Blocken, Bert

Montazeri, Hamid

Rezaeiha, Rahim

English

The current study systematically analyzes the impact of number of blades (n) on the aerodynamic performance of 2-, 3- and 4-bladed Darrieus H-type vertical axis wind turbines (VAWTs). A large number of operational parameters, i.e., tip speed ratio (λ), Reynolds number (Re), turbulence inten-sity and reduced frequency (K) are investigated to provide a deeper insight into the impact of n on the dynamic loads on the blades, the turbine performance and the wake. High-fidelity unsteady Reynolds-averaged Navier-Stokes (URANS) simulations, extensively validated with experiments, are employed. The results show that (i) within the turbine optimal operational range, the turbine power coefficient (CP) is almost independent of n; (ii) when dynamic stall is present, CP values are dependent on n due to the impact of K; and (iii) decreasing n leads to an increase in the maximum lift coefficient, while the drag coefficient of the blade(s) reduces due to the higher K. The present findings support the optimal aerodynamic design of small- to large-scale VAWTs

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 Numerical analysis of the influence of number of blades on thepower performance of vertical axis wind turbinesCitation for published version (APA):Rezaeiha, R., Montazeri, H., & Blocken, B. (2019). Numerical analysis of the influence of number of blades onthe power performance of vertical axis wind turbines. In The 15th International Conference on Wind Engineering,Beijing, China; September 1-6, 2019Document license:CC BYDocument status and date:Published: 01/09/2019Document Version:Publisher’s PDF, also known as Version of Record (includes final page, issue and volume numbers)Please check the document version of this publication:• A submitted manuscript is the version of the article upon submission and before peer-review. There can beimportant differences between the submitted version and the official published version of record. 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Oct. 2023 The 15th International Conference on Wind Engineering Beijing, China; September 1-6, 2019  Numerical Analysis of the Influence of Number of Blades on the Power Performance of Vertical Axis Wind Turbines Abdolrahim Rezaeiha a, Hamid Montazeri a,b, Bert Blocken a,b  a Eindhoven University of Technology, Eindhoven, Netherlands   b KU Leuven, Leuven, Belgium  KEYWORDS: VAWT; Urban; Offshore; Optimal Design; CFD; URANS. INTRODUCTION Vertical axis wind turbines (VAWTs) have recently received renewed interest for wind energy harvesting in two new potential locations, i.e., far offshore and in urban environments [1-6]. VAWTs have several advantages compared to horizontal axis wind turbines (HAWTs) [7]: omni-directionality, low noise, simple design and low costs. However, their aerodynamic per-formance is currently lower than HAWTs. Therefore, to benefit from their many advantages, their aerodynamic performance needs to be further improved. To improve their aerodynamic per-formance, the impact of operational [8, 9] and geometrical [10, 11] parameters needs to be well understood. Number of blades is an important geometrical parameter, which significantly affects the aerodynamic performance of VAWTs. However, to the best of our knowledge, its impact on the turbine performance and the dynamic loads of the blade is not well understood. Therefore, in this paper, such an impact is studied for 2-, 3- and 4-bladed turbines for different solidities and within a wide range of operational parameters. The evaluation is based on high-fidelity CFD simulations, extensively validated with experiments. The computational settings and parameters are described in Section 2. The results and conclusions are presented in Section 3 and 4, respec-tively.  CFD SIMULATIONS The reference turbine is a Darrieus H-type VAWT with the characteristics shown in Table 1. The blade cross-section is the NACA0018 airfoil. The 2D computational domain is 35d × 20d and consists of a rotating core and a fixed domain surrounding the core. The size of the computation-al domain is based on the guidelines for CFD simulations of VAWTs [12, 13]. The computation-al grid consists of approximately 395,851 quadrilateral cells with a maximum y+ of 3.8. The grid is based on a grid sensitivity analysis using three uniformly refined grids. Further details of the ABSTRACT: The current study systematically analyzes the impact of number of blades (n) on the aero-dynamic performance of 2-, 3- and 4-bladed Darrieus H-type vertical axis wind turbines (VAWTs). A large number of operational parameters, i.e., tip speed ratio (λ), Reynolds number (Re), turbulence inten-sity and reduced frequency (K) are investigated to provide a deeper insight into the impact of n on the dynamic loads on the blades, the turbine performance and the wake. High-fidelity unsteady Reynolds-averaged Navier-Stokes (URANS) simulations, extensively validated with experiments, are employed. The results show that (i) within the turbine optimal operational range, the turbine power coefficient (CP) is almost independent of n; (ii) when dynamic stall is present, CP values are dependent on n due to the impact of K; and (iii) decreasing n leads to an increase in the maximum lift coefficient, while the drag coefficient of the blade(s) reduces due to the higher K. The present findings support the optimal aerody-namic design of small- to large-scale VAWTs. grid study is presented in Ref. [13]. The boundary conditions at the inlet and outlet of the domain are a uniform velocity inlet and zero gauge static pressure outlet. Symmetry conditions are used for the side faces. No-slip condition holds on the airfoil and shaft walls. Sliding grid interface is employed for the interface between the rotating and fixed grids. In the CFD simulations, the ap-proach-flow (i.e. inlet) total turbulence intensity is 5% with a turbulence length scale equal to the turbine diameter, i.e., 1 m. The incident-flow total turbulence intensity is 4.42% representing the real value experienced by the turbine [14]. The four-equation transition SST model [15] is em-ployed to model the turbulence [16-18]. Incompressible unsteady Reynolds-Averaged Navier-Stokes (URANS) simulations are performed using the ANSYS Fluent 16.1 with the SIMPLE scheme for pressure-velocity coupling and the second-order temporal and spatial discretization. The azimuthal increment, dθ, is 0.1°, which is based on CFD guidelines for VAWTs [12, 13]. The number of iterations per time step is 20. A number of 20 turbine revolutions are performed, and the results are sampled at the 21st turbine revolution. This value is based on a comprehensive convergence analysis and allows the results to reach a statistically steady-state condition [12, 13]. Two sets of validation studies have been performed and presented in detail in Ref. [1, 13]. Table 1. Geometrical and operational characteristics of the reference turbine. Parameter Value Parameter Value Number of blades, n 2 Airfoil chord, c [m] 0.06 Diameter, d [m] 1 Shaft diameter, ds [m] 0.04 Height, h [m] 1 Freestream velocity, U∞ [m/s] 9.3 Swept area, A [m2] 1 Rotational velocity, Ω [rad/s] 27.9 – 102.3 Solidity, σ 0.12 Tip speed ratio, λ 1.5 – 5.5 Blade aspect ratio, h/c 16.67 Chord Reynolds number, Rec 0.69×105 – 2.14×105 RESULTS Fig. 1 shows the power coefficient versus tip speed ratio and solidity for 2-, 3-, and 4-bladed VAWTs with constant Rec at identical solidities and tip speed ratios. It can be seen that except for λ < 2.5, the turbine CP is weakly sensitive to the number of blades. In the optimal operating range of turbines with different solidities, i.e. in the vicinity of λopt, CP is almost n-independent. This is an important finding which implies that for variable-speed VAWTs maintaining their λopt at a given constant Rec, the number of blades could be selected based on the other design param-eters such as uniformity of the output power, structural loads and vibrations, and cost. The same applies to constant-speed low-solidity urban VAWTs, at a given constant Rec, frequently operat-ing at moderate to high λ where the CP is almost insensitive to the number of blades. Note that the urban VAWTs need to have a low solidity due to their dominant moderate to high λ.  However, in practice for small- to medium-scale turbines due to the low mean wind speed, e.g., in the urban environment, Rec is typically in the low to moderate regime, ≤ 2×105, where Re number effects are significantly influencing the turbine CP [8]. Therefore, to avoid the low Reynolds number effects, the blade chord length needs to be sufficiently large. Hence, from an aerodynamic point of view and for a given solidity, the smaller number of blades will yield a higher CP due to the Reynolds number effect. Therefore, the choice of the optimal number of blades with respect to the turbine CP needs to consider the Rec. Note that to select the number of blades there exists other important considerations, i.e., uniformity of structural loads, turbine vi-brations, power uniformity, and cost.  The 15th International Conference on Wind Engineering Beijing, China; September 1-6, 2019   Figure 1. Power coefficients versus tip speed ratio and solidity for 2-, 3-, and 4-bladed VAWTs with fixed Rec at identical λ – σ positions (TI = 5%). In addition, at a given solidity, the turbine with less number of blades will operate at a higher re-duced frequency K due to the larger blade chord length. The higher K will improve the turbine aerodynamic performance at low λ by delaying/avoiding the flow separation and dynamic stall and the consequent load fluctuations. The higher CP for the turbine with less number of blades at λ < 2.5, therefore, could be a result of the higher K. For instance, this is more pronounced for the 2-bladed turbine compared to the 3- and 4-bladed turbines at λ = 1.5 and 2.0, see Fig. 1b.  In the full paper, further results analyzing the impact of number of blades on the dynamic loads of the turbine blade at constant Rec will be presented and discussed in detail. CONCLUSIONS Number of blades n is an important geometrical design parameter for vertical axis wind turbines. The selection of the number of blades for a turbine is a function of several parameters, namely uniformity of output power, turbine loads and vibrations, cost as well as turbine aerodynamic performance. The focus of the present study is confined to the aerodynamic performance of the turbine to provide a profound understanding and to help the designers/manufacturers with this aspect of the design. In the present study, high-fidelity CFD simulations, extensively validated with experimental data, are employed where the main findings of the study can be summarized as follows: (i) at a given Rec, the turbine CP is independent of n within the optimal operational range, i.e., in the vicinity of λopt; (ii) for a given σ and at low λ where dynamic stall is present, CP values are dependent on the number of blades due to the impact of K. This means that at a given solidity, the smaller number of blades (higher chord length) delivers a higher K and thus a higher CP; and (iii) decreasing the n is found to increase the Cl,max and reduce the Cd due to the higher K. From an aerodynamic point of view, at a given σ, the less number of blades is favorable due to the higher Rec and K. However, as discussed above, the choice of the number of blades is also driven by several other important design parameters, such as uniformity of output power and structural loads and cost. A larger number of blades yields more uniform instantaneous loads and power during the revolution while the length scale of the load fluctuations is also comparatively smaller due to the smaller blade chord length at the given σ. ACKNOWLEDGEMENTS The authors acknowledge support from the EU Horizon 2020 (H2020-MSCA-ITN-2014), the TU1304 COST AC-TION “WINERCOST, the partnership with ANSYS CFD, the NWO and FWO 12M5316N. REFERENCES [1] Rezaeiha A, Kalkman I, and Blocken B, "Effect of pitch angle on power performance and aerodynamics of a vertical axis wind turbine," Applied Energy, vol. 197, pp. 132-150, 2017.  [2] Rezaeiha A, Kalkman I, Montazeri H, and Blocken B, "Effect of the shaft on the aerodynamic performance of urban vertical axis wind turbines," Energy Conversion and Management, vol. 149 (C), pp. 616-630, 2017.  [3] Hand B and Cashman A, "Conceptual design of a large-scale floating offshore vertical axis wind turbine," Energy Procedia, vol. 142, pp. 83-88, 2017.  [4] Zanforlin S, "Advantages of vertical axis tidal turbines set in close proximity: A comparative CFD investigation in the English channel," Ocean Engineering, vol. 156, pp. 358-372, 2018.  [5] Rezaeiha A, Montazeri H, and Blocken B, "A framework for preliminary large-scale urban wind energy potential assessment: Case study for the Netherlands," Submitted, 2020.  [6] Rezaeiha A, Montazeri H, and Blocken B, "Active flow control for power enhancement of vertical axis wind turbines: leading-edge slot suction," Energy, vol. 189C, p. 116131, 2019.  [7] Rezaeiha A, Pereira R, and Kotsonis M, "Fluctuations of angle of attack and lift coefficient and the resultant fatigue loads for a large horizontal axis wind turbine," Renewable Energy, vol. 114 (B), pp. 904-916, 2017.  [8] Rezaeiha A, Montazeri H, and Blocken B, "Characterization of aerodynamic performance of vertical axis wind turbines: impact of operational parameters," Energy Conversion and Management, vol. 169 (C), pp. 45-77, 2018.  [9] Bachant P and Wosnik M, "Effects of Reynolds number on the energy conversion and near-wake dynamics of a high solidity vertical-axis cross-flow turbine," Energies, vol. 9 (73), 2016.  [10] Rezaeiha A, Montazeri H, and Blocken B, "Towards optimal aerodynamic design of vertical axis wind turbines: Impact of solidity and number of blades," Energy, vol. 165 (B), pp. 1129-1148, 2018.  [11] Sagharichi A, Zamani M, and Ghasemi A, "Effect of solidity on the performance of variable-pitch vertical axis wind turbine," Energy, vol. 161, pp. 753-775, 2018.  [12] Rezaeiha A, Montazeri H, and Blocken B, "Towards accurate CFD simulations of vertical axis wind turbines at different tip speed ratios and solidities: Guidelines for azimuthal increment, domain size and convergence," Energy Conversion and Management, vol. 156 (C), pp. 301-316, 2018.  [13] Rezaeiha A, Kalkman I, and Blocken B, "CFD simulation of a vertical axis wind turbine operating at a moderate tip speed ratio: guidelines for minimum domain size and azimuthal increment," Renewable Energy, vol. 107, pp. 373-385, 2017.  [14] Blocken B, Stathopoulos T, and Carmeliet J, "CFD simulation of the atmospheric boundary layer: wall function problems," Atmospheric Environment, vol. 41 (2), pp. 238-252, 2007.  [15] Menter FR, Langtry RB, Likki SR, Suzen YB, Huang PG, and Völker S, "A correlation-based transition model using local variables—part I: model formulation," Journal of Turbomachinery, vol. 128 (3), pp. 413-422, 2006.  [16] Rezaeiha A, Montazeri H, and Blocken B, "On the accuracy of turbulence models for CFD simulations of vertical axis wind turbines," Energy, vol. 180 (C), pp. 838-857, 2019.  [17] Rezaeiha A, Montazeri H, and Blocken B, "CFD analysis of dynamic stall on vertical axis wind turbines using scale-adaptive simulation (SAS): Comparison against URANS and hybrid RANS/LES," Energy Conversion and Management, vol. 196 (C), pp. 1282-1298, 2019.  [18] Rezaeiha A, Montazeri H, and Blocken B, "Scale-Adaptive Simulation (SAS) of dynamic stall on a wind turbine," in Notes on Numerical Fluid Mechanics and Multidisciplinary Design - Progress in Hybrid RANS-LES Modelling (HRLM 2018). vol. 143, 1 ed: Springer International Publishing, 2020, pp. 323-333.  

Numerical analysis of the influence of number of blades on the power performance of vertical axis wind turbines

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Numerical analysis of the influence of number of blades on the power performance of vertical axis wind turbines

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