Using the CBS (Characteristic-Based Split) finite element method, this paper studies in detail the nonlinear dynamics of stall of airfoil NACA0012.First, the Instantaneous streamline patterns and the angle of attack lift coefficient curves of flows around the static airfoil are presented, and much attention is paid to the hysteresis and jumping phenomena in the angle of attack lift coefficient curve.Next, on the basis of the fixed point bifurcation theory in the map, by introducing a map into the flow field numerical simulation the static stall is proved numerically to be a kind of saddle-node bifurcation which involves the hysteresis and jumping phenomena. Additionally the dynamic stall of the airfoil is investigated by the ALE (Arbitrary Lagrangian-Euler) method, since the saddle-node bifurcation is sensitive to external excitation, which is the pitching-motion of the airfoil around the stall attack angle.The numerical results show that the specific external excitation could significantly enhance the lift coefficient and effectively delay the stall, and it may be considered a powerful control strategy of stall.
ZHANG Jiazhong, LI Kailun, CHEN Liying
. Nonlinear Dynamics of Static Stall of Airfoil and Its Control[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2011
, 32(12)
: 2163
-2173
.
DOI: CNKI:11-1929/V.20110726.1650.004
[1] Mittal S, Saxena P.Prediction of hysteresis associated with static stall of an airfoil[J]. AIAA Journal, 2000, 38(5): 933-935.
[2] 上官云信,周瑞兴,高永卫,等. 翼型相对厚度对失速分离特性的影响[J]. 空气动力学学报,2000,18(增刊):21-26. Shangguan Yunxin, Zhou Ruixing, Gao Yongwei, et al. The effect of relative thickness of airfoil on stall separate character[J]. Acta Aerodynamica Sinica, 2000, 18 (Supplement): 21-26. (in Chinese)
[3] 李栋,Igor Men'shov,中村佳朗. 薄翼失速翼型前缘分离泡对失速特性的影响[J]. 空气动力学学报,2006,24(3):361-366. Li Dong, Igor Men'shov, Yoshiaki Nakamura. The effect of bubble in leading edge region to the thin airfoil stall[J]. Acta Aerodynamica Sinica, 2006, 24(3): 361-366. (in Chinese)
[4] Ham N D. Aerodynamic loading on a two-dimensional airfoil during dynamic stall[J]. AIAA Journal, 1968, 6 (10): 1927-1934.
[5] McCroskey W J, Pucci S L. Viscous-inviscid interaction on oscillating airfoil in subsonic flow[J]. AIAA Journal, 1982, 20(2):167-174.
[6] McCroskey W J, Carr L W, McAlister K W. Dynamic stall experiments on oscillating airfoils[J]. AIAA Jour-nal, 1976, 14(1): 57-63.
[7] McCroskey W J, Philippe J J. Unsteady viscous flow on oscillating airfoils[J]. AIAA Journal, 1975, 13(1): 71-79.
[8] Carr L W. Progress in analysis and prediction of dynamic stall[J]. Journal of Aircraft, 1988, 25(1): 6-17.
[9] Ekaterinaris J A, Platzer M. Computational prediction of airfoil dynamic stall[J]. Progress in Aerospace Sciences, 1998, 33(11-12): 759-846.
[10] 王友进,闫超,周涛. 不同厚度翼型动态失速涡运动数值研究[J]. 北京航空航天大学学报,2006,32 (2):153-157. Wang Youjin, Yan Chao, Zhou Tao. Numerical investigation of dynamic stall vortex movement of different-thickness airfoils[J]. Journal of Beijing University of Aeronautics and Astronautics, 2006, 32(2): 153-157. (in Chinese)
[11] Sarkar S, Venkatraman K. Influence of pitching angle of incidence on the dynamic stall behavior of a symmetric airfoil[J]. European Journal of Mechanics/B Fluids, 2008, 27(3): 219-238.
[12] Witteveen J A S, Sarkar S, Bijl H. Modeling physical uncertainties in dynamic stall induced fluid-structure interaction of turbine blades using arbitrary polynomial chaos[J]. Computers and Structures, 2007, 85(11-14): 866-878.
[13] Gaitonde A L. A dual-time method for two-dimensional unsteady incompressible flow calculations[J]. International Journal for Numerical Methods in Engineering, 1998, 41(6): 1153-1166.
[14] Breuer M, Hnel D. A dual time-stepping method for 3D, viscous, incompressible vortex flows[J]. Computers & Fluids, 1993, 22(4-5):467-484.
[15] Nithiarasu P. An arbitrary Lagrangian Eulerian (ALE) formulation for free surface flows using the characteristic-based split (CBS) scheme[J]. International Journal for Numerical Methods in Fluids, 2005, 48(12):1415-1428.
[16] Zienkiewicz O C, Taylor R L, Nithiarasu P. The finite element method for fluid dynamics[M]. 6th ed. Beijing: World Publishing Corporation, 2009:79-105.
[17] 孙旭, 张家忠. 具有运动边界不可压缩粘性流动的CBS有限元方法[J]. 西安交通大学学报, 2011, 45(1): 99-104. Sun Xu, Zhang Jiazhong. A characteristic based split-FEM scheme for incompressible viscous flow with moving boundaries[J]. Journal of Xi'an Jiaotong University, 2011, 45(1):99-104. (in Chinese)
[18] Lippolis A, Vacca G, Grossman B. Incompressible Navier-Stokes solutions on unstructured grids using a co-volume technique//Lecture Notes in Physics, 1993, 414:270-274.
[19] Johnson A A, Tezduyar T E. Mesh update strategies in parallel finite element computations of flow problems with moving boundaries and interfaces[J]. Computer Methods in Applied Mechanics and Engineering, 1994, 119:73-94.
[20] Mittal S, Saxena P. Hysteresis in flow past a NACA0012 airfoil[J]. Computer Methods in Applied Mechanics and Engineering, 2002, 191: 2179-2189.
[21] 张家忠. 非线性动力系统的运动稳定性、分岔理论及其应用[M]. 西安:西安交通大学出版社, 2010: 96-110. Zhang Jiazhong. Stability and bifurcation of nonlinear dynamic systems and their applications[M]. Xi'an:Xi'an Jiaotong University Press, 2010: 96-110. (in Chinese)
CJA