A theoretical investigation of initiation of travelling combustion fronts in fuel beds from embedded hotspots

The critical initial conditions for establishing a self-propagating reaction front in a moderately exothermic fuel bed are investigated using numerical techniques. The progenitor is a spherical hot ball of specified radius and initial temperature embedded in the fuel bed (as opposed to a constant power or constant temperature hotspot investigated in other contributions). As the ball cools, heat is transferred to the fuel bed, and if this occurs at a sufficiently great rate, a steadily propagating travelling wave will be established that will eventually consume the entire bed. However, there are well-defined sets of initial conditions for which the travelling wave stalls, resulting in partial consumption of the fuel. Understanding and predicting this behaviour is important in fire-safety applications involving transport or storage of moderately reactive substances such as organic powders (flour, custard powder and so on) or materials such as fertilizers or weedkillers. The approach also has relevance in the spread of wild fires through fuel beds such as dry grass or leaves.