Enhancements to integral solutions to ablation and charring

Abstract

Two new enhancements to the heat-balance integral (HBI) technique improve the rapid prediction of aerothermal response of heat shields of high-speed vehicles. The first enhancement uses a generalized cubic in-depth thermal profile to mitigate the well-known overreaction of classical HBI techniques to rapid changes in aerodynamic heat load. The second enhancement involves a direct method for solving in-depth charring problems in the context of an HBI solution. Together, these enhancements extend approximate HBI techniques to a broader range of aerothermal problems with improved accuracy at only a modest cost in computational speed.

Verification and Application of the Sam Re-Entry Model

“…A bulk heating model is employed for conductors, and insulator response is calculated via a simple correlation [10], or by use of an HBI method [11]. Both of these have been designed to be appropriate for use with ablative materials in conjunction with a heat of ablation approach for the surface recession.…”

Thermo-chemical ablation during reentrant and high altitude skipping flight

“…al. 2 For the finite difference and finite element methods, the heat flux is a nonlinear boundary condition. At each time step the conduction equation is repeatedly solved until the temperature dependent heat load converges.…”

“…The transient heating and chemical evolution of the surface and interior of both carbon and silicon based materials experiencing atmospheric reentry remain subjects of vigorous inquiry 1,2,3,4,5,6,7,8 . Among these, material response calculations have been done using the heat-balance integral 1,2 (HBI), finite element 3 (FE) and finite volume 4 (FV) techniques.…”