Dynamic Modeling and Optimization of a Wind Turbine with Savonius-Type Rotor

A. Zachr* and N. Burny** * College of Dunajvros, Dunajvros, Hungary; Zachar.Andras@gek.szie.hu,

** Subotica Tech, Subotica, Serbia; Burany.Nandor@gmail.com

AbstractA wind turbine with a patented Savonius-type rotor is built and tested under different loading conditions and wind velocities. Numerical investigation was carried out to study the flow around the rotor. The turbine is modeled and simulated in computational fluid dynamics software. Detailed description of the 3D modeling procedure is given. Effects of different meshing approaches are discussed. Measurement and simulation results are given. Strong unsteady effects, including separation and vortex shedding are observed due to the continuous variation of flow angle with respect to blades. Turbine modifications for achieving higher torque and power coefficient are suggested and analyzed.

I. INTRODUCTION Vertical Axis Wind Turbines (VAWT) are ideal options

for small scale generation of electricity from wind. Savonius-type rotor is one of the widely developed and used VAWTs. Earlier most research is focused on theory and experiments. In the last two decades, thanks to the development of computational fluid dynamics software, the focus is moving to simulations. Computer models provide the user with the privilege to change inputs and see the outcome instantly, without fabricating a prototype. However, computer models are only approximations of the experiments and are limited in modeling the actual physics. Special care is necessary to verify the credibility of simulation results.

There are many patent documents describing wind turbines applicable in turbulent winds. Mainly these turbines are some derivatives of the Savonius rotor [2] or the Darrieus rotor [3]. Unfortunately the patent files usually do not report about the torque and power coefficients of these constructions or the reports are not based on thorough measurements and calculations. Sometimes it is purely believed that the preferred embodiment of the patent gives optimum results.

The authors built a real size prototype of the patented construction [2] and tested it for different wind speeds which occurred in the period of the investigation Wind tunnel for the real size turbine was not available. Measured torque and power values were well below the expectations based on the patent file.

This discrepancy turned the authors to further investigations by use of software tools. The aim is to evaluate different turbine shapes by use of computational fluid dynamic (CFD) modeling and analysis. Analytical modeling of turbines is difficult even in 2D cases so it is not preferred.

Figure 1. Cross sectional drawing of the patented Savonius-type wind turbine [1].

II. MODEL OVERVIEW The turbine construction reported in US patent

5,494,407 [1] by Benesh is modeled and analyzed through this research, first in its original form and later with a changed blade overlap. The horizontal cross sectional drawing of the turbine is shown in Fig. 1. It is stated by the patent holder that the turbine will generate maximum power for some special ratios of the diameter to other dimensions of the rotor, given in the patent document.

The construction built by the authors shown in Figure 2 includes two turbines on the same axis, rotated relative to one another for 90o, to achieve less pulsation of torque and acceptable starting torque [4,5]. The blade height for both turbines is the same, 0.9 m, the diameter is D1=1.3 m, so the effective vertical cross section area of the turbine is A=2.34 m2.

The total theoretical power possessed by the wind [4] with velocity v on cross section A is given by formula:

where: =1.29 kg/m3 is the air density. For the given size of the wind turbine and for wind

velocity v=10 m/s, the total wind power is PW=1510 W. Power coefficient value of CP=0.37 is reported in the

patent document. Accepting this value, the power extractable from the turbine for the same wind speed, neglecting bearing losses is:

Measurements done on the turbine have shown almost ten times lower output power for the given wind speed. To find the reasons for this disagreement, CFD analysis of the turbine is done. Commercially available CFD analysis software is used to evaluate the dynamic torque on the turbine for different wind speed and angular speed of the rotor.

Static CFD analysis of the same turbine is done earlier and reported in [6]. Using a dynamic analysis, the torque and power coefficients of the turbine and the speed-torque characteristic can be evaluated. These results are reported in this paper.

Figure 2. The wind turbine built by the authors.

III. MATHEMATICAL FORMULATION

A. Conservation equations The usual Reynolds-type averaged time dependent

Navier Stokes equations have been used to model the impulse transport of the flowing air around the Savonius rotor. The Boussinesq hypothesis is assumed to link the Reynolds stresses to the mean rate of fluid deformation. U1, U2, U3, P, k and as functions of x, y, z, t describes the flow field and the intensity of the turbulence around the studied Savonius rotor. The conservation equations are formulated in the Cartesian coordinate system because the applied flow solver (Ansys CFX 12.0) uses the Cartesian system to formulate the conservation equations for all (vector Ui and scalar P, k, ) quantities. Description of the entire geometry of the studied problem is incorporated into the generated unstructured numerical grid.

The shear stress transport (SST) turbulence model has been used to model the turbulent effects of the developed

flow field around the Savonius rotor. The SST model is based on the k- and the k- turbulence models where the near wall regions have been calculated by the k- and the fully turbulent regions calculated by the k- model. The appropriate blending functions have been used in the transitional region, between the two models.

For coupling the stator and the rotor domain of the studied flow geometry the Transient Rotor model has been applied. This model makes it possible to study the time evolution of the different flow parameters of the Savonius rotor.

B. Domain of discretization Fig. 3 indicates the generated grid for the rotor

domain on the surface of the studied Savonius rotor.

Figure 3. Details of the generated grid

C. Initial and boundary conditions The initial velocity field is zero everywhere inside the

calculation domain. Constant air velocity is assumed at the inlet position of the stator domain. The gradient of the velocity profile and the gradient of the turbulent quantities are assumed to be zero at the end of the outlet.

D. Numerical solution of the transport equations The corresponding transport equations with the

appropriate boundary conditions have been solved a commercially available CFD code (Ansys CFX 12.0). A "High Resolution Up-Wind like" scheme is used for discretizing the convection term in the transport equations. The resulting large linear set of equations is solved with an algebraic multi-grid solver. The applied grids for the different geometries have been generated with the WorkBench grid generator.

IV. MODEL GEOMETRY The 3D model of the turbine is constructed in the CFX

module of the Ansys software. The actual 3D geometry is shown in Fig. 4. The original mechanical drawings are prepared in AutoCAD software and imported to a 3D geometric modeling program to convert the DWG file to IGES type and after this the file has been imported into the Ansys WorkBench as an IGES file. Only one stage of the turbine is modeled and its height and diameter are both adjusted to 1 m. It is different from the prototype size to facilitate scaling of the calculation results.

Figure 4. Geometrical model of the Savonius-type wind turbine

V. ANALYSIS RESULTS First, the turbine is analyzed qualitatively: the flow field

is demonstrated, based on CFD analysis. Second, the analysis results are used to achieve quantitative characterization of the turbine.

A. Dynamic flow field description The dynamic flow field is analyzed for fixed wind

velocity of 10 m/s and fixed angular speed of the rotor of 4 rad/s. Fig. 5 has been created by the CFD software postprocessor that represents the local air speed with arrows. Arrow direction shows the local air movement direction, different colors stands for different speed intensity.

Figure 5. The dynamic flow field for two different angular positions

The flow field is far to be laminar. Forming of vortices on the inlet and the outlet side is evident. The flow is even not periodic; this leads to non periodic variation of the torque and the power during multiple revolutions of the rotor.

B. Calculated performances of the turbine Power and torque of the turbine is evaluated from the

CFD analysis for different wind speeds and angular speeds. Better performances are obtained for the coarse mesh applied first. The number of finite elements in this case was 800533.

Applying finer mesh in the second series of analyses the performances are deteriorated but they are more acceptable due to the finer representation of the air flow. The number of finite elements in this case was 3684975. The torque dependences on angular position for wind speed 10 m/s and angular speed 2 rad/s, for both meshes, are given in Fig. 6.

-40-35-30-25-20-15-10-505

10

0.31 1.57 2.83 4.08 5.34 6.60 7.85 9.11 10.37 11.62

Torque

[Nm]

Angel around the vertical (rotational axis) [rad]

Coarse Finer

Figure 6. Dependence of the turbine torque on angular position of the rotor for both meshes

The dependence of the output power on the rotors angular position for the same wind speed and the same angular speed of the turbine is given in Fig. 7.

-50

0

50

100

150

200

250

0.31 1.57 2.83 4.08 5.34 6.60 7.85 9.11 10.37 11.62

Power

[W]

Angel around vertical (rotational axis) [rad]

Coarse Finer

Figure 7. Dependence of the output power on angular position of the rotor for both meshes

The torque and the power are calculated and averaged for two revolutions. More revolutions are not analyzed as the simulation process is very time consuming.

Averaging the torque for the coarse mesh 16.1 Nm is obtained, but it is lowered to 8.5 Nm for the finer mesh.

The turbine average output power for the coarse mesh is 101 W but only 53.5 W is obtained for the finer mesh. This large deviation in torque and power is supposed to be caused by the fact that the coarse mesh is not applicable for the analysis of the real air flow.

The torque diagram and the power diagram for the coarse mesh is almost periodic, repeated for every 180o. In contrast, the finer mesh gives large deviations from periodicity.

This is the more realistic result as vortices cause aperiodic tilting in the air flow. Flow is always unsteady, separation and vortex shedding is happening.

Even more authentic values could be obtained with further refinement of the mesh and through analysis for more turns of the rotor but with the available computer resources this was the maximum.

The turbine torque and power depends on its angular speed. CFD analyses for five angular speed values in the range from rad/s to 4 rad/s are accomplished (Fig. 8). The maximum power point is obtained for about 3 rad/s, for both meshes. This is a somewhat lower value compared to values for other turbine geometries reported in the literature [7].

For the coarse mesh, in the maximum power point, the power coefficient of the turbine is Cp=23%, but the more realistic value is the one obtained for the finer mesh, equal to 12%.

0

20

40

60

80

100

120

140

160

2 4 6 8 10 12 14

Power [W]

Angular speed [1/rad]

Coarse Finer

Figure 8. Dependence of the output power on angular speed of the rotor for both meshes

VI. DISCUSSION Doing analyses for a coarser and a finer mesh have

shown that the application of finer mesh is essential for wind turbine analysis with turbulent air flow. CFD analysis with turbulence modeling by means of detached eddy simulation is necessary for representation of the actual physics.

Calculation of the torque for a model with smaller overlap of the blades has shown that shortening the overlap of the straight ends of the blades increase the torque. Further analyses are necessary to find the optimum overlap.

ACKNOWLEDGMENT The authors wish to express their thanks for Mr.

Gellrt Burny for his help preparing the technical drawings necessary for CFD analysis.

REFERENCES [1] A. H. Benesh, Wind Turbine with Savonius-type Rotor, US

Patent Number 5,494,407, Feb. 27, 1996. [2] S. J. Savonius, Rotor, sterreichisches Patentschrift Nr. 103819,

July 10, 1925. [3] G.J.M. Darrieus, Turbine having its rotating shaft transverse to

the flow of the current, US Patent Number 1,835,018, Oct. 1, 1926.

[4] T. Hayashi, Y. Li, Y. Hara, Wind tunnel tests on a different phase three-stage Savonius rotor, JSME International Journal 48 (1), 916.

[5] T. Hayashi, Y. Li, Y. Hara, K. Suzuki, Wind tunnel tests on a three-stage out-phase Savonius rotor, Tottori University, Tottori, 2011.

[6] N. Burny, A. Zachr, Evaluation of a wind turbine with Savonius-type rotor, EXPRES 2012 Conf. Rec., Subotica, March 2012.

[7] S. Kolachana, A computational framework for the design and analysis of Savonius wind turbine, Master thesis, Indian Institute of Technology, Madras, 2012.