Evaluation of Estimation Methods for High Unsteady Heat Fluxes from Surface Measurements

Shock interactions such as those that occur during atmospheric re-entry can produce extreme thermal loads on aerospace structures. These interactions are reproduced experimentally in hypersonic wind tun-nels to study how the flow structures relate to the deleterious heat fluxes. In these studies, the fluid jets created by shock interactions impinge on a test cylinder, where the temperature resulting from the heat flux is measured. These measurements are used to estimate the heat flux on the surface as a result of the shock interactions. Finding the boundary flux from discrete unsteady temperature measurements is char-acterized by instabilities in the solution. The purpose of this work is to evaluate existing methodologies for the determination of the unsteady heat flux and to introduce a new approach based on an inverse technique. The performance of these methods is measured in terms of accuracy and their ability to handle inherently unstable or highly dynamic data such as step fluxes and high-frequency oscillating fluxes. The inverse methods proved to be the most accurate and stable of the methods examined. Nomenclature cp = specific heat, kJ/kg K H = order of regularization matrix, dimensionless k = thermal conductivity, W/m K q = integrated heat flux, W s/m2 q = heat flux, W/m2 S = objective function T = calculated temperature, K t = time, s x = space coordinate, m Y = measured temperature, K a = regularization parameter, K2 m4/W2 ft ' = variable property correction factor, 1/K A * = distance between nodes, m rj = transformed coordinate, dimensionless K = thermal diffusivity, m2/s p = density, kg/m3 cf) = Kirchoff temperature, K /Vfr~1 = matrix of measurement variances, 1/K2 Subscripts n = time step 0 = nominal value I