Flame Spread and Group-Combustion Excitation in Randomly Distributed Droplet Clouds with Low-Volatility Fuel near the Excitation Limit: a Percolation Approach Based on Flame-Spread Characteristics in Microgravity

Abstract

Stable operation of liquid-fueled combustors requires the group combustion of fuel spray. Our study employs a percolation approach to describe unsteady group-combustion excitation based on findings obtained from microgravity experiments on the flame spread of fuel droplets. We focus on droplet clouds distributed randomly in three-dimensional square lattices with a low-volatility fuel, such as n-decane in room-temperature air, where the pre-vaporization effect is negligible. We also focus on the flame spread in dilute droplet clouds near the group-combustion-excitation limit, where the droplet interactive effect is assumed negligible. The results show that the occurrence probability of group combustion sharply decreases with the increase in mean droplet spacing around a specific value, which is termed the critical mean droplet spacing. If the lattice size is at smallest about ten times as large as the flame-spread limit distance, the flame-spread characteristics are similar to those over an infinitely large cluster. The number density of unburned droplets remaining after completion of burning attained maximum around the critical mean droplet spacing. Therefore, the critical mean droplet spacing is a good index for stable combustion and unburned hydrocarbon. In the critical condition, the flame spreads through complicated paths, and thus the characteristic time scale of flame spread over droplet clouds has a very large value. The overall flame-spread rate of randomly distributed droplet clouds is almost the same as the flame-spread rate of a linear droplet array except over the flame-spread limit.