Multi-dimensional modeling of charring ablators

Abstract

During an atmospheric entry/re-entry, when a spacecraft travels at hypersonic speed, a strong bow shock is formed in front of the entering vehicle. Such a shock results in an enormous amount of aerodynamic heat, part of which is transferred to the thermal protection system (TPS). Of the many TPS options, charring ablators have gained popularity in recent years for their e↵ectiveness and light weight. They are made of a fibrous non-pyrolyzing matrix (usually carbon or silicon carbide) and impregnated with pyrolyzing material (often phenolic resin). Phenolic Impregnated Carbon Ablator (PICA), as used for the MSL and the Stardust missions, is one such kind of material.1 The idea behind this type of material is to dissipate part of the energy through pyrolysis and ablation. Pyrolysis is the process in which the phenolic polymer gradually carbonizes at high temperature, losing mass and generating pyrolysis gases. These gases are then expelled through the porous structure of the material and blown into the chemical reacting boundary layer. The other phenomenon, surface ablation, refers to the mass removal of the char (composed of non-pyrolyzed and residual carbonized material) through oxidation, sublimation and spallation. Much research has been done on this topic. However, most of the simulation tools available in the literature are one or two-dimensional.2–6 Admittedly, a one-dimensional solution is mostly adequate for design purposes; for predictive analysis, however, it might not be su cient to take into account all phenomena taking place inside the charring ablator. For example, materials like PICA possess orthotropic properties. The thermal conductivity in the “in-plane” direction is significantly higher than in the “through-the-thickness” direction. Thus, the one-dimensional response models usually underestimate the centerline temperature rise.7 Similarly, the permeability of PICA material is higher in the “in-plane” than in the “through-the-thickness” direction, which is in accord with the anisotropic microstructure of the carbon fiber matrix.8 If the pyrolysis gases blowing rate along a curved surface is concerned, a one-dimensional model might not be accurate. But more importantly, it has been hypothesize that surface mass fluxes are greatly influenced by the geometry of the material tested.9 This is of great importance when small test-articles are employed to derive and validate models that are used in very di↵erent geometrical configurations. For instance, as it is not feasible to fit an entire heat-shield in ground tests facilities such as arc-jets or ICP torches, samples of a few inches are being used for validation and model calibration.10–17 Most ablation code, if not all, use simple analysis for the gas transport; the pyrolysis gas is either assumed to instantly exit at the surface (0D assumption), or simply travel along a normal line (1D assumption). In this research e↵ort, the multi-dimensionality behavior of the pyrolysis gas inside samples are presented. Using samples comparable to the ones used in ground testing facilities, it is shown that those assumption