Dynamics of Particle-Shock Interactions: Part II: Effect of the Basset Term

Abstract

Small particles and droplets encounter normal shocks in a variety of applications. The particle-shock interaction subjects the particles to large unsteady drag forces behind the shock front. In the present paper, an analysis has been made of the relative importance of the Basset history integral in the equation of motion for particle displacement and velocity behind a normal shock wave. The effect of the Basset integral has been related to gas stagnation conditions upstream of the shock and the local gas Mach number. In the present theoretical study it has been demonstrated that particle velocity and displacement relative to the gas behind the shock is unaffected by the inclusion of the Basset term until the latter stages of particle relaxation. The effect of the Basset history integral, that results from diffusion of vorticity from the decelerating particle, has been shown to decrease the particle drag or increase the displacement of the particle behind the shock. The effect is magnified with increasing stagnation pressures and particle diameters but with decreasing gas stagnation temperatures.