Development and calibration of a thermal model of a Schmidt-Boelter gauge to quantify environmental and installation effects on heat flux measurements for launch vehicles

Abstract

Aerothermal heating is the primary driver for launch vehicle external thermal protection system (TPS) design, except for the smaller areas exposed to high plume radiation heating rates. Aerothermal heating models are frequently calibrated via the data from cylindrical, in-flight, flush-mounted surface heat flux gauges. These sensors, typically copper or aluminum Schmidt-Boelter gauges taking advantage of the one-dimensional Fourier’s law of heat conduction, are used to measure the incident heat flux. This instrumentation, when surrounded by relatively low-conductivity materials (such as cork), can have wall temperatures significantly lower than the surrounding wall temperature. As a result of this substantial disturbance to the convective heating profile, the heat flux indicated by the gauge tends to be considerably higher (potentially by factors higher than 2) than it would have been had the calorimeter not been there. The contributors to this include thermal boundary layer disturbances and radial conductive heat transfer from the hotter insulation. These measurements, if uncorrected, can lead to highly conservative TPS designs. An effort to quantify the radial conduction effects will be presented here. A three-dimensional computational thermal math model has been developed, and includes the details of a Schmidt-Boelter gauge. These details of the model are presented. Calibration of the model was performed via comparison with data collected on flat plates exposed to an aerothermal environment in the Marshall Space Flight Center (MSFC) Improved Hot Gas Facility (IHGF). The analysis includes a study of the sensitivity of results and corrections to gauge design parameters. Analyzed parameters include gauge orientation (i.e. the direction of the high and low thermopile bead lines) with respect to flow direction, the axial location of the thermopile beads and the separation between the high and low beads, and the contact conductance from the calorimeter to the surrounding material.