Numerical study of the propagation of a small shock wave intensity from a homogeneous gas to an electrically charged dusty environment

Abstract

The paper is devoted to numerical modeling of the process of propagation of a low-intensity
shock wave from a pure gas into an inhomogeneous medium, which is a gas suspension
of solid particles. Computational experiments considered both electric neutral and charged
suspensions of solid particles. In the mathematical model used in the work, the conservation
of the momentum components of the carrier medium was described by the system of Navier-
Stokes equations for a compressible gas in a two-dimensional formulation. When describing
the interaction of the carrier and the dispersed phase of the gas suspension, the Stokes law,
Archimedes’ principle, the virtual masses force were considered, interphase heat transfer was
also taken into account. For the dispersed component of the mixture, a complete hydrodynamic
system of equations of motion was solved. It included the equation of continuity, the equation
of conservation of momentum and energy. The system of equations of the mathematical model,
supplemented by boundary conditions, was solved by an explicit finite-difference method of
the second order of accuracy. In the numerical model, an algorithm for suppressing numerical
oscillations was also used. Numerical modeling showed that the presence of an electric charge in
the dispersed component of the mixture affects the movement of the dispersed component and,
due to interfacial interaction, the gas flow. As a result of numerical calculations, it was found
that an increase in particle size leads to a significant increase in interfacial velocity slip. It was
determined that the intensity of the velocity slip between the carrier and the dispersed phases in
an electrically charged dusty medium occurs in the direction of increasing the specific Coulomb
force. While in an electrically neutral gas suspension, the growth of velocity slip occurs in the
direction of motion of the shock wave.