Inverse Ablation Analysis and the Calibration Integral Equation Method

Abstract

The calibration integral equation method has been demonstrated for resolving inverse heat conduction problems based on an invariant sample geometry. This paper proposes to extend its applicability to the investigation of ablation through an abstraction based on forming a fictive surface temperature poised at the nonrecessive origin. Resolving this time-dependent temperature history provides a boundary condition that can be used in a restricted space defined between the nonrecessive origin and an in-depth thermocouple. This fictive temperature (or heat flux) provides an equivalence-based formulation defined in the original spatial domain because the calibration integral equation method is based on conservation principles. The extraction of the fictive boundary condition does not require knowledge of the thermophysical properties or probe position(s) because it is based on calibration. The complexity of ablation requires a compromise between a fully calibrative technique and forward solving approaches. The second step of the two-step process now requires the specification of the thermophysical and geometrical parameters. For this preliminary study, the classical single-ablation temperature inverse problem is revisited but without any additional constraints being imposed. The recession, recession rate, and recession heat flux for a single-temperature ablative material can be solved for by direct means. This paper presents the first test study illustrating the concept and provides highly favorable results using simulated test data based on a Teflon sample with known ablation temperature while under significant thermal loading conditions.