Heat Flux Data Reduction Using a Preconditioning Trial Function

Abstract

This paper presents 1) a new preconditioned data reduction formulation, and 2) enhanced thin-film temperature gauge model for estimating the source heat flux applicable to impulsive test facilities used in hypersonic test programs. In such short-time tests, the heat flux is recovered from an active temperature-sensitive thin film. The physical situation permits a constant-property, semi-infinite substrate heat conduction model to be formulated relating the net substrate heat flux to the thin-film interface. Conventional lumped models assume no volumetric effects in the thin film. An enhanced boundary condition for the substrate is proposed that includes the storage of energy in the thin film. There are cases when the energy storage in the thin film should not be neglected. A parameter-free, physically motivated preconditioner is introduced to the integral equation system. This concept is applied to both the conventional and enhanced thermal models for predicting the source heat flux. A future-time method is proposed as the regularization scheme. The optimal future-time parameter is identified using a thermal phase-plane analysis that provides both a qualitative and quantitative means for estimating optimality. Highly favorable results are demonstrated for the simulated data sets based on a constant heat flux pulse.