Shock transition to detonation in channels with obstacles

Abstract

Multidimensional numerical simulations of an unconfined, homogeneous, chemically reactive gas were used to study interactions leading to deflagration-to-detonation transition (DDT). The configuration studied was a long rectangular channel with regularly spaced obstacles containing a stoichiometric mixture of ethylene and oxygen, initially at atmospheric conditions and ignited in a corner with a small flame. The compressible reactive Navier–Stokes equations were solved by a high-order numerical algorithm on a locally adapting mesh. The initial laminar flame develops into a turbulent flame with the creation of shocks, shock–flame interactions, shock–boundary layer interactions, and a host of fluid and chemical-fluid instabilities. The final result may be eventual deflagration-to-detonation transition (DDT). Here two types of simulations are described, one with DDT occurring in a gradient of reactivity, which is common in the channels with higher obstacles, and another in which DDT arises from energy focusing as shocks converge. For the latter case, the rate of energy deposition necessary to initiate a detonation in the unburned gas is analyzed using a control volume analysis.