Dynamics of Particle—Shock Interactions: Part I: Similitude

Abstract

The equation of particle motion is normalized for either relaxation behind a shock front or particle impaction from supersonic streams. Algebraic expressions are introduced for the drag coefficient in both cases to account for non-Stokesian drag and free molecular flow. Expressions are developed for the particle Knudsen, Reynolds, Mach, and Stokes numbers and for the ratio of the local gas-to-particle density and maximum particle drag. It is demonstrated that knowledge of the particle stagnation Knudsen number, local gas Mach number, and specific heat ratio are sufficient to predict the particle Knudsen, Reynolds, and Stokes numbers and the maximum drag behind the shock front. Graphs are also provided to estimate these important particle parameters.