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. Keywords: Near-limitfireflameletsreduced buoyancyspread ratethermally-thininstabilityfingeringcombustionpopulationlogistic modelbifurcationextinctiontime lag Acknowledgements The authors gratefully acknowledge the contributions of MSU graduate students Lisa Oravecz-Simpkins and Stefanus Tanaya who designed the Hele-Shaw facility and conducted the experiments that were discussed herein, and Karin Aditjandra, who conducted similar analyses on numerous other tests. The authors also are indebted to the ATHINA project team, who provided engineering support for the work. This research was supported by the NASA Office of Biological and Physical Research Cooperative Agreement No. NCC3-1053 to Michigan State University, and through internal funding at NASA Glenn Research Center at Lewis Field.