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MECHANICS
Stability of the Couette flow of a diatomic gas in conditions of viscous stratification and vibrational mode excitation
I. V. Ershov Novosibirsk State University of Architecture and Civil Engineering (Sibstrin), Novosibirsk, Russian Federation
Abstract:
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.
Keywords:
linear stability, Sutherland formula, vibrational relaxation, acoustic modes.
Received: 16.06.2016
Citation:
I. V. Ershov, “Stability of the Couette flow of a diatomic gas in conditions of viscous stratification and vibrational mode excitation”, Vestn. Tomsk. Gos. Univ. Mat. Mekh., 2016, no. 4(42), 84–99
Linking options:
https://www.mathnet.ru/eng/vtgu540 https://www.mathnet.ru/eng/vtgu/y2016/i4/p84
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Abstract page: | 83 | Full-text PDF : | 25 | References: | 28 |
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