Premixed flames in narrow heated channels of circular cross-section: Steady-state solutions, their linear stability analysis and the multiplicity of stable dynamic modes

Abstract

Premixed flames in narrow heated circular channels subjected to a Poiseuille flow are investigated within the constant density model for various Lewis numbers using irreversible one-step Arrhenius kinetics. A global stability analysis of steady-state axisymmetric solutions is carried out, together with time-dependent direct numerical simulations. The analysis reveals the criteria for the appearance of oscillatory and three-dimensional cellular flame structures. The problem is also studied separately within the framework of the narrow-channel approximation.Among the results obtained, the following can be singled out as the main ones. First, the multiplicity of stable dynamic modes, oscillatory and steady-state, taking place for the same set of parameters for flames with Le<1 is demonstrated. The actual occurrence of one mode or another depends on the initial conditions. Second, the appearance of chaotic regimes is shown for flames with Le>1. The chaotic dynamics occurs in a narrow range of values of the flow rate, with Feigenbaum period-doubling cascades taking place both before and after this interval. The results of this study could be useful in the development and use of small-scale combustion devices.Novelty and significance statement: A systematic study of premixed flames in narrow heated circular channels in the presence of Poiseuille flow is carried out for various Lewis numbers using irreversible one-step Arrhenius kinetics. One of the novelties presented in the paper is the linear global stability analysis of steady state axisymmetric solutions of this problem, which has not been reported before. Also, for the first time, the existence of multiple stable dynamic modes, oscillatory and time-independent, which occurs at the same parameter values, is demonstrated for flames with Lewis number smaller than one. For flames with a Lewis number greater than one, cases with chaotic dynamics are found that manifest themselves in a narrow range of the flow rate. Finally, it is demonstrated that the Feigenbaum cycle-doubling cascade can appear before and after this interval of chaotic dynamics. Such analysis has not been reported before for this problem of flames in partially heated channels.