OpenFOAM capabilities for the analysis of Vertical-Axis Wind Turbine aerodynamics

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1 OpenFOAM capabilities for the analysis of Vertical-Axis Wind Turbine aerodynamics Diego Domínguez 1, a), Daniel Fernández 1, Tim De Troyer 2, Mark C. Runacres 2 1 Aerospace Engineering Area, Universidad de León, Campus de Vegazana s/n, León, Spain 2 Thermo and Fluid Dynamics (FLOW), Faculty of Engineering, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussel, Belgium a) Corresponding author: diego.dominguez@unileon.es ABSTRACT Modelling and understanding VAWTs aerodynamics is quite complex. In the present work, 2D numerical analysis is performed in order to compare not only capabilities of RANS and LES methods implemented within OpenFOAM, but also to define the basic set-up of the solver parameters. Simulations have been addressed using the Arbitrary Mesh Interface (AMI) technique in order to provide movement to the mesh. The following turbulence models have been used: a k-ω SST for RANS and a k-ω SST Scale Adaptive Simulation (SAS) model for the LES. Under these conditions, different mesh refinements have been tested. Also, the importance of defining a time-step that limits maximum Courant number to 1 when using the PIMPLE algorithm has been stablished. For 2D simulations, the proposed LES method shows better capabilities than RANS for the CFD simulation of VAWTs. 1 INTRODUCTION The interest in Darrieus Vertical-Axis Wind Turbines (VAWTs) is growing due to some advantages that can make them an alternative for electricity generation in scenarios where Horizontal-Axis Wind Turbines (HAWTs) are less efficient [1]. Modelling and understanding VAWTs aerodynamics is quite complex. Research has been done applying a variety of techniques. With respect to turbulence models, Reynolds-Averaged Navier-Stokes (RANS) is the most widely used in both 2D [2] [3] and 3D simulations [4], due to its lower computational cost compared to Large Eddy Simulation (LES). In fact, the latter method has not been combined yet with a 3D simulation. Moreover, 2.5D simulations are an intermediate solution between 2D and 3D with a promising accuracy-time ratio [5]. The two-dimensional analysis is chosen here in order to compare not only capabilities of RANS and LES methods implemented within OpenFOAM, but also to define the basic set-up of the solver parameters. It is important to point out that there is hardly any reference to previous work on the analysis of 2D LES model capabilities. This makes sense, as turbulence is inherently a 3D phenomenon and using LES for two-dimensional flows is generally not recommended. 2 TURBINE CHARACTERISTICS AND EXPERIMENTAL DATA In order to study the suitability of the OpenFOAM solvers for the simulation of Vertical Axis Wind Turbines a test case must be defined. This work will make use of available experimental

2 data from the HyBlade Turbine [6]. The HyBlade project was conceived with the aim of reducing manufacturing costs by replacing fiber-reinforced materials by metals, keeping a good performance. The result of that project was a turbine whose characteristics are described in Table 1. Field test was performed at the Greenbridge Incubator & Science Park in Ostend (Belgium) under different wind conditions and with different electric resistances over which electrical power was measured. The results, once measurements were properly corrected, are presented in Figure 5. Table 1. Dimensions and characteristics of the HyBlade turbine D [m] 2 H [m] 2.8 N [-] 3 Blade Shape Straight c [cm] 37 Spoke-blade connection 0.5 c Blades airfoil NACA0018 AR [-] σ [-] NUMERICAL MODEL CONFIGURATION Although the two-dimensional simulations have limitations to reproduce the power coefficient (Cp) curve of the turbine, they were carried out in order to understand OpenFOAM s sensitivity to different configuration parameters. 3.1 Domain and mesh definition As the turbine is rotating the computational domain will not be static. In order to enable such a rotating movement it will be divided in two different subdomains: - An internal circular region where the turbine will be located. The mesh of this region will rotate at the prescribed angular velocity for each Tip Speed Ratio (TSR). - A rectangular static region that defines the domain size in the horizontal plane. L 1 L2 inlet D H outlet L = 120 L 1 = 40 L 2 = 80 H = 80 D = 3 L Figure 1. Computational domain (the figure is not to scale) Table 2. Dimensions of the computational domain (all units in m).

3 It is important to properly define the different dimensions of the computational domain, avoiding any blocking effect that would distort the results. A very interesting literature survey about this issue (and others) can be found in [3]. In accordance with the guidelines given in the literature, the domain for our case has been defined as stated in Figure 1 and Table 2. The meshing was done with the blockmesh and snappyhexmesh utilities included in OpenFOAM. The outer domain presents the coarser mesh; two refinement boxes are then defined surrounding the rotating region (Figure 2). This region, as well as its interface with the non-rotating one, has two additional refinement levels. Finally, higher refinement has also been defined close to the turbine profiles, including the necessary boundary layer. The 2D mesh was generated by extruding the three-dimensional one generated by the snappyhexmesh. Figure 2. Three different views of the generated mesh after extrusion An Arbitrary Mesh Interface (AMI) has been defined at the interface between the rotating and non-rotating regions. Mesh movement is defined in the dynamicmeshdict, where the option solid body motion and the function rotating motion are selected. Three different meshes were defined (Table 3), with an increasing refinement level, in order to analyze numerical convergence. Table 3. Characteristics of the different meshes used in the simulation Reference frame Number of elements (N E ) Rotating Stationary domain domain (N ER ) (N ES ) Number of nodes on the airfoil (N N ) Number of quads rows (N BL ) Grow factor Element sizing [mm] Sliding y p interface Mesh Mesh Mesh

4 3.2 Numerical model configuration Based on simulation characteristics the most suitable solver shall be selected and numerical model configuration shall be also defined. The aerodynamic speed of the blade is low, reaching a maximum value of 28 m/s for the case of highest tip speed ratio. That means Mach number is very low and fluid motion can be considered as incompressible. A pressure-based solver is then a suitable option. The selected solver is pimpledymfoam. It makes use of the PIMPLE algorithm and also enables mesh motion. Spatial discretization schemes for all the variables were second order. Temporal discretization is also a critical issue for this kind of simulations. Making use of a fixed time-step is the most common approach when an AMI has been defined within the domain because it facilitates the coupling process between the dynamic and static regions. However, it is not so easy to define the right value for the time-step. Usually, it is defined based on the rotational angle that the blade advances for the specified time-step. In the literature, it is possible to find rotational values between 1 15 and 2 [3] [7]. Nevertheless, the work of Trivellato and Castelli [8] has already pointed that the angular marching step has a notable influence in the results, particularly at low tip speed ratios, when its value is larger than 1 15 and close to 1. Another important parameter is the Courant number. When using the PIMPLE algorithm it should be possible to employ a Courant number higher than 1, although it is unclear what the effect is on the results. In the literature it is possible to find simulations where local Courant number, in the smaller cells, is as high as 50 [3] [7]. As stated above, time-step definition is a non-closed issue and its influence in the simulation will be further analyzed in this work. 3.3 Turbulence models One-equation models do not exhibit a good performance when used in fully detached flows, which is why they are less used than two-equation models for the aerodynamic analysis of VAWT s. There is no clear agreement about the most suitable model. Different versions of the k- ε turbulence model have been widely used (e.g. [8] [9] [10]) although k-ω SST is gaining an increasing popularity [3] [11] [12]. The following turbulence models have been used in the present work: a k-ω SST for RANS and a k-ω SST Scale Adaptive Simulation (SAS) model for the LES. SAS models can dynamically adjust to resolved structures in a transient simulation, which results in a LES-like behaviour in unsteady regions of the flowfield. At the same time, the model provides standard RANS capabilities in stable flow regions [13]. The use of wall functions has required an average y + value close to for optimal results. 4 RESULTS AND DISCUSSION Wind velocity for all the simulations in this work has been fixed at 8 m/s. Different values of tip speed ratios have been achieved modifying the rotational velocity of the turbine between 38.2 rpm (TTTTTT = 0.5) and 191 rpm (TTTTTT = 2.5). 4.1 Mesh sensitivity Some simulations are performed in order to test the influence of mesh refinement on the achieved results. Simulating the full range of TSR for each mesh would require an unreasonable

5 computational power. Therefore, the three meshes are tested for two different tip speed ratios and the results can be seen in Figure 3. When the number of elements in the mesh is increased, the Cp value rises and asymptotically approaches a certain value. Third mesh still gives a value higher than the second one at the cost of a notably larger number of cells. Slightly higher values could be potentially achieved by further increasing the number of cells; however, the slope of the graph indicates that this would require a mesh 3 or 4 times larger. Therefore, it was decided that third mesh meets the requirements sufficiently well, providing a reasonably good accuracy at moderate computational cost. Figure 3. Sensitivity analysis: Cp as a function of the number of cells in the rotating domain 4.2 Influence of temporal discretization As was previously pointed out, temporal discretization has been revealed as a critical issue. Three different configurations have been tested for the same tip speed ratio: - Fixed time-step, tt = s, maximum Courant number close to 3. - Fixed time-step, tt = s, maximum Courant number close to 1. - Variable time-step, a maximum value of 1 is given for the Courant number (C max ), tt is dynamically calculated to meet such requirement. Table 4. Analysis of the effect of time discretization in the accuracy of the results Case Cp Difference [%] Experimental tt = 1ee 4 ss tt = 5ee 5 ss C max The results of such simulations can be seen in Table 4. When the maximum Courant number goes significantly above 1, the calculated Cp dramatically changes. This reveals that the solver presents a very important sensibility to time discretization. It is important to note that only a very small number of cells present a Courant number higher than 1, the average value of the overall mesh is notably smaller than 1. Finally, the use of the variable time-step option gives worse results than tt = s but better than high Courant numbers, confirming the hypothesis that was already presented in previous sections.

6 4.3 Power coefficient curves for RANS and LES models The power coefficient is a key performance indicator not only for the wind turbine design, but the accuracy of the numerical simulation. TTTTTT = 1 TTTTTT = 1.5 TTTTTT = 2 Figure 4. Comparison between RANS and LES instantaneous power coefficients; Cp vs. azimuthal position (in degrees) of one blade during the last revolution An easy way to understand how the wind turbine works is by means of the instantaneous Cp value calculated during a single revolution by each turbulence model (Figure 4). Every plot shows three regions of high Cp value produced by each of the three blades when they travel through the region where angle of attack presents moderate values and the flow is not detached. At low TSR values (e.g. TTTTTT = 1), wind turbine produces a lower torque value which is even negative during part of the revolution, although average value is clearly positive. That explains common difficulties faced by VAWT during starting. At high TSR values (e.g. TTTTTT = 2), maximum Cp values have already diminished because angle of attack is now too small and the blade profile is operating at smaller values of C l. Figure 5. Comparison between experimental and numerical results: power coefficient vs. TSR Differences in the way RANS and LES models resolve turbulence in the flow produce changes between the results of both of them. This is clear at low tip speed ratios, when the angle of attack seen by the blades reaches very high values, the flow is totally detached most of the time and turbulent patterns in the flow are of paramount importance. When the rotational velocity increases, the variation in the angle of attack diminishes and turbulence modelling is not so critical. In such conditions, both turbulence models present a more similar behavior as can be

7 seen in both Figure 4 and Figure 5. It is also important to notice that maximum Cp is achieved at a higher value of TSR (1.75 instead of 1.5). Differences in the Cp value can be related to the differences in flow structures. Figure 6 shows how vorticity in the wake is stronger for the LES model as well as the difference between both models in the detached flow within the upper side of the blade which is producing torque. Max. Cp position Min. Cp position RANS LES Figure 6. Differences in vorticity magnitude between LES and RANS methods at TTTTTT = CONCLUSIONS Vertical Axis Wind Turbines are well known for the complexity of their aerodynamic behaviour. Numerical simulations are usually the easiest and cheapest way to study this problem but accurate procedures should be defined in order to achieve useful results. Within the present work the possibility of making use of a LES turbulence model has been tested and validated as a useful alternative to more common RANS models. Also the importance of the time-step value has been established: the results presented in this work show that the Courant number should be kept close to one even if the PIMPLE algorithm is used and the angular step is already close or smaller than 1 15.

8 It will be of interest to know if the results here presented can be also applied to 2.5 or 3D simulations. 3D simulations for VAWT require an extraordinary computational power and 2.5D could be a compromise between accuracy and needed resources. Initially, the method presented here should be valid for the 2.5D case, only an extrusion of the currently existing mesh in the normal direction should be needed. Some preliminary attempts have already been performed by the authors although difficulties have appeared due to still very high computational time and convergence issues. ACKNOWLEDGES The authors gratefully acknowledge the collaboration of Fundación del Centro de Supercomputación de Castilla y León (FCSCL) for granting the use of the supercomputer Calendula for this work. REFERENCES [1] M. M. Aslam Bhutta, N. Hayat, A. U. Farooq, Z. Ali, S. R. Jamil and Z. Hussain, Vertical axis wind turbine A review of various configurations and desing techniques, Renewable and Sustainable Energy Reviews, vol. 16, no. 2012, pp , [2] L. A. Danao, J. Edwards., O. Eboibi and R. Howell, A numerical investigation into the influence of unsteady wind on the performance and aerodynamics of a vertical axis wind turbine, Applied Energy, vol. 116, no. 3, pp , [3] F. Balduzzi, A. Bianchini, R. Maleci, G. Ferrar and L. Ferrari, Critical issues in the CFD simulation of Darrieus wind turbines, Renewable Energy, vol. 85, pp , [4] R. Howell, N. Qin, J. Edwards and N. Durrani, Wind tunnel and numerical study of a small vertical axis wind turbine, Renewable Energy, vol. 35, pp , [5] C. Li, S. Zhu, Y.-l. Xu and Y. Xiao, 2.5D Large eddy simulation of vertical axis wind turbine in consideration of high angle of attack flow, Renewable Energy, vol. 51, pp , [6] D. Domínguez, M. Pröhl, T. De Troyer, M. Werner and M. C. Runacres, Design of a hydroformed metal blade for vertical-axis wind turbines, Journal of Renewable and Sustainable Energy, vol. 7, no. 4, [7] K. Almohammadi, D. Ingham, L. Ma and M. Pourkashanian, Modeling dynamic stall of a straight blade vertical axis wind turbine, Journal of Fluids and Structures, vol. 57, pp , [8] F. Trivellato and M. R. Castelli, On the Courant Friedrichs Lewy criterion of rotating grids in 2D vertical-axis wind turbine analysis, Renewable Energy, vol. 62, pp , [9] M. R. Castelli, A. Englaro and E. Benini, The Darrieus wind turbine: Proposal for a new performance prediction model based on CFD, Energy, no. 46, pp , [10] M. Mohamed, Performance investigation of H-rotor Darrieus turbine with new airfoil shapes, Energy, no. 47, pp , [11] T. Maîtrea, E. Ametb and C. Pellone, Modeling of the flow in a Darrieus water turbine: Wall grid refinement analysis and comparison with experiments, Renewable Energy, vol. 51, pp , [12] S. Lain and C. Osorio, Simulation and evaluation of a straight-bladed darrieus-type cross flow marine turbine, Journal of Scientific and Industrial Research, vol. 69, no. 12, pp , [13] F. Menter and Y. Egorov, A Scale Adaptive Simulation Model using Two-Equation Models, in 43rd AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, 2005.