无限薄平板边界层前缘感受性过程的数值研究

Numerical study of leading-edge receptivity on the infinite-thin flat-plat boundary layer

在边界层流中层流向湍流转捩机理的研究一直是人们所关注的重要理论课题之一.感受性阶段是边界层内整个转捩过程中的初始阶段,它在层流向湍流转捩过程中起着关键性的作用.但是,在过去的边界层前缘感受性研究中大多数都是针对外部声波小扰动,很少见到考虑在自由流中普遍存在的自由来流湍流作用下边界层内诱导前缘感受性问题的相关报道.本文采用直接数值模拟的方法,研究自由来流湍流与无限薄平板前缘驻点扰动作用下边界层流中前缘感受性过程的内在机理.数值结果发现,在自由来流湍流与无限薄平板前缘驻点扰动作用下边界层流中能被感受出一组小扰动波,且它们的色散关系、增长率、中性曲线等结果都与流动稳定性中的线性理论获得的理论解相一致,由此可知在边界层内被激发产生的一组小扰动波就是Tollmien-Schlichting波,这也证明自由来流湍流与无限薄平板前缘驻点扰动相互作用是激发边界层流中前缘感受性过程的另一种物理机理;另外,还探讨了自由来流湍流度以及自由来流湍流的运动方向对无限薄平板边界层前缘感受性过程有何影响等.总之,开展边界层前缘感受性过程的深入研究,有益于完善流动稳定性理论,将为层流向湍流转捩过程的预测提供合理的理论依据.

The laminar-turbulent transition has always been one of the most concerned and significant research topics. Receptivity is the first stage of the laminar-turbulent transition process in the boundary layer, and also plays a key role in the laminar-turbulent transition. However, previous studies for leading-edge receptivity mostly focused on the external sound disturbances, while it is seldom to see the relevant research on the leading-edge receptivity to free-stream turbulence in the boundary layer which is universal in the free stream. In view of this, direct numerical simulation is utilized in this paper to study the leading-edge receptivity to free-stream turbulence exciting the Tollmien-Schlichting（T-S） wave in the boundary layer. The high-order high-resolution compact finite difference schemes based on non-uniform meshes and fast Fourier transform are used in spatial discretization, and the fourth order modified Runge-Kutta scheme is used in temporal discretization to solve Navier-Stokes equations for direct numerical simulation. Perturbation waves with short wavelengths, whose wavelengths are approximately one-third of the disturbance wavelengths of free-stream turbulence,are excited in the boundary layer under the free-stream turbulence; and our numerical results show that the dispersion relations, growth rates and neutral stability curve of the group of the excited perturbation waves with different frequencies are in line with the solutions obtained from the linear stability theory. These obtained numerical results confirm that the group of the excited perturbation waves with different frequencies are a group of T-S waves with different frequencies and the interaction between leading-edge of flat plate and free-stream turbulence to excite unstable waves in the boundary layer is one of the receptivity mechanisms. Furthermore, it is found that the amplitudes of the excited T-S waves in the boundary layer increase linearly with increasing the amplitude of the free-stream turbulence; while the normal wave number and incident angle of free-stream turbulence are approximately 60 and 20？, the leading-edge receptivity coefficient KIreaches a maximum; and the values of leading-edge receptivity coefficient KIof high-frequency disturbances are larger than those of low-frequency disturbances. Above all, the further study of leading-edge receptivity is of benefit to improving the hydrodynamic stability theory, and providing the theoretical foundation for predicting the prediction of laminar-turbulent transition.