A comparison of extinction limits and spreading rates in opposed and concurrent spreading flames over thin solids

Flame-spread phenomena over thin solids are investigated for purely forced-opposing and concurrent flows. A two-dimensional, opposed-flow, flame-spread model, with flame radiation, has been formulated and solved numerically. In the first part of the paper, flammability limits and spread rates in opposed flow are presented, using oxygen percentage, free-stream velocity, and flow-entrance length as parameters. The comparison of the flammability boundaries and spread-rate curves for two different entrance lengths exhibits a cross-over phenomenon. Shorter entrance length results in higher spread rates and a lower oxygen-extinction limit in low free-stream velocities, but lower spread rates and a higher oxygen-extinction limit in high free-stream velocities. The entrance length affects the effective flow rate that the flame sees at the base region. This affects the radiation loss and gas residence-time in an opposing way to cause the cross-over. Radiation also affects the energy balance on the solid surface and is in part responsible for the solid-fuel non-burn-out phenomenon. In the second part of the paper, a comparison of flammability limits and flame-spreading rates between opposing and concurrent spreading flames are made; both models contain the same assumptions and properties. While the spread rate in concurrent spread increases linearly with free-stream velocity, the spread rate in opposed flow varies with free-stream velocity in a non-monotonic manner, with a peak rate at an intermediate free-stream velocity. At a given free-stream velocity, the limiting oxygen limits are lower for concurrent spread, except in the very low free-stream-velocity regime, where the spreading flame may be sustainable in opposed mode and not in concurrent mode. The cross-over disappears if the two spread modes are compared using relative flow velocities with respect to the flames rather than using free-stream velocities with respect to the laboratory.