Predictions of laminar flame in aluminium dust clouds with a cylindrical two-dimensional analytical model

Abstract

A simple two-dimensional analytical model of laminar flame in aluminium dust clouds is developed for predicting temperature profiles, flame speed, and flammability limit. This study follows previous studies, in which the models were developed in one-dimensional and 2D in Cartesian coordinate forms, and considers cylindrical coordinates since a tubular space is where most of the experimental works on the subject of dust combustion have been carried out. This article aims mainly to study the effect of the heat loss that happens from the surrounding wall on important combustion parameters including the flame speed and lean flammability limit, with more accuracy. The equations are written in the fuel–lean condition and a tube with constant temperature boundary conditions is assumed as well. The zones constructing the structure of a flame include preheat, reaction, and post-flame zones, for which the equations are solved using the method of separation of variables. The model is used to generate a correlation for the variations of flame speeds in terms of particles’ diameter, equivalence ratio, and tube diameter. The results show that the flame speed increases with decreasing particle size. It increases with increasing equivalence ratio and the tube diameter, as well.