Fig. 6.5 in chapter 6.2.1.2. However, these curves are
actually recorded for five different inlet speeds. The objective of the variation of inlet
speed is to obtain a Reynolds-independent result, i.e. that the dimensionless curves do not
change above a certain wind speed. The curves acquired for wind speeds of
,
Fig A.1:
,
and
,
are presented in Fig. A.1.
CP and CT curves of second turbine operating unobstructed at five different inflow
wind speeds
It can be observed, that the performance curves are not yet fully developed at
and
of
inflow speed. A distinct drop around the design tip speed
can be observed in the power and thrust curves for these inlet speeds. The inlet
speed is too low that the flow entirely adheres on the blade profile. According to Karlsen
[16], who comprehensively investigated the blade profiles of the model wind turbines, this
effect can be ascribed to laminar separation bubbles near the blade leading edge, which
can cause the flow to separate at too low Reynolds numbers.
These phenomena are consistent with the results found by Adaramola and Krogstad [28]
on the same turbine. The power and thrust curves as recorded by Adaramola and Krogstad
are shown in Fig. A.2.
113
Appendix
Fig A.2:
Reynolds number effect on model turbine performance characteristics [28]
In contrast to the newly recorded performance curves, Adaramola and Krogstad found a
certain drop in the power curves already for a wind speed lower than
[28].
Also, laminar separation effects in certain sections of the blades were suspected to be
responsible for this phenomenon.
Furthermore, Adaramola and Krogstad found Reynolds-independent power and thrust
curves already at a wind tunnel inflow speed above
[28]. In the present
measurements as shown in Fig. A.1, however, the curves for
and
are very similar, but still not identical. Judging this correctly, the recorded
performance curves are not yet Reynolds-independent.
114
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