Numerical Investigation on the Effect of Spectral Radiative Heat Transfer within an Ablative Material

The spectral radiative heat flux could impact the material response. In order to evaluate it, a coupling scheme between KATS - MR and P1 approximation model of radiation transfer equation (RTE) is constructed and used. A Band model is developed that divides the spectral domain into small bands of unequal widths. Two verification studies are conducted: one by comparing the simulation computed by the Band model with pure conduction results and the other by comparing with similar models of RTE. The comparative results from the verification studies indicate that the Band model is computationally efficient and can be used to simulate the material\u27s response when exposed to spectral radiative heat flux. To further evaluate the effectiveness of the spectral form of heat transfer, material response simulations were run by taking into account spectral data as the boundary condition. The results indicate a significant difference in temperature and density distributions within the sample. The internal temperatures are predicted higher with early decomposition when the spectral radiative heat flux is considered

Fully Coupled Internal Radiative Heat Transfer for the 3D Material Response of Heat Shield

The radiative transfer equation (RTE) is strongly coupled to the material response code KATS. A P-1 approximation model of RTE is used to account for radiation heat transfer within the material. First, the verification of the RTE model is performed by comparing the numerical and analytical solutions. Next, the coupling scheme is validated by comparing the temperature profiles of pure conduction and conduction coupled with radiative emission. The validation study is conducted on Marschall et al. cases (radiant heating, arc-jet heating, and space shuttle entry), 3D Block, 2D IsoQ sample, and Stardust Return Capsule. The validation results agree well for all the cases within a margin of error of 10%. Thus, the validation results indicate that the coupling approach can simulate the thermal response of material accurately. The coupling scheme is then used to simulate a laser heating experiment that studied the impact of spectral radiate heat transfer on ablative material. The results from the laser ablation simulations indicate the expected behavior and match well with experimental ones implying the effect of spectral radiative flux on the material response

Numerical Reconstruction of Spalled Particle Trajectories in an Arc-Jet Environment

To evaluate the effects of spallation on ablative material, it is necessary to evaluate the mass loss. To do so, a Lagrangian particle trajectory code is used to reconstruct trajectories that match the experimental data for all kinematic parameters. The results from spallation experiments conducted at the NASA HYMETS facility over a wedge sample were used. A data-driven adaptive methodology was used to adapts the ejection parameters until the numerical trajectory matches the experimental data. The preliminary reconstruction results show that the size of the particles seemed to be correlated with the location of the ejection event. The size of the particles ejected from the bottom edge of the wedge varies over three orders of magnitude, whereas the size of the ones ejected from the top (inclined) surface were more uniform (around 10 microns). On the bottom edge, the particles ejected near the leading edge were bulkier (10-1000 microns), where those that ejected further along, had a smaller size (0.1-1 microns)

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We present a novel approach for deriving analytical solutions to transport equations expressed in similarity variables. We apply a fixed-point iteration procedure to these transformed equations by formally solving for the highest derivative term and then integrating to obtain an expression for the solution in terms of a previous estimate. We are able to analytically obtain the Lipschitz condition for this iteration procedure and, from this (via requirements for convergence given by the contraction mapping principle), deduce a range of values for the outer limit of the solution domain, for which the fixed-point iteration is guaranteed to converge