Effect of external heat loss on the propagation and quenching of flames in small heat-recirculating tubes

This study investigates the effect of external heat loss on the slow propagation of strongly-burning flames inside narrow heat-recirculating tubes. The system is studied using a two-dimensional numerical model for reactive flow, including conjugate heat transfer, over a range of tube diameters spanning the micro- and the meso-scale. Increasing external heat loss decreases the propagation speed of the slowly-propagating flames, leading to a transition from upstream to downstream propagation, until a heat loss limit is reached. Flames in micro-scale tubes are subjected to an extinction limit, while flames in larger diameter tubes, in the meso-scale range, are subjected to a blowout limit. While the absolute value of the external convective heat loss coefficient at the extinction/blowout limit increases with diameter, the dimensionless volumetric heat loss coefficient decreases with an increase in diameter until an approximately constant value, for the studied conditions, is reached at the blowout limit in the mesoscale range. Discrepancies in the predicted trends of 1-D and 2-D models indicate that 2-D effects play a significant role at larger diameters, not only at the meso-scale, but also in the upper-range of the micro-scale. These 2-D effects, associated with changes in flame shape that allow an increase in burning surface area, are seen to promote stability of the system. Results have implications on the choice of tube diameter to be used in the design of a stable burner optimized for heat transfer to an external heat load.