小扰动在二维超声速边界层中的弱非线性传播

Weak Nonlinear Evolution of Small Amplitude Disturbances in 2D Supersonic Boundary Layer

采用非线性抛物化稳定性方程(PSE)研究了非平行边界层的弱非线性稳定性。通过在流向采用一阶向后差分,法向采用四阶中心差分,并用预估-校正迭代来耦合非线性项,发展出了求解非线性PSE的数值方法。研究了不同幅值扰动及其高倍谐波的演化情况,发现随着基频扰动幅值的增大,高倍谐波可能失稳,而且失稳的位置会随着基频扰动的增大而向上游移动。通过观察涡量的发展可以发现涡破碎现象。算例与Navier-Stokes方程的直接数值模拟(DNS)结果作了比较,初步检验了其正确性。

The weak nonlinear instability of a nonparallel boundary layer is studied by nonlinear parabotized stability equations（PSE）. The PSEs are solved by employing a first--order backward difference scheme in streamwise direction and a fourth-order central difference scheme in the wall-normal direction. The nonlinear terms are acquired by the predictor-corrector and iterative approach. The evolution of some small amplitude disturbances and their high-order harmonic waves are studied. The results show that stable harmonic waves may become unstable with the existence of strong basic disturbance, and the critical positions at which they become unstable tend to move upwind with the increasing amplitude of the basic disturbance. The results also show that large vortices are likely to break into small vortices. The nonlinear nonparallel results are compared with data of direct numerical simulations （DNS） based on Navier-Stokes equations, which indicated the correctness of the PSE approach.