基于调和线性化 Navier-Stokes 方程的局部感受性

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.