Influence of heat-loss on compressibility-driven flames propagating from the closed end of a long narrow duct

This study focuses on the dynamics of compressibility-driven flames that emerge in narrow tubes, closed at their ignition end, when conductive heat losses through the walls are appreciable. A narrow gap approximation is used to reduce the governing equations to an effectively one-dimensional problem. In long channels this problem admits traveling-wave solutions which we have investigated numerically for finite values of the Zel’dovich number, and asymptotically in the limit of large Zel’dovich numbers. In particular, we describe the flame structure and the dependence of the propagation speed on the physico-chemical parameters, including the heat loss and compressibility parameters, and examine the transition from compressibility-driven to isobaric flames when systematically reducing the representative Mach number.