Heterogeneous Continuum Model of Aluminum Particle Combustion in Explosions

A heterogeneous continuum model is proposed to describe the dispersion and combustion of an aluminum particle cloud in an explosion. It combines gasdynamic conservation laws for the gas phase with a continuum model for the dispersed phase, as formulated by Nigmatulin. Interphase mass, momentum, and energy exchange are prescribed by the phenomenological model of Khasainov. It incorporates a combustion model based on mass conservation laws for fuel, air, and products. The source/sink terms are treated in the fast-chemistry limit appropriate for such gasdynamic fields, along with a model for mass transfer from the particle phase to the gas. The model takes into account both the afterburning of the detonation products of the booster with air and the combustion of the Al particles with air. The model equations are integrated by high-order Godunov schemes for both the gas and particle phases. Numerical simulations of the explosion fields from 1.5-g shock-dispersed-fuel charges in 3 different chambers are performed. Computed pressure histories are similar to measured waveforms when the ignition temperature model is employed. The predicted product production is 10–14% greater than that measured in the experiments. This fact can be ascribed to unsteady ignition effects not included in the modeling.