Intercalibration Results. MOPAR: Results of the Inter-code Calibration of Charring Material Response

As the part of an ongoing study on heat flux and ablation on hypersonic vehicles, a one dimensional material response implicit solver with solid ablation and pyrolysis has been developed at the University of Michigan. This code, named MOPAR, uses the Control Volume Finite-Element Method (CVFEM) to model surface ablation with wall recession, as well as inner decomposition and pyrolysis gas behavior. The code solves the solid and gas phase mass conservation equations, the total energy (solid and gas) conservation equation as well as the momentum conservation equation. The latter is pore-averaged to the Forchheimer Law. In addition, MOPAR also takes into account variable coordinate systems (cylindrical and spherical), and allows ablation on both sides of the domain, using a new tri-diagonal solver. The code has been verified and validated, and has been compared to both CMA and FIAT. It also has been strongly coupled to LeMANS, a hypersonic CFD code, to solve integrated problems, ranging from re-entry capsules to kinetic energy penetrators. The results presented here are part of the inter-code calibration exercise. The values for all of the in-depth temperatures, the surface temperatures and blowing rates agree identically to the reference output obtain with FIAT. It is to be noted that MOPAR solved the momentum equation for the test problem, through Darcyʼs Law, and FIAT does not. For such a material, with those general simulation conditions, it is clearly not necessary to do so. Finally, the test-case was run at a much finer resolution, both in space and time, than the output provided from FIAT. It is therefore possible to observe, in great detail the first few seconds of the simulation. During this time, the blowing rate peaks at much higher values than the FIAT code predicts, before asymptotically decreasing