For centuries, mankind has harnessed the power of wind to sail ships and drive
wind mills to grind grain. The earliest-known design is the vertical axis system
developed in Persia about 500-900 A.D and the first known documented design
is also of a Persian windmill, which had a shield to block the wind from the
half of the rotor moving upwind (Erich, 2006). It is widely
believed that vertical axis windmills have existed in China for 2000 years,
however the earliest documentation of a Chinese windmill was in 1219 A.D. by
the Chinese statesman Yehlu Chhu-Tshai. Here also, the primary applications
were apparently grain grinding and water pumping. The modern VAWT was first
patented in France (1925) and in the U.S. (1931) by Georges Jean-Marie Darrieus
Wind energy became significant in the energy crises experienced in the early
1970s to generate electrical energy instead of mechanical energy and currently
there are two categories of modern wind turbines, namely Horizontal Axis Wind
Turbines (HAWT) and Vertical Axis Wind Turbines (VAWT) (Izli
et al., 2007). VAWT is classified into two categories:
||Savonious type VAWT
||Darrieus type VAWT
The Savonius-type VAWT was invented by a Finnish engineer S.J. Savonius in
1922 (Savonius, 1931). The speed of the Savonius wind
turbine cannot rotate faster than the speed of the wind and so they have a Tip
Speed Ratio (TSR) of 1 or below. The working principle of Savonius wind turbine
is shown in Fig. 1.
Darrieus VAWTs are mainly of two types, namely Eggbeater Darrieus rotor and
H-Darrieus or simply H- rotor. It was first patented in France (1925) and in
the U.S. (1931) by Georges Jean-Marie Darrieus which included both the Eggbeater
Curved Bladed) and Straight-bladed VAWTs. His idea received little attention
and in the late 1960s, the design was independently re-invented by Canadian
researchers South and Rangi at the National Research Council in Ottawa
(South and Rangi, 1973). Figure 2 shows
the concept of the two types of Darrieus type vertical axis wind turbine.
A Darrieus wind turbine can spin at many times the speed of the wind hitting
it (i.e., the Tip Speed Ratio (TSR) is greater than 1). Hence, a Darrieus wind
turbine generates less torque than a Savonius but it rotates much faster .
Early developments in the 1970-80s demonstrated that though the VAWT are slightly
less efficient than their HAWT counterpart, they have some clear advantages
(Islam et al., 2005). The main difference between
VAWTs and HAWTs is that the VAWTs ability to accept wind from any direction,
i.e., it is omni-directional.
||(a) Concept of Savonius VAWT (b) Savonius VAWT and air flow
||(a) concept of curved blade (eggbeater (b) concept of three
This has several advantages. The turbine does not require a yaw system, which
is costly and could fail during operation. The yaw system includes both a control
system and a drive mechanism. The costs associated with such a system include
the cost of the equipment itself, installation cost and costs for operation
and maintenance. Furthermore, with an omni-directional turbine there are no
power losses during the time it takes for the turbine to yaw or during short
wind gusts with temporary changes in wind direction (Roynarin
et al., 2002).
An omni-directional turbine can be situated at places where the wind is turbulent
and where the wind direction changes often. For this reason, VAWTs have an advantage
over HAWTs in high mountain areas, in regions with extremely strong or gusty
winds and in urban areas. Furthermore, the VAWT is less noisy than the HAWT,
which becomes even more important in urban areas (Riegler,
2003). Investigations indicate a clear advantage in using VAWTs at rooftops
Blades of VAWT may be of uniform section and untwisted, making them relatively
easy to fabricate or extrude, unlike the blades of HAWT, which should be twisted
and tapered for optimum performance. Furthermore, almost all of the components
requiring maintenance are located at the ground level facilitating the maintenance
work appreciably (Islam et al., 2005). However,
its high torque fluctuations with each revolution, no self-starting capability
are the drawbacks (Kirke, 1998; The worlds
of David Darling, 2009).
The majority of research on VAWT design was carried out during the late 1970s
and early 1980s, notably at the USA Department of Energy Sandia National Laboratories
(Dodd, 1990) and in the UK by Reading University and VAWT
Ltd, who erected several prototypes including a 500 kW version at Carmarthen
Bay (Price, 2006). When it became accepted that HAWTs
were more efficient at these large scales, interest was lost in VAWT designs
and HAWTs have since dominated wind turbine designs. Due to this, very little
research can be found in the last couple of decades on the VAWT.
It is common to find on various literature and commonly believed that VAWTs
are less efficient than the commonly known HAWTs. However, as some literature
shows, that does not really indicate the truth. VAWT technology is not widely
commercialized, not because of it has been shown to be inferior to HAWT technology.
Rather, it appears to be because the VAWT technology is much different from
HAWT technology and relatively few companies have made the investment required
to truly understand and objectively evaluate the VAWT (Berg,
1996). VAWTs could develop similarly as HAWTs if money and time was invested
in research (Eriksson et al., 2008).
According to Kirke (1998) majority of the previously
conducted research activities on VAWT focused on straight bladed VAWTs that
equipped with symmetric airfoils like NACA0012, NACA0015 and NACA0018 profiles
which were unable to self-start. Due to the cyclical variation in angle of attack,
blades are stalled and generate low or negative (i.e. reverse) torque for most
azimuth angles at low tip speed ratio. To solve this problem, numerous attempts
were made to improve self staring of VAWT by different scholars including (Lazauskas,
1992; Dereng, 1981; Barker, 1983;
Hurley, 1979; Wakui et al.,
2005; Drees, 1979; Liljegren,
1984) and others. Though the approaches were tend to contribute in the increases
of starting torque, reductions in peak efficiencies and working on the operating
range were some of the major problems.
These days, there is revival of interests regarding VAWTs as several universities
and research institutions have carried out extensive research activities and
developed numerous designs based on several aerodynamic computational models
(Islam et al., 2008). A comparative study made
by Eriksson et al. (2008) cited above shows
that VAWTs are advantageous to HAWTs in several aspects. Other many research
works showed that VAWT has the potential to compete with the more widely used
conventional HAWTs if the inability of the turbine to self-start is resolved.
The present paper attempts to show self-starting capability of darrieus type
VAWT by modifying the conventional symmetrical airfoil which is not self starting
itself. NACA0018 airfoil was made to be divided into two parts at about 70%
of the chord length as shown in Fig. 3. The trailing edge
inclined at 15° from the main blade axis was modeled in gambit modeling
software. The model created was then read into commercial CFD software, Fluent
6.3.26 version for computational analysis of the two dimensional (2D) unsteady
flow around the turbine. 2D unsteady flow analysis for the modeled airfoil section
VAWT was analyzed based on Reynolds Averaged Navier-stokes (RANS) equation using
moving mesh technique.
The basic idea for the modification of the airfoil was to make use of high
lift forces for self -staring capability. As the velocity of the wind that passes
on the top surface is greater than the velocity of the wind on the lower surface
of the modified airfoil, high pressure difference that contribute to self starting
of the turbine assumed to be created at low tip speed ratio. Then the trailing
edge can be allowed to take the same axis orientation as the main airfoil for
the operation of the turbine at higher tip speed ratios.
MATERIALS AND METHODS
Computational fluid dynamic, CFD tool solving the Reynolds-averaged navier-stroke
equations based on moving mesh technique was conducted on October 8, 9 and 10,
2010 using high speed processor computer. The laboratory is located in the zoo
campus of Harbin Institute of Technology, Department of Manufacturing and Automation.
The analysis incorporates 2D unsteady flow of vertical axis wind turbine model
with NACA0018 modified airfoil blade section at different tip speed ratios and
steady flow conditions at three different orientations of the airfoils. The
procedures followed in the analysis are as follows.
Computational analysis: The basic structure of the vertical axis wind
turbine selected for the computational analysis is as shown in Fig.
4. It is a fixed pitch type with three straight blades of modified airfoil.
The basic analysis system of the turbine is shown in Fig. 5.
As the blades turn about the central shaft, they encounter an incident wind
that is composed of the ambient local wind velocity and the blade rotational
velocity as indicated in Fig. 5.
|| Modified geometry of NACA0018 airfoil
|| Schematic representation of VAWT model created with solid
||Topographic view of the model with lift and drag component
This incident wind velocity generates lift and drag forces on the blades, which
can be decomposed into a thrust force and a radial force on the turbine arms.
||Note: Lift is defined as the force perpendicular to
incident wind velocity and drag is defined as the force parallel to the
incident wind velocity
|| Boundary conditions
|| Mesh near airfoil
Computational domain: The modified NACA0018 airfoil was used for the
analysis of 2D unsteady flow. The airfoil was set to 0.2 m chord length and
the turbine radius was set to 2 m. Gambit 2.3.16 version modeling software was
used to create 2D model and to generate mesh. The domain size was created with
a rotating sub-domain surrounding the blades and stationary sub domains in the
remaining region. Mesh for the rotating sub-domain, central stationary sub-domains
and stationary sub domain located to the right side of rotating sub-domain were
generated with square pave. Frontal stationary sub-domain and the last stationary
sub-domain located at far end of the outlet are generated with structured type
of grid. The rotating sub-domain was set to a major diameter of 5 m and minor
3 m. The inlet width and out let width were set to 3 times the major diameter
of rotating sub-domain. The inlet was located 3 times the major diameter of
rotating sub-domain upstream and outlet 6 times the major diameter of the rotating
Computational method: The model and mesh generated in gambit modeling
software were read into the commercial CFD code, fluent V.6.2.30 for numerical
iterative solution. The RANS equations were solved using the green-gauss cell
based gradient option and the sliding mesh method was used to rotate the sub-domain
for the turbine blades. For pressure-velocity coupling, the simple algorithm
|| Rotating sub-domain
Standard was set as pressure discretization and first order upwind was set
for momentum. Time integration was done implicitly and the minimum convergence
criteria were set to 1e-06. The RNG k-epsilon model was adapted for the turbulence
For the moving mesh simulations, the computational sub-domain is split into
a moving part around the turbine and a fixed part for the fixed environment.
The rotational motion is simulated by allowing the mesh block around the wind
turbine to rotate at constant angular velocity. The mesh movement is defined
explicitly by specifying time-varying positions for all of the moving mesh block
cell vertices. An interface boundary surrounding the moving mesh part within
the model slides at the specified velocity. This represents the relative motion
between the rotating wind turbine and the fixed environment.
Boundary conditions: The boundary conditions are shown in Fig.
6. The inlet was defined as a velocity inlet, which has constant inflow
velocity while the outlet was set as a pressure out let, keeping the pressure
constant. The velocity at the out let was determined by the extrapolation from
inside. The no slip shear condition was applied on the turbine blades, which
sets the relative velocity of blades to zero. There were four domains in the
computational domain with 522 cells around each blade. The cells were concentrated
near the blades as shown in Fig. 7 for better result.
The flow condition used for the analysis is shown in Table 1.
Time step size was set corresponding to 2 degree for each rotational speed of
the rotor (ω) given in Table 1 corresponding to each
|| Lift coefficient comparison, for Re=360,000
|| Flow conditions
One hundred and twenty iterations were used per time step.
The operating speed of the turbine, expressed as tip speed ration (TSR) was
set between 0.1 and 1.
||Note: TSR(λ) is defined as:
where, R is the turbine radius, ω is angular velocity and V∞ is
the free stream velocity
Code verification: To verify the reliability of the computational method,
hydrodynamic forces acting on the conventional symmetrical airfoil, NACA0018
was computed from different angles of attack. The cord length was set to 1m
and the corresponding cord -based Reynolds number Re, was 360,000. The converged
solution was obtained after 1500 iterations. Figure 9 shows
the comparison of the computational solutions and experimental data (Sheldahl
and Klimas, 1981). The computed lift forces are in good agreement with the
experimental data for angles of attack between -10 and 10 degree which is considered
to be the normal operating range of turbine blades. The drag coefficient comparison
is also shown in Fig. 10.
|| Drag coefficient comparison, for Re=360,000
Figure 11 shows simulated torque values for the modeled
NACA0018 modified airfoil at lower TSR. It shows the torque values at different
azimuth angle in N-m for complete revolution of TSRs 0.1, 0.25, 0.5, 0.75 and
1. The torque values were obtained from coefficient moment (Cm) of the modeled
airfoil, air density, turbine area, free stream velocity chosen and the radius
of the turbine modeled. The graph shows that the average torque values at each
of the TSR simulated are positive.
Figure 12 shows simulated torque values for NACA2415 cambered
airfoil modeled in the same way as the modified NACA0018 using the same parameter
for comparison. It shows the torque at different azimuth angles in N-m for complete
revolution of TSRs 0.1, 0.25, 0.5, 0.75 and 1. The torque values were obtained
using the same principle as mentioned above. As can be seen from the graph,
the torque values are higher for the modified airfoil compared to the camber
Figure 13 shows the coefficient of moment (Cm) of the simulated
model for NACA0018 and NACA2415. This coefficient determines the average torque
of wind turbines. The Cm values were obtained from the average moment of the
three airfoils modeled through CFD computational analysis. As can be seen, Cm
near zero is higher and seems to reduce up to TSR = 0.5 and then starts to rise.
It is also clear that the Cm of modified NACA0018 is greater than that of NACA2415
Figure 14 shows the Coefficient of Power (Cp) for the modified
NACA0018 airfoil. The graph is generated by combining the performance of turbine
trailing edge inclined modeled for TSR 0.1 to 1 and without inclination of the
trailing edge for TSR greater than 1.
|| Torque for modified NACA0018
|| Torque for NACA2415 camber airfoil
||Comparison of Cm for NACA2415 and NACA0018 modified airfoil
The Cp was obtained from the ratio of the modeled turbine power to the available
wind power in the air and used to determine the performance of the turbines.
Figure 15 shows the steady state torque values at TSR 0
for different wind speeds at three different orientations of the blades. The
blade orientations were taken at three different azimuth angles of 0, 45 and
90° as shown in Fig. 16. This helps to show the performance
of the turbine at its steady state. The simulation result shows that the torque
values are positive at all the orientations and increases with increase of wind
|| Cp Curve of the modified airfoil
||Torque versus velocity at three locations of blades
|| Blades orientation at different azimuth angle
With this result it is possible to conclude that the turbine can self start
from steady state at any orientation of the blades.
In Fig. 16, Blade 1, 2 and 3 represent the steady state
orientation of the turbine at azimuth angle of 0°. B1′, B2′,
and B3′, represent the orientation of the turbine at azimuth angle of
45°. Lastly B1, B2 and B3′′ represent the third steady state
orientation of the turbine at azimuth angle of 90°.
Blade aerodynamic forces and torque are computed from the solution of RANS
equations through the integration of the pressure and shear stress over the
blade surface. The total wind turbine force components and torque are obtained
by adding the 3 blade force components and torque. The driving torque is obtained
by calculating the average of the instantaneous values corresponding to the
last revolution of the rotor. These values were used to derive the expected
wind turbine power coefficient (Cp). The turbine was allowed to turn until stable
torque was created and the minimum number of turns used for this model was 6
Power of the turbine is defined as:
where, p is expected output power of turbine, ω is angular velocity of
turbine, T averaged torque.
Cp is then calculated as:
where, ρ is the air density, V∞ free stream velocity, A frontal
area of the turbine
Symmetrical airfoils NACA0012, NACA0015 and NACA0018 are the conventional airfoil
sections used in Darrieus type VAWTs. However, the main drawbacks with these
types of sections are their minimum or negative torque generation at lower TSRs.
For comparison of the modified airfoil result, NACA 2415 camber airfoil was
numerically analyzed with computational fluid dynamic analysis taking the same
parameter as the modified airfoil. The simulation result is in agreement with
previous works (Lazauskas, 1992; Barker,
1983; Kirke and Lazauskas, 1991; Healy,
1978; Kotb, 1990; Habtamu and
Yingxue, 2011) that camber airfoil can increase staring torque but reduction
in peak efficiency and operating in narrower ranges are the draw backs.
The self- starting capability of the modified airfoil is then compared to the
cambered airfoil as shown in Fig. 13. As can be seen from
the simulation result, the modified airfoil has shown a better coefficient of
moment for the simulated model than the camber airfoil. This indicates that
the turbine can accelerate at lower TSR which cannot be possible using symmetrical
The steady state result shown in Fig. 15 at TSR 0 also indicates
that the modeled turbine can generate positive torques at all the selected three
orientations. This indicates that the turbine can start to turn from stationary
||Static pressure contour at 0° angle of attack in Pascal
||Static pressure contour at 10° angle of attack in Pascal
||Static pressure contour at 16° angle of attack in Pascal
The coefficient of moment and the steady result implies that the modified airfoil
has shown good self- starting for the modeled turbine at low tip speed ratios.
Figure 17 to 19 shows the static pressure
distribution around the airfoil in Pascal for angle of attacks 0, 10 and 16
degrees, respectively. Depending on the color of the static pressure contour,
one can predict where the pressure is high and lower around the airfoil using
the value of pressure displayed on the status bar for the modeled airfoil. Referring
back the relationship between pressure and velocity from the Bernoulli equation
one can also able to predict where the flow velocity of the wind high and low
around the airfoil.
The present work has attempted to analyze the performance of Darrieus type
VAWT with three fixed straight blades from different perspective through modification
of existing airfoil at low tip speed ratios. The research is aimed to contribute
to the current literature in renewable energy and self staring studies of vertical
axis wind turbine which is a promising design for diversified applications.
2D unsteady flow of VAWT with NACA0018 modified geometry blade section based
on fixed pitch three blades was analyzed using computational fluid dynamics.
The model was analyzed at lower TSRs 0.1, 0.25, 0.5, 0.75 and 1. The model was
also analyzed for its performance at its steady state or TSR = 0. The coefficients
of moments were then compared with NACA2415 camber airfoil which is self- starting
that is analyzed using the same parameter. Coefficients of moments for the higher
torque were also analyzed without the inclination of the trailing edge for performance
prediction. The simulation result shows that the modified airfoil has shown
better performance in self- staring of the turbine at lower TSRs for the modeled
turbine. The power coefficient of the simulated model obtained through combination
is also in the normal range of turbine performance. Optimization of the airfoil
through CFD is an extension of future work.