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.