CFD modelling investigation of a straight-blade vertical axis wind turbine

Khaled M Almohammadi a, D B Ingham b, L Ma c, M Pourkashanian d

aUniversity of Leeds, Leeds, West Yorkshire, United Kingdom, doctorkms@hotmail.com bUniversity of Leeds, Leeds, West Yorkshire, United Kingdom, d.b.ingham@leeds.ac.uk

cUniversity of Leeds, Leeds, West Yorkshire, United Kingdom, L.Ma@leeds.ac.uk dUniversity of Leeds, Leeds, West Yorkshire, United Kingdom, fue6mtz@leeds.ac.uk

1 INTRODUCTION

In the new economic climate around the globe, the demand for the efficient use of energy resources, such as wind energy, has become a significant issue. Wind energy has become one of the most promising and reliable sources of energy. The development of modern Vertical Axis Wind Turbine (VAWT) designs (Darrieus Type) has become a field of much competition between companies in order for wind turbines to be used in urban re-gions. This is because of the rapidly increasing consumption of energy and fossil fuel re-sources are being depleted. Therefore, it is essential to develop a turbine that is relatively small, quiet and efficient. Also, the esthetical appearance, operation safety and mainte-nance cost are things to be considered (Van Bussel et al., 2004). The original form of the Darrieus turbine was invented by the French engineer Georges Jeans Darrieus and patented in 1931 (Paraschivoiu, 2002). The blades were originally curved and of troposkein shape (eggbeater shape), which is the shape generated by rotat-ing a rope around a vertical axis. This configuration reduces the bending moments ex-erted on the blades due to centripetal acceleration. Therefore, tensile stresses are the only forces experienced by the blades and there would be no tip losses. It has been shown that the main drawback of this type of blade is its poor performance at low tip speed ratios (Kirke et al., 1998). The simple design of the straight blade VAWT has attracted designers to effectively re-duce the manufacturing cost. Paraschiviou and Delclaux (Paraschivoiu, 2002) concluded that the straight blade shape has more aerodynamic performance compared to the egg-beater or curved type shaped blades. One drawback of this type of blade is that they re-quire strong radial arms which exert bending stresses. As a result, the turbine may experi-ence resonance and this may end with fatigue failure due to severe vibrations (Islam et al., 2008). This type of turbine should be designed and modelled carefully in order to re-duce the noise and the vibrations that they usually produce. Many attempts have been carried out in the past few years to build a general understand-ing of the straight blade vertical axis wind turbine aerodynamics. For this purpose many models have been developed. These models may be classified into four main categories: momentum, vortex, cascade and computational fluid dynamic based modelling. The computational fluid dynamics modelling has become more favourable due to the model-ling aerodynamical complexity involved in the other modelling approaches. This ap-proach has become more feasible in the last few years as the computational power has been significantly improved by the development of high performance computers. How-ever, there has not been enough investigations on computational fluid dynamics simula-tions in the application of straight blade vertical axis wind turbines in the literature. This

paper focuses on the computational fluid dynamics modelling aspects and their effects on the prediction accuracy of vertical axis wind turbines performance.

1.1 Small wind turbines Over the last decade, the interest in small wind turbines has significantly increased in both turbine types, namely HAWT and VAWT. This is due to its flexibility in usage in utilizing power. It could be used as a stand-alone system, part of a grid system, mounted on top of a building, or simply anywhere one would like (Bwea, 2006). It is necessary to clarify exactly what is meant by small wind turbines. There is no international agreement about the scale for which the turbine is considered to be a small wind turbine. However, the UK standard for classifying small wind turbines, table 1, appears to be reasonable (Renewableuk, 2010). The turbine investigated in this paper is a micro wind turbine which makes its modelling more aerodynamically complex.

Table 1. UK standard for small wind turbines.

Small Wind Systems Power (KW)

Annual Energy Production

(KWh)

Total Turbine Height

(m)

Total Installed Cost (£k)

Micro Wind 0 - 1.5 Up to 1000 10 - 18 0.5 - 5 Small Wind 1.5 - 15 Up to 50000 12 - 25 2 - 50

Small-Medium Wind 15 - 100 Up to 200000 15 - 50 50 - 250

1.2 Wind turbine modelling The straight blade vertical axis wind turbines usually operate in the turbulent flow regime and it is very difficult to trace a fluid particle in a turbulent flow. When transport quanti-ties in the Navier-Stoke equations, namely mass, momentum, and energy, exhibit irregu-larities and periodic fluctuations in space and time, then the flow experiences turbulence phenomena. Most engineering problems, including wind turbines, develop turbulence. This has motivated engineers and scientists up to this day to analysis and understand tur-bulence. Unfortunately, there is no universal reliable approach to solving flows that ex-perience turbulence. However, there are many turbulence models available that may be used and the choice of the turbulence model depends on many factors, such as the accuracy required, the physics of the problem, and the computational power available. The straight blade vertical axis wind turbine investigated in this study operates in a rela-tively low Reynolds number regime, of the order of 10 , and the tendency of separation is high. As a result, the analysis of the forces around the airfoils requires a detailed con-sideration, especially near the airfoils and up to the wall surface. Also, the effect of the molecular viscosity in the eddies must be included in the selected model. Therefore, modelling vertical axis wind turbines includes mainly the following challenges:

High adverse pressure gradients. Presence of flow recirculations. Separation instability (statistically varying).

There is a lack of literature to explain the most appropriate approach on how to model straight blade vertical axis wind turbines using computational fluid dynamics. In this pa-per, analysis of different modelling techniques (by changing one factor and keeping all

the other factors the same) is discussed in detail in both the meshing and simulation phases in order to investigate their effects on the overall prediction accuracy.

2 CFD VALIDATION OF A WIND TUNNEL EXPERIMENT For the purpose of validating the computational fluid dynamics approach, the simulations presented in this paper are based on the experimental work proposed in the paper titled “Performance Testing of a Small Vertical-Axis Wind Turbine” (Bravo et al., 2007). Fig-ure 1 shows the SB-VAWT and the power curve for various wind speeds produced by Bravo et al. (2007). ANSYS FLUENT is the control volume based software used to per-form the numerical computations.

2.1 Turbine configuration and flow conditions The turbine consists of three straight NACA0015 airfoils with a chord length of 0.4m and span length 3m. The turbine diameter is 2.5m and it is installed in a 9m by 9m wind tun-nel. The maximum power produced experimentally is 0.3 which is obtained at a wind speed 10 m/s, where all the simulations in this paper are performed. Since the simulations are a 2-D cross section of the turbine, the struts (arms) were not in-cluded. Therefore, the power loss caused by them is not included. Also, the losses caused by the 3-D effects are not considered and they are assumed to be small due to operating at a low tip speed ratio, i.e. ratio of less than 2. As a result, the power coefficient produced is expected to have a value higher than that obtained experimentally.

2.2 SST transition turbulence model It has been found in the literature that the SST-transition model, which was originally de-veloped from the SST 푘-휔 model, is capable of predicting flows with severe separations to an acceptable accuracy (Menter et al., 2006). In this model, two transport equations are coupled with the SST 푘-휔 model. One of the equations that accounts for the intermit-tency and the other one accounts for the transition onset is based on the principle of mo-mentum thickness and this makes it a 4-equations model, i.e.

( ) + ( ) = 퐺 − 푌 + 푆 + (1)

Figure 1. The SB-VAWT and the power curve for various wins speeds produced by Bravo et al. (2007).

( ) + ( ) = 퐺 − 푌 + 퐷 + 푆 + (2)

( ) + ( ) = 푃 − 퐸 + 푃 − 퐸 + 휇 + (3)

( ) + ( ) = 푃 + 휎 (휇 + 휇 ) (4)

where 퐺 , 푌 , 푆 , 퐺 , 푌 , 퐷 , 푆 , 푃 , 퐸 , 푃 , 퐸 and 푃 are the source terms, and 푘, 휔, 훾 and 푅푒 are the transport quantities. Further details of the model may be found in Langtry et al., 2006, and Menter et al., 2006.(Langtry et al., 2006, Menter et al., 2006).

The SST transition turbulence model has been applied in all the computations presented in this paper at a tip speed ratio (TSR) of 1.75, for the purpose of illustrating the results obtained.

2.3 Mesh generation The mesh generation phase is extremely important because, if we are to rely on the pre-dicted results, we must do this well. The domain should be carefully meshed by consider-ing the factors explained in the next subsections. Structured quadrilateral cells on the air-foil surface is used in order to resolve the boundary layer (Tu et al., 2008). In the domain, unstructured quadrilateral and triangular cells are generated with the recommended qual-ity constrains. Gambit is the software used in generating all the meshes employed in this paper.

2.3.1 Domain cell type In 2-D simulations, there are mainly two cell types that could be generated in order to

apply control volume methods, namely quadrilateral and triangular cells as shown in fig-ures 2 and 3, respectively. It is crucial to understand their advantages and disadvantages in describing the fluid flow characteristics.

The quadrilateral cells are known to be stable in simulations but they are more difficult to be generated in contrast to triangular cells where they are less stable but easier to generate (Tu et al., 2008).

Figure 2. Quadrilateral based mesh. Figure 3. Triangular based mesh.

-50

0

50

100

150

0 60 120 180 240 300 360To

rque

(N.m

)

Azimuth angle (degree)

Torque Profile for different cell types

Quadrilateral

Triangular

The power coefficient obtained from the quadrilateral based mesh is 0.371, whereas it is 0.351 for the triangular mesh and it is about 0.275 in the experimental results (Bravo et al., 2007). It can be clearly seen from figure 4 that the differences in the torque profiles is not significant, even though the power coefficient prediction differ by about 5%. These differences may be caused by numerical diffusion, namely false diffusion, generated dur-ing the computations. It is known that numerical diffusion is related to the cell shape. Quadrilateral cells produce lower numerical diffusion than triangular cells (Versteeg and Malalasekera, 2007). Higher discretization schemes should be investigated in order to re-duce the numerical diffusion, which is clearly significant.

2.3.2 Aspect ratio on the airfoil surface The measure of the cell stretch is known as the cell aspect ratio. It is important to

evaluate how this will affect the simulation stability and accuracy in modelling vertical axis wind turbines as it is imposed on a complex flow situation.

Table 2. Power coefficients at different aspect ratio airfoil surfaces.

Aspect ratio on airfoil surface

Predicted Power Coefficients

Quadrilateral cells Triangular cells

2.5 5

0.371 0.276

0.351 0.283

10 30

0.267 0.218

0.310 0.263

It has been found that when using a large aspect ratio (by increasing the number of com-putational points on the airfoil surface) causes a poor prediction since the power coeffi-cient should be higher than the experimental value 0.275. As shown in table 2, the power coefficients differ by about 35-50% and this means this factor is significant when consid-ering modelling vertical axis wind turbines. It can be seen that the results produced using the quadrilateral cells changes consistently on increasing the aspect ratio on the airfoil surface. This is not similar to the triangular cells domain where the power coefficient predicted fluctuates.

2.3.3 Domain mesh size Increasing the domain cell size may significantly reduce the overall number of cells

and, as a result, save simulation time and resources. Also, it decreases the false diffusion,

Figure 4. Torque profile for quadrilateral and triangular based meshes at TSR 1.75.

which is generated numerically, and this has an adverse effect on the accuracy and the stability of the results obtained. However, this has been investigated in this paper in order to assess its impact on the performance predictions and solver stability.

Table 3. Power coefficient for different domain mesh sizes.

Mesh domain size Predicted Power Coefficients

Quadrilateral cells

Triangular Cells

150,000 0.276 0.310 250,000 0.292 0.305 350,000 0.287 0.257

Table 3 shows that the quadrilateral meshes based domain results are reasonably close to each other and appear not to be affected by the change in the domain mesh size. The re-sults obtained are in good agreement with the experiment data. On the other hand, the tri-angular based meshes show significant instability when using a coarse mesh and the pre-diction is close to the quadrilateral meshes. However, the triangular fine mesh simulation is stable and also the results obtained using this mesh are poor compared to the experi-ment data. The results obtained are lower than the experimental data, where it is expected to be higher due to the losses due to the 3D effects and the strut losses which are not in-cluded. It is possible that increasing the number of the triangular cells could have ampli-fied the numerical diffusion and caused the poor prediction. 2.4 Time steps / Courant number The time steps / Courant number relates the transient time step to the characteristic time of the control volume. In this study, it has been observed that when the Courant number is larger than about 40 then this leads to poor, inaccurate predictions of the turbine per-formance and may severely influence the solution stability. Table 4 shows that when the Courant number is high, the predicted value is lower than the experimental data.

Table 4. Power coefficient at different time steps.

Time Steps (Courant number)

Predicted Power Coefficients

Quadrilateral cells

Triangular cells

500 (≈ ퟏퟓퟎ) 0.256 0.228 1000 (≈ ퟗퟎ) 0.256 0.229

5000 (≈ ퟐퟎ) 0.276 0.310

Figure 5 shows that the torque profiles for the quadrilateral based mesh are reasonably similar, even thought the value of the power predicted at low Courant number differs by about 8%. On the other hand, the triangular based mesh shows a clear difference in the torque profiles, as shown in figure 6. It is clear that in both cases researchers may have concluded that time steps of 500 could be sufficient since the power predicted is almost identical to that for 1000 steps. However, in this example it is clear that if the Courant number is not small (<40) then the time step independency analysis is questionable.

-50

0

50

100

150

0 90 180 270 360

Torq

ue (N

.m)

Azimuth angle (degree)

Torque profile at different time steps for quadrilateral mesh

5000 steps

1000 steps

500 steps

-50

0

50

100

150

0 90 180 270 360

Torq

ue (N

.m)

Azimuth angle (degree)

Torque profile at different time steps for triangular mesh

5000 steps1000 steps500 steps

2.5 Turbulent length scale and turbulence flow intensity The turbulent length scale is a scale used to measure the size of the energy contained in the eddies of turbulent flows, whereas the turbulence intensity is used to measure the level of the turbulence in the flow.

Table 5. Power coefficient at different

intensity levels.

Intensity (%)

Predicted Power Coefficients

Quadrilateral cells

Triangular cells

0.5 0.276 0.310 1 0.301 0.327 10 0.390 0.388

Estimating the length scale value on the boundaries at the beginning of the computations showed no significant difference in the power coefficient predicted, seen table 6. How-ever, the estimation of the intensity value, as shown in table 5, appears to be significant and shows about 25-40 % difference in the predicted results. The intensity value of the fluid flow in this experiment is not provided in the published paper (Bravo et al., 2007). However, the intensity is expected to have a low value since it is a wind tunnel experi-ment and the results obtained at low intensity value are in a good agreement with the ex-perimental data.

3 CONCLUSIONS

The aim of this paper was to investigate some modelling aspects of computational fluid dynamics, in particular mesh generation and simulation. Two cell types have been stud-ied, namely quadrilateral and triangular shapes. It has been found that the cell shape is re-sponsible of about 5% difference in the power predicted. However, the error could be more due to the false diffusion, which is more enhanced when using the quadrilateral cells. The numerical diffusion is significantly harmful to the solution accuracy and the stability of the solver in modelling straight blade vertical axis wind turbines. This prob-lem could be reduced by increasing the domain mesh size and applying higher discretiza-tion schemes.

Length Scale (m)

Predicted Power Coefficients

Quadrilateral cells

Triangular cells

0.028 0.273 0.316 0.048 0.276 0.310

1 0.272 0.309

Figure 5. Torqueprofile at different time steps for quadrilateral cells.

Figure 6. Torque profile at different time steps for triangular cells.

Table 6. Power coefficient at different length scales.

Also, we have found that the aspect ratio on the airfoil surface is a significant factor in modelling vertical axis wind turbines. It is crucial to analyse how many computational points are required on the surface of the airfoil in order to obtain good grid independent solution. The results obtained using different domain mesh sizes of quadrilateral based meshes are similar. However, the triangular based mesh results are found not to be similar. Also, It is has been found that the estimation of the intensity level could significantly affect the re-sults obtained. However, the turbine power coefficient value obtained is almost the same for different length scale values. Understanding the advantages and the limitations of the parameters investigated on the computations will be a key factor to researchers, designers, and manufacturers who use CFD as a design tool to obtain reliable predictions of VAWT.

The future work is to study these factors at higher tip speed ratios, where the 3D effect is more significant, in order to compare the results obtained for each factor.

4 ACKNOWLEDGEMENTS

Khaled M. Almohammadi would like to express his gratitude to Taibah University, Kingdom of Saudi Arabia for supporting him to perform his PhD study.

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