A theoretical investigation of particle motion in an oscillating gas

Abstract

An investigation is made of the drift motion of small particles under the influence of acoustic oscillations. The investigation is made to determine if the motion has a magnitude great enough to produce significant changes on the fuel distribution in the chamber of a liquid propellant rocket motor. The calculations are made for the motion in both a rectangular and a cylindrical chamber. In the rectangular chamber the gas oscillation is restricted to the fundamental transverse mode and motion in only one dimension is considered. The particle drift velocity, that is the non-oscillating, non-damped term in the expression for the particle velocity is found in the solution of the second order equation. For particle motion in the cylindrical enclosure, only gas oscillations in the first transverse or sloshing mode is considered and motion is restricted to a transverse plane of the cylinder. The particle drift velocity, again a second order term, is determined. The magnitude of the drift velocity is calculated using conditions found in a liquid propellant rocket combustion chamber. Distances a typical fuel droplet would move during its average life time are calculated. The distances are small compared to the size of most rocket combustion chambers.