Model for Chapman-Jouguet deflagrations in open ended tubes with varying vent ratios

Abstract

We present a gas dynamic model for Chapman-Jouguet deflagrations driving a shock in tubes or congested configurations with rear venting. The model extends the previous work of Chue, Clarke and Lee (Proc. Roy. Soc. 1993) to include rear venting. Two models are formulated, one for a perfect gas with constant heat of combustion, and the second by assuming chemical equilibrium in the product gases and temperature dependent specific heats. In the presence of rear venting, much slower flames and shock strengths are generated; these are controlled by the vent ratio, which reduces the post shock strength and speed of the gas convecting the flame forward. Calculation results are presented for small hydrocarbon-air and hydrogen-air deflagrations. The results of the model are found in good agreement with the critical deflagration speed measured experimentally in large scale weakly confined congested experiments for auto-ignition insensitive mixtures. This suggests that flames in these experiments have reached their maximum Chapman-Jouguet deflagration speed prior to transition. We present a time scale estimate for flame acceleration and auto-ignition behind reflected shocks. For sensitive mixtures for which the flame acceleration time is longer than the auto-ignition time (hydrogen, acetylene), limited experimental evidence indicate transition to detonation at critical speeds lower than the CJ deflagration condition. The time scale ratio thus provides the conditions for which reaching the CJ deflagration condition can be taken as a necessary condition for DDT.