Origins of instabilities in turbulent mixing layers behind detonation propagation into reactive–inert gas interfaces

Abstract

Interactions of mildly irregular detonation waves with sharp interfaces separating combustible mixtures from an inert gas were modeled numerically using the compressible linear eddy model for a large eddy simulation (CLEM-LES) approach. In recent experiments of Lieberman and Shepherd [“Detonation interaction with an interface,” Phys. Fluids 19, 096101 (2007)], such interactions resulted in a transmitted shock-turbulent mixing zone (TMZ) complex as the reactive wave traveled through the interface separating fuel rich ethylene–oxygen mixtures and nitrogen. Kelvin–Helmholtz (K–H) instability was proposed as the main mechanism contributing to the formation of the turbulent mixing zone. This work aims to determine to what extent K–H plays a role and whether or not other sources of instability contribute to the observed evolution of the TMZ. The results show that full-scale simulations using CLEM-LES reproduce well (qualitatively and quantitatively) the experimental flow features. Upon recasting the simulations in the frame of reference of the node (i.e., the location where the detonation wave meets the interface) and by removing the cellular instability from the front, the growth rates of the TMZ only due to K–H instabilities originating from the velocity difference across the mixing layer were found to be insignificant. Conversely, the addition of controlled perturbations to the detonation front pressure resulted in significant growth of the TMZ. This outcome suggests that the TMZ formation and evolution are heavily influenced by instabilities originating at the front. In this regard, transverse waves associated with the detonation front cellular structure are likely to provide the bulk of TMZ growth through additional Richtmyer–Meshkov instabilities.