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Aerodynamic modeling of wind turbine airfoil concerning dynamic stall and Gurney flap

考虑动态失速和Gurney襟翼的风力机翼型气动建模

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Abstract

The prediction of the unsteady aerodynamic load on an airfoil has frequently used the Leishman-Beddoes (L-B) model. Meanwhile, flow control techniques could change the flow around the blade, increase the effectiveness of wind energy conversion, and reduce the wind load. However, there have been a limited number of investigations examining this semi-empirical model taking into account the effects of such aerodynamic add-ons. As a result, this study intends to extend and modify the L-B model so that it can predict the unsteady aerodynamic characteristics of a wind turbine airfoil equipped with a Gurney flap. According to the unsteady aerodynamic changes of the Gurney flap during the oscillation period, the prediction module was proposed by the circulation changes, as well as characteristics of vortex generation and shedding traveling on the airfoil surface. These predicting results were preliminarily confirmed through a wind tunnel experiment, which illustrated that this approach has high practical potential. Nevertheless, the aerodynamic coefficients slightly deviated in the deep stall region. Adopting such a wind turbine optimization technology might improve the prediction and evaluation of the aerodynamic characteristics of a flapped airfoil under varying turbulent flow conditions.

摘要

Leishman-Beddoes模型(L-B模型)常被应用于动态失速时的非定常载荷预测. 同时, 加装气动附件的方法可以改善叶片周围的绕 流状况, 提高能量转换效率并减小载荷. 然而, 目前考虑此类气动附加件影响的动态失速半经验模型气动力预测的研究还较少. 为此, 本研究基于L-B模型进行扩展和修正, 使其能够预测加装Gurney襟翼的风力机翼型的非定常气动特性. 针对Gurney襟翼在俯仰振荡期 间的非定常气动变化, 即环量变化以及在翼型表面的涡的产生和脱落运动特性, 提出了对应的预测模块. 通过风洞实验的方式对预测 结果进行了初步验证, 表明所述方法具有较高的实用潜力, 但气动系数试验结果在深失速区略有偏差. 通过这种风力机优化技术, 所得 结果有助于更好地理解及评估不同湍流来流工况时加装Gurney襟翼的风力机翼型动态特性变化规律.

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References

  1. W. J. McCroskey, Unsteady airfoils, Annu. Rev. Fluid Mech. 14, 285 (1982).

    Article  MATH  Google Scholar 

  2. H. Fatahian, H. Salarian, M. Eshagh Nimvari, and J. Khaleghinia, Effect of Gurney flap on flow separation and aerodynamic performance of an airfoil under rain and icing conditions, Acta Mech. Sin. 36, 659 (2020).

    Article  MATH  Google Scholar 

  3. A. R. Mamouri, A. B. Khoshnevis, and E. Lakzian, Experimental study of the effective parameters on the offshore wind turbine’s airfoil in pitching case, Ocean Eng. 198, 106955 (2020).

    Article  Google Scholar 

  4. G. Bangga, Numerical studies on dynamic stall characteristics of a wind turbine airfoil, J. Mech. Sci. Technol. 33, 1257 (2019).

    Article  Google Scholar 

  5. K. Gharali, E. Gharaei, M. Soltani, and K. Raahemifar, Reduced frequency effects on combined oscillations, angle of attack and free stream oscillations, for a wind turbine blade element, Renew. Energy 115, 252 (2018).

    Article  Google Scholar 

  6. C. Zhu, M. Li, Y. Liu, Y. Qiu, Y. Feng, and T. Wang, Aerodynamic modelling of wind turbines concerning rotational augmentation and dynamic stall (in Chinese), Proc. CSEE 42, 4363 (2022).

    Google Scholar 

  7. J. G. Leishman, and T. S. Beddoes, A generalized method for unsteady airfoil behavior and dynamic stall using the indicial method: Proceedings of the 42nd Annual Forum of the American Helicopter Society, Washington DC, 1986.

  8. J. G. Leishman, and T. S. Beddoes, A semi-empirical model for dynamic stall, J. Am. Helicopter Soc. 34, 3 (1989).

    Google Scholar 

  9. C. T. Tran, and D. Petot, Semi-empirical model for the dynamic stall of airfoils in view of the application to the calculation of response of a helicopter blade in forward flight, Vertica 5, 35 (1981).

    Google Scholar 

  10. F. J. Tarzanin, Prediction of control loads due to blade stall, J. Am. Helicopter Soc. 17, 33 (1972).

    Article  Google Scholar 

  11. M. H. Hansen, M. Gaunaa, and H. A. Madsen, A Beddoes-Leishman Type Dynamic Stall Model in State-Space and Indicial Formulations (Risø National Laboratory, Roskilde, 2004).

    Google Scholar 

  12. J. Boutet, G. Dimitriadis, and X. Amandolese, A modified Leishman-Beddoes model for airfoil sections undergoing dynamic stall at low Reynolds numbers, J. Fluids Struct. 93, 102852 (2020).

    Article  Google Scholar 

  13. K. Pierce, and A. C. Hansen, Prediction of wind turbine rotor loads using the beddoes-leishman model for dynamic stall, J. Sol. Energy Eng. 117, 200 (1995).

    Article  Google Scholar 

  14. X. Liu, C. Lu, S. Liang, A. Godbole, and Y. Chen, Improved dynamic stall prediction of wind turbine airfoils, Energy Procedia 158, 1021 (2019).

    Article  Google Scholar 

  15. S. Øye, Dynamic stall simulated as time lag of separation: Proceedings of the 4th IEA Symposium on the Aerodynamics of Wind Turbines, 1990.

  16. J. W. Larsen, S. R. K. Nielsen, and S. Krenk, Dynamic stall model for wind turbine airfoils, J. Fluids Struct. 23, 959 (2007).

    Article  Google Scholar 

  17. Y. N. Zhang, H. J. Cao, and M. M. Zhang, Investigation of leading-edge protuberances for the performance improvement of thick wind turbine airfoil1, J. Wind Eng. Ind. Aerodyn. 217, 104736 (2021).

    Article  Google Scholar 

  18. S. Li, L. Zhang, J. Xu, K. Yang, J. Song, and G. Guo, Experimental investigation of a pitch-oscillating wind turbine airfoil with vortex generators, J. Renew. Sustain. Energy 12, 063304 (2020).

    Article  Google Scholar 

  19. S. Perez-Becker, D. Marten, and C. O. Paschereit, Active flap control with the trailing edge flap hinge moment as a sensor: Using it to estimate local blade inflow conditions and to reduce extreme blade loads and deflections, Wind Energ. Sci. 6, 791 (2021).

    Article  Google Scholar 

  20. C. Zhu, J. Chen, J. Wu, and T. Wang, Dynamic stall control of the wind turbine airfoil via single-row and double-row passive vortex generators, Energy 189, 116272 (2019).

    Article  Google Scholar 

  21. R. H. Liebeck, Design of subsonic airfoils for high lift, J. Aircraft 15, 547 (1978).

    Article  Google Scholar 

  22. G. Sun, Y. Wang, Y. Xie, K. Lv, and R. Sheng, Research on the effect of a movable gurney flap on energy extraction of oscillating hydrofoil, Energy 225, 120206 (2021).

    Article  Google Scholar 

  23. Q. Liu, W. Miao, Q. Ye, and C. Li, Performance assessment of an innovative Gurney flap for straight-bladed vertical axis wind turbine, Renew. Energy 185, 1124 (2022).

    Article  Google Scholar 

  24. M. Masdari, M. Mousavi, and M. Tahani, Dynamic stall of an airfoil with different mounting angle of gurney flap, Aircr. Eng. Aerosp. Tec. 92, 1037 (2020).

    Article  Google Scholar 

  25. F. Ajalli, M. Mani, and M. Tadjfar, Plunging wake analysis of an airfoil equipped with a gurney flap, Exp. Tech. 39, 48 (2015).

    Article  Google Scholar 

  26. M. S. Chandrasekhara, P. B. Martin, and C. Tung, Compressible dynamic stall performance of a variable droop leading edge airfoil with a gurney flap, J. Am. Helicopter Soc. 53, 18 (2016).

    Article  Google Scholar 

  27. T. Liu, and J. Montefort, Thin-airfoil theoretical interpretation for gurney flap lift enhancement, J. Aircraft 44, 667 (2007).

    Article  Google Scholar 

  28. D. I. Greenwell, Gurney flaps on slender and nonslender delta wings, J. Aircraft 47, 675 (2010).

    Article  Google Scholar 

  29. S. Li, Study of Dynamic Stall Model and Flow Control Mechanism of Wind Turbine Airfoil (in Chinese), Dissertation for Doctoral Degree (Institute of Engineering Thermal physics Chinese Academy of Sciences, Beijing, 2021).

    Google Scholar 

  30. A. J. Niven, and R. A. M. D. Galbraith, Modelling dynamic stall vortex inception at low Mach numbers, Aeronaut. J. 101, 67 (1997).

    Article  Google Scholar 

  31. S. Gupta, and J. G. Leishman, Dynamic stall modelling of the S809 aerofoil and comparison with experiments, Wind Energy 9, 521 (2006).

    Article  Google Scholar 

  32. W. Sheng, R. A. M. D. Galbraith, and F. N. Coton, A modified dynamic stall model for low Mach numbers, J. Sol. Energy Eng. 130, 031013 (2008).

    Article  Google Scholar 

  33. W. Sheng, R. A. M. D. Galbraith, and F. N. Coton, Return from aerofoil stall during ramp-down pitching motions, J. Aircraft 44, 1856 (2007).

    Article  Google Scholar 

  34. B. Hand, G. Kelly, and A. Cashman, Employing computational fluid dynamics to derive Beddoes-Leishman model airfoil parameters for vertical axis wind turbines, J. Sol. Energy Eng. 143, 044501 (2021).

    Article  Google Scholar 

  35. B. Huang, P. Wang, L. Wang, T. Cao, D. Wu, and P. Wu, A combined method of CFD simulation and modified Beddoes-Leishman model to predict the dynamic stall characterizations of S809 airfoil, Renew. Energy 179, 1636 (2021).

    Article  Google Scholar 

  36. T. Wang, A brief review on wind turbine aerodynamics, Theor. Appl. Mech. Lett. 2, 062001 (2012).

    Article  Google Scholar 

  37. L. E. Ericsson, Dynamic airfoil flow separation and reattachment, J. Aircraft 32, 1191 (1995).

    Article  Google Scholar 

  38. B. A. O. Vieira, and M. D. Maughmer, Unsteady aerodynamic model for deployable gurney flaps based on indicial concepts, J. Aircraft 54, 1375 (2017).

    Article  Google Scholar 

  39. K. Yee, W. Joo, and D. H. Lee, Aerodynamic performance analysis of a gurney flap for rotorcraft application, J. Aircraft 44, 1003 (2007).

    Article  Google Scholar 

  40. J. Yang, H. Yang, X. Wang, and N. Li, Experimental study of a gurney flap on a pitching wind turbine airfoil under turbulent flow conditions, J. Mar. Sci. Eng. 10, 371 (2022).

    Article  Google Scholar 

  41. D. De Tavernier, C. Ferreira, A. Viré, B. LeBlanc, and S. Bernardy, Controlling dynamic stall using vortex generators on a wind turbine airfoil, Renew. Energy 172, 1194 (2021).

    Article  Google Scholar 

  42. Q. Li, Y. Kamada, T. Maeda, J. Murata, and Y. Nishida, Effect of turbulent inflows on airfoil performance for a horizontal axis wind turbine at low Reynolds numbers (Part II: Dynamic pressure measurement), Energy 112, 574 (2016).

    Article  Google Scholar 

  43. A. Björck, M. Mert, and H. A. Madsen, Optimal parameters for the FFA-beddoes dynamic stall model, Int. J. Environ. Sci. Technol. 12, 237 (1999).

    Google Scholar 

  44. J. G. Leishman, and T. S. Beddoes, A generalized model for unsteady aerodynamic behaviour and dynamic stall using the indicial method, J. Am. Helicopter Soc. 36, 14 (1990).

    Google Scholar 

  45. W. Sheng, R. A. Galbraith, and F. N. Coton, Improved dynamic-stall-onset criterion at low Mach numbers, J. Aircraft 44, 1049 (2007).

    Article  Google Scholar 

  46. A. A. Singapore Wala, E. Y. K. Ng, and S. Narasimalu, A Beddoes-Leishman-type model with an optimization-based methodology and airfoil shape parameters, Wind Energy 21, 590 (2018).

    Article  Google Scholar 

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Acknowledgements

This work was supported by the Natural Science Foundation of Jiangsu Higher Education Institutions of China (Grant No. 22KJD480003), and the Curriculum Construction Project of Guangling College, Yangzhou University (Grant No. KCSZ202210).

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Contributions

Junwei Yang designed the research, carried out the modeling, tests, and results analysis, and wrote the first draft of the manuscript. Hua Yang and Xiangjun Wang contributed to the study conception and provided a critical review. All authors have read and agreed to the published version of the manuscript.

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Correspondence to Hua Yang  (杨华) or Xiangjun Wang  (王相军).

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On behalf of all the authors, the corresponding author states that there is no conflict of interest.

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Yang, J., Yang, H. & Wang, X. Aerodynamic modeling of wind turbine airfoil concerning dynamic stall and Gurney flap. Acta Mech. Sin. 39, 323056 (2023). https://doi.org/10.1007/s10409-023-23056-x

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