1. Study of Unsteady Aerodynamic Effects for a Vertical Axial Wind Turbine
Tzong-Hann Shieh1,2,3,a,#
, Charng-Chin Hsiao2
, Yung-Ting Chen1,2,b
, Ya-Tzu Hsu3,c
and
Yang-Hsu Liao1,d
1
Department of Aerospace and Systems Engineering, Feng Chia University,
No.100 Wenhwa Rd., Seatwen, Taichung, Taiwan 40724, R.O.C.
2
Ph.D. Program of Mechanical and Aeronautical Engineering, Feng Chia University,
No.100 Wenhwa Rd., Seatwen, Taichung Taiwan40724,R.O.C.
3
Master Program in Creative Design, Feng Chia University,
No.100 Wenhwa Rd., Seatwen, Taichung, Taiwan 40724, R.O.C.
a
thshieh@fcu.edu.tw, b
m0211619@fcu.edu.tw, c
tarisa284@gmail.com, d
yanghsuliao@hotmail.com
#
corresponding author / TEL: +886-4-24517250 EXT.3960-, FAX: +886-4-24510862
Keywords: VAWT, Dynamic Mesh, Tip Speed Ratio, Blade Force, Dynamic Stall
Abstract. This study is investigated through a two dimensional model of vertical-axis wind turbine
generator. The aerodynamic disturbances during operation of three types of blades design are
discussed. The simulation model is built by lateral section profile of the vertical-axis wind turbine.
Varied tip speed ratios are involved in the simulating conditions. Computational domain contains
both dynamic and stationary mesh. Numerical method is used to solve unsteady Reynold’s average
Navier-Stokes (RANS) equations and k-ω SST turbulence model with near wall correlation function
such that can simulate the motion of blades. The interactions of blades are indicated by distribution of
action forces, average torque and dynamic stall in different rotational position of blades. The results
are preliminary discussions of structural and aerodynamic effects of vertical-axis wind turbine
generator, and will be validated through experiment in the future.
Introduction
In recent years, the global renewable energy and new energy developing area, wind power is the
one of the most potential renewable energy, no matter based on requirement of world economic or
business development. The principles of wind power is that blades of wind turbine can be rotated
through breeze flow by and then to drive the converting mechanism. The generator is connected with
the mechanism such that can convert rotational power into electricity. To obtain the optimized
converting efficiency of the turbine, however, the aerodynamic performance of blades and overall
flow design of the wind turbine has to be achieved first. There are two types of wind turbine,
vertical-axis and lateral-axis, which are defined by the axial direction of the generator of wind turbine.
The vertical-axis wind turbine has specific advantages on aerodynamic properties if compared with
lateral wind turbine. But on commercial market development, the advantages will be taken over by
lateral-axis type. The specific aerodynamic property of vertical-axis wind turbine is it can accept
wind from any direction without yawing. The blades of vertical-axis wind turbine have uniform wing
sections in the direction of span and untwist, which is the biggest difference comparing with lateral
one. Therefore, vertical type is more easily manufactured than lateral type. For vertical-axis wind
turbine, the maintainance of its components can be finished on the ground, and this also cost saved for
logisitic. However, torque differences between each rotation are significant and it cannot be
self-activated [1].
Moreover, the design of blade is the most important factor of wind turbine’s performance.
Vertical-axis wind turbines can be classfied into three major groups by silhouette of blade [1]. There
are Savonius type of wind turbine invented by Sigurd Johannes Savonius from Finland [2], Darrieus
wind turbine which is invented by French engineer Georges Jean Marie Darrieus [3], and Darrieus
type with straight blads, also called H-rotor type. The important parameters of design are mainly on
modifying the shape of blade and how to control the feedback of blades when approaches to

2. maximum loading. In addition, generator’s property, and strength and stiffness of blades both are
considered. Consquently, the optimized design of a vertical-axis wind turbine can be obtain. How to
optimize the converting efficiency, from wind energy to electricity, the blade‘s aerodynamic property
has a significant effect influence. Ferreira et al. [4] mentioned that the angle of attack of blades can be
larger than the static stall angle if the tip speed ratio dynamic stall was less than 4. That can also
induce the dynamic stall since the blades are in unsteady flow field. To reduce the cost of experiments,
applying CFD in simulating the fluid deattached phenomenon during dynamic stall situation of
vertical-axis wind turbine in preliminary study is much valuable.
Computational Method
This study uses numerical method to solve two dimensional problem of unsteady flow, and the
coupling effects between turbine and fluid under 7m/s free stream condition. Pressure based and finite
volume method both are utilized in discrete numerical model and the Navier-Stokes equations are is
solved through Reynold averaged method. For discrete space model, pressure and velocity are
coupled via SIMPLE method. For discrete momentum equations, the power law is considered in
solving fluid flow with low Reynold number so that the results are more accurate than using first
order formulation. Otherwise, to solve large pressure gradient in highly rotional flow, the PRESTO
method is considerd. In time discrete, implicit and second order method are considerd hence the
periodic unsteady phenomenon of relative motion, rotational velocity, and numbers of blade can be
investigated. Time step is also setup for distrete computation. Moreover, two equation ω−k
SST(Shear-Stress Transpor) turbulence model is used to resolve inverse pressure gradient and
detached phenomenon on blades. Considering the detached problem in boundary layer, the near wall
correction formula is also involved into analysis to improve accuracy computational results of inverse
pressure gradient.
Physical Model and Meshes
The model in this research is refered to the real model of cyclic subsonic wind tunnel experiments
we built. The model of wind tunnel test section and wind turbine are indicated in Fig. 1. The initial
wind speed is also refered to real operating condition, 7m/s. To reduce the difficulty of manufacturing
blades, low Reynold number airfoil – NACA0015 is chosed as the turbine’s blade (shown as Fig. 2).
Two tips of blade are cut vertically with repect to span direction. The whole wind turbine model are
built with three blades as a rotor. The rotor’s related dimentions are shown in Table 1.
Fig. 1 Computational model and dimension Fig. 2 Dimensionless of NACA0015
airfoil

3. Table 1 Geometric properties of blades and rotor
Name Number Dimension Unit Note
Airfoil NACA0015 -/- -/-
Chord Length -/- 0.05 m
Ridus of Rotor -/- 0.165 m
Ridus of Pole -/- 0.023 m
Blade Span (Z Dir.) -/- 1 m 2D
To simulate the flow of inside rotor’s domain of a vertical-axis wind turbine, dimensionless near
wall distance
( ) μρ τuyy =+
should be as low as possible. The phenomena of dynamic stall,
interaction between blades and air, and vortex detachment on blade during the turbine rotating can be
resolved. Hence, the meshes near blades are refined to approach the analytical requirements.
Dynamic mesh is used to simulate the rotational motion of turbine. The fluid model is divided into
three calculation domains, stationary, rotational, and near wall meshes. The combination of
non-sturctured and structured meshes is used in this study (shown as Fig. 3). Fig. 4 indicates refined
structured meshes around the blade. The meshes assist to solve reaction force, dynamic stall, and
vortex detachment of blades. Besides the near wall domain, fluid meshes are built in non-sturctured
type. Total meshes are nearly 230,000.
Fig. 3 Whole meshes Fig. 4 Structured meshed near wall
Results and Discussions
To obtain the average torque, the tip speed ratio (TSR) is defined as Eq. 1.
V
R
TSR
ω
= (1)
R, ω , and V are radius of rotor, rotaitional speed, and free stream speed respectively. By the
defination of TSP, the optimized value of the simulation model is shown in Fig. 5. The optimized
average torque can be obtained when TSP equals to 1.3. The TSP over 2, however, the greater TSP
the smaller average torque is obtained. According to the result, this paper uses 1.3 as the optimized
TSP condition, means that rotional speed equals 55 RPM and free stream speed equals 7 m/s. The
reaction force of blade and dynamic stall phenomenon is investaged under the condition.
Reaction forces of vertical-axis wind turbine, the action force indeuced by inverse tangent force
affects the torque of turbine directly. That also means the torque of turbine will increase if the tangent
force of blade increases. The tangent force coefficient of blade is defined as Eq. 2.
cVFC tt
22
2
1
∞= ρλ (2)
Which Ft is tangent force, λ is TSP, and ∞V is speed of free stream. The variance of tangent force
coefficient with azimuth is shown in Fig. 6. The maximum tangent force of blade is achieved when
rotor at 50 degree of rotational position. Additionally, the moment of rotor which induced by the axial

4. force of bla
turbine. Th
Fig
Fig
Fig. 7 a
position re
phenomeno
There are n
appeared a
potition eq
isosurface
unsteady f
performanc
Summary
The two
between bl
center pole
increase th
TSP. The a
The dyn
turbulence
dynamic, s
ade is not ev
he effect of
g. 5 Varianc
re
g. 7 Isosurfa
rota
and Fig. 8 d
epectively.
on of fluid
no vortices w
at 90 degre
quals to 135
of vortices
flow. It will
ce becomes
o dimension
lades, and i
e is mainly
he distance. O
average torq
namic mesh
model and
such that dy
vident. The
axial force
ces of avera
espect to TS
ace of vertic
ational posi
display isos
The result
detach in n
which induc
ee rotationa
degree, sin
. Vortices d
l decrease t
s low.
n model use
interaction b
caused by t
Otherwise,
que decreas
method can
d near wall
ynamic stall
amplitude o
cannot be ig
age torque w
SR
ces at 90 de
ition.
surface of v
ts indicate
near wall bo
ced by fluid
al position a
nce vortices
detaching m
the tangent
ed in this st
between bla
the distance
for rotors w
es as TSP in
n simulate t
correlation
phenomena
of axial forc
gnored norm
with
c
egree Fig.
vortex grad
that ω−K
oundary laye
d detaching a
and show t
detaching t
may affect th
force of bl
tudy can re
ade and cen
e between b
with three bl
ncreases aft
he rotation
n function c
a between b
ce is the maj
mally but in
Fig. 6 Vari
coefficient o
8 Isosurfac
rota
dent in 90 d
ω SST turb
er and dyna
at lower rota
the trend of
the dynamic
he followin
ade and ave
solve the d
nter pole. O
blade and po
ades, the av
ter achievin
of blades w
can also be
blades and th
jor cause of
n this study.
ances of tan
of blade wit
azimuth
ce of vertice
ational posit
degree and
bulence mo
amic stall w
ational posi
f detaching
c stall can b
ng blades so
erage torqu
dynamic stal
Overall, the
ole. The eff
verage torqu
ng of optimi
well. The com
e applied in
he rotor can
f structure di
ngent force
th respect to
es at 135 deg
tion.
135 degree
odel can pr
when turbine
tion. The vo
g. When the
be discovere
o that the bl
ue so that th
ll of blade,
aerodynam
fect can be
ue is mainly
ized average
mbination o
n simulating
n be predict
isruption of
o
gree
e rotational
redict flow
e’s rorating.
ortices have
e rotational
ed from the
lades are in
he turbine‘s
interaction
mic effect of
reduced by
affected by
e torque.
of k-ω SST
g rotational
ted. Though
f
l
w
.
e
l
e
n
s
n
f
y
y
T
l
h

5. pressure coefficient and vortices distribution are used to demonstrate the dynamic effect of blade’s
vortice detaching, the mechanism of reduceing detaching at tail of blade and postpone votices
detaching can be investaged from the results. Three dimensional effects of fluid flow cannot be
simulated by two dimension model. To improve the model‘s accuracy, the three dimensional effects
need to be considered for further study.
Acknowledgement
This research project is supported by the Ministry of Science and Technology of Taiwan, ROC under
grant MOST103-2221-E-35-064 & NSC102-2221-E-035-029-.
References
[1] A. Goude, Fluid Mechanics of Vertical Axis Turbines:Simulation and Model Development, Acta
Universitatis. Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of
Science and Technology 998(2012).
[2] M. Islam, D. S.-K. Ting, and A. Fartaj, “Aerodynamic Models for Darrieus-Type Straight-Bladed
Vertical Axis Wind Turbines,” Renewable & Sustainable Energy Reviews, Vol. 12, pp.
1087-1109(2008).
[3] J. O. Ajedegba, Effects of Blade Configuration on Flow Distribution and Power Output of a
Zephyr Vertical Axis Wind Turbine, MS Thesis, University of Ontario Institute of
Technology(2008).
[4] B. K. Kirke, and L. Lazauskas, “Limitations of Fixed Pitch Darrieus Hydrokinetic Turbine and the
Challenge of Variable Pitch,” Renewable Energy, Vol. 36, Issue 3, pp. 893-897(2011).
[5] C. J. S. Ferreira, A. van Zuijlen, H. Biji, G. van Bussel, and G. van Kuik, “Simulating Dynamic
Stall in a Two-Dimensional Vertical-Axis Wind Turbine: Verification and Validation with
Particle Image Velocimetry Data,” Wind Energy, Vol. 13, pp. 1-17(2010).