Modelling of unsteady pool fires – fuel depth and pan wall effects

Abstract

This paper presents physics-inspired mathematical model to predict the time varying burn rate of unsteady pool fires. The model benefits from the observations on the thermal behaviour and select data from systematically and carefully designed experiments on small and large pool fires of n-heptane and small pool fires of diesel, kerosene and ethanol fuels. All modelling features are based on dimensionless quantities. Amongst the three controlling heat transfer mechanisms, convection is dealt with simply. However, conduction and radiant heat transfer models have needed new considerations. A combination of steady and unsteady conduction along the pan wall affected by the thermal properties of the wall material and liquid phase conduction are modelled and validated against specific experiments. Radiant heat transfer modelling differs from the conventional approach to account for fuel depth-dependent enhancement in burn flux in small pans to values comparable to large pool fires. The radiation view factor invokes mass flux based Reynolds number to account for fuel depth-related effects. Several constants are modelled in terms of dimensionless parameters constructed from a large number of physical variables of the pan and the fuel and used in the model such that they allow the best fits between the simulation and a part of the experimental data. All the sub-models combined into a surface heat flux balance provide the temporal variation of the mass depletion as also the relative magnitudes of the fluxes in a MATLAB code. Comparisons of the predictions on the dependence of the burn behaviour on fuel depth, free board, pan diameter and wall material with the experimental data of the present authors and from literature on n-heptane are set out. Comparisons between the predictions and experimental data on diesel, kerosene and ethanol are also set out to show the ability of the model to track the mass loss history based on fundamental properties of the fuel and the pan. The outstanding-to-good quality of predictions in most cases is attributed to the necessary physics taken into account in the model.

Keywords:

• pan fire
• pool fire modelling
• unsteady pan fire model

Acknowledgments

The authors are thankful to the authorities of Jain (Deemed-to-be-university) for encouragement in the conduct of this research.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article.