Reconstruction of Heat Flux Maps Using Embedded Multisensor Gauges for Hypersonic Applications

A novel approach to the reconstruction of the gauge heat flux based on discrete embedded temperature measurements is presented to improve the performance of inverse heat conduction methods when there is significant lateral heat flux. The technique aims at reconstructing both the lateral and normal components in space–time bases and introduces two main innovations: 1) a least-squares approach to balance the impulse response for mismatched gauge materials, and 2) an advanced regularization approach based on cross-validation of samples distributed in a K-fold time series. Validation is carried out on hypersonic wind tunnel tests with both matched and mismatched gauge article materials conducted in a Mach 6 facility. The main findings are that the intergauge heat flux due to mismatched materials is important and accounts for more than 10% of the normal heat flux, that the multidimensional reconstruction is superior to the one-dimensional method that uses single-surface sensors, that glue layers have a marginal effect on embedded sensor gauges, and that the novel approach to regularization can resolve strong lateral heat flux with few sensors. A new predictive elastic-net model is derived from the time-series cross-validation that leads to properly accounting for the variation of the model’s effective degrees of freedom.