Non-Darcian Behavior of Pyrolysis Gas in a Thermal Protection System

To improve heat and ablation rate modeling of the thermal protection system for reentry vehicles, a material response model with surface ablation and pyrolysis is developed. To accurately model the effects of the pyrolysis gas within the ablator, Darcy’s law is replaced by Forchheimer’s law for flow through porous media. The use of Forchheimer’s law accounts for the inertial effects of the gas and removes any dependency on microscopic parameters, such as pore size. To characterize theflow, the Forchheimer number is proposed because it depends only on macroscopic quantities. To verify and validate the model, comparisons to experimental data and to prior computational results are presented. Applying Ergun’s equation to evaluate the inertial parameter of the Forchheimer number, a simple test case is run. For the case of a generic carbon-phenolic ablator subjected to a typical reentry trajectory, conditions for non-Darcian behavior are investigated by way of a parametric study. Finally, the necessary conditions required for gas kinetic energy to be relevant are highlighted.