Table Of ContentTitle
The Influence of Blade Chord on the Aerodynamics
and Performance of Vertical Axis Wind Turbines
A Thesis Submitted for the Degree of Doctor of Philosophy
by
Okeoghene Eboibi
The University of Sheffield
Mechanical Engineering Department
October 2013
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Abstract
The climate change due to emissions from the combustion of fossil fuel to
meet the ever increasing energy demands of the growing world population
has roused the attention of governments and individuals to protect the
environment. The formulated policies to protect the environment have
aroused interest in wind turbines as an alternative source of energy. The
suitability of the vertical axis wind turbines (VAWTs) in harnessing energy
from the wind in the built areas have been shown, but there still exists a
large knowledge gaps in the aerodynamics and performance of the VAWT
especially in the design and selection of an appropriate blade chord. This
thesis studied the influence of the blade chord on the aerodynamics and
performance of vertical axis wind turbines through experimental and
computational fluid dynamics methods. Two VAWT configurations of blade
chords 0.04m (AR = 15) and 0.03m (AR = 20) with corresponding solidities of
0.34 and 0.26 were used for the investigations. The performance and the flow
fields of the two configurations were measured experimentally through the
use of performance measurement method and Particle Image Velocimentry
(PIV) measurement techniques. All the experimental tests were conducted in
a low-speed open suction wind tunnel and the results are presented.
Computational fluid dynamics modelling based on the Unsteady Reynolds
Average Navier-stokes (URANS) was employed to simulate the two
configurations at the same wind tunnel test conditions to complement the
revelations from the experimental tests. The developed CFD models after a
parametric study that enabled the selection of the model’s features were
validated against experimental data by comparing both forces and the flow
physics. Vorticity of the CFD flow visualisation and blade forces provided an
additional and penetrating insight into the aerodynamics and performance
of the VAWTs by linking flow physics, and performance to the aerodynamics.
The VAWT flow physics, aerodynamics and performances have been shown
to depend on the Reynolds numbers that ranges from 1.27x103 to 1.1x105, the
blade chord (solidity), the azimuth angle blade stall is initiated and the
dynamic stall associated with the flow fields around the blade. At 6m/s test
condition, the C = 0.04m VAWT attained peak CP = 0.165 at λ = 4, while the C =
0.03m VAWT performed in the negative region at all the λ. The better
performance attained by the C = 0.04m VAWT over the C = 0.03m VAWT was
repeated at all other wind speeds tested in the experiments and also in the
computational fluid dynamics investigations. The C = 0.04m VAWT attained
a higher peak CP = 0.326 at 8m/s at λ = 3.75 indicating increased performance
with increases in Reynolds numbers. This trend was equally seen with the C
= 0.03m VAWT in the experiments and also the computational fluid
dynamics results. The VAWT with σ = 0.34 performed better than σ = 0.26
VAWT in all the conditions tested due to its higher Reynolds numbers and
solidity differences that influence the nature of the dynamic stall
phenomenon associated with the flow fields around the blades.
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Declaration
The work presented in this thesis is carried out in the Mechanical
Engineering Department at the University of Sheffield between November
2010 and September 2013. I declare that no part of the work has been
submitted before to the University of Sheffield or at any other University for
the award of a degree. The work presented in this thesis is entirely the
results of my own efforts and does not include collaborative work except
stated otherwise. The thesis contains about 120 figures and approximately
64,000 words.
Signed:
Okeoghene Eboibi
Date: 14/11/2013
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This thesis is dedicated to my wife, Carol.
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Acknowledgements
First, my acknowledgements go to my supervisor, Dr. Robert Howell, for
his helpful expertise, encouragements, and advice during the research
period. His amiable disposition, penetrating critiques and consistent
mentoring have made my study and stay in Sheffield memorable, indeed I am
very grateful.
My acknowledgements go to the research group members including those
who have successfully concluded their studies; Jonny, Louis, Dorit, Jon,
Kanok, Ethan, Cora, Stu and Danial. Thank you all for your good company.
To Jonny and Louis, I am grateful for all the assistance provided to me, in
the understanding of the basics of experimentation in VAWTs and also CFD
modelling. My gratitude also goes to the technicians in the workshop for the
assistance provided for the fabrication works of the experimental
equipment. Also, I thank my friends and the Nigerian community in
Sheffield.
The Tertiary Education Trust Fund and the Management of the Delta
State Polytechnics, Ozoro, Nigeria are appreciatively acknowledged for the
financial assistance that enabled me to pursue and accomplish this
endeavour. Also, I thank the Ozoro Polytechnic community, especially the
School of Engineering for filling in the gaps created by my absence.
To my parents, brothers and sisters, I say thank you for all your supports
through prayers and advice of encouragements to hold on, especially when
my morale was low. I appreciate you all for your genuine concerns. I am
gratefully indebted to my wife, Carol, and our children, Ewomazino D.,
Elozino F., and Orozino N for all your courage and strength to carry on while
I was away from the family for these years. May the good Lord grant our
wishes so we can be happier ever when the family reunites. Finally, I thank
the almighty God for the strength, guidance, provisions, and also for his
grace and the gift of perseverance all through the period of this journey. He
has been and remained God forever.
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Nomenclature
Symbol
A hot wire anemometry, constant 1
AR aspect ratio
B hot wire anemometry, constant 2
C blade chord
C drag coefficient
D
C lift coefficient
L
C moment coefficient
M
CP power coefficient in experiment
CP power coefficient in experiment
cfd
D wind turbine diameter
d pressure outlet boundary distance from VAWT axis
o
d particle displacement
p
E hotwire voltage
F capacity factor
F drag force
D
F lift force
L
g acceleration due to gravity
I rotor rotational mass moment of inertia
rig
k–ε the turbulence model based on turbulent kinetic energy and turbulent
dissipation
k–ε RNG the variant of k–ε using Re-Normalisation Group methods
k–ω turbulence model based on turbulent kinetic energy and specific
dissipation
k–ω SST the variant of k–ω by Menter (1993)
L aerodynamic loss factor
M particle magnification
p
N the number of blades
n hot wire anemometry, constant 3
P pressure, rated power
PB the blade power (three blades)
Pw the wind power
q dynamic pressure
R rotor radius,
R gas constant
g
Re blade Reynolds number
R radius of particle
p
S wind turbine spacing
S-A Spallart Allmaras turbulence model
T temperature
t time
Δt inter image time, change in time step
T blade torque
B
T the resistive torque
res
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Symbol continued…
T turbulence intensity
u
u' standard deviation of velocity fluctuations
U mean velocity
mean
U particle velocity
p
V wind velocity
V the blade velocity
b
V relative velocity
R
V free stream wind speed
w
V settling velocity of particle
S
y dimensionless wall distance
Greek symbol
α angle of attack
ΔCP change in CP
θ azimuth position
λ tip speed ratio
dynamic viscosity of fluid
f
ξ rotor angular acceleration
vorticity
circulation
air density
density of fluid
f
density of tracer particle
p
σ rotor solidity
ω rotor angular speed
Abbreviations
CFD Computational Fluid Dynamics
DES detached eddy simulation
FOV field of view
HAWT horizontal axis wind turbine
LES large eddy simulation
LEV leading edge vortex
NACA National Advisory Committee for Aeronautics
PIV Particle Image Velocimetry
RANS Reynolds Averaged Navier–Stokes
TEV trailing edge vortex
URANS Unsteady RANS
VAWT vertical axis wind turbine
VTM vorticity transport model
WPD wind farm power density
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Table of Contents
Title ........................................................................................................................................ 1
Abstract ................................................................................................................................ 2
Declaration .......................................................................................................................... 3
Acknowledgements ........................................................................................................... 5
Nomenclature ..................................................................................................................... 6
Table of Contents .............................................................................................................. 8
List of Figures .................................................................................................................... 13
Introduction ..................................................................................................................... 19
1.1 The Environment and Wind Energy ........................................................... 19
1.2 The Wind Machine ........................................................................................... 20
1.3 Kinematics of VAWT ....................................................................................... 23
1.4 Aim of the Study ............................................................................................... 26
1.5 The Thesis Outline ........................................................................................... 28
Literature Review ............................................................................................................ 30
2.1 Introduction ...................................................................................................... 30
2.2 VAWT Performance Assessment Parameters ........................................... 31
2.2.1 Aerofoil Thickness and Camber ........................................................... 31
2.2.2 Solidity ........................................................................................................ 33
2.2.3 Flow Curvature and Blade Sweep ....................................................... 42
2.2.4 Reynolds Number Effects ....................................................................... 44
2.2.5 Dynamic Stall ........................................................................................... 46
2.2.6 Summary ..................................................................................................... 49
2.3 VAWT Investigative Methods and Application ....................................... 50
2.3.1 Experimental Methods .......................................................................... 50
2.3.1.1 Performance and Aerodynamics ....................................................... 51
2.3.1.2 Particle Image Velocimentery and Flow Physics ........................ 55
2.3.1.3 Summary ................................................................................................. 56
2.3.2 Numerical Modelling .............................................................................. 57
2.3.2.1 Momentum and vortex Methods ...................................................... 58
2.3.2.1.1 Momentum Models......................................................................... 58
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2.3.2.1.2 Vortex Models .................................................................................. 59
2.3.2.1.3 Summary ........................................................................................... 62
2.3.2.2 Computational Fluid Dynamics Methods...................................... 62
2.3.2.2.1 Aerodynamics and Performance ................................................ 63
2.3.2.2.2 CFD Model Verification and Validation ................................... 65
2.4. Summary ................................................................................................................. 71
Methods .............................................................................................................................. 74
3.1 Introduction ...................................................................................................... 74
3.2 The Wind Tunnel ............................................................................................. 75
3.3 Wind Tunnel VAWT Models ......................................................................... 77
3.4 VAWT Performance Measurement Apparatus ........................................ 77
3.4.1 Start-up Apparatus .................................................................................. 78
3.4.2 Measurement Apparatus ........................................................................ 78
3.5 Performance Measurement Method ........................................................... 82
3.5.1 Calibration ................................................................................................ 82
3.5.2 Velocity Profile and Turbulence Intensity Measurement ............ 85
3.5.3 Power Coefficient Measurement ......................................................... 87
3.6 Particle Image Velocimentery (PIV) Method............................................ 90
3.6.1 PIV Equipment ......................................................................................... 90
3.6.1.1 Tracer Particle Generator................................................................... 91
3.6.1.2 Pulsed Light Sheet Source.................................................................. 92
3.6.1.3 Camera Synchronised with the Laser ............................................. 92
3.6.1.4 Image Acquisition and Processing Software ................................. 93
3.6.2 PIV Experimental Set-up and Test Cell .............................................. 94
3.6.3 Blade Surface Treatment ....................................................................... 95
3.6.4 Verification of Test Settings .................................................................. 96
3.6.4.1 Seeding Concentration ........................................................................ 96
3.6.4.2 Laser Power ............................................................................................ 97
3.6.4.3 Time Between Pulses ........................................................................... 98
3.6.4.4 Number of Images .............................................................................. 100
3.6.5 Testing and Image Acquisition Procedure ..................................... 100
3.6.6 Image Evaluation and Data Analysis ................................................. 101
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3.6.6.1 Image Masking ..................................................................................... 102
3.6.6.2 Correlation of Image .......................................................................... 102
3.6.6.3 Moving Average Validation and Vector Statistics ..................... 104
3.7 Computational Fluid Dynamics Method ................................................. 106
3.7.1 CFD Solver ............................................................................................... 106
3.7.2 CFD Model Development .................................................................... 107
3.7.3 Parametric Studies ................................................................................. 114
3.7.3.1 Time Step Size ....................................................................................... 114
3.7.3.2 Mesh Sensitivity ................................................................................... 115
Turbulence Modelling and CFD Model Validation................................................ 118
4.1 Introduction ..................................................................................................... 118
4.2 Turbulence Modelling .................................................................................... 119
4.3 Model Validation ............................................................................................ 122
4.3.1 Power Coefficient .................................................................................. 123
4.3.2 Flow Physics .............................................................................................127
4.3.2.1 Flow Fields at λ = 2.5, C = 0.04m ...................................................... 128
4.3.2.2 Flow Fields at λ = 4, C = 0.04m ......................................................... 130
4.3.2.3 Flow Fields at λ = 3, C = 0.03m ......................................................... 130
4.4 Summary .......................................................................................................... 134
Experimental Results ....................................................................................................135
5.1 Introduction .....................................................................................................135
5.2 Performance of VAWTs ................................................................................ 136
5.2.1 Power Coefficient Determination ..................................................... 136
5.2.1.1 Blade Chord = 0.03m (σ = 0.26) ........................................................ 136
5.2.1.2 Blade Chord = 0.04m (σ = 0.34) ........................................................ 139
5.3 Flow Field Visualization and PIV Measurements ................................. 142
5.3.1 Blade Interaction with 6m/s Wind Speed, C = 0.03m (σ = 0.26).. 143
5.3.1.1 Flow Fields at λ = 2.5 .......................................................................... 143
5.3.1.2 Flow Fields at λ = 3.............................................................................. 146
5.3.1.3 Flow Fields at λ = 4 ............................................................................. 148
5.3.2 Blade Interaction with 8m/s Wind Speed, C = 0.03m (σ = 0.26).. 150
5.3.2.1 Flow Fields at λ = 2.5 .......................................................................... 150
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Description:performance of vertical axis wind turbines through experimental and Computational fluid dynamics modelling based on the Unsteady Reynolds.
