Characterizing fingering flamelets using the logistic model

Abstract

We apply the logistic equation to a class of flame spread that occurs in near-extinction, weakly convective environments such as microgravity or vertically confined spaces. The flame under these conditions breaks into numerous ‘flamelets’ which form a Turing-type reaction–diffusion fingering pattern as they spread across the fuel. Flamelets are steady, based on flame spread measurements, and reach a critical state near extinction where a spread rate plateau reflects a critical heat flux for ignition. Our analysis of experiments performed in a buoyancy-reducing, vertically confined flow tunnel reveals the presence of statistical order in the seemingly random patterns. Flamelets as a group form a dynamic population that interacts competitively for the limited available oxygen. Flamelets bifurcate and extinguish individually, but as a whole, the group maintains a stable size. Flamelets show an exponentially decaying lifetime and a uniform pattern of dispersion. We utilize the continuous logistic model with a time lag to describe the flamelet population growth and fluctuation around a stable population characterized by the carrying capacity based on environmental limitations. We discuss how the physics of the system is expressed through the model parameters.