Edge-flames in circular channels: Multiplicity of steady-state axisymmetric solutions

Abstract

A numerical study of the combustion process occurring after separate injection of fuel and oxidizer through an end-wall porous plug into a semi-infinite circular channel is presented. The fuel flow is injected into the center of the channel, surrounded by the oxidizer flow in an axisymmetric manner. It is assumed that the channel walls and the porous plug are kept at constant (cold) temperature. The study is based on the coupled Navier–Stokes and transport equations with one-step Arrhenius-type combustion kinetics. The structure of the combustion field consists of an edge flame located in the reactants mixing layer and a diffusion flame following it. The study is limited to finding axisymmetric solutions. It is found that, for certain values of the parameters, the system can have multiple (up to four) axisymmetric solutions. Particular attention is paid to finding the bifurcation points bounding these multiple solution regions in parametric space. It is shown that in all likelihood the effect of the fuel Lewis number, 𝐿𝑒𝐹 , is decisive for the emergence of multiple modes. For 𝐿𝑒𝐹 = 1 only two modes appear, while with a decrease in 𝐿𝑒𝐹 the number of modes can increase to four. Although the analysis of the stability of the different regimes remains outside the scope of this work, the shape of the curve relating the flame position to the reaction Damköhler number suggests that only two of them can be simultaneously stable.