Modeling Mismatched Materials in Heat Flux Reconstruction with Embedded Sensors

Creating heat flux maps is one of the major data reduction tasks of ground-test hypersonic facilities. The ability to embed multiple high-frequency sensing elements improves the perfor- mance of Schmidt-Bolter gauges when there is significant lateral heat flux, i.e., close to the leading edge of fin elements and wings. Hypersonic flow heat transfer tests with mismatched materials were conducted in a Mach 6 quiet facility to demonstrate the ability of embedded- sensor gauges to measure the vector heat flux. A novel algorithm to reconstruct the thermal field in the gauge and extract both the lateral and normal components of the heat flux vector is discussed. This work presents two main innovations: i) a least squares approach to balance the impulse response for mismatched gauge materials, 2) an advanced regularization approach based on cross validation of samples distributed in a K-folded time-series. The reconstruction approach is verified using virtual tests carried out with finite element simulations on gauges with different distributions of epoxy and metal. Validation is carried out on hypersonic wind tunnel tests with both matched and mismatched gauge-article materials. The main findings of this research are that the intergauge heat flux that arises due to mismatched materials is important and accounts for more than 20% of the normal heat flux and that the novel approach to regularization is able to resolve such a lateral heat flux in space-time bases with few sensors (number of spatial splines greater or equal than number of sensors).