Multi-droplet interaction effects in dense sprays

Abstract

A new approach for dense-spray modeling is employed to develop a model for multi-droplet interaction effects. A statistical description of droplets in a cloud and correlation functions for the effects of interactions between neighboring droplets are used to extract correction factors for various parameters that are affected by droplet interactions (e.g. drag cofficient, Nusselt number and Sherwood number). The correction factors enable the calculation of the drag coefficient, evaporation rate and heat transfer of a droplet in a cloud based on models for a single droplet. The model is employed to study the effects of droplet interactions on the evaporation and motion of a dense spray in a hot gaseous environment. It is shown that interaction effects are important during a larger fraction of the droplet lifetime as the droplet size decreases. The multi-droplet interactions cause the drag coefficient of a droplet in a dense spray to be lower—and hence its velocity higher—than that for an isolated droplet. For 100 μm droplets, as expected, the evaporation rate decreases and the droplet lifetime increases due to multi-droplet interactions. For 40 μm droplets, however, the evaporation rate increases and the droplet lifetime decreases. Although heat transfer to an interacting droplet is slower than to an isolated droplet, at the same gas-phase conditions and relative velocity of the droplets, the higher relative velocity of a 40 μm interacting droplet more than compensates for this effect to result in a shorter droplet lifetime.