Abstract
We examine random packs of discs or spheres, models for ammonium-perchlorate-in-binderpropellants, and discuss their average properties. An analytical strategy is described for calculating the mean or effective heat conduction coefficient in terms of the heat conduction coefficients of the individual components, and the results are verified by comparison with those of direct numerical simulations (DNS) for both two-dimensional (disc) and three-dimensional (sphere) packs across which a temperature difference is applied. Similarly, when the surface regression speed of each component is related to the surface temperature via a simple Arrhenius law, an analytical strategy is developed for calculating an effective Arrhenius law for the combination, and these results are verified using DNS in which a uniform heat flux is applied to the pack surface, causing it to regress. These results are needed for homogenization strategies necessary for fully integrated two- or three-dimensional simulations of heterogeneous propellant combustion, and some sample two-dimensional results are presented.
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