See

discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/308968618

Effect of blade number on performance of drag

type vertical axis wind turbine

Article in Applied Solar Energy · December 2016

DOI: 10.3103/S0003701X16040150

CITATIONS READS

0 81

6 authors, including:

M. Zheng Y. Li
Northwest University 1,307 PUBLICATIONS 31,781 CITATIONS
241 PUBLICATIONS 1,395 CITATIONS
SEE PROFILE

SEE PROFILE

Huang Teng J. Hu
Beihang University (BUAA) Harbin Institute of Technology
61 PUBLICATIONS 279 CITATIONS 21 PUBLICATIONS 4 CITATIONS

SEE PROFILE SEE PROFILE

Some of the authors of this publication are also working on these related projects:

Solar thermal energy storage View project

Renewable energy View project

All content following this page was uploaded by M. Zheng on 10 October 2016.

The user has requested enhancement of the downloaded file. All in-text references underlined in blue are added to the original document
and are linked to publications on ResearchGate, letting you access and read them immediately.
M. ZHENG 1, Y. LI1, H. TENG1,
J. HU1, Z. TIAN1, Y. ZHAO1

EFFECT OF BLADE NUMBER ON PERFORMANCE OF DRAG TYPE VERTICAL

AXIS WIND TURBINE
In this paper, the effect of blade number on performance of drag type vertical axis wind turbine (VAWT)
is studied by Ansys numerical simulation, it involves 3-blade, 5-blade and 6-blade VAWTs. The optimized
width of blade for each VAWT at maximum power efficiency is obtained, and simulation for the wind turbine
with different number of blade is conducted for the VAWTs with turbine radius of 2m at the inlet wind speed
8m/s. By simulations, it gets the evolution curve of torque with respect to time, and the cyclical
characteristics for these wind turbines. The results show that the maximum power efficiency and the stability
of the wind turbine increase with the number of blade of the wind turbine, however the optimal d/D
decreases with the number of blade of the wind turbine. The maximum power efficiencies are 20.44%,
24.30% and 26.82% for 3-blade, 5-blade and 6-blade wind turbines, and the correspondingly optimal d/D
are 0.66, 0.40 and 0.35, respectively. While the optimal rotational rate of turbine decreases with blade
number.

1. Introduction

Renewable energy includes wind, solar, biomass, hydro and geothermal energy. Wind turbine is the
main tool for the use of wind energy, through which wind energy can be converted into mechanical
energy, and then converted into other types of energy, such as electricity, heat, etc. So the design of wind
turbine is the most important part of the study for wind energy utilization. Vertical wind vertical axis
wind turbine (VAWT) and the parallel horizontal axis wind turbines (HAWT) are two types of wind
turbine.VAWT can be clarified into two main types, i.e., drag - type and lift - type [1]. Drag – type
includes Savonius type turbine, wind cup type, flat type and Madras type.
Chen et al studied the effect of tip speed ratio on power efficiency of the Darrieus - type wind
turbines [2], it showed that the optimized tip speed ratio is 4. Li et al analyzed the advantages and
disadvantages of VAWT and HAWT comparatively [3], it found that the efficiency of VAWT could be
improved by changing blade geometry.
Rosario Nobile studied the performance of lift-type VAWT numerically for a 3 blades turbine with
8 air concentrated stators around the wind turbine introduced simultaneously [4]. It showed that such
stators raise the power and torque coefficients by around 30–35% as compared to the stator-free case.
S. Rolland et al used CFD software to analyze the aerodynamic performance of a new type of
vertical axis wind turbine (VAWT). The new turbine is with crescent-shaped blade airfoil, the diameter of
the turbine is 1.6 m with 8 blades [5]. In the simulation, the effects of some key operational parameters,
such as wind speed, rotation rate, yaw angle and blade pitch angle, etc., are studied. The result shows that
the turbulence modeling technique is sufficient to evaluate the performance of the turbine in the definite
operating conditions and can give proper predictions.
J. Kumbernuss et al studied the performance of Savonius-type vertical axis wind turbines (VAWT)
with varying overlap ratios and shift angles experimentally [6]. Each wind turbine was tested under 4 inlet
wind speeds. The results show that a higher overlap ratio has a higher effect on the starting characteristics
of the Savonius wind turbine, and the phase shift angle could change its power efficiency. The highest
power coefficient is about 18%-20% for inlet wind speed 6m/s at the phase shift angle 15°.
In reference [1], the dynamic characteristics of 5-blade drag-type VAWT for the wind speed from
6.0 to 10.0m/s is studied, it shows that the critical length of the simulated region and the optimized rotor’s
rate increase with the inlet wind speed linearly within the scope of the simulation; the power efficiency of
5-lade drag type VAWT increases with the inlet wind speed exponentially.
It can be seen from above analysis that the power coefficient of wind turbine deponds upon many
factors, such as the vane shape, the number and width of blade, etc. Here in this paper the effect of blade
number on the performance of drag-typed VAWT at optimized blade width is conducted by numerical
simulation.

2. Geometric parameters of blade

The shape of drag-type blade VAWT could be in a semi-cylindrical, semi-spherical, spiral, conical
forms and so on. The helical and conical blade is complex in machining and inconvenient in long -
distance transportation. While the semi - cylindrical blade possesses advantages of larger effective area
and easier molding process, which is also widely used in engineering as compared to others [7-9].
Therefore, the analysis in this paper is focused on this type of semi-cylindrical shaped blade, and the
simulation is devoted to the effect of blade number on power efficiency of turbine.
The schematic view of 3-blade wind turbine is shown in Fig. 1, in which D is the wheel radius of
the wind turbine, which is invariable in the following calculation; d is the width of a wind turbine blade,
which varies in the simulations.

Fig. 1 Schematic view of 3-blade wind turbine

3. Calculation model
3.1 2-dimensional flow model
Appropriate simplified model should be considered so as to simplify the computation and keep a
suitable accuracy of the calculation.
Since the rotation of the turbine blades belongs to low-speed one, the lateral flow field at any blade
height position is almost the same for the same cross-section blade, flow velocity along the direction of
the blade height is approximately zero according to the geometric features and operating characteristics of
straight blade wind turbine, so the simulation can be reasonable to be simplified as a two - dimensional
one so as to reduce the amount of computation [1,10].
Fig. 2 is a simplified 2-dimensional flow model for 3-blade turbine. The geometric parameters of
the VAWT are as follows: the rotation radius D of the turbine is 2m, the blade height is 1m, and the
simulation area is 140m ×70m [1,10]. The inlet wind is from the left into the flow field, and flows out
from the right edge, wind turbine is at the position 20m away from the front; the turbine rotates in
clockwise direction.

Fig. 2 Simplified 2-dimensional flow model for 3-blade turbine

Because the entire simulation process of windmill is dynamic[1,10], it needs to consider the rotating
regional area and the static regional area in the calculation separately. In Fig. 2, the calculation region is
divided into 3 parts, i.e., Z1, Z2 and Z3. Z1 is central and static area inside the circular rotating blade, its
radius changes with the specific value of blade width, the formula for setting this radius is 2.2m – 0.4m –
blade width; Z2 is circular dynamic area with a outer radius of 2.2m, including the rotating blades; Z3 is
static rectangular area excluding Z1 and Z2, the scale is 70m × 140m.
3.2 Controlling equations
SST k-ω turbulence model is selected for this research, which is to be amended and improved on
the basis of k-ω turbulence model; it has advantages in studying the aerodynamics around the wind
turbine blade. It is more convenient to simulate the near-wall boundary layer and free shear flows at low
Reynolds numbers, and also convenient to be used to simulate the boundary layer separation under
adverse pressure gradient, and the results are comparatively higher accuracy additionally [11]. SST k-ω
turbulence model combines the features of the two types of two-equation models in both near wall and
far-field, i.e., k-ω equation model at near the wall and k-ε equation model at far-field; it gives good
predictions for the flow field of separated flow, and therefore exhibits certain advantages in dealing with
rotating machinery problem.
3.3 Calculation
 Once the turbulence model is determined, the most important thing is to solve the equations in the
calculation process numerically. The finite volume method is selected in this study [12], which concerns
the division of the computing grid so that the control body doesn’t overlap each other around each mesh
node; it derives discrete equation group by integrating the differential equations for each control body.
The PISO algorithm is employed to solve the discrete equation numerically, a multi - step correction is
involved at each calculation step; it derives an accurate pressure equation from continuous and discrete
equations, and then the velocity field is obtained from the pressure field, the calculation continues
repeatedly until the convergence velocity field and pressure field are obtained [13]. In addition, the
sliding mesh technique is chosen for rotational flow field simulation of the two-dimensional flow field in
the VAWT, this technique is the most accurate method in solving flow field of multi-body problem
directly. Meshed region rotates as a whole with time, the mesh nodes at both sides can not be overlapped,
while remaining the flux equal at the interface, it enables the region-coupling problem to be solved [14],
the detail of the grid division can be found in [10].
3.4 Boundary conditions
In this paper, the boundary conditions are set as follows:
(1) The wind from infinite position is set to be as the initial value of the entrance, i.e., the inlet
wind velocity (velocity inlet) is chosen for the entrance boundary conditions.
(2) The free outflow (outflow) is set for the outlet boundary condition. In this case, the disturbance
of the air flow due to wind turbine wake could be observed.
(3) The initial symmetry boundary (symmetry) is set down for both sides of the border; while the
flow field in the dynamic area of blade rotates together with the ring-shaped region, without sliding
relative to the surrounding fluid, so setting at the blade surface boundary is wall (wall) condition.
(4) The interface boundary conditions are set for the interfaces of the regions, since the numerical
results of the flow field need exchange mutually to get interpolation at the interface.
3.5 Treatment of the calculated results
Since only a part of wind energy can be absorbed by wind turbine, which is converted into mechanical
energy, so the power efficiency of wind energy is introduced to measure wind capacity of turbine to
absorb the kinetic energy from the wind, the greater the power efficiency the higher the conversion of the
wind energy into mechanical energy. The definition of power efficiency of wind energy into mechanical
energy is as follows,
1
C p = P /( ρSv 3 ) (1)
2
P is the actual power of the wind turbine, ρ is the air density, S is the swept area of the wind turbine
blades, and v is the wind speed.
The wind power efficiency Cp is an important parameter to assess the aerodynamic performance of
wind turbine, and it might change with the variations of wind speed and rotational rate of turbine. After a
lot of simulation trial, the time step is chosen as 0.02s, a total of 4000 steps, i.e., the simulation is
conducted in 80s. Since the output from computer is a dimensionless quantity, a coefficient is need to be
transferred from the instantaneous torque Cm into the actual moment M. Fig. 3 shows variation of the
instantaneous torque Cm with time. The torque coefficient changes periodically with time, it achieves to a
steady state after some cycles. One could take the average in one or two cycles in steady state as the final
calculated value for the torque.

Fig. 3 Variation of moment coefficient with time

The actual moment M can be obtained from the torque coefficient Cm through Eq. (2),
M = Cm ⋅ C (2)
in which, Cm is the instantaneous torque with the unit of N⋅m, and the coefficient C = 0.6125.
The actual power of wind turbine can be obtained through Eq. (3),
P = M ⋅ 2π ⋅ n / 60 (3)
in which, n is the rotational rate of turbine, in rpm. Then the power efficiency can be further calculated
from the actual power of wind turbine, i.e.,
1
C p = P /( ⋅ ρ ⋅ v 3 ⋅ h ⋅ D) (4)
2
in which, h is the height of the turbine, D is the diameter of the turbine, and ρ v3hD/2 is power of inlet
wind.

4. Calculation results
4.1 Calculation result and analysis for a 3-blade wind turbine case
As to the case of 3-blade wind turbine, the width of blade d is set as 1.26m, 1.28m, 1.30m, 1.32m
and 1.34m for the simulation, respectively. The turbine radius is fixed at D = 2m. In addition, the
rotational rate n of turbine is set as 17rpm, 18rpm, 19rpm, 20rpm and 21rpm, respectively, for the inlet
wind speed of 8m/s. The result of power efficiency is shown in Table 1 for the above cases.
Table 1 Variation of power efficiency with blade width and rotation rate for 3-blade turbine (%)

d(m)
1.26 1.28 1.30 1.32 1.34
n(rpm)

17 19.31 19.32 19.02 18.95 18.92

18 19.44 19.78 19.69 19.67 19.80

19 19.64 20.07 20.43 20.53 20.40

20 19.56 19.77 20.02 20.54 20.52

21 19.20 19.36 19.86 20.09 20.20

Table 1 shows that the maximum power efficiency for the 3-blade turbine is 20.54% at the inlet
wind speed 8m/s, it corresponds to the rotational rate of 20rpm and the blade width of 1.32m for this 3-
blade turbine.
Fig. 4 shows the variation of power efficiency with rotation rate for 6-blade turbine at different ratio
of blade width d to the wheel radius of the wind turbine D. Fig. 4 indicates that the most highest power
efficiency occurs at d/D about being 0.66 to 0.67 for the 3-blade turbine.
21 d/D = 0.63
d/D = 0.64
d/D = 0.65
Efficiency (%)

d/D = 0.66
20 d/D = 0.67

19

18
15 17 19 21 23
Rotational rate (rpm)

Fig. 4 Variation of power efficiency with rotation rate for 6-blade turbine at different d/D
Analyzing the results of power efficiency in Table 1 and Fig. 4, it can be found that the power
efficiency varies with width of the blade and rotation rate of turbine, the optimal value of blade width
might correspond to the greatest area for sweeping the wind field without the blades shading each other,
the optimal value of rotation rate of turbine might correspond to the optimal rotation rate for adsorbing
wind energy.
4.2 Results of the 5-blade wind turbine
For the 5-blade wind turbine, the turbine radius is fixed at D = 2m. The blade width d takes 0.76m,
0.80m, 0.82m and 0.86m, etc, to simulate the effect of blade width and rotation rate on power efficiency.
The inlet wind speed is 8m/s. Four rotation rates for n, 16rpm, 17rpm, 18rpm and 19rpm are selected. The
power efficiency is obtained and shown in Fig. 5. It can be seen from Fig. 5 that the maximum power
efficiency for the 5-blade turbine is 24.30%, it corresponds to the rotational rate of 17rpm and the blade
width d of 0.80m (i.e., d/D = 0.40) for the 5-blade turbine at the inlet wind speed 8m/s.
 Fig. 5 Variation of power efficiency with blade width and rotation rate for 5-blade turbine

4.3 Results of the 6-blade wind turbine

For 6-blade wind turbine, the turbine radius is fixed at D = 2m. Six blade widths for d, 0.60m,
0.66m, 0.68m, 0.70m and 0.72m are selected for the simulation, the inlet wind speed is 8m/s. The results
are shown in Table 2.

From Table 2, it can be seen that the maximum power efficiency for the 6-blade turbine is 26.82%,
it corresponds to the rotational rate n of 18rpm and the blade width d of 0.68~ 0.70m (i.e. d/D = 0.34~
0.35) for the 6-blade turbine at the inlet wind speed 8m/s.
Table 2 Variation of power efficiency with blade width and rotation rate for 6-blade turbine (%)
d(m)
0.60 0.66 0.68 0.70 0.72
n(rpm)
16 23.11 24.45 26.47 26.51 24.89
17 23.57 24.73 26.51 26.64 25.07

18 23.69 24.64 26.82 26.82 25.82

19 23.64 24.48 26.59 26.34 25.48

20 23.39 24.18 26.18 26.16 25.20

4.4 Comparison of wind turbine performance with different blade number

Above results indicate that the optimal blade width for each type of wind turbine varies with blade
number. From the data above, the optimal blade width d is 1.32m for 3-blade wind turbine at inlet wind
speed 8m/s, the corresponding power efficiency is 20.44%; the optimal blade width d is 0.80m for 5-
bladed wind turbine, the corresponding power efficiency is 24.30%; the optimal blade width d is 0.70m
for 6-blade wind turbine, the corresponding power efficiency is 26.81%. This indicates that the optimal
power efficiency of wind turbine increases and optimum blade width decreases with the number of blades
for the same wind turbine and inlet wind speed.
In addition, for the same wind turbine (turbine radius of 2m) and inlet wind speed 8m/s, the tend of
optimal rotation rate deceases with the number of blades for the same wind turbine. This is helpful to the
design of windmill.
Figs. 6-8 display the variations of steady torque with time after reaching to steady state for the 3-
blade turbine, 5-blade turbine and 6-blade turbine, respectively. Fig. 6 is for the 3-blade wind turbine at a
wind speed of 8m/s, rotation rate of 20rpm and blade width 1.32m. Fig. 7 indicates that the curve changes
periodically with period of about 3.24s; Fig. 7 is for the 5-blade wind turbine at a wind speed of 8m/s,
rotation rate of 17rpm and blade width 0.80m. Fig. 7 indicates that the curve changes periodically with
period of about 3.18s; Fig. 8 is for the 6-blade wind turbine at a wind speed of 8m/s, rotation rate of
18rpm and blade width 0.70m. Fig. 8 indicates that the curve changes periodically with period of about
2.98s. In addition, Figs. 6, 7 and 8 show that the averaged torque of the corresponding wind turbine
increases with number of blades for the same turbine radius and inlet wind speed. The values of torque for
the above three wind turbines are, 199.97, 279.69 and 291.44, respectively. By using Eq. (2), it gives the
values of the averaged moment for the above three wind turbines, and the corresponding values are
122.48Nm, 171.31Nm and 178.51Nm, respectively. By using the relative standard deviation analysis, the
relative errors of the instant moment with respect to the averaged one can be obtained, which is shown in
Table 3 as well. Table 3 shows that the relative standard deviation decreases with the number of blades,
which indicates that the stability of the wind turbine increases with the number of blades, this is helpful to
the design of windmill.

Fig. 6 Variation of steady torque coefficient - time for 3-blade wind turbine

Fig. 7 Variation of steady torque coefficient - time for 5-blade wind turbine

Fig. 8 Variation of steady torque coefficient - time for 6-blade wind turbine
Table 3 Relative standard error of moment for three wind turbines
Number of blades 3 5 6
Averaged Torque（Nm) 122.48 171.31 178.51
Relative standard error (%) 13.42% 6.82% 6.55%

5. Conclusion
Through above analysis for wind turbine with the same turbine radius (2m) and the inlet wind speed
8m/s, it concludes:
1) The optimal d/D varies with blade number of wind turbine;
2) The optimal d/D for the 3-blade wind turbine is 0.66-0.67; its optimum power efficiency is 20.44%, the
corresponding rotation rate is 20rpm;
3) The optimal d/D for the 5-blade wind turbine is 0.40, its optimum power efficiency is 24.30%, and the
corresponding rotation rate is 17rpm;
4) The optimal d/D for the 6-blade wind turbine is 0.34 ∼ 0.35, its optimum power efficiency is 26.82%,
and the corresponding rotation rate is 18rpm;
5) The stability of the wind turbine and the optimum power efficiency increase with the number of blades
for turbine with the same radius and the inlet wind speed.

Acknowledgement: this work is supported by the special sci. & tech. innovation program of Shaanxi
province and the innovation foundation for postgraduate of Northwest University.

REFERENCES
[1] Zheng M., Guo L., Li Y., Tian Y., Teng H. P., Hu J., Zhao Y., Yu L. J. Power Efficiency of 5 Blade
Drag Type Vertical Axis Wind Turbine [J], Applied Solar Energy, 2015; 51(3): 225–231.
[2] Z. Chen, Analysis of tip speed ratio for vertical axis wind turbine [J], Renewable Energy, 2008; 26 (5):
 76-82.
[3] C. Li, X. Li, X. Ye, Progress of structure and performance of vertical axis wind turbine [J], Turbine
Technology, 2013; 1: 67-73.
[4] R. Nobile, M. Vahdati, J. F. Barlow, A. Mewburn-Crook, Unsteady flow simulation of a vertical axis
augmented wind turbine: A two-dimensional study [J], J. of Wind Engineering & Industrial
Aerodynamics, 2014; 125:168-179.
[5] S. Rolland, W. Newton, AJ Williams, TN Croft, DT Gethin, M. Cross, Simulations technique for the
design of a vertical axis wind turbine device with experimental validation [J], Applied Energy, 2013;
111, 1195-1203.
[6] J. Kumbernuss, J. Chen, H.X. Yang, L. Lu, Investigation in to the relationship of the overlap ratio and
shift angle of double stage three bladed vertical axis wind turbine (VAWT) [J], Journal of Wind
Engineering and Industrial Aerodynamics, 2012; 107-108, 57-75.
[7] F. Feng, Y. Li, L. Chen, et al, Simulation and experimental study of aerodynamic characteristics for
combination-type vertical axis wind turbine [J], Solar Energy Journal, 2014; 35 (5): 855-859.
[8] C. Ye, X. Zhao, J. Wang, Analysis and numerical simulation of vertical axis wind turbine
aerodynamic performance [J], Machinery and Electronics, 2012; (1): 20-23.
[9] X. Xu, Z. Zhou, M. Qiu, Simulation of aerodynamic performance for vertical axis wind turbine
impeller [J]; Solar Energy Journal. 2012; 33 (2): 197-203.
[10] M. Zheng, Y. Li, Y. Tian, et al, Effect of blade installation angle on power efficiency of resistance
type VAWT by CFD study, Int. J. Energy Environ. Eng., 2015; 6(1): 1-7.
[11] C. Yang, F. Wu, Y. Zhang, Unsteady numerical simulation based on sliding mesh for vertical axis
wind turbine [J] Agricultural Machinery, 2009; 40 (6): 98-102.
[12] B. Yan, X. Han, X. Kong, et al, Improved diffusion discrete finite volume method format item [J],
Huazhong University of Science and Technology (Natural Science), 2012; 40(5): 20-23.
[13] W. Liu, Study of PISO algorithm using second-order upwind scheme [J] Journal of Aerospace
Power, 1998; 13(1): 81-84.
[14] L. Zhang, L. Hu, X. Shao, Unsteady flow field in pump under slip grid computing [J],
Hydrodynamics Research and Development, 2013; 28 (1): 10-16.

1
Institute for Energy Transmission Technology and Application, School of Chemical Received
Engineering, Northwest University, Xi’an 710069, China

View publication stats