A Green’s function approach to heat-flux estimation from temperature-sensitive paint measurements

Abstract

A method for estimating global heat flux from measurements of surface temperature using temperature-sensitive paint (TSP) in hypersonic wind tunnels is introduced. Exact solutions to the one-dimensional heat-conduction equation for two- and three-layer solids of finite depth are obtained using a Green’s function (GF) formulation. GFs describing both the temperature change anywhere within the solid and the mean temperature across the TSP form the basis of an inverse heat-conduction problem, which is then solved using regularized deconvolution to mitigate amplification of measurement noise. The disparity between apparent and true TSP temperatures, arising from the integrated emission intensity across the paint, is minimized by means of an iterative routine considering the statistics of a virtual temperature profile. Numerical simulations of heat conduction in various scenarios are then conducted to verify the validity of the method, while its effectiveness is assessed in the analysis of exemplary wind tunnel experiments.