Material Response Reconstruction of Ablative TPS Using Accurate Boundary Layer Modeling

In hypersonic atmospheric entry missions, charring ablators are often used. These materials are made of a non-pyrolyzing matrices (carbon, ceramic, etc.) combined with pyrolyzing materials (phenolic, silicon resin). Pyrolysis is the process in which the polymer gradually carbonizes at high temperature, losing mass and generating pyrolysis gas. Once generated inside the matrix, the gas is expelled at the surface, therefore changing the chemical composition of the boundary layer, and influencing the thermal conductivity. Pyrolysis gas transport is modeled using porous media flow equations. The gas is usually assumed to travel along a line, either instantaneously (in so-called 0D, like STAB, FIAT), or according to Darcy's Law (in 1D, like CHAR). Since the gas is blown into the chemical reacting boundary layer, models of the transport are crucial to determining the boundary conditions for the solution of the flow field. As oppose to other recent TPS, such as the one used for MSL, Stardust or Dragon-X, the Orion heat shield is made of AVCOAT, which is a much more complex material. First, AVCOAT is not made of a solid preform, but of an epoxy novolac resin to which carbon and silica fibers are added. The material is injected into a fiberglass honeycomb matrix, which is bonded to the structure. When subjected to high temperature, the resin pyrolysis, leaving behind a carbon/silica char. The char itself also starts to reacts, and recesses, which leaves the honeycomb structure protruding at the surface. The silica also melts, resulting in glassy streaks on the surface of the material. A high fidelity simulation of such material therefore requires to take all these physical, chemical and geometrical phenomenon in consideration. The material models currently used for sizing TPS are based on models that have been designed during the Apollo era. Although tit has been "modernized" to better replicated the behavior of modern-day AVCOAT, but remains very similar to the original one. This model performs well enough to provide analyses that leads to successful missions, but they certainly could benefit from being updated. so that they could be used in more sophisticated material response codes. For instance, the pyrolysis gas flow is not taken into account, leading to some uncertainties in the boundary layer effects and in the convective transport at the surface. Moreover, certain phenomenon, such as a mysterious "hump" that appears in the data and that has been attributed to the presence of water, is not modeled at all. Finally, reaction kinetic at the surface often assume chemical equilibrium, which provides good results in certain regime, but erratic behavior in other (the so-called "end game" effect). The current proposal aims at using a statistical approach to redesign from he ground up the AVCOAT material model currently used by NASA. Using uncertainty analysis, the extensive AVCOAT arc-jet data will be thoroughly analysis, and used to estimate the best parameters to be used for simulations. This new material model will then be applied to the EFT-1 flight data, and its accuracy will be assessed. An inverse problem approach will also be used on the flight data itself to estimate the transmitted heat flux from the aerothermodynamic heating. This will therefore allow to fully estimate the accuracy of the boundary layer approximations used in the hypersonic CFD code used to reconstruct the flow field. This analysis will be performed using the high-fidelity Material Response code KATS, which solves the conservation equations for mass (gas and solid), momentum (in 3D), and energy. The momentum equation is a steady-state version of Darcy's Law, also known as the Darcy- Brinkman equation. The code uses a multi-scale approach to solve the interaction of the fibers with the pyrolysis gas, and can be efficiently coupled to a hypersonic aerothermodyanmics code. Using KATS, incertainty quantification (UQ) and sensitivity analysis (SA) will be applied to the experimental measurements and computational simulations. With UQ, a formal comparison between the experimental data and simulations will allow the proper validation of the computational models. SA will enable the determination of important model parameters and variables measured in the experiments and included in the simulations that a.ect the output quantities of interest. The UQ and SA will be performed with methods based on stochastic expansions, which have been shown to be computationally efficient and e.ective for modeling and propagating uncertainty in complex physics simulations with high non-linearity and large number of uncertain variables. As a second task, a new integrated modeling approach will be developed and tested. Contrary to the state of the art approach which consist of coupling (loosely or not) a CFD code to a Material Response code, the new method proposes to solve the whole domain using one general set of equations for both the flow field and the porous ablator. This approach has the advantage of e.ectively removing all boundary layer assumption currently used in aerothermal boundary conditions by letting the code calculate the surface fluxes intrinsically, and not by imposing approximate surface balance equations. This new approached has been implemented in the KATS framework, and has been tested on simple problem, using simplified geometry. More development will be needed to fully accomplish the tasks. For instance, the current implementation uses an AUSM+-UP shock capturing scheme, which works well for supersonic and subsonic region, but might need to be modified for hypersonic flow so that accurate heat fluxes are computed. The fully-integrated method will first be tested on simple problem (1D, 2D, arc-jet article) and then will be ported to larger problem such as certain section of the EFT-1 heat shield. Since this approach necessitate a time accurate simulation, it is unlikely that the whole spacecraft could be modeled this way, because of the vast amount of computational resources needed. Finally, a complementary third task is included in this proposal. Since the AVCOAT material is considered ITAR restricted, it is very difficult to use in the open research community. However, publications made during the Apollo era are still openly available, and present enough data to provide the basis of a working material model. Although the modern version of AVCOAT is different than that was used on Apollo spacecrafts, it remains similar enough that general behaviors would still be reproduced. As a parallel effort, it is proposed that this published data be used to design a material model similar to AVCOAT. Such a model will allow the international community to participate openly, and transparently in the development of physical models that are pertinent to AVCOAT, without having to worry about ITAR restrictions. A similar effort was made in the past for NASA's lightweight charring ablator PICA, with the TACOT material model.