Percolation theory for flame propagation in non- or less-volatile fuel spray: A conceptual analysis to group combustion excitation mechanism

A percolation theory for flame propagation in non- or less-volatile fuel spray is developed based on a cubic lattice model representing a local spray state. The interdroplet flame propagation characteristics found from microgravity experiments on flame spread along a linear droplet array are applicable to describing interdroplet flame propagation between neighboring droplets in any distribution of droplets because the effect of heat conduction from the flame front is shielded by the nearest unburned droplet, which acts as a heat sink. Thus, once the method by which the unburned droplet nearest to the flame front is ignited is identified and formulated into a simple algorithm rule, we can examine by computer simulation the statistical flame propagation behavior in a non- or less-volatile fuel spray in the framework of the percolation theory. In non- or less-volatile fuel, an unburned droplet swallowed by an envelope diffusion flame of other droplets is heated and becomes a new supplier of fuel vapor to the flame front, allowing the flame front to advance. For randomly distributed droplets, the flame front selects the path that minimizes its propagation time. These two phenomena occur when the grid spacing of the cubic lattice model is equal to the maximum flame radius of an isolated droplet immersed in the same air conditions as the local spray state. Furthermore, physical considerations reveal that the lattice size that leads to statistically meaningful information can be rather small, i.e., 20×20×20 vertices. Therefore, the proposed percolation theory is tractable and useful in finding the probability that a flame front propagates across a spray element and for exploring the mechanism of the excitation of group combustion for non- or less-volatile fuel sprays.