Analysis of the convective evaporation of nondilute clusters of drops

Abstract

A model for the convective evaporation of nondilute clusters of drops has been developed. The critical parameter which controls the different evaporation modes has been identified to be the penetration distance of the outer flow into the cluster volume. A dynamic criterion has been developed to differentiate between penetration and no penetration. Convective evaporation was modeled using a Reynolds number correlation between the evaporation rate with and without convection. Other equations, previously developed [Combust. Flame51, 55–67 (1983)] for quiescent, nondilute-spray evaporation, have been used here as well, with the exception of a new kinetic-evaporation law at the droplet surface and a nonuniform interior temperature model which have both been developed here. The model is shown to perform well for low penetration distances which are obtained for dense clusters in hot environments and low relative velocities between outer gases and cluster. For dense clusters with low penetration distances the results of the model predict that for the same initial velocity the evaporation time is shorter as the cluster becomes more dilute. For dilute clusters and large penetration distances, the opposite was found. Since for large penetration distances the predictive ability of the model deteriorates, these last trends are questionable. Furthermore, the evaporation time was found to be a weak function of the initial relative velocity and a strong function of the initial drop temperature. The initial surrounding gas temperature was found to have a strong influence in the lower temperature regime, 750–1500 K, whereas in the higher temperature regime the influence was very weak. The vitiation of the ambient gas by fuel vapor was found to have a very small influence upon the evaporation time for rich mixtures when the cluster is introduced in a strongly convective, high temperature surroundings. In all cases the results show that the interior drop-temperature was transient throughout the drop lifetime, but nonuniformities in the temperature persisted up to at most the first third of the total evaporation time.

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