Drag coefficients of inert and burning particles accelerating in gas streams

Abstract

The effects of burning and acceleration on the drag coefficients of particles suspended and accelerating in gas streams were studied in a Reynolds number range extending from 250 to 1600. The model chosen for the analytical study was a spherical particle with mass flux through the surface to simulate burning. The governing equation was the integrodifferential representation of the tangential equation of motion of a thin boundary layer on a sphere. The solutions indicated that burning and acceleration tend to reduce the drag coefficient. The fractional reduction was found to be a function of the ratio of mass flux from the surface to that in the free stream f for the burning particle and the acceleration modulus Ac for the accelerating particle. The effects of burning and acceleration were studied experimentally by subjecting burning particles (gunpowder) and nonburning particles to the convective flow behind a shock wave in a shock tube. The variation in particle size and displacement with time were obtained by photographing particle shadows with a high speed framing camera and concentrated light source. The particle density, the shock wave velocity, and the atmospheric conditions together with the photographic data provided sufficient information to calculate the particle's drag coefficient. The analytical expressions predicted and experimental results verified that the particle drag coefficient was insensitive to burning and accelerative effects if Ac ≤10 −2 and f <0.025. When these conditions are met, other phenomena such as free stream turbulence, particle rotation and roughness can create large variations in the drag coefficient than the mechanisms considered in this study.