MATHEMATICAL MODEL OF VISCOUS GAS DYNAMICS IN A CHANNEL WITH FIBROUS FILLER

The paper presents a numerical implementation of a mathematical model of gas flow in a channel with fibrous filler. Gas dynamics are described by a two-dimensional non-stationary Navier-Stokes equation. The mathematical model is based on the continuum technique of modeling the dynamics of inhomogeneous media − it was assumed that the volumetric fractions within the total volume of the mixture are specified for the carrier and dispersed phases. The volumetric content of the dispersed phase is a constant. When modeling the dynamics of an inhomogeneous medium, homogeneous Dirichlet boundary conditions were set for the velocity vector components. The equations of the mathematical model were solved by the explicit McCormack finite-difference method of the second order of accuracy. To suppress numerical oscillations, a nonlinear correction scheme of the grid function was used. The grid convergence of the numerical model of gas dynamics in a channel with a fibrous filler was investigated. The results of numerical calculations of the propagation of a low-intensity shock wave in a homogeneous gas and in inhomogeneous media were compared. A gas suspension and a channel filled with a fibrous filler were considered as inhomogeneous media. The comparison demonstrates that when a low-intensity shock wave interacts with a gas suspension, the flow velocity decreases, while the interaction of the gas flow with the fibrous filler leads to a significantly greater loss of kinetic energy of the gas. The mathematical model of gas dynamics in a fibrous filler can be used in shock wave suppression calculations.