Grigor'ev Y.N.   Ershov I.V.  

Stability Investigations of Relaxing Molecular Gas Flows. Results and Perspectives

Reporter: Grigor'ev Y.N.

Survey of the systematic authors’ investigations of a dissipative effect arised in the molecular gas flows is presented. Such an effect is connected with thermal relaxation, in particular, of nonequilibrium vibrational modes of molecules. The full system of two-temperature aerodynamics equations is used in general case of high vibrationally excited molecular gas. The system contains the Landau-Teller equation which describes a relaxation process in terms of vibrational temperature.

Analysis of linear stability of plane parallel flows of inviscid nonheat-conducted vibrationally excited gas is fulfilled. Generalization of the classical first and second Raley’s theorems and Howard’s “semicircle” theorem is given for such flows. The calculation data on decreasing maximal growth rates of most unstable inviscid modes are presented. Their dependencies on Mach number of carrier flow, characteristic relaxation time and degree of vibrational modes exciting are analyzed.

The plane Couette flow was considered for investigation of internal flows. The energy stability theory generalized on compressible thermally nonequilibrium flows was used for subsonic case. Neutral stability curves and critical Reynolds numbers were calculated by solving a variational problem for specially constructed energy functional. It was shown the critical Reynolds numbers grow with growth of bulk viscosity coefficient, Mash number, characteristic relaxation time and degree of vibrational modes exciting. Under limiting values of regime parameters their values in two and half times more then in equilibrium case.

Supersonic flow was considered on the base of classical modal linear stability theory. It was shown for Mach number values from three up to five a growth of the critical Reynolds numbers connected with vibrational exciting can reach above twelve percentages.

For independent confirmation of numerical calculation results an asymptotic theory of stability of plane parallel flows of compressible thermally nonequilibrium gas was developed. In its frameworks two-point spectral problem for supersonic Couette flow was considered which didn’t previously solve even for the perfect gas case. The results of analytical and numerical solving demonstrate a good correspondence similarly to classical case of boundary layer.

In supercritical domain of the Reynolds numbers a numerical modeling of nonlinear development of the Kelvin–Helmholtz instability which reproduces a local mechanism of turbulization was carried out. The calculation results show relative dumping of kinetic energy of the vortex "cat's-yey"structure on a background of relaxation process reaches  near fifteen percentages.

At all carried out investigations such exciting degrees were considered which one can reach for diatomic gases in nozzle flows, underexpanded jets or by laser pumping vibrational molecular modes. The results of these studies allow us make a conclusion about essential damping influence of relaxation on linear and nonlinear dynamics of flow disturbances.

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