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

Abstract

In the present study, with the assumption of a laminar, steady and uniform flow and with the purpose of gaining flame speed, quenching distance, lean flammability limit, and temperature distribution, a two-dimensional (2D) analytical model of micro-sized aluminium dust cloud combustion in a channel is presented. In the previous analytical models, energy conservation equations of laminar flame had been solved one-dimensionally and flame speed and quenching distance had been obtained assuming that heat loss to the wall is linear. This model is developed with the assumption that the particle burning rate in the flame front is controlled by the process of oxygen diffusion, and a channel with constant temperature boundary conditions, similar to those of quenching plates and experimental aluminium dust cloud combustion channels, is assumed as well. In order to examine more precisely the impact from the amount of heat loss originating from the channel wall on combustion parameters including flame speed, energy equations are written in two-dimensions. The equations are written in two limiting cases: lean and rich mixtures. Flame structure consists of preheat, reaction, and post-flame zones for the lean mixture and preheat and reaction zones for the rich mixture. Although equations in the lean mixture are solved using the separation of variables method, Laplace method is used for their solution in the rich mixture. By solving the energy equations in each zone and matching the temperature and heat flux at the interfacial boundaries, algebraic equations of flame speed are obtained. The obtained gas temperature distribution in different flame zones in the channel and also flame speed changes in terms of particles' diameter, equivalence ratio, and channel width in both lean and rich mixtures are presented in the results section. Generally, the results of the study shows that solving equations in 2D models leads to higher agreements between the theoretical and experimental results in flame speed, lean limit, and quenching distance terms.