Effect of Viscous Unsteady Aerodynamics on Flutter Calculation
Effect of Viscous Unsteady Aerodynamics on Flutter Calculation
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DOI：
10.2514/6.2019-2036
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发表时间：
2019-01
期刊：
影响因子：
--
通讯作者：
H. Taha;A. Rezaei
中科院分区：
文献类型：
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作者：
H. Taha;A. Rezaei
20世纪60年代的许多研究报告称，即使在零攻角和/或升力条件下，使用经典非定常空气动力学理论也无法准确预测颤振边界。由于颤振现象是非定常空气动力学和结构动力学的交叉问题，且细长梁的结构动力学可以较好地预测，因此可以推断该问题源于经典的非定常空气动力学理论。因此，在20世纪70年代和80年代出现了一股研究热潮，研究这种理论，特别强调库塔条件对非定常流的适用性。人们几乎一致认为，在高频率和低雷诺数下必须放宽库塔条件，这也是最近几项生物动力飞行的非定常空气动力学研究得出的结论。意识到涡度的产生和升力的发展本质上是粘性过程，我们发展了非定常空气动力学经典理论的粘性扩展，相当于边界层理论的非定常扩展。我们依靠一种特殊的边界层理论，它密切关注后缘附近的细节：三层甲板理论。我们利用这一理论放宽了库塔条件，并确定了对无粘非定常升力的粘性修正。利用所建立的粘性非定常模型，我们建立了雷诺数相关的升力频率响应（即Theodorsen的粘性扩展）。研究发现，粘度对超出Theodorsen无粘度溶液的升力发展产生了显著的相位滞后，特别是在高频率和低雷诺数时。由于颤振类似于任何典型的hopf分岔，主要由施加载荷和运动之间的相位差决定，因此预计粘滞将影响颤振边界。为了评估这种影响，我们将发展的非定常粘性气动理论与典型截面的结构动力模型相结合，进行气动弹性模拟和分析。我们将所建立的粘性非定常模型与Theodorsen模型所确定的颤振边界进行了比较。
Many studies over the 1960’s reported failure in predicting accurate flutter boundaries using the classical theory of unsteady aerodynamics even at zero angle of attack and/or lift conditions. Since the flutter phenomenon lies in the intersection between unsteady aerodynamics and structural dynamics, and because the structural dynamics of slender beams can be fairly predicted, it was inferred that the problem stems from the classical theory of unsteady aerodynamics. As a result, a research flurry occurred over the 1970’s and 1980’s investigating such a theory, with particular emphasis on the applicability of the Kutta condition to unsteady flows. There was almost a consensus that the Kutta condition must to be relaxed at high frequencies and low Reynolds numbers, which was also concluded from several recent studies of the unsteady aerodynamics of bio-inspired flight. Realizing that vorticity generation and lift development are essentially viscous processes, we develop a viscous extension of the classical theory of unsteady aerodynamics, equivalently an unsteady extension of the boundary layer theory. We rely on a special boundary layer theory that pays close attention to the details in the vicinity of the trailing edge: the triple deck theory. We use such a theory to relax the Kutta condition and determine a viscous correction to the inviscid unsteady lift. Using the developed viscous unsteady model, we develop a Reynolds-number-dependent lift frequency response (i.e., a viscous extension of Theodorsen’s). It is found that viscosity induces a significant phase lag to the lift development beyond Theodorsen’s inviscid solution, particularly at high frequencies and low Reynolds numbers. Since flutter, similar to any typical hopf bifurcation, is mainly dictated by the phase difference between the applied loads and the motion, it is expected that the viscosity-induced lag will affect the flutter boundary. To assess such an effect, we couple the developed unsteady viscous aerodynamic theory with a structural dynamic model of a typical section to perform aeroelastic simulation and analysis. We compare the flutter boundary determined using the developed viscous unsteady model to that of Theodorsen’s.