# Ablation and Material Response

Accurate prediction of ablation and material response requires coupled analysis of both the flow field and the material that is used. The approach taken in this work to simulate the fluid-solid coupling is to use a previously developed CFD code, LeMANS, and couple it via boundary conditions to a material response code. This leads to an iterative solution process during which the two codes are run sequentially to provide updated boundary conditions for one another. This iterative process is continued until the coupled problem is converged.

Currently, there are two material response codes that have been developed for use in this coupled framework. The first is a one-dimensional code called MOPAR (Modeling of Pyrolysis and Ablation Response) which uses a Control Volume Finite-Element Method (CVFEM) and can model both charring and non-charring (surface ablative) materials. The code solves the mixture energy equation, the solid phase continuity equation, the gas phase continuity equation, and the momentum equation. The first two equations are solved implicitly on a contracting grid using Landau coordinates and Newton's method for non-linear systems. The third equation is solved via direct integration of the kinetic equations, and so a numerical solution technique is not needed. Finally, the momentum equation is averaged to Forchheimer's Law for flow through a porous medium, and directly integrated in the gas phase continuity equation. Figure 1 shows the results of a validation study performed with MOPAR.

Figure 1: Comparison of 1D MOPAR results to experimental arc-jet measurements of surface temperature.

The second material response code is a multidimensional extension of MOPAR. This code is currently used for non-charring ablative materials, and solves the energy equation implicitly for 2D/axisymmetric and 3D geometries. Extending the material response predictions to multidimensional geometries provides two major benefits: the capability to model "sharp" geometries such as leading edges where a 1D material approximation breaks down, and the capability to model anisotropic materials.

Both material response codes have been coupled to the CFD code, LeMANS. Figures 2 and 3 show a comparison between the 1D and multidimensional (axisymmetric in this case) material response codes for one trajectory point of the IRV-2 vehicle's flight path. These results are for a fully coupled fluid-solid simulation and show the temperature contours for both the flow and the solid in Figure 2, and the temperature and heat flux results at the IRV-2 surface in Figure 3.

Figure 2: Comparison of flow and solid temperature contours for the 1D and axisymmetric material response codes for the IRV-2 vehicle. The bottom figure is close-up of the nose region in the left figure.

Figure 3: Comparison of surface properties for the IRV-2 vehicle predicted by the 1D and axisymmetric material response codes.

As can be seen from the above figures, the axisymmetric results predict a higher surface temperature than the 1D model. This is due in part to a lower predicted rate of heat conduction away from the surface and into the material in the axisymmetric model. In addition, the temperature contours in the axisymmetric case are more swept back near the vehicle's shoulder than in the 1D case due to the ability of heat to diffuse within the material. This also demonstrates the need for multidimensional modeling of material response to obtain accurate results for geometries with relatively high curvature such as the nose region of the IRV-2 vehicle.

Current work is focused on continuing the development of the multidimensional material response code to allow for, among things, the prediction of material stresses due to flow induced thermal loads. In addition, work is being done to ensure the robustness and accuracy of simulations involving multiple coupled codes by developing effective convergence criteria and verification tests.

### Acknowledgments

Funding for this work is provided by the Air Force Research Laboratory through the Collaborative Center in Aeronautical Sciences.

### Recent Publications

- Wiebenga, J.E. and Boyd, I.D.,"Computation of Multi-Dimensional Material Response Coupled to Hypersonic Flow",
*43rd AIAA Thermophysics Conference*, New Orleans, Louisiana, June 25-28 2012, AIAA paper 2012-2873.