Modeling maximum flame speeds

A simple gold model for flame acceleration in tubes, caused by repeated obstacles, has been developed using a ''boxcar'' approach. The tube is assumed to consist of a series of chambers separated by obstacles. The feedback mechanism for flame acceleration is modeled by assuming that the effective burning velocity in the nth chamber depends on the same quantity in the (n-1)th chamber. The equation for flame propagation is shown to be a logical difference equation. The equation predicts the various experimentally observed end results of flame acceleration such as total flame extinguishment after a flame has reached a certain critical flame speed, subsonic steady-state flame propagation, and continuous flame acceleration leading to transition to detonation. This equation models flame acceleration phenomenologically by associating various terms with effects such as flame folding, fine-scale turbulence, quenching and gas dynamics. The predicted maximum flame speeds (subsonic flame propagation) for various mixture compositions, obstacle spacings, obstacle blockage ratios, and initial gas temperatures agree with the experimental results fairly well. (orig.)