Transition to detonation in inhomogeneous hydrogen-air mixtures: The importance of gradients in detonation cell size

Abstract

This paper presents a numerical study of flame acceleration and deflagration-to-detonation transition (DDT) of hydrogen-air mixtures in a channel with obstacles, where the mixture composition has a spatial gradient perpendicular to the wave propagation direction. The mixture composition gradient corresponds to a detonation cell size gradient, which characterizes the detonability or the detonation sensitivity. We use a recently developed chemical-diffusive model (CDM) to investigate the influence of the cell size gradient on the detonability of an inhomogeneous mixture and examine characteristic behaviors of flame acceleration and DDT. The CDM is a parametric model for chemical reaction and diffusive transport processes in compressible Navier-Stokes simulations. When optimized, the CDM can reproduce the correct flame and detonation properties, particularly the detonation cell size. The simulation results show that the ease with which an inhomogeneous mixture can detonate is bounded by the detonation limits of the most and least detonable homogeneous mixture. That is, the run-up distance to DDT of inhomogeneous mixtures with 0.8<ϕ<1.0 is found to be greater and less than the most and the least detonable mixtures with ϕ=1.0 and ϕ=0.8, respectively. Other macroscopic observables in the inhomogeneous mixture such as the average combustion wave speed and the total flame surface area are also in between those in these two homogeneous mixtures. The simulation data showed that pressure waves generated by a deflagration play an important role to re-distribute the prescribed mixture composition. The combustion process occurs preferentially in mixtures that initially concentrate along the unobstructed channel centerline. The numerical results agree with prior experimental findings that the averaged equivalence ratio cannot adequately estimate the detonability of an inhomogeneous mixture.