关键词:激波;热气动弹性;稳定性;壁板颤振;当地活塞流理论 Abstract In order to analyze the aeroelastic stability of heated flexible panel in shock-dominated flows, a systematic theoretical analysis model is established, and then test its correctness by the numerical simulation method. First of all, based on Hamilton principle and Von-Karman large deflection plate theory, the coupled partial differential governing equations are established with thermal effect based on quasi-steady thermal stress theory. Local first-order piston theory is employed in the region before and after shock waves. The Galerkin discrete method is employed to truncate the partial differential equations into a set of ordinary differential equations. The nonlinear flutter equation is linearized in the equilibrium position based on Lyapunov indirect method,and then Routh-Hurwits criterion is employed to analyze stability of the linear system. Finally, aeroelastic stability of the nonlinear flutter system is obtained. In order to verify the correctness of theoretical results, the nonlinear flutter equations are solved by the fourth-order Runge-Kutta numerical integration method to obtain time history of panel response. The results show that stability of the panel is reduced in the presence of the oblique shock. In other words, the heated panel becomes aeroelastically unstable at relatively small flight aerodynamic pressure. And the LCO amplitude and frequency are observed to increase with shock strength; the stability boundaries of heated flexible panel in shock-dominated flows are distinct from that in regular supersonic flows; only if the non-dimensional dynamic pressure upstream of the shock impingement location and the non-dimensional dynamic pressure downstream of the shock impingement location of the panel satisfy critical condition of flutter stability, will the heated panel be aeroelastically stable.
本文针对激波主导流动下壁板的热气动弹性稳定性问题,建立了基于当地活塞流理论的分析模型,并用数值仿真方法来验证其正确性. 分别研究了只一面作用气动载荷及两面同时受不同动压的气动载荷的薄壁板受斜激波冲击时的热气动弹性稳定性,给出了使壁板发生气动弹性失稳的边界条件. 得到以下结论: (1)不论是只一面受气动载荷还是两面同时受不同动压的气动载荷作用,当壁板受激波作用时更容易发生热气动弹性失稳,并且随着激波强度的增大,受热壁板的稳定性也越来越差,极限环幅值和频率增大. (2)当激波强度较小时,气动弹性稳定性边界仍将“壁温/动压”平面(图3(a))分成4个区域:渐进稳定区、屈曲区、基本型颤振区和过渡稳定区,但是随着激波强度的增大,壁板的临界屈曲温升减小;当激波强度更大时,气动弹性稳定性边界将平面的四个区域进一步分成5个部分,连续的渐进稳定区被屈曲区隔开成为两部分,并且即使温升为零时受热壁板也会发生屈曲. (3)对于单面受气动载荷并且有激波作用的壁板,只有在激波前后的动压都满足稳定性边界条件下,壁板才可能保持气动弹性稳定性;对于双面受气动载荷并且一侧有激波作用的壁板,只有在激波前后的动压以及另一侧的动压都满足稳定性边界的条件下,壁板才可能保持气动弹性稳定性. (4)与单面受气动载荷的情况相比,在两面受气动载荷的情况中,气动弹性稳定性边界对于激波强度的变化敏感度降低;在温升不变的情况下,气动弹性临界稳定动压会随着激波强度的增大而明显减小;在温升较小时,气动弹性临界稳定动压的增量随着温升的增大而减小,而当温升较大时,气动弹性临界稳定动压的增量保持不变. (5)壁板上壁面的激波强度确定时,下壁面不同的超音速气流对气动弹性稳定性边界有影响;随着下壁面超音速气流的无量纲动压越大,受激波作用的受热壁板稳定性也越来越差,但临界屈曲温升在增大. The authors have declared that no competing interests exist.
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