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.

Time-resolved heat flux determination from fast-responding temperature-sensitive paint measurement in a shock tunnel using transient in-situ calibration

“…The specific definition of the apparent temperature given by Liu et al [13] is complex. For practical convenience, the mean temperature has been considered a reasonable approximation of the apparent temperature [14,17]:…”

“…In addition, Cai et al [16] proposed a numerical iterative method to solve the inverse problem of 1D double-layer semi-infinite heat conduction by addressing the issue of non-linearity due to temperature-dependent thermal properties. Recently, Whalen et al [17] used Green's function for the inverse problem of 1D double-and triple-layer finite heat conduction and adopted an iterative routine to minimize the discrepancy due to the apparent temperature.…”

Fabrication of thin inorganic temperature-sensitive paint using ball milling and its temporal response delay

“…The finite thickness of a TSP brings major issues such as delayed temporal response and spatial diffusion. The heat capacity and thermal conductivity of a TSP lead to a temporal response delay [6][7][8][9][10]. This is a problem in dynamic measurement environments.…”

“…Nagai et al [9] experimentally evaluated that the thickness of a polymerbased TSP (1-10 µm, respectively) can result in heat flux errors. Whalen et al [10] theoretically and numerically showed that the thickness of the TSP can lead to errors in the heat flux. Clearly, the thickness and composition of the TSP layer are crucial factors for TSP measurements.…”