Simulation of unsteady gas-particle flow induced by the shock-wave interaction with a particle layer

A numerical simulation of the unsteady gas-particle flow arising from the shock-wave interaction with a layer of inert particles is performed based on a continuum model. Each phase is described by a set of equations describing the conservation laws of mass, momentum and energy. The interphase interaction is taken into account using source terms in the momentum and energy equations. The governing equations for the gas and dispersed phases are of a hyperbolic type, they can be written in a conservative form and can be solved with a Godunov-type numerical method. A third order Runge-Kutta method is used to discretize the governing equations in time. The proposed model allows one to calculate a wide range of gas-particle flow regimes occurring when the volume concentration of the dispersed phase varies. The closure of the mathematical model and some details of numerical model implementation are discussed. The shock-wave flow structure as well as the space-time dependencies of particle concentration and other flow parameters are presented.