Revisiting slug calorimeters for hypersonics

This paper describes the first steps toward developing a highly-accurate multi-layered slug calorimeter for estimating the surface heat flux in high-enthalpy flows associated with hypersonic ground test campaigns. Slug geometry, material choices, test conditions, manufacturing method, mathematical modeling and instrumentation selection must be integrated into the design process in order to achieve the desired accuracy outcome. Integration is often overlooked in lieu of simplified data reduction equations that relate in-depth temperature measurements to the desired surface heat flux. Simplified models are often physics deficient and can lead to misleading interpretations. This paper illustrates the need for inclusive modeling in arriving at the data reduction equation for the heat flux gauge. Several important results are highlighted in this paper including the: (a) identification of data reduction model discrepancies; (b) significance of Volterra integral formulations for algorithm development; (c) implementation of a parameter-free preconditioner operated on data reduction model for low-pass filtering; (d) development of the approximation thread for uncertainty propagation; (e) achievement of stability through the future-time method; and, (f) extraction of the optimal regularization parameter through phase-plane and cross-correlation concepts for estimating the “best” heat flux.