Flame acceleration in a narrow channel with flow compressibility and diverging or converging walls

We study the effects of non-parallel (diverging or converging) channel walls on flame propagation and acceleration in planar and cylindrical narrow channels, closed at the ignition end and open at the other, accounting for thermal expansion in both the zero Mach number and weakly compressible flow limits. For parallel channel walls, previous work has shown that thermal expansion induces an axial flow in the channel, which can significantly increase the propagation speed and acceleration of the flame. In this study, we consider examples of diverging/converging linear walls, although our asymptotic analysis is also valid for curved walls. The slope of the channel walls is chosen so that the magnitude of the thermal-expansion induced flow through the channel obtained for parallel walls is modified at leading-order, thereby influencing the leading-order flame propagation. For zero Mach number flows, the effect of the diverging/converging channel walls is moderate. However, for weakly compressible flows, the non-parallel walls directly affect the rate at which pressure diffuses through the channel, significantly inhibiting flame acceleration for diverging walls, whereas the flame acceleration process is enhanced for converging walls. We consider several values of the compressibility factor and channel wall slopes. We also show that the effect of a cylindrical channel geometry can act to significantly enhance flame acceleration relative to planar channels. The study reveals several new physical insights on how non-parallel channel walls can influence the ability of flames to accelerate by modifying the flow and pressure distribution induced by thermal expansion.