RI 7908 Mathematical Study of a Propagating Flame and Its Induced Aerodynamics in a Coal Mine Passageway

The unsteady, one-dimensional, compressible-flow equations have been solved numerically for a deflagration propagating through a gallery of finite length closed at the ignition end and open at the opposite end. These equations were solved for two situations wherein (1) the propagating flame was extinguished after 0.1 sec or before the return of aerodynamic disturbances reflected from the open end, and (2) the flame was allowed to propagate a full 0.8 sec until it was extinguished. It was found that the process of sudden flame extinguishment creates rarefaction waves that, upon entering the burned zone, produce resonance within the burned cavity. For the relatively small value of the product of the expansion ratio (8.5) and the effective burning velocities of 7.4 m sec-1 for the first experiment and 4.9 m sec-1 for the second experiment, it was found that the acoustic approximation provides an adequate estimate of the pressures developed ahead of the flame during the system's early history.