Inverse heat transfer methods for global heat flux measurements in aerothermodynamics testing

This review provides a systematical description of the inverse heat transfer solutions applied to global heat-flux measurements using temperature-sensitive-coating techniques in hypersonic wind tunnels. The analytical inverse heat transfer solutions for a two-layer structure (typically a polymer sensor coating on a base) are focused to elucidate the effects of the relevant parameters including the polymer and base thicknesses, the thermal properties of materials, and the convective heat transfer at the base backside. Then, the numerical inverse heat transfer method is developed by incorporating the temperature-dependencies of the thermal properties in heat-flux calculation. Furthermore, correcting the lateral heat conduction effect is formulated as an image deconvolution problem based on a convolution-type integral equation with a Gaussian kernel. Other relevant topics are also discussed, including determining the non-uniform paint thickness distribution, in-situ correction for the effect of the temperature-dependent diffusivity, and in-situ calibration for the thermal penetration parameter of the polymer coating. Examples are given to demonstrate the applications of these inverse solutions in temperature-sensitive-paint (TSP) measurements.