Asymptotic and numerical study of variable-density premixed flame propagation in a narrow channel

Abstract

The influence of thermal expansion on the dynamics of thick to moderately thick premixed flames (flame thickness less than or comparable to the channel height) for a variable-density flow in a narrow, rectangular channel is explored. The study is conducted within the framework of the zero-Mach-number, variable-density Navier–Stokes equations. Both adiabatic and non-adiabatic channel walls are considered. A small Péclet number asymptotic solution is developed for steady, variable-density flame propagation in the narrow channel. The dynamics of channel flames are also examined numerically for O(1) Péclet numbers in configurations which include flame propagation in a semi-closed channel from the closed to the open end of the channel, flame propagation in a semi-closed channel towards the closed end of the channel and flame propagation in an open channel in which a Poiseuille flow (flame assisting or flame opposing) is imposed at the channel inlet. Comparisons of the finite-Péclet-number dynamics are made with the behaviour of the small-Péclet-number solutions. We also compare how thermal expansion modifies the flow dynamics from those determined by a constant-density model. The small-Péclet-number variable-density solution for a flame propagating in a circular pipe is given in the Appendix.