Analytical methods for determination of heat transfer fields from temperature sensitive paint measurements in hypersonic tunnels

This paper describes the analytical methods used for temperature sensitive paint (TSP) measurements to obtain quantitative global heat-flux diagnostics in the hypersonic environment on important physical phenomena like laminar-turbulent transition, near-surface stationary vortices and separation. This problem is generally considered as an inverse heat transfer problem. The exact analytical solution of the 1D unsteady heat conduction for a polymer layer (TSP or TSP/insulating-layer) on a base of any material is obtained and used to calculate heat flux into the polymer surface as an explicit function of a time-dependent surface temperature change measured by TSP in hypersonic tunnels. In addition, an analytical solution of the 3D unsteady heat conduction equation is given to include the effect of the lateral heat conduction. Simulations and experiments are conducted to examine the analytical method and assess the relevant factors regarding the measurement uncertainty.

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