The unsteady Reynold averaged Navier-Stockes (URANS) equation was adopted to simulate unsteady aerodynamic force in stall flutter.Coupled with a structure’s dynamic equation, the time domain aero-elastic analysis method was established.The structure’s dynamic equation was solved in time domain using the fourth order implicit Adams linear multi-step method based on the prediction-correction technique.Firstly, the aerodynamic response of dynamic stall and the prediction accuracy of frequency locking region were verified to ensure the CFD solver being suitable to stall flutter simulation.Then, this aero-elastic analysis method was used to simulate the flutter boundary of NACA23012 airfoil.The results showed that the flutter velocity boundary predicted with the proposed method agrees well with the test results.Through analyzing structural motion responses and flow characteristics in stall flutter, it was found that the generation of leading edge vortices and wake shedding in stall flutter is an energy conversion and an injection mechanism to keep the constant amplitude oscillation of the airfoil; meanwhile, the frequency locking phenomenon occurring in stall flutter is the main reason to cause flutter frequencies abruptly dropping when the initial attack angle are 15°, 16°and 17°, respectively.
[1] Li Jing. Experimental investigation of the low speed stall flutter of an airfoil[D]. Manchester: The University of Manchester, 2008.
[2] Dowell H E, Robert Clark, David Cox. A modern course in aeroelasticity[M]. U.S.: Springer, 2004:194-206.
[3] Jones W P. Aerofoil oscillations at high mean incidences[R]. R. & M. No.2654(11,502), London: Her Majesty's Stationery Office, 1953.
[4] McCroskey W J, Philippe J J. Unsteady viscous flow on oscillating airfoils[J]. AIAA Journal, 1975, 13(1): 71-79.
[5] 金琰，袁新，申炳録. 机翼大攻角下失速颤振的气动弹性研究[J]. 工程热物理学报, 2002,23(5): 573-575.
JIN Yan, YUAN Xin, SHIN Byeong-Rog. Aeroelastic analysis of an airfoil's stall flutter at large mean incidence angle[J]. Journal of Engineering Thermophysics, 2002,23(5): 573-575 (in Chinese).
[6] 李迺璐，穆安乐，Balas M J. 基于Floquet理论的旋转风机叶片动力失速气弹稳定性研究[J]. 振动与冲击, 2015, 34(24): 82-88.
LI Nai-lu, MU An-le, BALAS M J. Aeroelastic stability analysis on rotating stall blade of wind turbine based on floquet theory[J]. Journal of Vibration and Shock, 2015, 34(24): 82-88 (in Chinese).
[7] 任勇生, 刘廷瑞. 具有结构阻尼的复合材料薄壁梁的动力失速非线性颤振特性[J]. 振动与冲击, 2013, 32(18): 146-152.
REN Yong-sheng, LIU Ting-rui. Stall nonlinear flutter behavior of a thin-walled composite beam with structural damping[J]. Journal of Vibration and Shock, 2013, 32(18): 146-152(in Chinese).
[8] Grigorios Dimitriadis, Li Jing. Bifurcation behavior of airfoil undergoing stall flutter oscillations in low-speed wing tunnel[J]. AIAA Journal, 2009, 47(11):2577-2595.
[9] Razak N A, Thomas Andrianne, Grigorios Dimitriadis. Flutter and stall flutter of a rectangular wing in a wind tunnel[J]. AIAA Journal, 2011, 49(10): 2258-2271.
[10] Sacha Yabili, Smith M J, Grigorios Dimitriadis. Unsteady Navier-Stokes simulation of low-Reynolds stall flutter[R]. AIAA 2012-1706, Tennessee: AIAA, 2012.
[11] Damien Watrin, Grigorios Dimitriadis. Computational considerations for the prediction of stall flutter[R]. AIAA 2012-1706, Hawaii: AIAA, 2012.
[12] Besem F M, Kamrass J D, Thomas J P, et al. Vortex-induced virbration and frequency lock-in of an airfoil at high angles of attack[J]. Journal of Fluids Engineering, 2016, 138(1): 1-9.
[13] Deman Tang, Dowell E H. Experimental aerodynamic response for an oscillating airfoil in buffeting flow[J]. AIAA Journal, 2014, 52(6): 1170-1179.
[14] Zhu B, Lei J, Cao S. Numerical simulation of vortex shedding and lock-in characteristics for a thin cambered blade[J]. Journal of Fluids Engineering, 2007, 129(10):1297-1305.
[15] Young J, Lai J C S. Vortex lock-in phenomenon in the wake of a plunging airfoil[J]. AIAA Journal, 2007, 45(2): 485-490.
[16] Ashraf M A, Young J, Lai J C S. Oscillation frequency and amplitude effects on plunging airfoil propulsion and flow periodicity[J]. AIAA Journal, 2012, 50(11): 2308-2324.
[17] Young J, Ashraf M A, Lai J C S. Numerical simulation of fully passive flapping foil power generation[J]. AIAA Journal, 2013, 51(11): 2727-2739.
[18] McAlister K W, Pucci S L, McCroskey W J. An experimental study of dynamic stall on advanced airfoil sections volume2. pressure and force data[R]. TR-82-A-8, California: NASA, 1982.
[19] 叶正寅, 张伟伟, 史爱明等. 流固耦合力学基础及其应用[M]. 哈尔滨: 哈尔滨工业大学出版社, 2010:171-173.
YE Zheng-yin, ZHANG Wei-wei, SHI Ai-ming. Fundamentals of fluid-structure coupling and its application[M]. Harbin: Harbin Institute of Technology Press, 2010:171-173 (in Chinese).
[20] Kiran Ramesh, Joseba Murua, Ashok Gopalarathnam. Limit-cycle oscillations in unsteady flows dominated by intermittent leading-edge vortex sheddingp[J]. Journal of Fluids and Structures, 2015, 55: 84-105.
[21] William Bollay, Charles D. Brown. Some Experimental Results on Wing Flutter[J]. Journal of the Aeronautical sciences, 1941, 8(8): 313-318.
[22] Alexander Mendelson. Effect of Aerodynamic Hysteresis on Critical Flutter Speed at Stall[C]. Washington: National Advisory Committee for Aeronautics, 1948: 1-24.
[23] Shantanu S. Bhat, Raghuraman N. Govardhan. Stall Flutter of NACA 0012 Airfoil at Low Reynolds Numbers[J]. Journal of Fluids and Structures, 2013, 41(1): 166-174.
