Numerical study of the velocity slip of a carrier and a dispersed phase in the interaction of a shock wave with an electrically charged gas suspension
In this paper, we consider the propagation of a shock wave from a pure gas into a heterogeneous mixture con-sisting of solid particles suspended in a gas and having an electric charge. The applied mathematical model takes into account the speed and thermal interaction of the carrier and dispersed components of the mixture. The mathematical model assumed a monodisperse composition of the solid component of the mixture, that is, it was assumed that all particles have the same linear size, shape and consist of one material. The force interaction of particles and gas included the Stokes force, the strength of the attached masses, as well as the dynamic force of Archimedes. The carrier medium was described as a viscous compressible heat-conducting gas. The equations of the mathematical model were solved by the explicit finite-difference method of the second order of accuracy, using the non-linear correction of the grid function. The system of equations of the mathematical model was supplemented by boundary and initial conditions for the desired functions: at the boundaries of the computational domain, the Dirichlet boundary conditions were set for the velocity components of the carrier and dispersed phase for the remaining dynamic functions Neumann conditions were set. For the Poisson equation describing the distribution of the internal electric field of a charged gas suspension, homogeneous Dirichlet boundary conditions were specified. As a result of numerical calculations, differences were revealed in the velocity slip of the carrier and dispersed phases, in cases where the shock wave propagates into a neutral and electrically charged dusty medium. It was also revealed the effect of particle size on the speed of sliding of the carrier and dispersed components of a heterogeneous mixture during the propagation of a shock wave into a neutral and electrically charged gas suspension.