This contribution presents an alternative to classical data reduction techniques to measure the heat transfer using thin-film gauges. A finite-element model of the two-dimensional unsteady heat conduction equation is solved in the cross-sectional area of a metallic airfoil bounded with a polyamide sheet on which thermal sensors are deposited. This novel methodology allows capturing all 2D heat conduction effects that are irremediably neglected with the 1D data reduction technique. The application of this technique in a compression tube facility allows an exact evaluation of the initial wall heat flux into cooled rotor blades. During the spinning-up period, the rotor is spun up to nearly its nominal speed (from 0 rpm to 6200 rpm) resulting in preheating due to drag losses. The long duration of this experiment $(∼450 s)$ and the magnitude of the wall temperature increase result in significant 2D conduction effects that are not accounted for using the 1D approach. In addition, short-duration experiments confirm the existence of 2D effects at smaller time scales $(∼0.5 s)$, as well as the influence of the initial nonuniform temperature distribution in the rotor blade. The resulting flux with such an initial condition appears to be the superposition of the wall heat flux at the end of the spinning up before the test and the flux due to the blow-down itself.

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