Building a model of a gas mixture flow in a plane channel with absorbing walls


Аuthors

Nikitchenko Y. A.*, Sergeeva N. I.**

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: nikitchenko7@yandex.ru
**e-mail: natasg777@yandex.ru

Abstract

The paper presents a physical and mathematical model of the flow of a mixture of gases in a plane channel with absorbing walls. The model considers a mixture of two gases, one of which condenses on the surface of the channel. The surface temperature is lower than the temperature of the gas mixture at the entrance to the channel. The computational domain of the channel is divided into two subdomains: in the near-wall, kinetic domain, the model kinetic equation of polyatomic gases is solved, while in the remaining, hydrodynamic domain, a system of equations of a two-temperature model is solved.
The Knudsen number calculated from the cross-section of the channel is 0.01, which corresponds to the upper boundary of the transition region. The computational grids of the computational domains have the following characteristics. The grid step of the hydrodynamic domain, both in the longitudinal and transverse directions, is equal to the average free path of the molecule. The grid step of the kinetic domain in the longitudinal direction is five times the free path. The grid step in the transverse direction near the channel surface is 0.1 of the free path.
In the area of the two-temperature model and the model kinetic equation crossover, an approximating Navier-Stokes type function is constructed by the parameters of the two-temperature model. The model kinetic equation is integrated along the longitudinal axis of the velocity space and is solved only along the transverse axis. 
The boundary conditions on the surface of the channel were set as follows: - for the non-condensable component, the diffuse law of reflection of molecules was adopted,
- for the condensed component, in the case of its condensation, the density and pressure were assumed to be equal to the pressure of the saturated vapor of this component; if the density of the molecular flux falling on the surface became less than the density of the molecular flux created by the liquid phase, then the diffuse law of reflection of molecules from the surface was adopted.
The calculations showed that at approximately five hundred mean free paths of the molecule, almost complete condensation of the component occurs. In the area of intensive condensation, the speed of both components decreases (diffuser effect), and then increases.

Keywords:

nonequilibrium flows, gas mixtures, gas flow in a plane channel

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