Numerical study of the influence of initial volume content of dispersion component of mixture on the leakage of dusty medium in vacuum

The following work mathematically models the flow of homogeneous gas and inhomogeneous medium in the form of a suspending matter of solid particles in gas – gas suspension. The aim of the work is to study the influence of the initial volumetric content of the solid component of the mixture on the process of its flow into a vacuum and to identify its differences from the process of the homogeneous gas leakage into a vacuum. When simulating the outflow process, we took into account the viscosity, compressibility, and thermal conductivity of gas. The mathematical model used in this work implements a continuous methodology for modeling the flow of an inhomogeneous medium. This kind of methodology for modeling the mixture motion involves solving the complete hydrodynamic system of equations of motion for each of the components of the mixture. In contrast, the system of equations of motion of the components of the mixture is connected with components responsible for the inter-phase force and thermal interaction. The system of equations of the mathematical model includes continuity equations for the density of the carrier medium and "average density" of the dispersed component of the mixture. The Navier-Stokes equation was solved to describe the momentum conservation of the carrier medium; the equation of momentum conservation was also written for the dispersed component of the mixture with regard to components responsible for the inter-component interaction. The energy conservation equations for the mixture components were solved, taking into account inter-component heat transfer. The system of equations of the mathematical model, supplemented by boundary conditions, was solved by the explicit finite-difference method of the second order of accuracy.