Assessment of evaporation equilibrium and stability concerning an acoustically excited drop in combustion products

Abstract

The evaporation of drops in a sound field has been the subject of numerous studies aimed at determining its role in combustion instability. The models generally assume local equilibrium evaporation at the interface. We determine here the conditions of validity of this assumption, without calling into question other a priori assumptions of the classical model, in particular spherically symmetric quasi-steady evolution in the gas phase and liquid phase thermal unsteadiness with pure heat conduction.Another possible phenomenon concerns the differential recoil of the vapor. In the case of rapid evaporation, a pressure difference appears between both sides of the interface, even if the latter is plane. This pressure difference, usually neglected, is proportional to the square of speed and the resulting force is oriented toward the denser fluid, i.e. the liquid. A very fast evaporation may even cause local deformation, i.e. Hickman instability. The stability condition concerning this phenomenon has also been determined.This study was co-funded by CNES (French Space Agency) and ONERA and was performed in the framework of CNES–ONERA French Research & Technology activities on the high-frequency combustion stability of liquid–propellant rocket engines.