A discrete dynamical model for flame spread over combustible flat solid surfaces subject to pyrolysis with charring: An application example to upward flame spread

A discrete dynamical approach for modelling the early phase of the spread of a flame over a pyrolysing surface of a charring solid is developed. The discrete dynamical model (DDM) consists of a two-dimensional upward spread model coupled with a one-dimensional pyrolysis submodel. One numerical example of applying the DDM to the upward flame spread on a wooden board is provided. The goal of this numerical simulation was to investigate the possibility that the model could describe the transient behaviour of the spread. A qualitative comparison with one test from the literature is performed. In the numerical example, the following features are qualitatively captured: evolution of the pyrolysing area on the surface, transient pyrolysis depth, transient ‘flame spread patterns’ (two-dimensional contour maps of mass flux of gasified fuel, of surface temperature and of pyrolysis depth) and the total mass loss rate.