The heating of a stream of particles by thermal counter radiation

Introduction. It is accepted that the depth of heating of the dust/gas/air mixture by the radiation of combustion products SR is equal to the length LR of the free path of radiation in the mixture. Numerical simulation of combustion of a gas-air mixture that has inert particles, taking into account the re-radiation of heat by heated particles of the fresh mixture, led to ratio SR >> LR. In this work, the analytical assessment of ratio χS = SR/LR is performed. One-dimensional problem model. The co-authors determined stationary temperature distribution over the flow of initially cold monodisperse particles suspended in vacuum. Particle velocity V is directed toward a heat-radiating, absolutely black surface that is permeable by particles. Simplifying assumptions are used: radiation consists of two oppositely-directed flows of electromagnetic energy; interaction between particles and radiation is described in the approximation of geometric optics; the temperature inside the particle is the same. Problem solving. It is shown that χS is determined by V=Vcp / (εT 0,5, σTb)3 , where cp, εT, σ, Tb are, respectively, heat capacity per unit volume of the suspended matter, integral emissivity of the particle material, the Stefan-Boltzmann constant, and the surface temperature. For ≤ 2.8, re-emission can be neglected: χS ≈ 1. At ≤ 1.2, temperature distribution regulates re-emission: χS ≈ 5 –1/(2 – εT) >> 1. Solution discussion. The analytical solution satisfactorily describes the available numerical solutions and experimental data for the case of combustion of a dust/gas/air mixture after specifying the parameters of a simplified model: the radiating surface should be understood as the flame front, Tb is the combustion temperature, and cp is the overall heat capacity of the mixture. The estimate ≤ 1.2 indicates the final high temperature of the gas suspension, the possibility of its autoignition far from the flame, and the need to change initial assumptions when simulating re-emission. Conclusions. Analytical evaluations make it possible to employ ratios SR >> LR and SR ≈ LR for the suspension over a thermal radiation source in vacuum. Conditions for the application of the results of simplified simulation of re-emission to the combustion of a dust/gas/air mixture are formulated.