Simulation of hypersonic flows in chemical and thermodynamic nonequilibrium at low and moderate reynolds numbers

Autor: G. A. Tirskii, G. G. Chernyi, Yu. V. Glazkov
Rok vydání: 1995
Předmět:
Zdroj: Computational Mathematics and Modeling. 6:278-283
ISSN: 1573-837X
1046-283X
Popis: In studies of rarefied gas flow it is relevant to consider the limits of applicability of the continuum model. In problems of hypersonic flow past bodies the deviation from the continuum model, reflected in breakdown of the linear relationship between fluxes and "forces," is manifested primarily near the surface and within the head shock, the thickness of which is proportional to the Knudsen number. Since the equations of hydrodynamics are an asymptotic limit of solutions of Boltzmann equations at Knudsen numbers that tend to zero, in the absence of reliable experimental data we can naturally try to compare the solutions of the Navier-Stokes equations at small Reynolds numbers Re~ with the solution of Boltzmann equations. In [1] the solution has been obtained in the framework of the locally self-similar approximation of the Navier-Stokes equations and it has been established that the flow near the body is characterized by absence of equilibrium between translational and vibrational degrees of freedom. All vibrational temperatures of the molecular components were assumed equal in this study. In the framework of parabolized Navier-Stokes equations, which are an asymptotic form of the Navier-Stokes equations retaining terms of order O(1) and O(Re~) [6], a numerical solution has been obtained for the two-dimensional axisymmetric problem of flow past a hyperboloid of revolution, which approximately models the flow in the neighborhood of the stagnation line of a reentrant spacecraft in the range of altitudes from 85 to 110 kin. The method of global iterations by the pressure gradient is used; this method was previously proposed in [2] for homogeneous gas flows. In this article, we consider a model with different temperatures of the molecular components, which contrary to [3] allows for feedback from the chemical reactions to vibrational relaxation. The boundary slip conditions include a jump of vibrational energy at the surface. The calculations are compared with direct Monte-Carlo simulation results [4] obtained under the same conditions. For flows of a chemically reactive gas, this comparison has been previously carried out ignoring vibrational relaxation [4, 5]. We consider stationary supersonic flow past a smooth blunt body immersed in a viscous dissociated air mixture in chemical and thermodynamic nonequilibrium. In the coordinate system attached to the surface of the immersed body (the coordinate x is measured along the surface and y along the normal to the surface) we write the following equations [7]: the equation of continuity; two projections of the momentum equation; the equation of heat influx, with explicit terms associated with relaxation of vibrational degrees of freedom (as thermodynamic equilibrium is approached, the additional terms vanish and the heat influx equation takes the standard form, with vibrational and translational degrees of freedom in equilibrium); the equation of balance of vibrational energy for each species of molecules; the equation obtained by summation of the equations of balance of vibrational energy for each species of molecules assuming equal vibrational temperatures; equations of diffusion of the reaction products; equations of diffusion of chemical elements closing these equations; Stefan-Maxwell equations; state equation. When specifying boundary conditions on the surface of the impermeable body, we allow for slip effects, temperature discontinuity, and catalytic recombination of atoms on the wall [8]. For the equations of vibrational energy balance of each species of molecules, new boundary conditions are proposed that allow for the discontinuity of the vibrational energy on the surface of the body. Conditions corresponding to the impinging flow parameters are specified on the outer boundary. Five components are assumed present in the perturbed flow region: N 2, 02, NO, N, O. All these components participate in dissociation, recombination, and exchange reactions.
Databáze: OpenAIRE
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