Computational Fluid Dynamic Solutions of Optimized Heat Shields Designed for Earth Entry

Abstract : Computational fluid dynamic solutions are obtained for heat shields optimized for aerothermodynamic performance using modified Newtonian impact theory. Aerodynamically, the low-order approach matches all computational simulations within 10%. Benchmark Apollo 4 solutions, at the moment of maximum heating, show that predicted heat fluxes using this approach under-predict convective heat flux by approximately 30% and over-predict radiative heat flux by approximately 16% when compared to computational results. Parametric edge radius studies display a power law reliance of convective heat flux on local edge radius of curvature. A slender, oblate heat shield optimized for a single design point is shown to produce heat fluxes that are 1.8 times what was predicted using the Newtonian approach. For this design, maximum heat flux decreases with the inverse cube of the base cross section sharpness. Uncoupled radiative heat flux results based on CFD solutions for a slender heat shield show that the lower-order approach under-predicts the heating from the radiating shock layer by 70%, suggesting the infeasibility of empirical relations used to predict radiative heat ux for eccentric blunt-body heat shields. Coupled vehicle/trajectory optimized designs are examined for both lunar return (11 km/s) and Mars return (12.5 km/s) and show possible discrepancies for eccentric cross sections using low-order semi-empirical correlations. Ultimately gains suggested by the lower order approach using more complex geometries are not reflected in these high- fidelity simulations. In some respects (especially with regards to the heating environment), the simpler shape (i.e. a 25 spherical segment) is the ideal one.

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