Effect of decreasing blockage ratio on DDT in small channels with obstacles

Abstract

Multidimensional numerical simulations of an unconfined, homogeneous, chemically reactive gas were used to catalog interactions leading to the deflagration-to-detonation transition (DDT). The configuration studied was an infinitely 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 channel height is kept constant at 3200 µm and obstacle heights varied from 2560 µm to 160 µm to decrease the blockage ratio (br) from 0.8 to 0.05. The compressible reactive Navier–Stokes equations were solved by a high-order numerical algorithm on a locally adapting grid. The initially laminar flame develops into a turbulent flame with the creation of shocks, shock-flame interactions, shock-boundary layer interactions, a host of fluid and chemical-fluid instabilities, and DDT. Several different DDT mechanisms are observed as the br is reduced. For br in the range of 0.5–0.35, the shocks in the unburned material diffract over the obstacles and reflect against the channel wall, forming Mach stems that increase in strength with every obstacle traversed. Eventually, the Mach stem strength is sufficient for the unburned mixture to detonate after it reflects from an obstacle. For br outside of this range, DDT may occur either through Mach-stem reflection or through direct initiation due to shock focusing. Stochasticity of the turbulence leading to DDT in channels with low br is considered.