One Dimensional Heat Flux History Estimation From Discrete Temperature Measurements

Extreme thermal environments such as atmospheric reentry can generate unsteady heat fluxes on aerospace vehicles. These high heat fluxes are typical of shock interactions and will produce extreme thermal loads on materials exposed to such environments. Such heat fluxes are reproduced experimentally in a hypersonic wind tunnel. The fluid jets created by shock interactions impinge on a test cylinder, where the temperature due to the heat flux is measured. Finding the boundary flux from discrete unsteady temperature measurements in the interior of a material is often referred to as the inverse heat conduction problem and is characterized by instability in the solution. These instabilities are further magnified by experimental measurement errors. Even though the measured temperatures in this case are on the surface, the approach will be to employ an inverse technique so that a stable solution can be obtained in the presence of random experimental errors. The inverse technique, based on a least squares fit of measured and calculated temperatures, introduces a regularization (or smoothing) term to maintain stability in the solution. This method proved to be more accurate and flexible in reducing measured temperature data into boundary heat flux histories than traditional techniques.