The dynamics of dense and dilute clusters of drops evaporating in large, coherent vortices

Abstract

The behavior of evaporating clusters of drops embedded into large, coherent vortices is described using a formulation which is valid for both dense and dilute clusters. Drops and gas interact both dynamically and thermodynamically. Dynamic coupling occurs through a force on the drops due to drag resulting from a slip velocity between the two phases The net interaction force on the gas with drops is due to a source thrust from evaporation plus drag on each drop. The drag coefficient accounts for blowing from the drop surface. Thermodynamic coupling is a result of drop heating and evaporation. Limitations due to drop proximity on heating and evaporation are taken into account. The vortical motion of the drops in the cluster results in the formation of a core region devoid of drops at the center of the vortex, and a shell region containing the drops and surrounding the inner core. Results are presented showing the dependence of the evaporation time, the final to initial volume ratio and the final to initial shell thickness ratio upon the initial air/fuel mass ratio and as a function of the initial tangential velocities, upon the initial Stokes number, initial drop radius and initial outer cluster radius. Differences in behavior between and control parameters of dense and dilute clusters are pointed out by these new results. It is found that for dense clusters the final to initial volume ratio and final to initial shell thickness scale with the initial Stokes number, a new result which must be validated experimentally.

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