CFD analysis of low speed vertical axis wind turbine with twisted blades.

M., Manzoor Hussain ; Mehdi, S. Nawazish ; Reddy, P. Ram 等

Introduction

Wind energy is the kinetic energy associated with the movement of atmospheric air due to uneven heating and cooling of earth surface. Wind power is the extraction of this energy by wind turbines. The wind has played a long and important role in the history of human civilization. Savonius wind turbines are a type of vertical-axis wind turbine (VAWT), used for converting the power of the wind into torque on a rotating shaft. Aerodynamically, they are drag-type devices, consisting of two or three scoops. The features of this windmill are easy to make, independent of direction of wind, low speed and high torque [8]. Much larger Savonius turbines have been used to generate electric power or draw deep-water, which need small amounts of power and get very little maintenance. Design is simplified because, unlike horizontal-axis turbines, no pointing mechanism is required to allow for shifting wind direction and the turbine is self-starting [1]. Savonius and other vertical-axis machines are not usually connected to electric power grids. They can sometimes have long helical scoops, to give smooth torque.

Savonius Turbine Rotor with Semi Circular Straight Blades

A simple vertical axis Savonius rotor with two straight blades, semi circular in cross-section is shown in figure 1.

[FIGURE 1 OMITTED]

It consists of two straight blades which are semi circular in cross-section attached to a shaft. Two thin discs are welded at the top and bottom surfaces of this whole arrangement for balancing and stability of the turbine blades. The turbine is called a vertical axis type as the whole turbine is arranged vertically and also the axis of the rotor shaft is vertical. Taking into account the comparative character of the analysis, the momentum model predicts in a simple and fairly accurate way VAWT overall performance [2]. The power co-efficient of the turbine of this type of rotor is around 25.62%, which shows that the above configuration is less efficient.

Savonius Rotor with Twisted Blades

The present analysis is on the enhancement of efficiency by modifying the blade configuration from straight semi circular to a twisted semi circular one. The sample models of different twist angles of the blades are shown in figure 2. The twist in this turbine is assumed to be given as--the bottom cross-sectional surface of the blades is fixed and the top cross-sectional surface is given the desired twist with respect to the bottom fixed surface. Wind flow analysis is done over each configuration of the rotor with the blade twist angles ranging from 5[degrees] to 60[degrees] in steps of 5[degrees]. The optimum angle of twist at which the efficiency and the output power is maximum is evaluated.

[FIGURE 2 OMITTED]

Specifications

Rotor specifications

1. Base plate diameter: 112 cm

2. Rotor blade diameter: 54 cm

3. Base plate thickness: 4mm

4. Blade thickness: 2mm

5. Rotor height: 120cm

Mesh specifications

1. Hexahedral fine volume mesh at rotor blades

2. Tetrahedral coarse volume mesh at wind tunnel walls

3. Pyramidal volume mesh for smooth transition from Hexahedral to Tetrahedral mesh

Wind tunnel specifications

1. Test section CS: 130cm x 120.8cm

2. Test section length: 130cm

Flow specifications

1. Velocity of wind: 5 m/s

2. Reynolds number: 2x[10.sup.4]

3. Tip speed ratio = 0.8

[FIGURE 3 OMITTED]

* Boundary specifications

i. Inlet boundary condition for surface in -Z axis direction

ii. Outlet boundary condition for surface in +Z axis direction

iii. Wall boundary conditions for remaining surfaces

* Scale specifications

i. Model scale 1:3

ii. Wind tunnel scale 1:3

Cfd Software Star-Cd

a) Conservation of Mass

b) Conservation of Momentum

c) Conservation of Energy

The equation that results from applying the law of conservation of mass is the continuity equation. Conservation of momentum is based on application of Newton's Second law to a fluid element, which yields a vector equation, which is also called Navier-Stokes Equation. The Conservation of Energy is based on the application of First Law of Thermodynamics to fluid element. STAR-CD is a computer code which simulates fluid flow, heat transfer and related phenomena that occur in engineering applications. This software facilitates predictions of the behavior of the flow. STAR-CD simulations are mathematical deductions from established physical principles. These deductions therefore involve creation of representation of what takes place actually with in the simulated item.

Working out a modeling strategy.

This requires a precise definition of the physical system's geometry, material properties and flow conditions based on the best available understanding of the relevant physics. The necessary tasks include:

* Planning the computational mesh (e.g. number of cells, size and distribution of cell dimensions, etc.).

* Looking up numerical values for appropriate physical parameters (e.g. density, viscosity, specific heat, etc.).

* Choosing the most suitable modeling option from what is available (e.g. turbulence model, combustion option, etc.).

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

[FIGURE 6 OMITTED]

[FIGURE 7 OMITTED]

[FIGURE 8 OMITTED]

The five phases are repeated for all Savonius configurations and for each the parameters are obtained at different angles of attack.

[FIGURE 9 OMITTED]

Mesh Details

No. of fluid cells created : 281561

No. of shells at wall boundaries : 50394

No. of shells at non-wall boundaries : 14802

No. of iterations taken to converge : 115

Sub-Surface thickness : 2

Results and Discussion

From the analysis of flow of wind over various configurations of the rotor blades, it is found that the efficiency is maximum at [theta]=45[degrees] which is obtained as 33.85% when compared to 25.6% without twist, which could be accounted to the increase in the positive wetted part in the side projected area and hence increase in the average projected area. The developed twisted blade configuration of the rotor, in general would have the following performance characteristics:

* Increase in positive wetted area.

* Decrease in negative torque.

* Increase in torque and RPM.

* This design enhances the ability to utilize the power from the wind blowing in any direction as both the frontal and side projected area involves the concave part of the blade and hence insensitive to wind direction.

* This design proves to have a good self-starting ability.

The rotary motion to the rotor is provided due to the impact of the wind flowing with certain velocity over the blades. The concave part of the blade provides positive torque while the convex part provides negative torque. Hence these are the positive wetted and negative wetted areas respectively. Also, the difference in the velocity on both sides of the convex blade adds to the positive torque according to Bernoulli's principle. During a complete rotation, the air crosses the frontal area of the rotor for a part of time and the side area for the rest of the time. In the present analysis, the flow over both the areas is considered and the parameters like velocity, torque, force etc., are determined. The averages of the values obtained for both the projected areas are taken as the net values for further calculations.

For a given twist angle '[theta]',

The Frontal projected area is found to be: [D+D/2(1+cos[theta])] *L.

And the side projected area is found to be: [D+D/2(sin[theta])] *L.

The effective diameter is obtained as: 0.5 * [[D+D/2(1+cos[theta])] + [D+D/2(sin[theta])]].

During the calculation of [A.sub.f], As for the various twist angle configurations of the rotor, we found that as [theta] increases, [A.sub.f], decreases and As increases. At [theta]=45[degrees], the average projected area is found to be maximum. Hence the effective diameter is found to be maximum at the same angle. Both the above mentioned values decrease as the [theta] value increases beyond 45[degrees].

As [theta] increases, the positive wetted area of the side projected area and hence, the torque increases. This continues till [theta]=45[degrees] and beyond this angle of twist, the decrease in the positive wetted area of the front projected area is more than the increase in the positive wetted area of the side projected area. Hence, the high RPM and high Torque are obtained at an angle of twist of 45[degrees]. This design principle can be used in future to increase the efficiency of Savonius wind turbine.

References

[1] Baker J.R. Feature to aid or enable self starting of fixed pitch low solidity vertical axis wind turbines. J of wind Engineering and Aerodynamics, 15(1983)369-380.

[2] Martino Marini, Aristide Massardo and Antonio Satta. Performance of vertical axis wind turbines with different shapes. J of wind Engineering and Aerodynamics, 39(1992)83-93.

[3] Wilson RE, Lissaman PBS. Applied Aerodynamics of wind power machines. Oregon State University, May,1974.

[4] John. J Bertin, Aerodynamics for Engineers.

[5] Benesh, a.h., 1988., "wind turbine system using a vertical axis Savonius rotor, "U.S. patent, patent no.4784568"

[6] John D. Anderson, jr. (1995), Computational fluid dynamics: the basics with applications, McGraw-Hill.

[7] Jianhui Zhang, "Numerical Modeling of Vertical Axis Wind Turbine (VAWT)"

[8] Testuya Kawamura, Tsutomu Hayashi, Kazuko Miyashita. Application of the Domain Decomposition Method to the flow around the Savonius Rotor. 12th Int. conference on Domain Decomposition Methods. 2001

Manzoor Hussain M *, S Nawazish Mehdi **, P. Ram Reddy ***

* Department of Mechanical Engineering, J N T University, Hyderabad. E-mail: [email protected]

** Professor, Mechanical Engineering Department, MJ College of Engineering, Hyderabad.

*** Professor, Mechanical Engineering Department, CMR College of Engineering, Hyderabad.

Table 1 : Results of CFD Analysis at various twist angles

[??]   Af(m2)   (As(m2)    D(m)   N(rpm)   w(rad/s)   Tf(Nm)   Ts(Nm)

0      1.296     0.648    0.810   94.36     9.88      2.5300   1.2640
5      1.295     0.676    0.820   93.21     9.76      2.5380   1.3880
10     1.291     0.704    0.830   92.09     9.64      2.6510   1.4430
15     1.285     0.732    0.840   90.99     9.52      2.7152   1.9092
20     1.276     0.759    0.850   89.92     9.41      2.7201   2.0491
25     1.266     0.785    0.855   89.40     9.36      2.7281   2.1951
30     1.253     0.810    0.860   88.88     9.30      2.8115   2.2925
35     1.237     0.834    0.863   88.57     9.27      2.8407   2.5337
40     1.220     0.856    0.865   88.36     9.25      2.8788   2.7034
45     1.201     0.877    0.866   88.26     9.24      2.9128   2.8208
50     1.180     0.896    0.865   88.36     9.25      2.7891   2.6601
55     1.158     0.913    0.863   88.57     9.27      2.6010   2.5610
60     1.134     0.929    0.860   88.88     9.30      2.5855   2.1799

[??]   Tavg(Nm)    o/p     i/p    [eta]

0      1.8970     18.74   73.20   25.60
5      1.9630     19.16   74.26   25.77
10     2.0470     19.73   75.31   26.19
15     2.3122     22.01   75.99   28.96
20     2.3846     22.44   76.82   29.21
25     2.4621     23.05   77.57   29.72
30     2.5520     23.74   77.72   30.55
35     2.6847     24.89   78.02   31.90
40     2.7911     25.82   78.17   33.03
45     2.8668     26.49   78.25   33.85
50     2.7246     25.20   78.17   32.23
55     2.5800     23.92   78.02   30.65
60     2.3827     22.16   77.65   28.54