Predicting the pyrolysis temperature for thermally thin fuels in opposed-flow flame spread in the thermal regime

The thermal theory of opposed-flow flame spread assumes that the fuel pyrolyzes at a constant pyrolysis temperature. However, the pyrolysis temperature cannot be thermodynamically determined, and its value is usually assigned from limited amount of experimental data that are available for different fuels. Detailed numerical modeling which employs finite-rate pyrolysis kinetics indicate that the pyrolysis temperature is not a constant across the pyrolysis zone and its value can also depend on several parameters such as the opposed-flow velocity, fuel thickness, etc. This situation is more pronounced for thermally thin solids where steady state conditions at a constant pyrolysis temperature are not achieved. In this work, a simplified scale analysis is performed to understand the behavior and dependence of the pyrolysis temperature and pyrolysis length on the fuel and environmental conditions. Two non-dimensional numbers - a pyrolysis number and a radiation number - are identified in the energy balance relation that control a competing behavior on the pyrolysis temperature. A closed-form formula for the pyrolysis temperature is developed through this analysis in the thermal regime that explains and qualitatively predicts the parametric behavior of the pyrolysis temperature when compared to a comprehensive numerical model and available experimental results. The agreement of the simplified model with the numerical solution can be improved by more properly quantifying the magnitude of the flame heat flux in the pyrolysing region. (C) 2022 The Author(s). Published by Elsevier Inc. on behalf of The Combustion Institute. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/)