Linear stability of a supersonic boundary layer on a plate under conditions of vibrational excitation and of viscous stratification

Abstract

An asymptotic theory of the neutral stability curve for a supersonic boundary layer of a vibrationally excited molecular gas on a plate is developed. The initial mathematical model of flow consists of equations of two-temperature viscous heat-conducting gas dynamics, which are used to derive a spectral problem for a linear system of eighth-order ordinary differential equations within the framework of the classical linear stability theory. Unified transformations of the system for all shear flows are performed in accordance with the classical Lin scheme. The problem is reduced to an algebraic secular equation with separation into the inviscid and viscous parts, which is solved numerically. It is shown that the thus-calculated neutral stability curves agree well with the previously obtained results of the direct numerical solution of the original spectral problem. In this case, the critical Reynolds number increases with excitation enhancement of the internal degrees of freedom of molecules, and the neutral stability curve is shifted toward the domain of higher wave numbers. This is also confirmed by means of solving an asymptotic equation for the critical Reynolds number.