基于调和线性化Navier-Stokes方程的局部感受性

Local receptivity based on harmonic linearized Navier-Stokes equations

高超声速边界层中Mack模态的感受性决定了触发转捩的扰动的初始幅值,因而考虑感受性是构建合理的转捩预测方法的前提。壁面粗糙元与来流声波作用从而激发Mack模态是典型的局部感受性过程,对该过程的描述方法大致包括大雷诺数渐近理论、有限雷诺数理论和直接数值模拟。由于需要做小粗糙元线性假设,所以前两种方法无法有效预测有限高度粗糙元工况,而第三种方法则由于计算量庞大而无法进行参数化研究。本文发展了一套基于调和线性化Navier-Stokes方程的局部感受性高效算法,并针对马赫数5.92的高超声速平板边界层系统地研究了小尺度及有限高度粗糙元与声波引起的Mack模态感受性。结果表明,快声波诱导Mack模态的局部感受性显著强于慢声波。对于有限高度粗糙元,快声波的局部感受性在较大声波参数范围内随粗糙元高度增加而超线性增强。

The receptivity of Mack mode in the hypersonic boundary layer determines the initial amplitudes of disturbances that trigger transition.Therefore,considering the receptivity is a fundamental prerequisite for developing rational transition prediction methods.The excitation of Mack mode by the interaction between localized wall roughness and incoming acoustic waves is a typical local receptivity process,which can be generally described by three methods,i.e.,the large-Reynolds-number asymptotic theory,the finite-Reynolds-number theory,and direct numerical simulations.However,the first two theories become invalid under the condition of finite-height roughness due to the hypothesis of small(linear)roughness involved,whereas the third method is computationally intensive and not suitable for parametric study.In the present study,an efficient method for computing the local receptivity is developed based on the harmonic linearized Navier-Stokes equation(HLNS),and the local receptivity of Mack mode,induced by the interaction between the acoustic wave and the small/finite-height roughness,is systematically investigated in the hypersonic boundary layer at a Mach number of 5.92.The results suggest that the local receptivity of Mack mode induced by fast acoustic waves is significantly stronger than that of slow acoustic waves.For finite-height roughness,the local receptivity of fast acoustic waves shows a super-linear enhancement with the increase of roughness height within a large range of acoustic parameters.