Shock wave structure in two-phase flow of a dilute mixture of non-ideal gas and small solid particles

This study examines the structure of shock waves in two-phase flow of a dilute mixture of non-ideal gas and small solid particles employing the Navier-Stokes-Fourier model. The gas is assumed to follow the reduced van der Waals' equation of state while the solid dust particles are treated as pseudo-fluids. The mass and volume fraction, radius, and specific heat of the dust particles and the pre-shock Mach number and the non-idealness of the gas have been taken as the parameters for the flow. Initially, gas and dust particles are assumed to be in equilibrium, moving at a uniform speed. Upon the initiation of the shock formation process, the gas and solid particles transit into a non-equilibrium state, exhibiting different profiles and relax finally to achieve the equilibrium at distinct relaxation rates. It is found that only when the size of dust particles approaches the order of mean free path of the gas, the mixture exhibit behavior akin to single-phase fluid. The non-equilibrium intensifies as the size of the dust particles increases. The profiles of the gas and dust particles are found to differ considerably with the presence, size, and thermodynamic properties of dust particles, the non-ideal nature of the gas, and the Mach number of the flow.