Asymptotic Analysis of a Premixed Polydisperse Spray Flame

Abstract

An asymptotic analysis of a laminar adiabatic premixed fuel-rich polydisperse spray flame is presented. The mathematical model is based on a sectional approach used to describe the cloud of droplets, so that droplet-droplet interaction within the spray can be accounted for. Small spray parameters are identified and used for expansion purposes, together with the large activation energy approach. Analytic solutions are found and matched for the preheat, reaction, and postreaction zones that characterize these flames. The latter zone is absent from “classical” premixed flame analysis, but is a feature of the spray flames in which droplets that survive the reaction zone will continue to vaporize and mildly cool the surroundings. The influence of the initial flux of droplets of the spray upon flame temperature and burning velocity is examined.