Predictions of flame acceleration, transition to detonation, and detonation propagation using the Chemical-Diffusive Model

Abstract

This paper presents numerical simulations of the evolution of premixed flames in channels with obstacles using the Chemical-Diffusive Model (CDM) coupled to a compressible Navier-Stokes solver. The CDM is a parametric model for chemical reaction and diffusive transport, and it is calibrated to reproduce a set of properties of one-dimensional laminar flame and the Zel’dovich-Neumann-Döring (ZND) detonation. In this work, we use two different CDMs, one calibrated using the theoretical half-reaction distance of the ZND detonation and the other calibrated with the experimental detonation cell size, to simulate a stoichiometric hydrogen-air mixture and investigate flame acceleration, deflagration-to-detonation transition (DDT), and detonation propagation in obstacle-laden channels. As the channel geometry varies, both CDMs predict propagation of fast flames in the choking, quasi-detonation, and CJ-detonation regimes. When the channel width is much greater or smaller than the minimal scale requirement for the onset of DDT, both CDMs predict similar choked fast flames and CJ detonations. In cases where the channel widths are close to the critical conditions, deflagration waves are more likely to undergo DDT if the CDM is calibrated for the half-reaction distance, which produces smaller computed detonation cells than experiments. In numerical simulations of channels with the same geometries as prior experiments, using the cell size-constrained CDM improves predictions of DDT.