A Modified Directional Flame Thermometer: Development, Calibration, and Uncertainty Quantification

Abstract

The directional flame thermometer (DFT) is a robust device used to measure heat fluxes in harsh environments such as fire scenarios but is large when compared to other standard heat flux measurement devices. To better understand the uncertainties associated with heat flux measurements in these environments, a Bayesian framework is utilized to propagate uncertainties of both known and unknown parameters describing the thermal model of a modified, smaller DFT. Construction of the modified DFT is described along with a derivation of the thermal model used to predict the incident heat flux to its sensing surface. Parameters of the model are calibrated to data collected using a Schmidt–Boelter (SB) gauge with an accuracy of ±3% at incident heat fluxes of 5 kW/m2, 10 kW/m2, and 15 kW/m2. Markov Chain Monte Carlo simulations were used to obtain posterior distributions for the free parameters of the thermal model as well as the modeling uncertainty. The parameter calibration process produced values for the free parameters that were similar to those presented in the literature with relative uncertainties at 5 kW/m2, 10 kW/m2, and 15 kW/m2 of 17%, 9%, and 7%, respectively. The derived model produced root-mean-squared errors between the prediction and SB gauge output of 0.37, 0.77, and 1.13 kW/m2 for the 5, 10, and 15 kW/m2 cases, respectively, compared to 0.53, 1.12, and 1.66 kW/m2 for the energy storage method (ESM) described in ASTM E3057.