基于现有的Hopf分岔法动态失速模型(Hopf bifurcation model),引入Wagner函数计算其附着流下等效攻角,对原模型的边界层再附着项进行一定修改,使新模型可表示为状态空间的形式,并为原模型补齐了对于阻力和力矩系数的建模。相比于常见的ONERA和Leishman-Beddoes动态失速模型,新模型在附着流下拥有与解析理论最一致的幅值及相位特性;分离流下,新模型在大部分情况下的计算精度优于常见模型,且能更好地捕捉初级失速涡和深度失速下出现的多级失速涡现象。其中对轻度失速的分析表明,各动态失速模型在轻度失速下的环量项建模仍具有一定的提升空间。
Abstract
Improvement and modification have been done to the Hopf bifurcation dynamic stall model: introducing the Wagner function to compute the effective angle of attack under attached flow, redesigning the boundary layer reattachment term, and establishing the equations of drag and pitching moment. Compared with ONERA model and Leishman-Beddoes model, the new model shares the best coherence with analytical theory in amplitude and phase characteristics under attached flow. For separated flow, the new model has better accuracy than the others in most cases and captures better primary dynamic stall vortex fluctuation. The multi-stage vortex in deep stall can be also computed by the new model. Analysis under light stall reveals that the modeling of circulatory terms of all models can be further improved for this regime.
关键词
风力机 /
气动载荷 /
气动失速 /
数值模型 /
动态失速模型
Key words
wind turbines /
aerodynamic loads /
aerodynamic stalling /
numerical models /
dynamic stall model
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参考文献
[1] THEODORSEN T.General theory of aerodynamic instability and the mechanism of flutter[R]. 1949.
[2] 杨鹤森, 赵光银, 梁华, 等. 翼型动态失速影响因素及流动控制研究进展[J]. 航空学报, 2020, 41(8): 125-150.
YANG H S, ZHAO G Y, LIANG H, et al.Research progress on influence factors of airfoil dynamic stall and flow control[J]. Acta aeronautica et astronautica sinica, 2020, 41(8): 125-150.
[3] ROCCHIO B, CHICCHIERO C, SALVETTI M V, et al.A simple model for deep dynamic stall conditions[J]. Wind energy, 2020, 23(4): 915-938.
[4] SHENG W,GALBRAITH R A M,COTON F N. A modified dynamic stall model for low mach numbers[J]. Journal of solar energy engineering, 2008, 130(3): 031013-1.
[5] 戴玉婷, 严慧, 王林鹏. 基于非线性气动力的失速颤振计算与试验研究[J]. 工程力学, 2020, 37(8): 230-236.
DAI Y T, YAN H, WANG L P.Calculation and experimental study of stall flutter based on nonlinear aerodynamics[J]. Engineering mechanics, 2020, 37(8): 230-236.
[6] BOUTET J,DIMITRIADIS G,AMANDOLESE X.A modified Leishman-Beddoes model for airfoil sections undergoing dynamic stall at low Reynolds numbers[J]. Journal of fluids and structures, 2020, 93: 102852.
[7] LAXMAN V,VENKATESAN C.Chaotic response of an airfoil due to aeroelastic coupling and dynamic stall[J]. AIAA journal, 2007, 45(1): 271-280.
[8] AHAUS L A.An airloads theory for morphing airfoils in dynamic stall with experimental correlation[M]. St. Louis: Washington University in St. Louis, 2010.
[9] TRUONG V K.A semi-empirical model of unsteady aerodynamics for wind turbines and its application to the S809 airfoil[R]. 2018.
[10] LEISHMAN G J.Principles of helicopter aerodynamics [M]. Cambridge: Cambridge University Press, 2006.
[11] HANSEN M H,GAUNAA M,MADSEN H A.A Beddoes-Leishman type dynamic stall model in state-space and indicial formulations[R]. Risϕ National laboratory, 2004.
[12] MCALISTER K,PUCCI S,MCCROSKEY W, et al.An experimental study of dynamic stall on advanced airfoil sections. Volume 2.Pressure and force data[R]. NASA-TM-84245, 1982.
[13] BEDDOES T S.Practical computation of unsteady lift[R]. 1982
[14] BETHI R V, GALI S V,VENKATRAMANI J.Response analysis of a pitch-plunge airfoil with structural and aerodynamic nonlinearities subjected to randomly fluctuating flows[J]. Journal of fluids and structures, 2020, 92: 102820.
[15] ERICSSON L,REDING J.Fluid mechanics of dynamic stall part I. Unsteady flow concepts[J]. Journal of fluids and structures, 1988, 2(1): 1-33.
[16] HOLIERHOEK J,DE VAAL J,VAN ZUIJLEN A, et al.Comparing different dynamic stall models[J]. Wind energy, 2013, 16(1): 139-158.
基金
上海市浦江人才计划(2019PJD020); 上海市科技创新行动计划(20dz1205300)