Asymptotic Theory of Neutral Stability of the Couette Flow of a Vibrationally Excited Gas
Yu. N. Grigor'ev1,2, I. V. Ershov1,3
1Institute of Computational Technologies, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
2Novosibirsk State University, Novosibirsk, 630090, Russia
3Novosibirsk State University of Architecture and Civil Engineering, Novosibirsk, 630008, Russia
Keywords: линейная теория устойчивости, колебательно-возбужденный газ, кривая нейтральной устойчивости, критическое число Рейнольдса, linear stability theory, vibrationally excited gas, neutral stability curve, critical Reynolds number
Abstract
An asymptotic theory of the neutral stability curve for a supersonic plane Couette flow of a vibrationally excited gas is developed. The initial mathematical model consists of equations of two-temperature viscous gas dynamics, which is 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 particular, the critical Reynolds number increases with excitation enhancement, 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 at the Mach number M ≤4.
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