Evaluation of Directional Flame Thermometer for Real-Time Inversion of Heat Flux

The Directional Flame Thermometer (DFT) is often used to measure heat flux during room fire testing. In literature and practice, heat transfer solutions for the DFT have been post processed. It is important to develop real-time capability for calculating heat flux based on measured temperatures as such capability will allow control of fire testing furnaces. In this study, we show that if a user will accept moderate errors in the heat flux, then a simple forward solution methodology allows heat flux measurements to be made in real-time. Essentially, the “inverse” problem is sufficiently well-conditioned to allow for a simple solution. Both a simple spreadsheet type solution and a finite difference code were used to generate the heat flux. The code was verified in both forward and inverse senses. The calculations were verified through a convergence study of both the forward and inverse solutions in spatial discretization (dx) and temporal discretization (dt). The inverse solution showed expected convergence behavior in both spatial and temporal discretization. In all cases, the solution for the front plate produced a maximum error of around 5%, which decreased as the DFT reached a steady state temperature. The forward and inverse models were validated through experimental testing using a radiant heater panel. The inverse model’s calculations were compared to measurements from a Schmidt-Boelter gage. The front plate heat flux measurements of the DFT matched reasonably well with the Schmidt-Boelter gage (2–6% difference) during the majority of the testing. The heat flux was then used to drive a forward simulation, and the forward model’s calculations were compared to actual temperature data acquired by the tests, producing a difference no greater than 4%. The DFT was also placed into a room fire to evaluate its effectiveness in this environment. The DFT was placed near a sand burner and in a panel fire test. The DFT produced reasonable heat flux values, but had more noise than results from those in front of the radiant heater panel (standard deviation of 1500 W/m² compared to 400–600 W/m²).