Multiplicity of solutions of lifted edge flames: symmetrical and non-symmetrical configurations

Abstract

A numerical investigation of the combustion process taking place after fuel and oxidizer are injected separately into a planar channel from an end-wall porous plug is presented. A fuel stream injected in the middle of the channel is surrounded on both sides by oxidizer streams and two edge flames are formed after contact of reactants and ignition. The formulation of the problem is symmetrical with respect to the middle of the channel. The study is based on the coupled Navier-Stokes and transport equations with one-step Arrhenius-type combustion kinetics. The main focus is on the influence of the fuel Lewis number, the flow rate and the Damköhler number on the flame structure. It is shown that symmetrical and non-symmetrical configurations of edge flames are possible for the same set of parameters, and that these solutions can be simultaneously stable. At the same time, the areas of existence of symmetric and non-symmetric flame configurations turn out to be different. Further, it is demonstrated that there can be at least seven different (but not all stable) steady-state solutions for the same set of parameters, although the evidence for the absence of other solutions, in addition to those found, cannot be achieved within the framework of the methods used in the study. These results may be critical for flames with low fuel Lewis number (e.g. hydrogen flames) and highlight the importance of taking into account the possibility of non-symmetrical flame configurations in the design and operation of combustion devices based on diffusion flames.