Theoretical development of a new surface heat flux calibration method for thin-film resistive temperature gauges and co-axial thermocouples

This paper presents a theoretically developed and computationally demonstrated surface heat flux calibration method applicable to thin-film resistive temperature gauges and co-axial thermocouples. For this study, the physical situation of interest involves hypersonic shock-tunnel studies. For experiments instrumented with these gauges, constant thermophysical properties are assumed since small temperature variations normally occur in the short-duration run times. Extraction of the net surface heat flux is acquired by resolving a newly formulated first-kind Volterra integral equation that contains calibration data. The proposed calibration method is based on an inverse approach which contrasts system identification methods. Several key advantages to this approach are discussed and demonstrated in the context of these gauges. Advantages of the proposed approach include (a) only one unknown “regularization” parameter is required; (b) estimation of the optimal regularization parameter is systematically and theoretically developed and demonstrated through the energy residuals, (c) computational coding is minimal and computer run times are short, and (d) results indicate robustness, stability and accuracy in the methodology. This calibration formulation and its subsequent regularized numerical method do not explicitly require the thermal effusivity, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sqrt{\rho C k}$$\end{document} owing to its input–output based derivation.