Correlation for wall-temperature oscillations in unsteady stagnation point convective heating

Abstract

The purpose of this paper is to provide insight into how unsteady flow temperature affects the wall temperature of test articles exposed to convective heating. To this end, a simplified analytical correlation is derived that allows the determination of wall temperature fluctuation amplitude in the case of an unsteady freestream. Stagnation point flows with oscillating freestream temperature are analysed applying self-similar boundary layer theory. The correlation reveals that the problem is fully described by two non-dimensional parameters: the ratio of fluid and solid thermal effusivities, and the ratio $\sqrt{\mathrm{Sr}\mathrm{Pr}\mathrm{Re}}/\mathrm{Nu}$ of Strouhal, Prandtl, Reynolds, and Nusselt numbers. Numerical conjugate heat transfer simulations are performed for a solid test article subjected to convective heating. The derived analytical correlation agrees well with simulation results, spanning ten orders of magnitude in wall-to-freestream temperature amplitude ratio, with maximum discrepancies of 35%. Deviations from theory occur for low frequencies where the wall temperature of the solid medium undergoes significant temperature changes. Experimental measurements of an unsteady plasma freestream are analysed, predicting wall-temperature fluctuations of test articles of different sizes. High frequency content is shown to have little influence, while low frequencies contribute most to wall temperature fluctuations. Small sample sizes are shown to suffer from much larger wall-temperature fluctuation amplitudes, and high-density flow conditions are more severely affected. The derived theory can be applied to aid in both design and analysis of unsteady convective heating experiments.