Breakup of liquid drops due to convective flow in shocked sprays

Abstract

An analytical model of the breakup of droplets in a column or a spray subjected to shock waves is presented. The model is based on observation of the breakup of isolated drops and is an extension of the model for a column of droplets previously developed by the authors, wherein droplet motion was ignored. In this model, allowance for the simultaneous stripping and motion of the droplets is made and, in addition, a probability factor, accounting for the probablity of wake-droplet interactions, is included for the spray case. It is shown analytically that, in the range of spacing to drop diameter ratio, S/D 0 =10–25, of importance to two-phase detonations, and for 2≤ M ≤6, the breakup time of the drops can be 55% to 90% of the breakup time of an isolated drop under the same convective flow conditions. Experiments with columns of 1.94-mm water drops at S/D 0 =14.6, under the action of M =2 shocks, indicate, on the basis of the diameter growth, a breakup-time reduction in good agreement with the value of t bc /t b =0.62, predicted analytically, where t b and t bc are the breakup time for isolated drops and drops in column, respectively. Data for similar water columns at higher Mach Numbers up to M =3.3 indicate a qualitative agreement but not as good quantitative agreement as obtained at M =2. Previously published work on the ignition and detonation of 2.6-mm diethylcyclohexane drops in oxygen provides further qualitative verification of the model.