A unified theory of quasi-steady droplet combustion

Abstract

A unified theory is developed for the quasi-steady combustion of any cloud of liquid fuel droplets in a quiescent oxidizing atmosphere, based on the assumptions of a flame sheet model and of the potential representation for the overall mass flux. The latter gives a key to the closure of the equation system that governs the isobaric gas phase, which is not in general closed except for a one-dimensional case such as the spherical combustion of a single fuel droplet. The geometry of the droplet cloud may be arbitrary, and physical properties will depend on the thermodynamic variables. The theory allows us to reduce the problem to two much simpler ones. It is found that, given the electrical potential field surrounding an ensemble of conductors which has the same geometry as the droplet cloud, the thermodynamic fields surrounding the droplets and their combustion characteristics can be directly obtained from the results of the spherical combustion of a singel fuel droplet, by considering the electrical potential field as the mapping function between the gas-phase regions in both cases. As a fundamental and important example involving droplet interaction, the system of two spherical droplets is considered to give the explicit expression for the criterion which divides the two types of droplet combustion obtained, namely, two separate flames and one coalescent flame. This will be of interest in connection with the prediction of the so-called group combustion mode in sprays.