Two-phase reactive particle flow through normal shock waves

An analysis is presented for the steady one-dimensional flow behind a normal shock wave of a compressible gas containing small spherical particles of solid propellant. The solids mass fraction is assumed large enough to require that the void volume fraction be retained as a variable in the governing conservation equations. The particles are ignited by the shocked air and by viscous interaction. Propellant gases are then generated which depend on the instantaneous size of the particles and on the linear burning rate. The latter is assumed dependent upon the local pressure and the particle temperature. These calculations are of interest because of the potential hazards of such particle flows, in that extreme pressures are predicted within the relaxation zone, pressures even greater than those calculated for the final equilibrium conditions. The results stress the importance of the Mach number of the normal (strong shock) and the energy content of the propellant (J/kg).