A New Calibration Method for Thin-Film Resistive Temperature Gauges For Estimating Heat Flux in Shock Tunnel Applications

摘要

This paper describes a surface heat flux calibration method applicable to thin-film resistive temperature gauges; co-axial thermocouples; and, null-point calorimetry. A first-kind Volterra integral equation is derived from frequency analysis of the linearized, semi-infinite heat equation applicable to short-time applications. The resulting linearized calibration integral equation is developed in alternative forms involving temperature, Kirchhoff temperature and thermophysical properties. Data are simulated using the fully nonlinear heat equation that properly accounts for temperature dependent property variations. Simulated temperature data from the nonlinear problem attempts to emulate a physical experiment. Accurate and stable results are reported even in the presence of significantly noisy data. Several revelations are presented within the calibration framework including alternative linearizations based on thermophysical properties. Several advantages to this approach are discussed and demonstrated in the context of these gauges. Advantages of the 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.