Nonsteady burning of periodic sandwich propellants with complete coupling between the solid and gas phases

We develop a mathematical model that describes the unsteady burning of a heterogeneous propellant by simultaneously solving the combustion field in the gas-phase and the thermal field in the solid-phase, with appropriate jump conditions across the gas/solid interface. The model takes into account the ammonium perchlorate (AP) decomposition flame, reaction between the AP products and the binder gases, different properties (density, conductivity) of the AP and binder, temperature-dependent, gas-phase transport properties, and the unsteady nonplanar regressing surface. Propagation of the latter is described by using a level-set formulation which gives rise to a Hamilton-Jacobi equation. Numerical studies for a periodic sandwich geometry show that the surface evolves unsteadily into a steadily propagating front, and the effects of various parameters (pressure, stoichiometry, length scale) on the steady propagation speed are discussed. A variety of surface shapes are predicted, depending on the parameter values. It is shown that accounting for the full Navier-Stokes equation in the gas phase yields results that differ little from those generated when an Oseen model is adopted.