Numerical analysis of the bistable propagation of lean premixed hydrogen flames

Abstract

Premixed hydrogen-air flames that propagate in slender channels have been recently found to be bistable in the limit of fuel-lean mixtures and non-negligible heat losses. Specifically, two stable configurations conformed by either a circular or a double-cell flame front arise for the same combination of controlling parameters (fuel mixture, heat transfer). Nevertheless, this multiplicity of solutions lacks a satisfactory explanation that predicts the formation of either one or another structure given a particular ignition transient. In this work, the analysis of a set of numerical simulations is offered to unveil the underlying physics controlling the bistable behavior. The formulation employed here proves that simplified one-step Arrhenius reaction and quasi-two-dimensional equations suffice to reproduce the complex dynamics, rendering three-dimensional effects and detailed chemical kinetics as second-order contributions that may be important, however, to provide exact quantitative results. Specifically, the initial temperature profiles and subsequent expansion of the flow field prescribe the growth of the flame front leading to different curvatures and sizes of the kernel that control the evolution into one of the canonical structures. Moreover, the achievement of double-cell flames require splitting and reorientation processes prior to pairing of isolated flames, which call for specific initialization conditions that enable these transient dynamics.