Design of Phosphor Thermometry System for Transient High Heat Flux Surface Thermometry

Abstract

Abstract: A transformative calibration methodology is presented for predicting transient surface temperatures in a thermally conducting medium from in-depth, time-varying temperature measurements. The surface temperature is resolved using two experimental runs and a newly devised first-kind Volterra integral equation. The first experimental run involves calibration with known surface temperature while the second run involves resolving the surface temperature of interest through the ill-posed integral equation. This paper presents the concept genesis and numerically demonstrates the concept for feasibility, robustness, stability and accuracy. From this demonstration, we propose to implement surface placed thermographic phosphors in the calibration stage of the inverse method for estimating the required surface temperature. As a preliminary study, we consider transient, constant property, onedimensional heat conduction in a semi-infinite medium. It is mathematically demonstrated that a Volterra integral equation of the first kind is developed for estimating the surface temperature using a calibrated system (host material and sensor). Sensor characterization, explicit sensor positioning and thermophysical properties are implicitly contained in the new calibration integral equation. The calibration integral equation displays only four terms; namely, the measured front surface temperature and corresponding measured in-depth temperature response associated with the calibration run; and, the unknown surface temperature and its measured in-depth temperature response associated with the second run. Preliminary numerical results indicate the merit of the concept. This paper suggests using thermographic phosphors for estimating the surface temperature in the calibration portion of the process owing to their rapid thermal response, good surface thermal contact characteristics and lack of capacitance for assuring minimal delay. Though the present paper describes the theoretical basis for resolving such problems, it is intended for near-term application using the UTK’s high-heat flux laser facility which is presently under development