AN INVESTIGATION ON THE AERODYNAMIC
PERFORMANCE OF A VERTICAL AXIS WIND TURBINE
By
ETESH VAISHNAV
Bachelor of Science in Mechanical Engineering
Bhilai Institute of Technology
Durg, India
2007
Submitted to the Faculty of the
Graduate College of
Oklahoma State University
in partial ful llment of
the requirements for
the Degree of
MASTER OF SCIENCE
December, 2010
COPYRIGHT
c
By
ETESH VAISHNAV
December, 2010
AN INVESTIGATION ON THE AERODYNAMIC
PERFORMANCE OF A VERTICAL AXIS WIND TURBINE
Thesis Approved:
Dr. Khaled A. Sallam
Thesis Advisor
Dr. Andrew S. Arena
Dr. Frank W. Chambers
Dr. Mark E. Payton
Dean of the Graduate College
iii
ACKNOWLEDGMENTS
I would like to express my gratitude to my mentor Dr. Khaled A. Sallam for his
invaluable guidance. Without his advice this thesis would not have been possible.
I also would like to gratefully acknowledge my hearty appreciation to my advisory
committee: Dr. Frank W. Chambers and Dr. Andrew S. Arena.
I am forever indebted to my parents for their endless patience, encouragement and
love when it was most required. I owe a debt of gratitude to my girlfriend, Niraja
Singh, for her countless support. Khushwant Saini, Vivek Dubey, Rohit Pillay and
Siddarth Agrawal, I am privileged to have such roommates helping me at all moments.
I am also thankful to all those people who are directly or indirectly associated
with me and whose contribution made this project attain a successful completion.
iv
TABLE OF CONTENTS
Chapter Page
1 INTRODUCTION 1
1.1 General Statement of The Problem . . . . . . . . . . . . . . . . . . . 1
1.1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.2 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Previous Related Studies . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2.1 VAWT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2.2 Flapping Wings . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3 Speci c Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.4 Organization of The Thesis . . . . . . . . . . . . . . . . . . . . . . . 8
2 COMPUTATIONAL METHODS 13
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2 Governing Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3 Geometry of NACA 4 digit series . . . . . . . . . . . . . . . . . . . . 15
2.4 Geometry Creation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.5 Grid Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.6 Turbulence Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.7 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.8 Problem Set up in Fluent . . . . . . . . . . . . . . . . . . . . . . . . 18
2.9 Time Step Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.10 Reference Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.11 Airfoil Lifting Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
v
2.12 Tip Speed Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.13 Angle of Attack . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.14 Von Karman Vortex Street . . . . . . . . . . . . . . . . . . . . . . . . 22
2.15 Calculation of Torque Produced by Horizontal and Vertical Forces Act-
ing on Airfoils . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.16 Grid Independence . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.17 Validation of 2-D CFD simulation . . . . . . . . . . . . . . . . . . . . 24
3 RESULTS AND DISCUSSION 35
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.2 Coe cient of Performance of a VAWT (Cp) . . . . . . . . . . . . . . 36
3.3 E ect of Rotor Diameter on VAWT's Performance . . . . . . . . . . . 36
3.4 E ect of Laminar Flow on VAWT's Performance By Comparing the
Results From RANS Turbulence Model and Laminar Viscous Model . 37
3.5 E ect of Solidity on VAWT's Performance . . . . . . . . . . . . . . . 38
4 CONCLUSIONS AND RECOMMENDATIONS 58
4.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.2 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.3 Recommendations For The Future Work . . . . . . . . . . . . . . . . 60
BIBLIOGRAPHY 61
APPENDIX A: Steps Involved in Post-processing of VAWT 65
APPENDIX B: Airfoil Coordinates 74
vi
LIST OF TABLES
Table Page
2.1 Data sets used for simulation in FLUENT (V1 = 10 m/s, Rotor Di-
ameter = 2 m.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.1 Data sets used for simulation in FLUENT (V1 = 10 m/s, Rotor Di-
ameter = 1 m.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.2 Cp vs at V1 =10 m/s . . . . . . . . . . . . . . . . . . . . . . . . . 57
1 NACA 0018 Coordinates . . . . . . . . . . . . . . . . . . . . . . . . . 75
vii
LIST OF FIGURES
Figure Page
1.1 Darrieus type straight bladed VAWT (Islam et al., 2006). . . . . . . . 9
1.2 Savonius type VAWT (Islam et al., 2006). . . . . . . . . . . . . . . . 9
1.3 Helical type VAWT (Quiet Revolution Ltd, 2008). . . . . . . . . . . . 10
1.4 Worldwide electrical power generation (World Wind Energy Report,
2008). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.5 Installed capacity of wind energy on yearly basis (World Wind Energy
Report, 2008). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.6 Cp- curve for various types of wind turbines (Bragg and Schmidt, 1978). 11
1.7 Variation of Cp with pitch angles at = 4 (Chen and Zhou, 2009). . 12
1.8 In
uence of airfoil thickness on VAWT's performance at Re=200,000,
V=10 m/s [Kirke and Lazauskas (1991), Claessens (2006)]. . . . . . . 12
2.1 Solution strategy in FLUENT (Fluent 12.0.16 user guide). . . . . . . 25
2.2 Variation of angle of attack as a function of in degrees for a range of . 25
2.3 Schematic view of the geometry of rotor 120 with NACA 0018 airfoil. 26
2.4 Blocking with the application of quarter O-grid and periodic vertices. 26
2.5 Schematic view of the hexahedral meshing of 120 of rotor with NACA0018. 26
2.6 Closer view of the O-type grid around NACA0018 airfoil. . . . . . . . 27
2.7 View of the rotor (unstructured hexahedral mesh) with three airfoils. 27
2.8 Schematic views of the stationary far- eld and rotor (unstructured hex-
ahedral mesh). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.9 Schematic view of a six bladed VAWT with GUI of ICEM CFD. . . . 28
viii
2.10 Velocity vectors at the surface of the airfoil at = 2, = 360, V1 =
10 m/s, Reynolds number 106. . . . . . . . . . . . . . . . . . . . . . . 29
2.11 Velocity vectors at the out
ow at = 2, V1 = 10 m/s. . . . . . . . . 29
2.12 Velocity vectors at the leading edge of the airfoil at = 2, = 120,
V1 = 10 m/s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.13 Velocity vectors at the trailing edge of the airfoil at = 2, = 240,
V1 = 10 m/s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.14 Depiction of leading and trailing edge vortex formation . . . . . . . . 31
2.15 Formation of vortices at = 2 . . . . . . . . . . . . . . . . . . . . . 31
2.16 Grid-Independent result for cell size of 65000 and 140000 (Horizontal
component of the blade force at =1.88, V =10 m/s). . . . . . . . . 32
2.17 Horizontal component of the blade force at =1.88, V =10 m/s (Guerri
et. al, 2007). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.18 Grid-Independent result for cell size of 65000 and 140000 (Vertical
component of the blade force at =1.88, V =10 m/s). . . . . . . . . 33
2.19 Vertical component of the blade force at =1.88, V =10 m/s (Guerri
et. al, 2007). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.20 (A) Validation of Cp of VAWT with the experimental results by Claessens
(2006) as a function of (B) V1 = 10 m/s, Re = 106, Rotor diameter=
2 m. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.1 (A) In
uence of rotor diameter on the VAWT's performance for a range
of (B) V1 = 10 m/s, Re = 106, Rotor diameter 1m. and 2m. . . . 41
3.2 Contours of Vorticity for a range of for Laminar
ow at Rec =5000,
D = 0.1365 m. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.3 In
uence of Laminar
ow on Cp with the application of Laminar viscous
model at low Rec= 5000, V1 = 10 m/s, Rotor diameter= 0.1365 m. 43
3.4 Variation of torque generated by each blade as a function of = 1 . . 44
ix
3.5 Variation of torque generated by each blade as a function of = 2 . . 44
3.6 Variation of torque generated by each blade as a function of = 3 . . 45
3.7 Variation of torque generated by each blade as a function of = 4 . . 45
3.8 Variation of torque generated by each blade as a function of = 5 . . 46
3.9 Variation of torque generated by each blade as a function of = 6 . . 46
3.10 Variation of total torque generated by VAWT as a function of = 1 . 47
3.11 Variation of total torque generated by VAWT as a function of = 2 . 47
3.12 Variation of total torque generated by VAWT as a function of = 3 . 48
3.13 Variation of total torque generated by VAWT as a function of = 4 . 48
3.14 Variation of total torque generated by VAWT as a function of = 5 . 49
3.15 Variation of total torque generated by VAWT as a function of = 6 . 49
3.16 Contours of Velocity of airfoil-1 after two cycles at =5 and Rec = 106 50
3.17 Contours of Pressure of airfoil-1 after two cycles at =3 and Rec = 106 51
3.18 Contours of Velocity at = 1, 2, 3 and Rec = 106, for 3 bladed turbine
on left side and 6 bladed turbine on right side . . . . . . . . . . . . . 52
3.19 Contours of Velocity at = 4, 5, 6 and Rec = 106, for 3 bladed turbine
on left side and 6 bladed turbine on right side . . . . . . . . . . . . . 53
3.20 Contours of Vorticity at = 1, 2, 3 and Rec = 106, for 3 bladed turbine
on left side and 6 bladed turbine on right side . . . . . . . . . . . . . 54
3.21 Contours of Vorticity at = 4, 5, 6 and Rec = 106, for 3 bladed turbine
on left side and 6 bladed turbine on right side . . . . . . . . . . . . . 55
3.22 (A) In
uence of number of blades on the VAWT's performance for a
range of (B) V1 = 10 m/s, Re = 106, Rotor diameter= 2 m. . . . 56
x
NOMENCLATURE
CL Lift coe cient
A Frontal area of wind turbine [m2]
CD Drag coe cient
Cm Moment coe cient
Cp Power coe cient
D Tangential component of drag
DR Radial component of drag
F Total tangential force
FR Total radial force
L Tangential component of lift
LR Radial component of lift
P Power [watt]
p Pressure [atm]
R Length of the rotor arm [m]
Re Reynolds number
t Time [sec]
T Temperature [Kelvin]
T Torque [N-m]
V Wind velocity [m/s]
Greek Symbols
Air density
i
Angle of attack
Angular velocity [radian/s]
Dynamic viscosity [N-s/m2]
k Kinetic energy
Rotational angle of airfoil
Tip speed ratio
" Turbulence dissipation rate
ABBREVIATIONS
AR Aspect Ratio
CFD Computational Fluid Dynamics
DES Detached Eddy Simulation
DNS Direct Numerical Simulation
LES Large Eddy Simulation
NSE Navier Stokes Equation
RANS Reynolds Averaged Navier Stokes
RNG Renormalization Group
S-A Spalart Allmaras
S k-" Standard k- "
SST K-
Shear Stress Transport K-
ii
CHAPTER 1
INTRODUCTION
1.1 General Statement of The Problem
1.1.1 Background
Non-renewable resources of energy are limited in the world and are depleting at a
faster rate due to rapidly growing population. These energy resources are exhaustible
and are the main cause of pollution, which is eventually leading to another major
problem of global warming. Considering all these problems, it has now become a
dire need to nd another substitute of energy which is mainly pollution free and
available in abundance. Among all the available renewable energy resources, wind
energy has many advantages like it is available in abundance, does not contribute to
global warming, requires less installation and maintenance cost for power generation.
The top leading countries in the eld of wind energy production are USA, China,
Spain and Denmark. For many years wind energy has been used for many small
purposes like for water pumping with the capacity of 10 - 250 kW and for producing
mechanical power to operate some small devices, but nowadays it is also being used
to produce electricity with the application of wind turbines. Wind turbine consists
of a rotor shaft and a generator mounted in a nacelle.
Based on axis of rotation, wind turbines are divided into two types: Horizontal
axis wind turbines (HAWT) and vertical axis wind turbines (VAWT). In case of
horizontal axis wind turbines (HAWT), this arrangement is mounted at the top of a
tower with the rotor blades facing the wind directly. Whereas in case of VAWT, this
1
arrangement is mounted vertically hence provides better stability to rotor blades and
are easily accessible for maintenance. Apart from having this arrangement, rotor of
VAWT requires no yaw mechanism to maintain a proper stability. VAWT is further
divided into lift driven VAWT (Darrieus type) and drag driven VAWT (Savonius
type) as shown in gure 1.1 and gure 1.2 respectively. Darrieus type VAWT proves
to be more e cient than Savonius type turbine. G. J. M. Darrieus was the rst to
come up with an invention of VAWT in 1931 and since then study of wind turbine
has been of interest to many researchers. Figure 1.5 provides a statistical data of
world wide installed capacity of wind energy in MW.
After mid 80s, there has been a renaissance of interest regarding sources of renew-
able energy among numerous researchers (Bragg and Schmidt, 1978; Marini et al.,
1992; Wang, 2000; Chen and Zhou, 2009; Claessens, 2009; Ferreira, 2009) carrying
out extensive studies in the eld of wind turbines. These studies have led to a wide
range of designs of VAWT and suggested various improvements on a conceptual ba-
sis. Selection of a wind turbine depends on the required tip speed ratio for instance,
straight bladed-VAWT is generally suitable to operate at high to avoid the problem
of self-starting, whereas helical type VAWT as shown in gure 1.3 is generally suitable
to operate at comparatively lower value of .
Various authors investigated the performance of VAWT, mainly including Bragg
and Schmidt (1978), Cetin et al. (2005) and Ferriera (2009) to name a few. Figure
1.6 by Bragg et al. (1978), depicts a curve between Cp and for varieties of wind
turbines. With this gure he explained the e ciency limit of an ideal wind turbine,
rst proposed by a German physicist Betz in 1919, according to him no wind turbine
can have its e ciency (i. e. Cp ) more than 0.59 and this limit is called Betz limit.
Figure 1.7 shows a study by Chen and Zhou (2009) which explains the e ect of pitch
angle on a performance of VAWT. Claessens (2009) in his thesis investigated the e ect
of airfoil thickness on Cp of a wind turbine as shown in gure 1.8.
2
1.1.2 Problem Statement
The present study explores a range of factors in
uencing the aerodynamic perfor-
mance of a VAWT. The e ect of tip speed ratio has been examined which is considered
to be a prominent factor in deciding Cp of a wind turbine. In this regard, is opti-
mized for the maximum e ciency of the turbine. E ect of rotor diameter on Cp has
also been a part of this study. Furthermore, the blade and tower wakes at low and
high Reynolds numbers and their e ects on Cp has also been the area of concern in
the present study. In addition, present study elucidates the e ect of solidity on Cp of
a VAWT.
1.2 Previous Related Studies
1.2.1 VAWT
The research on VAWT aerodynamics began with the stream tube momentum
model and vortex model. There are many factors that a ect the propulsive perfor-
mance of an airfoil like angle of attack, tip speed ratio, thickness, symmetricity of
an airfoil, lift and drag coe cient. While designing a quasisteady model of an airfoil
these factors were not taken into consideration hence the model did not come out to
be a more practical model. Therefore, studies of
apping and plunging airfoil, mainly
by Sane et al. (2002), Lee et al. (2006) and Shyy et al. (2009) came into existence
where the forces acting due to the unsteady motion of a wing were calculated.
Guerri et al. (2007) and Chen and Zhou (2009) both analyzed the
ow around
a rotating VAWT by using Reynolds Averaged Navier Stokes (RANS) solver in 2-D
simulation. PISO discretization scheme with SST K-! model was used to get the
ow details near the wall of the blades. Sliding mesh technique was used to make
a moving mesh. NACA 0018 airfoil type was chosen for both the studies. Grid was
split into moving and rotary part. Guerri et al. (2007) calculated the horizontal
3
and vertical component of the forces acting on the airfoil to determine the value of
the total torque generated by VAWT whereas Chen and Zhou (2009) reported the
coe cient of moment. Moment coe cient of an airfoil is calculated by the following
formula:
Cm = Tmean/0.5 AV 2R (1.1)
Chen also investigated the e ect of pitch angle on VAWT aerodynamic perfor-
mance and obtained an optimum range of pitch angle which would give maximum
power output keeping tip speed ratio constant. Figure 1.7 shows the variation of Cp
with pitch angles. Guerri et al. (2007) analyzed the in
uence of tip speed ratio on
the aerodynamic performance of VAWT and also showed that the resulting value of
Cp obtained with RANS simulations is more accurate as the same Cp can be achieved
at relatively lower value of than obtained with the Multiple Stream Tube theory.
He also found that the computed force and torque vary periodically as a function of
angle of rotation .
Howell et al. (2009) and Claessens (2006) performed experimental and computa-
tional studies on 2-D and 3-D models at di erent Reynolds numbers. He obtained 3-D
computational results in a good agreement with the experiments. E ect of surface
roughness was also taken into consideration. It was concluded that 2-D CFD results
are always higher than 3-D CFD results and this is because of the presence of end tip
vortices which causes circulation in real wind turbine. In case of 2-D, losses due to the
end tip vortices and rotor arm are ignored. Periodic pattern of coe cient of moment
was also observed with three cycles per revolution. Claessens (2006) studied the ef-
fect of Reynolds number, airfoil thickness and tip speed ratio on NACA 0012, NACA
0015, NACA 0018, and NACA 0021. Figure 1.8 by Kirke and Lazauskas (1991) shows
the in
uence of airfoil thickness on the turbine performance at Re = 200000.
Tang et al. (2007) studied the e ect of structural
exibility of airfoils on the
4
uid
ow pattern around the VAWT. They found that structural
exibility causes
pitching and heaving motion to an airfoil when it comes to the e ect of aerodynamic
forces. This leads to signi cant changes in lift and thrust generation as explained
in the previous equation, hence propulsive performance of a VAWT. Geometry of an
airfoil is also an important factor that in
uences aerodynamic performance and cost
of the wind turbines. Marini et al. (1992) studied the di erent airfoil shaped blade of
a VAWT and their performances. They used Single stream-tube momentum model
and free wake vortex model for their experiments. Ferreira (2009) did a study on 2-D
and 3-D wake generation of VAWT.
1.2.2 Flapping Wings
Hover et al. (2004) have conducted studies on angle of attack pro les and their in-
uences on propulsive performance of a plunging and
apping airfoil. They employed
the method given by Read et al. (2003) that involved the comparison of performances
obtained by four di erent types of angle of attack pro les. The principle behind their
investigation was to vary the angle of attack to achieve a desired pro le so as to get
the enhanced thrust performance. Shape of the angle of attack pro le a ects the wake
pattern hence the coe cient of thrust. Thrust coe cient of an airfoil is calculated
by the following formula:
Cthrust = F /0.5 AV 2 (1.2)
Where F is the tangential force acting on airfoil.
Four major lift generating mechanism used by birds and insects have been iden-
ti ed by Ellington et al. (1996) and then experimentally con rmed by Tang et al.
(2007). Computational model proposed by Wang (2000) to solve Navier-Stokes equa-
tion for two-dimensional plunging airfoil proved to be very signi cant contribution
when it was compared with the results obtained by Birch and Dickinson (2001). Inves-
5
tigations have been made by Lee et al. (2006) on unsteady, viscous and incompressible
ows over a two dimensional
apping airfoil.
Tay and Lim (2009) considered several variables like Strouhal numbers, pitch
amplitude and phase angle to evaluate lift, thrust and e ciency of non-symmetrical
apping airfoil. They found that lift force depends on the shape of the airfoil whereas
thrust force depends on variables.
Strouhal number is a dimensionless parameter which describes the
apping
ow
mechanism and is given as:
St = fL
v (1.3)
Where:
f = Frequency of vortex shedding
L = Characteristic length (Chord length in present case)
V = Velocity of the
uid
Symmetrical airfoil contributes to only thrust and propulsive e ciency not to lift
whereas non-symmetrical
apping airfoil not only gives high thrust and e ciency but
high lift also. Sane and Dickinson (2002) modi ed quasi-steady model of a
apping
ight. They compared rotational force produced by hovering insect wing rotating at
a certain angular velocities with the force produced by translation of the wings of
quasi-steady model. Birch and Dickinson (2001), Ansari et al. (2006), Shyy and Liu
(2007), Shyy et al. (2009) conducted studies on Leading edge vortex phenomena of a
apping wing of an insect to improve the aerodynamic performance. Dynamic stall
is a mechanism that gives rise to leading edge vortex (LEV) which is accountable for
a good performance of
apping wings. This LEV detaches from the wing and forms
wake into the trailing edge. Ansari et al.'s (2006) study was focused on complex
interaction between leading edge vortex (LEV) and trailing edge vortex (TEV). Shyy
and Liu (2007) explained that both the phenomena pressure gradient and centrifugal
force in the momentum equation cause to generate LEV. They utilized results ob-
6
tained from experiments conducted by Birch and Dickinson (2001) on insect
ying
at low Reynolds number and concluded that reduction in e ective angle of attack
considerably reduces the e ect of downwash and hence reduces the growth of LEV.
Shyy et al. (2009) demonstrated that having a low aspect-ratio of a
apping wing
can increase lift even if the wing is surrounded with the tip vortices. Lee et al. (2006)
successfully proposed a theory that thrust and drag generation depends on leading
and trailing edge vortex.
Numerous aspects of an aerodynamic performance of VAWT have been questioned
throughout the literature concerning the performance optimization of wind turbines.
Plenty of literatures are available dealing with the performance optimization of wind
turbines at high Reynolds number above 106 whereas very few are available concerning
low Reynolds number
ow especially for Laminar
ow. This brings upon a need for
further investigations into Laminar
ow regimes over VAWTs. The e ect of solidity
on Cp was not in a preview of available literature which makes it an immediate need
to explore about. Therefore, in a view of current status concerning an aerodynamic
performance of VAWT, present study is extended to improve upon the conceptual
approach.
1.3 Speci c Objectives
Review of literature suggested the following speci c objectives to accomplish in the
present study:-
To investigate the aerodynamics of a moving airfoil (NACA0018) of VAWT in
two dimensional unsteady
ows at Reynolds number of 1.086 106 using ANSYS
FLUENT 12.0.16 for simulation and ICEM CFD to generate sliding mesh.
To study the variation of performance coe cient of VAWT at di erent tip speed
ratios and obtain an optimum value of tip speed ratio ( ) at which VAWT
7
produces maximum power output for NACA 0018 airfoil.
To investigate the in
uence of rotor diameter on aerodynamic performance of
VAWT.
To study the e ect of laminar boundary layer separation on Cp of a VAWT by
comparing the results of Laminar viscous model and RANS turbulence model.
To consider the e ect of solidity (which is given by = NbC/R) on VAWT's
performance at 1 = 0.321 for three bladed VAWT and 2 = 0.642 for six bladed
VAWT.
1.4 Organization of The Thesis
The thesis is organized into four chapters. The statement of the problem, speci c
objectives of the present study and literature review have been presented in the rst
chapter. The second chapter describes the computational methods used during the
present study. The results and discussions are presented in the third chapter. Finally,
the summary and main conclusions of the present study, including recommendations
for future study, are presented in the fourth chapter.
8
Figure 1.1: Darrieus type straight bladed VAWT (Islam et al., 2006).
Figure 1.2: Savonius type VAWT (Islam et al., 2006).
9
Figure 1.3: Helical type VAWT (Quiet Revolution Ltd, 2008).
Figure 1.4: Worldwide electrical power generation (World Wind Energy Report,
2008).
10
Figure 1.5: Installed capacity of wind energy on yearly basis (World Wind Energy
Report, 2008).
Figure 1.6: Cp- curve for various types of wind turbines (Bragg and Schmidt, 1978).
11
Figure 1.7: Variation of Cp with pitch angles at = 4 (Chen and Zhou, 2009).
Figure 1.8: In
uence of airfoil thickness on VAWT's performance at Re=200,000,
V=10 m/s [Kirke and Lazauskas (1991), Claessens (2006)].
12
CHAPTER 2
COMPUTATIONAL METHODS
2.1 Introduction
The governing equations in Computational Fluid Dynamics (CFD) basically con-
sist of Continuity Equation, Conservation of Momentum also known as Navier-Stokes
Equation and Conservation of Energy. Fluent deals with inviscid and viscous
ow
both, but in the present study we are dealing with the viscous
ow; therefore, Conti-
nuity Equation and Navier-Stokes Equation will be mainly the area of concern. Some
of the prominent advantages of using CFD methods include the accuracy and reliabil-
ity of the results and lower cost of application of CFD as compared to the expensive
experimental methods. CFD uses computational software which o ers a user-friendly
platform that enables users to simulate any
ow with various sets of test conditions.
CFD works on a principle of discretization where a
ow domain is discretized in
very small units called cells. This unit cell structure is known as mesh or grid. Several
discretization schemes are available in Fluent and choices can be made on the basis of
the needs of the end result. These cells are used for the analysis of the
ow problem.
Fluent gives the properties of the
uid at every single node. Spatial discretization
schemes available in Fluent are Least Squares Cell based, Green Gauss Node and
Cell based which is to be chosen according to the
ow pattern. A pre-processing
is required before proceeding to the post-processing. ICEM CFD has been used as
a pre-processor to generate the sliding mesh and FLUENT as a post-processor for
the simulation process. In addition to this, the boundary condition of the problem
is one of the decisive factors that plays a vital role in determining the accuracy of
13
the simulation process. Therefore, it is the matter of great importance to select an
appropriate boundary condition so as to achieve a desired result.
This chapter provides a detailed explanation of various parameters used to set up
the simulation of a
uid
ow around a two dimensional rotating VAWT using NACA
0018 airfoils. This chapter deals with the types of viscous model, boundary conditions,
discretization schemes, time step calculations, reference values and solver used. The
grid is generated using ICEM CFD and
ow is analyzed using FLUENT. Numerical
values of forces obtained from the simulation are validated with the research article
by Guerri et al. (2007) by plotting a graph between force and angle of rotation.
Another validation is made by comparing a graph between Cp and obtained by
CFD computations, with the experimental results by Claessens (2006).
2.2 Governing Equations
Computational Fluid Dynamics comprise the governing di erential equations and
applicability of these governing equations depend on the nature of the
ow. These
equations have their mathematical representations which can be employed individu-
ally or in a group depending on the need of the desired output. Three basic principles
which govern the characteristics of the
ow of any
uid are conservation of mass, mo-
mentum and energy. In present case, we are dealing with the equation of continuity
with the application of K-
model.
The Continuity Equation or Conservation of Mass given by White (2005), as
follows:
@
@t + @ u
@x + @ u
@y + @ u
@z = 0 (2.1)
Navier-Stokes Equation for an incompressible
ow given by White (2005), as fol-
lows:
14
[@ui
@t + @ukui
@xk
] = - @
@xi
+gi + @2ui
@xkxk
= 0 (2.2)
2.3 Geometry of NACA 4 digit series
NACA 4 digit airfoil family is de ned by a series of numbers where each number
has its own signi cance, for instance in NACA 0018 the rst digit represents maximum
camber as percentage of chord and it is denoted by `m'. Second digit refers to distance
of maximum camber from the leading edge in tenth of percentage denoted by `p'. Rest
of the two digits designate to maximum thickness of airfoil as a percentage of chord
denoted by `t'. Coordinates of NACA 0018 airfoil used for the present study has been
listed in Appendix (B). The coordinates of NACA 4 digit airfoil family are given by
the following equations as mentioned by Abbott and Doenho (1959):
y = tc
0:2 [0:2969
q
x=c 0:1260(x=c) 0:3516(x=c)2 + 0:3516(x=c)3 0:3516(x=c)4]
(2.3)
Where:
c is the chord length of the airfoil
x is the position along chord from 0 to c
y is the half thickness at a given value of x
t is the maximum thickness as a fraction of chord
The position of the coordinates on the upper curve of the airfoil (XU, YU) and lower
curve (XL, YL) of the airfoil is given by
XU = XL = X (2.4)
Similarly, the position of the coordinates on lower curve of the airfoil (XL, YL) is
given by:
YU =+Y (2.5)
15
YL = -Y (2.6)
2.4 Geometry Creation
ICEM CFD has been used as a pre-processor for the grid generation. Symmetrical
airfoil NACA 0018 has been used for the present study as shown in gure 2.3. Rotor
is equipped with three airfoils each with the chord length of 0.107 m. located at 120
from one another. Diameter of the rotor is set as 2 m. and far- eld is located at
168 chords from the center of the rotor. Formatted point data for airfoil come from
di erent sources. For this case NACA ASCII 4 digit series has been used. Two curves
with 100 node points on each of them is drawn using create/modify tool going all
the way from leading edge to trailing edge. All the curves and surfaces are assigned
separately with di erent part names, this helps setting up the boundary conditions
distinctly.
2.5 Grid Generation
Two separate zones are created, rotor being rotary and square far- eld being
stationary. The far- eld mesh which is of hexahedral type is less dense as compared
to hexahedral mesh in the rotary zone. 2-D planar blocking is created around the
120 section of rotor as depicted in gure 2.4. Having a proper edge-curve association
helps get a nice t of mesh around the edges. Among several types of grids available
in ICEM CFD like H-grid, O-grid, C-grid and Y or quarter O-grid, current meshing
uses quarter O-grid along with the C-grid around the airfoil. O-grid allows a uniform
orientation of mesh around the geometry and C-grid captures the geometry of the
airfoil as illustrated in gure 2.6. Block is then split to capture the airfoil geometry.
Blades of the vertical axis wind turbine are set to rotate by making a pair of opposite
nodes periodic. This is done by setting up base, axis and angle in global mesh
parameters and then selecting periodic vertices using the edit block tool. Hexahedral
16
meshing is used considering the fact that hexahedral mesh provides more uniform and
smooth meshing over tetrahedral or quad. Edge meshing parameters are used to get
a more uniform mesh distribution. Mesh around the airfoil needs to be dense enough
so as to have a smooth gradient change in
uid. Figure 2.5 shows the schematic
view of the hexahedral meshing of 120 section of a rotor. This 120 section is then
copied and rotated to get a complete 360 VAWT as shown in gure 2.7. FLUENT
does not accept structured mesh pattern therefore, the structured hexahedral mesh is
converted into unstructured mesh before exporting it to FLUENT. Figure 2.8 shows
the complete set up of a VAWT mesh.
2.6 Turbulence Model
The end result of the
ow problem primarily depends on the Reynolds number.
Working with high Reynolds number is comparatively complex as it requires more
precision and accuracy to deal with. Computational Fluid Dynamics o ers a gamut of
ow models which can be used individually as per the requirement of the end result.
Various turbulent modeling and simulation techniques like Direct Numerical Simula-
tion (DNS), Large Eddy Simulation (LES), Detached Eddy Simulation model (DES),
Reynolds Stress Model (RSM), K- model, K-! model, Spalart-Allmaras model are
available and each one of them can be e ectively used in particular area of applica-
tions.
In the present study, wall bounded turbulent
ows around the vertical axis wind
turbine has been modeled using SST K-! model. SST model for K-! di ers from
standard model in a context that SST provides a change in a gradual manner from
standard K-! model in the inner region to high Reynolds number
ow with K- model
in the outer region. In order to achieve this, K- model is transformed into a K-!
formulation. Two equation eddy viscosity turbulence model by Menter (1994) is given
by these equations:
17
@( k)
@t + @( ujk)
@xj
= P- ! k +
@[( + k t) @k
@xj
]
@xj
(2.7)
@( k)
@t + @( ujk)
@xj
=
t
P - !2 +
@[( + ! t) @!
@xj
]
@xj
+ 2(1 F1) !
!
@k
@xj
@!
@xj
(2.8)
2.7 Boundary Conditions
Boundary condition in Fluent de nes the
ow parameters at the boundaries of the
ow domain. The end result depends on the boundary condition to a great extent.
There are various boundary types available in FLUENT like pressure inlet, velocity
inlet, mass
ow inlet, pressure outlet, pressure far- eld, out
ow, stationary wall,
moving wall and axis. In our current study, periodic boundary condition is applied
to set the airfoils rotating. Boundary conditions used for the present case have been
shown in gure 2.8.
In order to use velocity inlet as a boundary type the magnitude and direction of
the velocity must be known. The possible pairs of boundary types at the inlet and
exit are:
Pressure inlet - Pressure outlet
Mass
ow inlet - Pressure outlet
Velocity inlet - Pressure outlet or Out
ow
For our study a boundary pair of velocity inlet and out
ow is used. Out
ow boundary
condition is generally suitable for the simulation of airfoil related problems. Airfoils
are considered to be a stationary wall in reference to a moving
uid zone.
2.8 Problem Set up in Fluent
Rotating hexahedral mesh of the rotor is merged with the stationary mesh of the
far- eld. Mesh is then checked into ICEM CFD for all possible errors like uncon-
18
nected vertices, periodicity, uncovered faces and single elements. ANSYS is used as
a common structural solver and Fluent V6 as an output solver to write a mesh le
which could be read into FLUENT. Two dimensional double precision solver with
parallel processing option is used. Mesh is checked again in Fluent for any negative
volumes and skewness. FLUENT also allows scaling the size of the working domain
and at the same time the user can set the units in SI, CGS and other format. In
order to apply periodicity turbo-outer and far-inner both the parts are changed from
wall boundary types to interface boundary types. Now mesh interface is created
by selecting both the interface zones which allows us to set the rotational periodic
boundary conditions. Moving mesh technique is applied for this simulation where
rotor is set to rotate at 380 RPM but the far- eld remains stationary. Various types
of pressure velocity coupling schemes are available in FLUENT and their selection
depends on various factors. The present study involves the application of SIMPLE
scheme. Among several special discretization schemes available in FLUENT, Green-
gauss node based gradient with Presto pressure and second order upwind scheme are
found to be appropriate for the present study. Simulation begins with rst order
upwind scheme and then continues with the second order after the rst convergence
is reached just to avoid instability in
ow. Convergence criterion for the solution
are set as 106. Appendix (A) describes the steps followed in FLUENT for a
ow
modeling of VAWT. Currently, our area of consideration is to determine the forces
acting on each of the three rotating airfoils and to obtain an optimum value of tip
speed ratio which gives the maximum power output when wind passes the turbine at
a speed of 10 m/s. In the present study Reynolds number is set as 1.086 106 for a
rotor diameter of 2 m. In the present case Reynolds number based on rotor diameter
(D) is given by:
ReD = V D
= 1 10 2
1:8421 105 (2.9)
19
2.9 Time Step Calculations
Unsteady simulation involves time dependent calculations. Time step is calculated
using speed of the rotor.
Rotational speed of the rotor N = 380 rpm = 380/60 revolution/sec = 6.33 rps
Or, Rotor makes 6.33 revolutions in one second
Or, it takes 0.1579 seconds to make 1 revolution or (360 )
Therefore, time taken to rotate 360 is 0.1579 seconds
Time step size is given as 1.052 104 seconds
Therefore number of time steps required for one revolution
= 0.1579/1.052 104 = 1500 time steps
Maximum iterations per time step = 80
The maximum iterations per time step in FLUENT basically sets the maximum
number of iterations to be performed per time step, which is generally used for un-
steady
ow calculations. If the convergence criteria are achieved before this particular
number of iterations is performed, the solution moves to the next time step.Therefore
it is recommended to set the value of maximum iterations per time step little high.
2.10 Reference Values
Chord length = 0.107 m
Reference Length = Radius of The Rotor = 1 m.
Area = Rotor Diameter span = 2*1 = 2 m2 for 2-D Span = 1
Enthalpy = 0 jule/kg
Pressure = 1 atm at the Velocity Inlet
Density = 1 kg/m3
Temperature = 288.16 k
Reynolds number = 1.086 106
20
Viscosity = 1.8421 105 kg-s/m
Turbulent Kinetic energy = 1.5 m2/ s2
Turbulent dissipation rate = 1386 s1
2.11 Airfoil Lifting Theory
Blades of a wind turbine is considered to be like an airfoil therefore, the same
airfoil lifting theory is applied to the blades of a wind turbine as well. Mechanism of
lift generation in airfoil is based on Bernoulli's principle, (White, 2005) which states
that velocity of the
uid increases where the pressure generated by the
uid decreases
or vice versa. This phenomenon causes lift to generate on airfoil. The velocity of the
wind passing over the upper surface of the airfoil is more than the one passing over
the lower surface and according to Bernoulli's principle, pressure on the lower surface
is more than the pressure on the upper surface which causes a pressure di erence and
this whole mechanism eventually leads to an aerodynamic lift generation. In case of
wind turbines, this aerodynamic lift causes rotation of the turbine blades.
2.12 Tip Speed Ratio
Tip speed ratio is an important factor that a ects power output of a wind turbine
greatly. Proper attention must be paid while designing a wind turbine so as to achieve
an optimum tip speed ratio. Angle of attack of blade varies as the turbine rotates.
Angle of attack is inversely proportional to the tip speed ratio. Therefore, at higher
tip speed ratio a blade experiences lower angle of attack leading to lower stall creation.
For a tip speed ratio of above 3 the stall produced by turbine is very low hence positive
torque is generated. Torque generation also depends on the type of airfoil chosen and
Reynolds number. According to Betz limit (Cetin et al., 2005) no wind turbine can
have its e ciency more than 0.593. Tip speed ratio is a ratio of linear velocity of the
blades to the free stream velocity of the wind. It is a dimensionless parameter which
21
is de ned as:
Tip Speed Ratio = linear velocity of the rotor blade/wind velocity
= ! r/V (2.10)
where:
= Tip Speed Ratio
! = Angular velocity of rotor blade
r = Rotor radius
V = Wind velocity
2.13 Angle of Attack
Angle of attack , is de ned as the angle subtended by an oncoming wind velocity
with the chord line of an airfoil. The angle of attack depends on the rotational angle
and tip speed ratio which is given as:
= tan1[ cos
sin ] (2.11)
As the blade rotates angle of rotation also changes and it causes a change in angle
of attack. As it is shown in gure 2.2, increases gradually for a range of = 0 -
45 then it decreases and goes negative from 45 - 60 and then increases between 60 -
225. A condition of stall occurs after reaches 40 degrees where drag force becomes
dominant over lift force.
2.14 Von Karman Vortex Street
Figure 2.15 (b) shows a phenomenon in
uid dynamics. When
uid
ows over
a cylindrical body it creates periodic pattern of swirling
ows which is called Von
Karman Vortex Street. This wake shedding is the result of a
ow separation usually
occur at low Reynolds number. Leading and trailing edge vortex formation is depicted
22
in gure 2.14 and gure 2.15 (a). The velocity vectors at V1 = 10 m/s, over the
surface of the airfoil, at the out
ow, leading edge and trailing edge is also shown in
gure 2.10 - gure 2.13 respectively.
2.15 Calculation of Torque Produced by Horizontal and Vertical Forces
Acting on Airfoils
Forces acting on each airfoil are sum of the two components that is pressure force
and viscous force. In order to calculate the torque produced by each airfoil, this
force is further split into horizontal and vertical direction. Component of these two
forces do not always contribute to the torque due to the rotary motion of the turbine.
The component of force for which axis of rotation of turbine lies in its direction,
produces no torque. Forces acting on each airfoil are set to be reported in FLUENT
in horizontal and vertical direction. The component of these forces in horizontal and
vertical direction obtained by using data sets by Guerri et al. (2007) is illustrated
in gure 2.16 and gure 2.18 respectively. Torque produced by each airfoil is then
calculated by following equations:
T1 = - Fx1.Rcos - Fy1.Rsin (2.12)
T2 = - Fx2.Rcos ( + 120) - Fy2.Rsin ( + 120) (2.13)
T3 = - Fx3.Rcos ( + 240) - Fy3.Rsin ( + 240) (2.14)
Total Torque T = T1 + T2 + T3 (2.15)
(Total Torque `T' is calculated for every 6 degrees of rotation)
Average Torque =
X
T/n (2.16)
where n is number of recorded values = 360/6 = 60
23
2.16 Grid Independence
Computational results obtained by CFD simulation must be grid independent.
The results should not vary with the number of cells in mesh. Therefore, grid in-
dependency is one of the important parameters to check the accuracy of the solution.
Simulation is run for a cell size of 65000 and 140,000 and then component of the forces
are plotted as a function of angle of attack. Results are found to be independent of the
number of cells with negligible di erence in their magnitude. Figure 2.16 and Figure
2.18 shows the grid independent solution obtained by simulations. These graphs also
serve the purpose of validation as gure 2.16 and 2.18 follows the same trend as shown
in gure 2.17 and 2.19 by Guerri et. al (2007).
2.17 Validation of 2-D CFD simulation
Simulation is set to run at several tip speed ratios ranging from 1- 6 at Reynolds
number of 106 and then a graph is plotted between Cp and . Results are found to
be in a good agreement with the experimental result by Claessens (2006) as shown
in gure 2.20. Maximum Cp = 0.34 is obtained at = 3.8.
Table 2.1: Data sets used for simulation in FLUENT (V1 = 10 m/s, Rotor Diameter
= 2 m.)
TSR Speed in RPM Total Time Steps Step Size t Total Time/cycle Cp(obtained)
1 95.5 1500 0.0004188 0.6282 0.004
2 191 1500 0.0002094 0.3141 -0.007
3 286.47 1500 0.0001396 0.2094 0.263
4 380 1500 0.0001052 0.1579 0.325
5 477.46 1500 0.0000837 0.1256 0.093
24
Figure 2.1: Solution strategy in FLUENT (Fluent 12.0.16 user guide).
Figure 2.2: Variation of angle of attack as a function of in degrees for a range of .
25
Figure 2.3: Schematic view of the geometry of rotor 120 with NACA 0018 airfoil.
Figure 2.4: Blocking with the application of quarter O-grid and periodic vertices.
Figure 2.5: Schematic view of the hexahedral meshing of 120 of rotor with
NACA0018.
26
Figure 2.6: Closer view of the O-type grid around NACA0018 airfoil.
Figure 2.7: View of the rotor (unstructured hexahedral mesh) with three airfoils.
27
Figure 2.8: Schematic views of the stationary far- eld and rotor (unstructured hexa-
hedral mesh).
Figure 2.9: Schematic view of a six bladed VAWT with GUI of ICEM CFD.
28
Figure 2.10: Velocity vectors at the surface of the airfoil at = 2, = 360, V1 = 10
m/s, Reynolds number 106.
Figure 2.11: Velocity vectors at the out
ow at = 2, V1 = 10 m/s.
29
Figure 2.12: Velocity vectors at the leading edge of the airfoil at = 2, = 120, V1
= 10 m/s.
Figure 2.13: Velocity vectors at the trailing edge of the airfoil at = 2, = 240, V1
= 10 m/s.
30
Figure 2.14: Depiction of leading and trailing edge vortex formation
(a) Leading edge vortex and trailing edge
vortex.
(b) The tower wake.
Figure 2.15: Formation of vortices at = 2
31
Figure 2.16: Grid-Independent result for cell size of 65000 and 140000 (Horizontal
component of the blade force at =1.88, V =10 m/s).
Figure 2.17: Horizontal component of the blade force at =1.88, V =10 m/s (Guerri
et. al, 2007).
32
Figure 2.18: Grid-Independent result for cell size of 65000 and 140000 (Vertical com-
ponent of the blade force at =1.88, V =10 m/s).
Figure 2.19: Vertical component of the blade force at =1.88, V =10 m/s (Guerri
et. al, 2007).
33
Figure 2.20: (A) Validation of Cp of VAWT with the experimental results by Claessens
(2006) as a function of (B) V1 = 10 m/s, Re = 106, Rotor diameter= 2 m.
34
CHAPTER 3
RESULTS AND DISCUSSION
3.1 Introduction
At the lower blade speed the blade torque is expected to be high but the power
delivered to the turbine shaft would be low due to the low rotational speed. On the
other hand at higher blade speed power would still be low due to the lower torque.
Hence, there would be an optimum speed at which turbine would deliver maximum
power. Therefore, having a proper ratio between the linear velocity of the tip of the
rotor blade and oncoming wind velocity is an important design consideration in order
to obtain maximum power output. This ratio is called Tip Speed Ratio. There are
several factors that tip speed ratio of the wind turbine depends on such as type and
shape of the airfoil used, number of blades, wind velocity and speed of the rotor.
This chapter mainly deals with computational methodology used and results ob-
tained from a proper assessment of an optimum tip speed ratio at which turbine pro-
duces maximum power output. Simulation is set to run at several tip speed ratios.
E ect of rotor's diameter on turbine's performance is investigated in this chapter.
Rotor's diameter is halved (D=1 m.), keeping the wind velocity and tip speed ratio
the same as earlier. Result is then analyzed and compared with the results from pre-
vious chapter where coe cient of performance of VAWT obtained by CFD simulation
was validated with the experimental result by Claessens (2006).
35
3.2 Coe cient of Performance of a VAWT (Cp)
Coe cient of Performance of a wind turbine is a factor that describes how e -
ciently wind power is utilized and transformed into useful turbine power. Coe cient
of Performance depends on the type of airfoils, blade thickness and Reynolds num-
ber. It has been found by experiment that performance increases with the increase
in thickness of airfoil. It is basically given by the ratio between power extracted by
the turbine and available wind power. It can be mathematically expressed as:-
Cp = Power generated by Turbine/Wind Power
= Pt/Pw
Cp = ! Tmean/0.5 AV 3 (3.1)
Average Torque is calculated by reporting coe cient of moment in FLUENT for one
complete revolution. It is given by the formula:-
Tmean = 0.5(Cm1 + Cm2 + Cm3) AV 2R/number of recorded values (3.2)
Where Cm1, Cm2, Cm3 are coe cient of moments of airfoil-1, airfoil-2 and airfoil-3
respectively.
3.3 E ect of Rotor Diameter on VAWT's Performance
Coe cient of performance is directly proportional to the radius of the rotor. If
size of the rotor increases Cp also increases. Following the objective of investigating
the e ect of turbine size on Cp, rotor's diameter is halved keeping the wind velocity
and tip speed ratio the same as earlier. Now in order to maintain the same angular
velocity of the rotor is doubled and then set up is simulated for a range of . Con-
clusion is drawn by considering the graph between Cp and in gure 3.1 that Cp of
a wind turbine remains almost same as long as the is constant. Fundamentally, the
reduction in rotor diameter increases the possibility of blade-blade interaction which
36
causes more wake generation but in the present case this interaction was not strong
enough to cause a decrease in Cp due to the fact that the ratio of chord length and
rotor radius ( i. e. c/R) were kept the same in both the cases.
3.4 E ect of Laminar Flow on VAWT's Performance By Comparing the
Results From RANS Turbulence Model and Laminar Viscous Model
Fluid
ow over a body is divided into two categories depending on the relative
motion between solid and
uid (White, 2005); one where frictional forces are signi -
cant to the
ow and another where their e ects are negligible. The
ow region which
is in immediate contact with the body is regarded as a boundary layer. Flow pattern
over the airfoil surface goes through several stages from zero velocity at the boundary
layer with high friction to maximum velocity away from the boundary layer. Based
on the Reynolds number,
ow in the boundary layer can be classi ed as Laminar
ow, Transition region
ow and Turbulent
ow. Reynolds number is the ratio of
inertial forces to viscous forces. Flow at low Reynolds number is considered to be
a
ow where viscous forces are signi cant whereas
ow at high Reynolds number is
turbulent due to the dominance of the inertial forces. In the current study both the
aspects of
uid
ow has been covered. SST k omega model as a RANS Turbulence
model is used at Reynolds number of 106. Inertial forces at this Reynolds number
are too high which causes better aerodynamic performance of NACA 0018 airfoil as
compared to low Reynolds number
ow. Contours of vorticity at various is shown
in gure 3.20 and gure 3.21 which illustrates the
ow pattern around VAWT at high
Reynolds number. Condition of dynamic stall is observed at few angle of attacks and
this e ect becomes even less signi cant at high . Reynolds number based on chord
is given by:
Rec = V c
(3.3)
On the other hand,
ow around the turbine is also investigated using Laminar
37
Viscous model at Reynolds number of 5000. As
ow velocity over the airfoil surface
decreases pressure increases. This causes
ow reversal in the boundary layer which
leads to
ow separation and this separation is called Stall, whereas the bubbles created
at leading edge is called leading edge separation bubble. Design of airfoils for low
Reynolds numbers are restricted to lift to drag ratio. Symmetrical airfoils like NACA
0018 cannot handle an adverse pressure gradient, causing lower L/D ratio, which
eventually leads to
ow separation. In order to avoid this problem and maintain a
proper lift to drag ratio, usually cambered airfoils are used at low Reynolds numbers.
Laminar
ow can sustain the pressure gradient to a certain extent after that there
may be three possibilities as mentioned by White (2005) (a) complete separation
and stall (b)
ow separation and then reattachment as turbulent (c) fully turbulent
ow. Contours of vorticity at various for laminar
ow is shown in gure 3.2 and
it shows vortices are trailing back due to the
ow separation. Wind turbine cannot
be conveniently operated below a speci c range of Reynolds number as it is obvious
from gure 3.3 that turbine produces negative torque at Re = 5000 therefore produces
negative power output.
3.5 E ect of Solidity on VAWT's Performance
Optimization of number of blades is really necessary to ensure maximum power
output from a wind turbine. If the numbers of rotor blades are less it is supposed
to rotate at a much faster rate to sweep out as much wind as possible which may
contribute to maximum power output for that con guration. On the other hand if
turbine has too many numbers of blades it will obstruct the
ow of the wind and
will not let su cient amount of wind to pass through it. Aerodynamic performance,
load bearing capacity and total manufacturing cost of the unit are some important
factors which must be given a thoughtful consideration while making a choice for the
number of blades to be used. Aerodynamic loading is another important factor to be
38
considered before making a selection of number of blades. In case of Vertical Axis
Wind Turbine the blades are not required to be directed towards the wind direction
as it is in case of Horizontal Axis Wind turbine. At the same time center of gravity
of VAWT lies near the ground as the generator is mounted nearby the ground. Along
with having some advantages over HAWT it also possess some disadvantages like
when VAWT rotates wind
ow produces very high drag force thereby causing a yaw
phenomena. This is where alignment of VAWT plays an important role. Cetin et al.
(2005) describes an empirical formula to determine the optimum tip speed ratio for
a particular number of blades, as follows:-
opt = 4 /n (3.4)
where n = number of blades. For a 3 bladed wind turbine it should be around 4.18.
In the present study opt = 3.8.
Individual torque generated by each blade at several tip speed ratios are shown
in gures 3.4 - 3.9 and it shows that torque increases for a range of of 2 - 4 and
then goes negative due to the generation of dynamic stall. Total torque produced
by the turbine at various tip speed ratios are also shown in gures 3.10- 3.15. In
order to get an accurate result, simulation is run until steady solution is reached. In
most of the cases simulation is found to reach steady state but still in few cases the
results are expected to change slightly in the next few cycles. Contours of velocity
and contours of pressure of airfoil 1 is shown in gure 3.16 and gure 3.17 at =
5 and 3 respectively. In order to make a better comparison of vorticity and wake
produced at each , for 3 bladed and 6 bladed VAWT, screen-shots of contours of
vorticity are attached side by side in gure 3.20 and gure 3.21. Contours of Velocity
for 3 bladed and 6 bladed VAWT are also shown in gure 3.18 and gure 3.19. All
the contours are clipped to the same range to bring consistency.
Solidity is de ned as the ratio of total blade surface area to the area swept by wind
turbine blades. Lack of information available regarding the e ect of number of blades
39
on overall performance of a wind turbine gives rise to further the present study in
this eld. In order to investigate the e ect of solidity on Cp, mesh is created for a six
bladed VAWT and then CFD simulation is carried out. Simulation is performed at V
= 10 m/s, Re = 106, D = 2 m. and at values of ranging from 1-5. Data sets used
for this simulation were kept exactly the same as used earlier for the simulation of 3
bladed wind turbine, just to make a better comparison between their performances.
Solidity can be mathematically expressed as follows:
= NbC
R (3.5)
Where:
Nb = Total number of blades (6 for the present case)
C = Blade chord length
R = Rotor radius
It is concluded from the CFD results that blockage e ect increases with the in-
crease in number of blades which causes low entrance velocity and leads to higher
torque generation. This e ect is more signi cant at higher values of . Another
conclusion that can be drawn from the result is, the corresponding value of for
Cp;max of wind turbine decreases with the increase in number of blades or in other
words maximum Cp is obtained at relatively lower value of as the number of blades
increases. It is obvious from the gure 3.22 that Cp;max = 0.34 is achieved at = 3.8
for 3 bladed VAWT whereas for 6 bladed VAWT Cp;max = 0.39 is achieved at =
2.8. A conclusion can be drawn from gure 3.20 and 3.21 that for 6 bladed turbine
wake interaction between blades take place more frequently as compared to 3 bladed
turbine which means that Cp;max could be obtained at relatively lower value of as
compared to 3 bladed VAWT.
40
Figure 3.1: (A) In
uence of rotor diameter on the VAWT's performance for a range
of (B) V1 = 10 m/s, Re = 106, Rotor diameter 1m. and 2m.
41
(a) after 1 cycle at =1 (b) after 1 cycle at =2
(c) after 3 cycles at =3 (d) after 2 cycles at =4
(e) after 2 cycles at =5 (f) after 3 cycles at =6
Figure 3.2: Contours of Vorticity for a range of for Laminar
ow at Rec =5000, D
= 0.1365 m.
42
Figure 3.3: In
uence of Laminar
ow on Cp with the application of Laminar viscous
model at low Rec= 5000, V1 = 10 m/s, Rotor diameter= 0.1365 m.
43
Figure 3.4: Variation of torque generated by each blade as a function of = 1
Figure 3.5: Variation of torque generated by each blade as a function of = 2
44
Figure 3.6: Variation of torque generated by each blade as a function of = 3
Figure 3.7: Variation of torque generated by each blade as a function of = 4
45
Figure 3.8: Variation of torque generated by each blade as a function of = 5
Figure 3.9: Variation of torque generated by each blade as a function of = 6
46
Figure 3.10: Variation of total torque generated by VAWT as a function of = 1
Figure 3.11: Variation of total torque generated by VAWT as a function of = 2
47
Figure 3.12: Variation of total torque generated by VAWT as a function of = 3
Figure 3.13: Variation of total torque generated by VAWT as a function of = 4
48
Figure 3.14: Variation of total torque generated by VAWT as a function of = 5
Figure 3.15: Variation of total torque generated by VAWT as a function of = 6
49
(a) t= 0.5s =360 (b) t = 0.631s =720
(c) t= 0.526s =432 (d) t =0.605s =648
(e) t= 0.552s =504 (f) t= 0.578s =576
Figure 3.16: Contours of Velocity of airfoil-1 after two cycles at =5 and Rec = 106
50
(a) t= 0.234s =360 (b) t = 0.267s =720
(c) t= 0.296s =432 (d) t =0.312s =648
(e) t= 0.362s =504 (f) t= 0.413s =576
Figure 3.17: Contours of Pressure of airfoil-1 after two cycles at =3 and Rec = 106
51
(a) =1 (b) =1
(c) =2 (d) =2
(e) =3 (f) =3
Figure 3.18: Contours of Velocity at = 1, 2, 3 and Rec = 106, for 3 bladed turbine
on left side and 6 bladed turbine on right side
52
(a) =4 (b) =4
(c) =5 (d) =5
(e) =6 (f) =6
Figure 3.19: Contours of Velocity at = 4, 5, 6 and Rec = 106, for 3 bladed turbine
on left side and 6 bladed turbine on right side
53
(a) after 1 cycle at =1 (b) after 1 cycle at =1
(c) after 2 cycles at =2 (d) after 2 cycles at =2
(e) after 2 cycles at =3 (f) after 2 cycles at =3
Figure 3.20: Contours of Vorticity at = 1, 2, 3 and Rec = 106, for 3 bladed turbine
on left side and 6 bladed turbine on right side
54
(a) after 3 cycles at =4 (b) after 3 cycles at =4
(c) after 3 cycles at =5 (d) after 3 cycles at =5
(e) after 2 cycles at =6 (f) after 2 cycles at =6
Figure 3.21: Contours of Vorticity at = 4, 5, 6 and Rec = 106, for 3 bladed turbine
on left side and 6 bladed turbine on right side
55
Figure 3.22: (A) In
uence of number of blades on the VAWT's performance for a
range of (B) V1 = 10 m/s, Re = 106, Rotor diameter= 2 m.
56
Table 3.1: Data sets used for simulation in FLUENT (V1 = 10 m/s, Rotor Diameter
= 1 m.)
TSR Speed in RPM Total Time Steps Step Size t Total Time/cycle Cp(obtained)
1 191 1500 0.0002094 0.3141 0.00271
2 382 1500 0.0001047 0.1570 -0.0054
3 572.94 1500 0.0000698 0.1047 0.267
4 760 1500 0.00005263 0.0789 0.354
5 954.92 1500 0.00004188 0.0628 0.087
Table 3.2: Cp vs at V1 =10 m/s
SST k-! model (Re=106) Laminar model (Re=5000) Solidity with 6 Blades, (Re=106)
D = 2 m. D = 1 m. D = 0.1365 m. D = 2 m.
1 0.004 0.0027 -5.03 0.1539
2 -0.007 -0.0054 -1.75 0.216
3 0.263 0.267 -6.25 0.33
4 0.325 0.354 -6.02 -0.68
5 0.093 0.087 -11 -2.48
57
CHAPTER 4
CONCLUSIONS AND RECOMMENDATIONS
4.1 Summary
In the present study, a 2-D unsteady model of a vertical axis wind turbine com-
prising three rotating symmetric airfoils (NACA0018) has been designed with the
consideration of a near wake. The
ow around the wind turbine is simulated using
ANSYS FLUENT 12.0.16 at Reynolds number of 106. ICEM CFD is used as a pre-
processor to generate hexahedral grid and sliding mesh technique is implemented to
create a moving mesh. SST k- ! Turbulence model is employed for the analysis and
simulation is set to run at several tip speed ratios ranging from 1 to 5. Variation of
Cp as a function of is then observed by plotting a graph between them. An appro-
priate validation is made by comparing CFD results with the experimental results by
Claessens (2006). Maximum Cp = 0.34 is obtained at = 3.8. In addition, the e ect
of rotor diameter on VAWT's performance is also investigated. In this regard, rotor
diameter is halved but the angular velocity is doubled to keep the tip speed ratio
constant. Furthermore, theory behind leading edge separation bubble is proposed
with the application of Laminar viscous model at low Reynolds number. E ect of
solidity on Cp is also included in this thesis for a six bladed turbine.
4.2 Conclusions
The following conclusions are drawn on the basis of results obtained from 2-D CFD
simulations of a VAWT as shown in previous chapter:
58
Tip speed ratio is one of the in
uential factors on which coe cient of perfor-
mance of a wind turbine depends.
Depending on the type of airfoil used, every wind turbine has a particular range
of operating tip speed ratios at which, turbine produces positive power output
and for the rest of the values of it goes negative. In general a VAWT with
xed pitch blades is unable to start by itself. The major problem with the
straight-bladed VAWT is the negative Cp at low tip speed ratios. A positive
Cp shows that the turbine is able to rotate independently and produce power,
whereas a negative Cp means the turbine needs extra power to be able to rotate.
Cp;max = 0.34 is achieved at = 3.8 for a 3 bladed VAWT whereas for a 6
bladed VAWT Cp;max = 0.39 is achieved at comparatively lower value of that
is 2.8.
In
uence of rotor diameter on the aerodynamic performance of a VAWT has
been investigated and found that Cp remains almost constant at the same value
of ranging from 1-5, this is due to the fact that the ratio of chord length and
rotor radius ( i. e. c/R) were kept the same in both the cases.
For Laminar
ow at low Reynolds number Cp was found to be low due to the
presence of leading edge separation bubble and reduced lift-to-drag ratio.
In order to increase Cp of a VAWT at low Reynolds numbers (e. g. small
VAWT), di erent blade geometry (e. g. cambered) and di erent propulsion
mechanism ( inspired by insect
ights) are needed.
In
uence of solidity was explored by involving six blades for the simulation and
it was concluded that blockage e ect increases with the increase in number of
blades which causes lower entrance velocity and hence leads to higher torque
generation. Maximum Cp is obtained at relatively lower value of as compared
59
to 3 bladed VAWT. It requires comparatively large torque to produce same
amount of Cp.
4.3 Recommendations For The Future Work
3-D model of a VAWT can be proposed in the future studies to account for
the tip vortices and rotor arms. The 2-D CFD simulation does not include the
e ects of the end tip vortices present on the real wind turbine and that is why,
2D simulations shows a signi cantly increased performance compared to the
3D simulations. Furthermore, the other reason for an overestimated numerical
value of Cp of 2-D calculations as compared to 3-D could be the absence of rotor
arms in 2-D simulations.
In lieu of having a blade xed to the rotor arm, a
apping or plunging mechanism
can be provided which will help reducing the condition of a dynamic stall. It is
the same phenomena used by insects.
60
BIBLIOGRAPHY
[1] Abbott, Ira H., and Von Doenho , Albert E., \Theory of Wing Sections: In-
cluding a Summary of Airfoil Data, Section 4.2", Dover Publications Inc., New
York, 1959, Standard Book Number 486-60586-8.
[2] Ansari, S. A., Zbikowski, R. and Knowles, K., \Non-Linear Unsteady Aerody-
namic Model For Insect-like Flapping Wings in the Hover. Part 1: Methodology
and Analysis", Journal of Aerospace Engineering, 2006, Vol. 220, pp. 61-83.
[3] Birch, M. J. and Dickinson, H., \Spanwise Flow and the Attachment of the
Leading-Edge Vortex on Insect Wings", Nature, 2001, Vol. 412, pp. 729-733.
[4] Bragg, G. M., and Schmidt, W. L., \Performance Matching and Optimization
of Wind Powered Water Pumping Systems", Energy Conversion, 1978, Vol. 19,
pp. 33-39.
[5] Cetin, N. S., Yurdusev, R. A., and Ozdemir, A., \Assesment of Optimum Tip
Speed Ratio of Wind Turbines", Mathematical and Computational Applications,
2005, Vol. 10, pp. 147-154.
[6] Chen, W. and Zhou, C. Y., \Application of Numercal Simulation to Obtain the
Optimization Pitch Angle for VAWT", IEEE, 2009, pp. 4244-4702.
[7] Claessens, M. C., \The Design and Testing of Airfoils for Application in Small
Vertical Axis Wind Turbines", MS Thesis, 2006, Delft University of Technology.
[8] Darrieus, G.J.M., \Turbine Having Its Rotating Shafts Transverse to the Flow
of the Current", United States Patent 1835018, 1931, pp. 1-4.
61
[9] Ellington, C. P., Berg, C. V. D., Willmott, A. P. and Thomas, A. L. R., \Leading-
Edge Vortices in Insect Flight", Nature, 1996, Vol. 384, pp. 626-630.
[10] Ferreira, C. J. S., \The Near Wake of the VAWT - 2D and 3D Views of the
VAWT Aerodynamics", PhD Dissertation, 2009, Delft University of Technology,
The Netherlands.
[11] Guerri, O., Sakout A. and Bouhadef, K., \Simulations of the Fluid Flow Around
a Rotating Vertical Axis Wind Turbine", Wind Engineering, 2007, Vol. 31, pp.
149-163.
[12] Howell, R., Qin, N., Edwards, J. and Durrani, N., \Wind Tunnel and Numerical
Study of a Small Vertical Axis Wind Turbine", Renewable Energy, 2009, Vol.
35, pp. 412-422.
[13] Hover, F., Haugsdal, O. and Triantafyllou, M. S., \E ect of Angle of Attack
Pro les in Flapping Foil Propulsion", Journal of Fluids and Structures, 2004,
Vol. 19, pp. 37-47.
[14] Islam, M., Ting, D. SK., and Fartaj, A., \Aerodynamic Models for Darrieus-
type Straight-Bladed Vertical Axis Wind Turbines", Renewable and Sustainable
Energy Reviews, 2006, Vol. 12, pp. 1087-1109.
[15] Lee, J. S., Kim, C. and Kim, K. H., \Design of a Flapping Airfoil for Opti-
mal Aerodynamic Performance in Low-Reynolds Number Flows", AIAA Journal,
2006, Vol. 44, pp. 1960-1972.
[16] Marini, M., Massardo, A. and Satta, A., \Performances of Vertical Axis Wind
Turbines With Di erent Shapes", Journal of Wind Engineering and Industrial
Aerodynamics, 1992, Vol. 39, pp. 83-93.
62
[17] Menter, F. R., \Two-Equation Eddy-Viscosity Turbulence Models for Engineer-
ing Applications", AIAA Journal, 1994, Vol. 32, pp. 1598-1605.
[18] Read, D. A., Hover, F. S. and Triantafyllou, M. S., \Forces on Oscillating Foils
for Propulsion and Maneuvering", Journal of Fluids and Structures, 2002, Vol.
17, pp. 163-183.
[19] Sane, S. P. and Dickinson, M. H., \The Control of Flight Force by a Flapping
Wing: Lift and Drag Production", The Journal of Experimental Biology, 2001,
Vol. 204, pp. 2607- 2626.
[20] Sane, S. P. and Dickinson, M. H., \The Aerodynamic E ects of Wing Rotation
and a Revised Quasi-Steady Model of Flapping Flight", The Journal of Experi-
mental Biology, 2002, Vol. 205, pp. 1087-1096.
[21] Shyy, W. and Liu, H., \Flapping Wings and Aerodynamic Lift: The Role of
Leading-Edge Vortices", AIAA Journal, 2007, Vol. 45, pp. 2817-2819.
[22] Shyy, W., Trizila, P., Kang, C. K. and Aono, H., \Can Tip Vortices Enhance
Lift of a Flapping Wing?", AIAA Journal, 2009, Vol. 47, pp. 289-293.
[23] Tang, J., Viieru, D. and Shyy, W., \A Study of Aerodynamic of Low Reynolds
Number Flexible Airfoils", 37th AIAA Fluid Dynamics Conference and Exhibit,
2007, Florida.
[24] Tay, W. B. and Lim, K. B., \Analysis of Non-Symmetrical Flapping Airfoils",
Acta Mechanica Sinica, 2009, Vol. 25, pp. 433-450.
[25] Wang, Z. J., \Two Dimensional Mechanism for Insect Hovering", Physical
review letters, 2000, Vol. 85, pp. 2216-2219.
63
Additional References
[26] ANSYS FLUENT 12.0.16 manual, 2009.
[27] Quiet Revolution Ltd, \Gallery", <http://www.quietrevolution.com/index.
htm>.
[28] White, F. M., \Viscous Fluid Flow," (2005), McGraw-Hill Companies, 3rd edi-
tion.
[29] World Wind Energy Association, (2008), <http://www.wwindea.org/home/
index.php?option=com_content&task=view&id=266&Itemid=43>.
64
APPENDIX A
Steps involved in post-processing of VAWT using ANSYS FLUENT 12.0.16
Figure 1: Fluent launcher panel
Figure 2: Read-case-data panel
65
Figure 3: General panel
Figure 4: Model panel
66
Figure 5: Materials panel
Figure 6: Cell zone conditions panel
67
Figure 7: Cell zone conditions panel
Figure 8: Boundary conditions panel
68
Figure 9: Boundary conditions panel
Figure 10: Mesh interface panel
69
Figure 11: Reference values panel
Figure 12: Solution methods panel
70
Figure 13: Under relaxation factor panel
Figure 14: Monitors residual panel
71
Figure 15: Monitors moment panel
Figure 16: Solution initialization panel
72
Figure 17: Calculation activities panel
Figure 18: Scaled residuals
73
APPENDIX B
In this appendix the coordinates of the NACA 0018 Airfoil pro les are given. These
are the coordinates used for the 2-D unsteady simulations.
74
Table 1: NACA 0018 Coordinates
x/c y/c z/c x/c y/c z/c
1 0 0 0.5 -0.0789 0
0.999 -0.0002 0 0.4686 -0.0818 0
0.9961 -0.0008 0 0.4373 -0.0843 0
0.9911 -0.0019 0 0.4063 -0.0864 0
0.9843 -0.0033 0 0.3757 -0.088 0
0.9755 -0.0051 0 0.3455 -0.0891 0
0.9649 -0.0073 0 0.3159 -0.0897 0
0.9524 -0.0099 0 0.2871 -0.0898 0
0.9382 -0.0127 0 0.2591 -0.0893 0
0.9222 -0.0159 0 0.2321 -0.0882 0
0.9045 -0.0193 0 0.2061 -0.0865 0
0.8853 -0.023 0 0.1813 -0.0842 0
0.8645 -0.0268 0 0.1577 -0.0813 0
0.8423 -0.0308 0 0.1355 -0.0778 0
0.8187 -0.0349 0 0.1147 -0.0737 0
0.7939 -0.0392 0 0.0955 -0.0691 0
0.7679 -0.0434 0 0.0778 -0.0639 0
0.7409 -0.0478 0 0.0618 -0.0583 0
0.7129 -0.0521 0 0.0476 -0.0522 0
0.6841 -0.0564 0 0.0351 -0.0457 0
0.6545 -0.0606 0 0.0245 -0.0388 0
0.6243 -0.0646 0 0.0157 -0.0316 0
0.5937 -0.0686 0 0.0089 -0.0241 0
0.5627 -0.0723 0 0.0039 -0.0163 0
0.5314 -0.0757 0 0.001 -0.0083 0
75
x/c y/c z/c x/c y/c z/c
0 0 0 0.5 0.0789 0
0.001 0.0083 0 0.5314 0.0757 0
0.0039 0.0163 0 0.5627 0.0723 0
0.0089 0.0241 0 0.5937 0.0686 0
0.0157 0.0316 0 0.6243 0.0646 0
0.0245 0.0388 0 0.6545 0.0606 0
0.0351 0.0457 0 0.6841 0.0564 0
0.0476 0.0522 0 0.7129 0.0521 0
0.0618 0.0583 0 0.7409 0.0478 0
0.0778 0.0639 0 0.7679 0.0434 0
0.0955 0.0691 0 0.7939 0.0392 0
0.1147 0.0737 0 0.8187 0.0349 0
0.1355 0.0778 0 0.8423 0.0308 0
0.1577 0.0813 0 0.8645 0.0268 0
0.1813 0.0842 0 0.8853 0.023 0
0.2061 0.0865 0 0.9045 0.0193 0
0.2321 0.0882 0 0.9222 0.0159 0
0.2591 0.0893 0 0.9382 0.0127 0
0.2871 0.0898 0 0.9524 0.0099 0
0.3159 0.0897 0 0.9649 0.0073 0
0.3455 0.0891 0 0.9755 0.0051 0
0.3757 0.088 0 0.9843 0.0033 0
0.4063 0.0864 0 0.9911 0.0019 0
0.4373 0.0843 0 0.9961 0.0008 0
0.4686 0.0818 0 0.999 0.0002 0
76
VITA
ETESH VAISHNAV
Candidate for the Degree of
Master of Science
Thesis: AN INVESTIGATION ON THE AERODYNAMIC PERFORMANCE OF
A VERTICAL AXIS WIND TURBINE
Major Field: Mechanical and Aerospace Engineering
Biographical:
Personal Data: Born in Bilaspur, India on April 22nd, 1985.
Education:
Received Bachelor of Engineering degree in Mechanical Engineering from
Bhilai Institute of Technology, Durg, India, 2007.
Completed the requirements for the degree of Master of Science with a
major in Mechanical and Aerospace Engineering from Oklahoma State
University in December 2010.
Experience:
Worked as a Graduate Research Student under the aegis of Dr. Khaled
A. Sallam in the area of CFD Simulation of a Vertical Axis Wind Turbine
(Aug 2009- Dec 2010).
Employed as a Teaching Assistant for Mechanical and Aerospace Engineer-
ing, Oklahoma State University (Aug 2010- Dec 2010).
Employed as a Graduate Research Assistant for Agricultural Economics,
Oklahoma State University (Jan 2009- May 2009).
Name: Etesh Vaishnav Date of Degree: December, 2010
Institution: Oklahoma State University Location: Stillwater, Oklahoma
Title of Study: AN INVESTIGATION ON THE AERODYNAMIC PERFOR-
MANCE OF A VERTICAL AXIS WIND TURBINE
Pages in Study: 76 Candidate for the Degree of Master of Science
Major Field: Mechanical and Aerospace Engineering
Scope and Method of Study:
The two dimensional unsteady
ow around a vertical axis wind turbine (VAWT)
comprising three rotating symmetric airfoils (NACA0018) was studied numerically
with the consideration of the near wake. The
ow around the wind turbine was
simulated using ANSYS FLUENT 12.0.16 at Reynolds number of 106. ICEM CFD
was used as a pre-processor to generate hexahedral grid and arbitrary sliding mesh
technique was implemented to create a moving mesh. SST k- ! turbulence model was
employed for the analysis and simulation was set to run at several tip speed ratios
ranging from 1 to 5. The variation of the performance coe cient (Cp) as a function of
tip speed ratio ( ) was investigated by plotting a graph between them. A validation
was made by comparing CFD results with experimental results. Maximum Cp of
0.34 was obtained at of 3.8. In addition, the e ect of the rotor diameter on the
VAWT's performance was investigated. In this regard, rotor diameter was halved and
the angular velocity was doubled to keep the tip speed ratio constant. Furthermore,
the e ect of laminar boundary layer separation on Cp of a VAWT was studied by
comparing the results of Laminar viscous model and RANS turbulence model. Apart
from that, the e ect of solidity on Cp was investigated by comparing the Cp obtained
from six bladed turbine with the three bladed turbine.
Findings and Conclusions:
In
uence of rotor diameter on the aerodynamic performance of a VAWT was inves-
tigated and found that Cp remained almost constant at the same value of ranging
from 1 to 5. This was due to the fact that the ratio of the chord length and the
rotor radius were kept the same in both cases. For Laminar
ow at low Reynolds
number, Cp was found to be low due to the presence of leading edge separation bubble
and reduced lift-to-drag ratio. Therefore, in order to increase Cp of a VAWT at low
Reynolds numbers (e. g. small VAWT), di erent blade geometry (e. g. cambered)
and di erent propulsion mechanism are needed. In
uence of solidity was explored
by involving six blades for the simulation and it was concluded that blockage e ect
increased with the increase in number of blades which caused the maximum Cp to be
obtained at a relatively lower value of as compared to three bladed VAWT.
ADVISOR'S APPROVAL: Khaled A. Sallam