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 to 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.

Models for shock-induced ignition evaluated by detailed chemical kinetics for hydrogen/air in the context of deflagration-to-detonation transition

“…The blast wave emanating from this local explosion may be strong enough to initiate detonation directly involving a gradient mechanism or through subsequent interactions with walls, other shock waves, or with a flame. This mechanism has been observed in experiments by, amongst others, Teodorczyk (1995), Kellenberger and Ciccarelli (2015), and Boeck M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT (2015), and in numerical simulations by, amongst others, Oran and Gamezo (2007), Gamezo et al (2008), 45 and Goodwin et al (2016).…”

Chemical-diffusive models for flame acceleration and transition-to-detonation: genetic algorithm and optimisation procedure

“…Goodwin et al [33,34] have simulated DDT in long rectangular channels containing a mixture of stoichiometric ethylene-air. The channel contained regularly spaced obstacles and the simulations were used to quantify the effects of decreasing the blockage ratio of those obstacles on the DDT mechanism [33]. Details of the computational geometry and simulation conditions can be found in [33,34].…”

“…The channel contained regularly spaced obstacles and the simulations were used to quantify the effects of decreasing the blockage ratio of those obstacles on the DDT mechanism [33]. Details of the computational geometry and simulation conditions can be found in [33,34]. Figure 4 shows a sequence of temperature images from a simulation in which the obstacle blockage ratio is 0.5.…”

“…Sequence of temperature images from a simulation of flame acceleration and DDT for a stoichiometric mixture of ethylene-air, in a channel with a blockage ratio of 0.5. Figure courtesy of Gabriel Goodwin[33,34].…”

Experimental and numerical investigations on propagating modes of detonations: Detonation wave/boundary layer interaction

“…Goodwin et al [25][26] studied DDT and the effect of decreasing blockage ratio in small channels with obstacles by solving the multidimensional reactive NS equations with one-step Arrhenius kinetics, mainly presenting two types of simulations: one with DDT occurring in a gradient of reactivity and another in which DDT arises from energy focusing as shocks converge. Cai et al [27] investigated the diffusion and mixing effects in hot jet initiation and propagation of hydrogen detonations using the two-dimensional reactive NS equations with one-step Arrhenius kinetics.…”