Stability of the Couette flow of a diatomic gas in conditions of viscous stratification and vibrational mode excitation

I. V. Ershov

Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 4 (2016), pp. 84-99

Résumé

Stability of the viscous two-dimensional perturbations in a supersonic plane Couette flow of perfect and vibrationally excited gases is investigated within the framework of the linear theory. In both cases, the transport coefficients were taken to be both constant and dependent on the static temperature of the flow. The Sutherland viscosity law was used in order to take into account the temperature dependence of shear viscosity. The thermal conductivity coefficients caused by the translational, rotational, and vibrational motions of gas molecules are determined by Eucken's relations. A detailed comparison of the stability characteristics of the acoustic modes I and II for both viscosity models is carried out for a perfect gas. It is shown that the «viscous» stratification significantly increases the flow stability as compared to the case of the constant viscosity model. At the same time, the characteristic features in the development of viscous disturbances, typical for the Sutherland model, remain valid in the case of a simpler constant viscosity model. The dissipative effect of the vibrational mode excitation is preserved in the case when the temperature dependence of the transport coefficients is taken into account. The relative reduction caused in the growth rates of viscous disturbances for modes I and II by the vibrational excitation is practically the same for both viscosity models. The increase in the critical Reynolds number is approximately 12% in both cases.

Détail

Keywords: linear stability, Sutherland formula, vibrational relaxation
Mots-clés : acoustic modes.