Non-linear Estimators for Hypersonic Heat Flux Reconstruction

A novel class of non-linear estimators that minimizes the projection of the error on a multi- resolution basis is developed to improve the accuracy and efficiency of the multidimensional reconstruction of the heat-flux from discrete temperature sensors in non-planar hypersonic boundary layers. This approach uses the local temperature time derivative as the pre-estimator of the heat flux estimation risk in the inverse heat conduction problem. This new approach leads to improved results both in terms of computational efficiency and signal-to-noise ratio when compared to both regularization of the linear response operator and filtering of the temperature measurements. The approach is verified against an analytical verification test case, which shows significant accuracy improvement compared to optimal linear estimators and L2 regularization. It is then applied to experimental data to resolve the heat flux from noisy temperature data collected using fast-response sensors in the Virginia Tech hypersonic wind tunnel at Mach 6. The heat flux agrees very well with the Fay-Riddel approximation. Moreover, the heat transfer coefficient variation over the surface of the test is consistent with Computational Fluid Dynamics simulations of the Reynolds Averaged Navier Stokes (RANS) equations