Stability of a supersonic couette flow of vibrationally excited diatomic gas

I. V. Ershov

Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 1 (2015), pp. 47-62

Résumé

Within the linear theory, we study stability of the Couette flow of vibrationally excited diatomic gas with a parabolic profile of static temperature. The original mathematical model of the gas flow is the system of equations of two-temperature aerodynamics. As a result, it has been shown that when a certain combination of values of the parameters of the test flow (Reynolds number $\mathrm{Re}$, Mach number $\mathrm{M}$, bulk viscosity $\alpha_1$, the degree of vibrational nonequilibrium $\gamma_{\mathrm{vib}}$, and vibrational relaxation time $\tau$), it can be both stable and unstable with respect to small perturbations. For viscous perturbations, the spectra of eigenvalues, the growth increments, and neutral stability curves in the plane $(\mathrm{Re}, \alpha)$ were calculated for the first and second growing modes in the range of numbers $\mathrm{M}=2$–$6$ and $\mathrm{Re}=10^4$–$10^7$. The range of variation of the critical Reynolds number $\mathrm{Re_{cr}}\approx(2$–$5)\cdot10^4$ was found. It is shown that the second mode is most unstable for all levels of excitation. The excitation does not actually change the shape of the region of instability, but its boundaries shift to higher wave numbers with increasing excitation. It can be stated that, in general, the excitation of internal degrees of freedom of the gas molecules reduces the disturbance growth increments and has a stabilizing effect on the flow.

Détail

Keywords: hydrodynamic stability, vibrational relaxation, equations of two-temperature aerodynamics, critical Reynolds number.
Mots-clés : unstable viscous excitation modes