Effects of gas compressibility on the dynamics of premixed flames in long narrow adiabatic channels

We examine the dynamics of premixed flames in long, narrow, adiabatic channels focusing, in particular, on the effects of gas compressibility on the propagation. Recognising the importance of the boundary conditions, we examine and compare three cases: flame propagation in channels open at both ends, where the pressure must adjust to the ambient pressure at both ends and the expanding gas is allowed to leave the channel freely, and flame propagation in channels that remain closed at one of the two ends, where the burned/unburned gas remains trapped between the flame and one of the two walls. Earlier studies have shown that a flame accelerates when travelling down a narrow channel as a result of the combined effects of wall friction and thermal expansion. In the present work we show that compressibility effects enhance the transition to fast accelerating flames in channels open at both ends and in channels closed at the ignition end. In both situations, the accelerating flames could reach values that, depending on the effective Mach number, are as large as fifty times the laminar flame speed. In contrast, when the channel is closed at the far end, the acceleration is limited and the propagation speed is damped as the flame approaches the far boundary. Moreover, we show that, in channels closed at their ignition end, the flame in sufficiently long channels evolves into a steadily propagating compression-driven flame. The propagation speed of these flames depends exponentially on the constant-volume equilibrium temperature, which is higher than the (constant pressure) adiabatic flame temperature, and is therefore larger than for ordinary isobaric flames. Fast propagating compression waves cannot emerge in channels that remain open at their ignition end because of the reduced pressure forced by the open boundary.