Transition characteristics of combustion modes for flame spread in solid fuel tube

This paper provides a new concept based on the Damköhler number (Da) to describe the complete transition behavior found in a flame spread in a solid combustible tube. Through a series of experiments performed with various diameters of the tube, ambient pressure, and oxidizer velocity within a wide range, three combustion modes are observed for the flame spread in a solid fuel tube namely combustion dominated by heat transfer (mode 1), by chemical kinetics (mode 2), and slow combustion sustained under very high blowing conditions (so-called “stabilized combustion”: mode 3). Previous studies on the flame spread in tubes have shown that each transition, from mode 1 to mode 2 (transition 1–2) and from mode 2 to mode 3 (transition 2–3), is characterized by an equivalent velocity and by a friction velocity respectively. Meanwhile, for a flame spread on a fuel plate, it is widely known that both transitions are summarized by the Da. To achieve a comprehensive understanding of the transition characteristics of the combustion modes for the flame spread in the tube, the flame-spread rates under various conditions are experimentally investigated to elucidate the parameters that determine both transitions. First, the authors introduce a laminar friction velocity for the laminar flow region and revealed that transition 2–3 is determined by the laminar and turbulent friction velocity for laminar flow and turbulent flow regime respectively. The correlation between the Da and the friction velocity was experimentally obtained to show that transition 2–3 is consequently determined by the Da. This finding suggests that transition 2–3 corresponds to a blow-off limit that is observed for flame spread on a fuel plate. Second, the same correlation between the non-dimensional flame-spread rate and the Da is obtained, and it clearly showed that the transition 1–2 was determined by the Da. In conclusion, both transition phenomena are physically identical to those observed for on-plate flame spread, except the transition 2–3 occurs instead of the blow-off.