Effect of the discrete nature of heat sources on flame propagation in particulate suspensions

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In some heterogeneous systems, such as dust clouds, the heat sources (i.e., particles) are separated by large spaces of a noncombustible, heat-conductive media. In spite of the clearly discrete nature of the heat sources in such systems, the source term in the energy conservation equation of the flame propagation models is commonly considered to be a continuous function of spatial coordinates. To analyze the validity of this assumption for dust flames, we have compared flame speeds predicted by two different flame models. One of the models is based on the common approximation of the heat sources by a continuos function of spatial coordinates, and the other considers the exact description of the coordinates of the burning particles. An analytical expression for the flame speed in the media with regularly distributed pointlike discrete heat sources (particles) has been obtained, and the parameter responsible for the relation between discrete and continuous models was identified. The flame speeds obtained from the continuous and discrete models coincide if the particle combustion time is much longer than the characteristic time of heat transfer between particles. In the opposite case, for the fast (compared with the time of heat transfer between particles) burning fuels, the flame speed in the discrete system is a weak function of the particle combustion rate and is an explicit function of the distance between particles. The effect of the discrete nature of the heat sources on flame propagation is illustrated by comparing flame speeds calculated both from continuous and discrete models in lean aluminum and zirconium particle-gassuspensions. Lower flame speeds and a weaker dependence of the speed on oxygen concentration are predicted by the discrete flame model. The possible effect of the nonuniform particle distribution in space on the flame propagation phenomena is also discussed in the present work.