Numerical Modeling of the Shock Waves Reflection from a Firm Surface in Mono- and Polydisperse Gas Suspensions

Abstract

In the paper flows of shock waves in multiphase media are described. Gas suspensions are considered as a multiphase medium—liquid drops or solid particles suspended in a gas. In this work, a continual approach in mathematical modeling of the dynamics of multiphase media is applied. The continual approach involves solving the complete hydrodynamic system of equations for each of the mixture components. The system of equations for the dynamics of each phase includes equation of continuity of density (average density for the dispersed phase), equations of conservation of momentum and energy. The carrier medium is described as a viscous, compressible heat-conducting gas. The mathematical model takes into account the velocity and thermal interaction of the phases of the mixture. The system of equations was solved by the MacCormack explicit finite-difference method of the second order of accuracy. To obtain a monotonic numerical solution, a nonlinear correction scheme was applied to the grid function. The influence of parameters of a disperse phase on speed and the shape of the reflected shockwave was numerically studied in the paper. Results of numerical calculations of the distribution of a shock wave from clean gas to a gas suspension, with the subsequent reflection from a firm surface, are given. Calculations allowed to establish that the intensity of a shock wave, reflected from a firm surface, in a gas suspension increases with a decrease of the number of dispersed particles. It is established that in polydisperse gas suspensions existence of fine fraction leads to an increase in the intensity of the reflected shock wave.