Modeling Sub-Surface Processes Within a Solid Fuel Ramjet

Combustion in a solid fuel ramjet (SFRJ) is a complex, multiphase, and multiscale process, where the heat transfer into the solid fuel causes temperature increase and phase change. The released vapor is transported and mixed with the air to react above the surface, and this provides a continuous heat transfer. The heat and mass transfer within the solid fuel and at the multiphase interface are referred to as the sub-surface processes, and their modeling, for representative fuels is the primary focus here. Reactive simulations of SFRJ resolve the gas-phase turbulence and combustion using high-fidelity large eddy simulation (LES), while the sub-surface processes are modeled in the past using an analytical steady-state model assuming only local, 1D wall-normal variation with an Arrhenius rate model for mass transfer at the interface. This work evaluates this approach against other possible and improved alternatives. For mass transfer, a heat-flux-based regression model is compared with the conventional Arrhenius rate model while for heat transfer, the conventional steady-state analytical model is compared against an unsteady numerical approach that is tightly coupled with the gas-phase combustion solver. The test configurations include a 1D steady opposed flame burner and an axisymmetric unsteady SFRJ combustor. The results show that, although the steady-state heat transfer may be sufficient for steady problems, e.g., an opposed-flame burner, it is not appropriate for unsteady combustion. Unsteady processes in an SFRJ is shown to be due to unsteady vortex shedding at the backward-facing step (BFS). It is also shown that the unsteady heat transfer promotes flame stability and also increases the overall regression rate predictions. In terms of mass transfer, the results show that both the Arrhenius rate and heat-flux-based approaches yield consistent results if the heat transfer is correctly modeled.