Theoretical and numerical study of flame propagation and transition to detonation.

摘要

The ability of accelerating, turbulent flames, which have been observed to reach velocities on the order of hundreds of meters per second, to generate precursor shock waves is of fundamental significance to the transition from deflagration to detonation (DDT) and in a variety of destructive explosions. For sufficiently high flame velocities, the precursor shock becomes strong enough to initiate an explosion in the region between the flame and the shock which can lead to transition to detonation.; Before attempting to model such accelerating flames, it is useful to consider the simpler problem of constant velocity flames. A comparative study of the use of a modified version of the Chi-Perlee numerical code and analytical methods of determining the strength of the shock wave generated by a flame propagating at a relatively high, but constant velocity, and the induction length and hence sensitivity of the combustible mixture behind the precursor shock wave have been reported in this study. Validation of the numerical code was provided by the excellent agreement of the numerical results with the exact non-linear solution of this problem. Above a flame burning velocity of 200 m/sec, it was found that the induction length behind the shock decreases to a small fraction of the flame-shock distance, providing a clear indication that the combustion reactions behind the shock must be taken into account. The numerical calculation was performed taking the combustion reaction behind the shock into account when the ratio L{dollar}sb{lcub}rm i{rcub}{dollar}/L{dollar}sb{lcub}rm sf{rcub}{dollar} of the induction length L{dollar}sb{lcub}rm i{rcub}{dollar} to the distance between the shock and the flame L{dollar}sb{lcub}rm sf{rcub}{dollar} becomes less than the value of unity. The result of numerical calculation clearly shows that a steady detonation has been established by initiation of explosion by a flame driven shock wave.; The numerical code validated for steady flames was also used to study the flowfields generated by accelerating flames for four different regimes of flame acceleration. It was found that due to the interaction between shock waves, flames, expansion waves, and contact surfaces which arises in the flowfields generated by accelerating flames, the overpressure generated by an accelerating flame may exceed that produced by a constant velocity flame propagating at the final or maximum velocity of the accelerating flame.