Models of CJ Deflagrations and Their Transition to Detonations from the Interaction of a Detonation Wave with a Perforated Plate

Abstract

The last stage of a deflagration-to-detonation transition (DDT) process involves the propagation and acceleration of a fast flame. This process is currently poorly understood. The difficulties lie in its complex structure, which is turbulent and involves multi-dimensional gasdynamic phenomena. Previous experimental studies have established these fast flames from the interaction of a detonation wave with a row of obstacles or porous plate. Two main questions remain unsolved: 1) What is the propagation speed of the fast flame obtained in these configurations and 2), Which factors dominate the occurrence of the DDT phenomenon? To answer these questions, two models have been constructed in the present work. Firstly, a quasi-1D gasdynamic model is proposed for estimating the transmitted reaction front speed and the strength of the transmitted shock. By alternately assuming a Chapman-Jouguet (CJ) deflagration or an inert shock, the model estimated the transmitted shock speeds. The comparison with extensive experimental data for a range of hydrocarbon fast flames revealed that the burning velocity required for transition to detonation was the CJ value. Secondly, a numerical shock-induced ignition model, which can impose mechanical fluctuations from a driven piston, was established in order to investigate the ignition and acceleration process, thereby clarifying the other question of interest. The results from the simulations indicated that the mechanical fluctuations can play an important role in triggering DDT by means of promoting the local ignition and amplification of the reaction front stemming from such ignition. It was also found that the maximum amplification effects occur with a fluctuation period between the non-fluctuated ignition delay and the time scale of chemical energy deposition. The inert simulation results show that two types of gasdynamic effects from the fluctuations were vital to the hot-spot formation. These hot spots make significant contribution to the detonation initiation.