Influence of turbulent fluctuations on detonation propagation

Abstract

The present study addresses the reaction zone structure and burning mechanism of unstable detonations. Experiments investigated mainly two-dimensional methane-oxygen cellular detonations in a thin channel geometry. The sufficiently high temporal resolution permitted to determine the PDF of the shock distribution, a power-law with an exponent of -3, and the burning rate of unreacted pockets from their edges -through surface turbulent flames with a speed approximately 3-7 times larger than the laminar one at the local conditions. Numerical simulations were performed using a novel Large Eddy Simulation method where the reactions due to both auto-ignition and turbulent transport and treated exactly at the sub-grid scale in a reaction-diffusion formulation. The model is an extension of Kerstein & Menon's Linear Eddy Model for Large Eddy Simulation to treat flows with shock waves and rapid gasdynamic transients. The two-dimensional simulations recovered well the amplification of the laminar flame speed owing to the turbulence generated mainly by the shear layers originating from the triple points and subsequent Richtmyer-Meshkov instability associated with the internal pressure waves. The simulations clarified how the level of turbulence generated controlled the burning rate of the pockets, the hydrodynamic thickness of the wave, the cellular structure and its distribution. Three-dimensional simulations were found in general good agreement with the two-dimensional ones, in that the sub-grid scale model captured the ensuing turbulent burning once the scales associated with the cellular dynamics, where turbulent kinetic energy is injected, are well resolved.

Dynamics of detonations with a constant mean flow divergence

“…For the acetylene mixture, the reduction in effective activation energy is 14%, while for propane, the reduction in the activation energy is by 54%! The significantly lower effective activation energy for the much more unstable propane mixture is not surprising, as it was already noted that the enhancement of burning mechanism in turbulent detonations by turbulent mixing suppresses much of the thermal character of the ignition mechanism, where the reaction zone length does not grow with velocity deficit, as anticipated from thermal ignition considerations (Radulescu Maxwell et al 2017). Instead, the rapid burn-out of non-reacted pockets by diffusive processes explains why the reaction zones remain substantially shorter.…”

“…These trends differed fundamentally from experimental observations, where the opposite trend was found, mainly that cellular detonations have an enhanced detonability than anticipated from ZND-type models neglecting the cellular structures, and that more unstable detonations were more detonable than stable ones. It was recently suggested that turbulent mixing in the reaction zone of unstable detonations, absent in the inviscid simulations of the above studies, may account for these discrepancies (Maxwell et al 2017). Indeed, diffusive effects were found to have profound differences even in onedimensional detonation dynamics (Romick et al 2012).…”

“…In gases, real detonations are multi-dimensional and their reaction zone is often turbulent; deviations from the ZND model are substantial (Lee 2008;Shepherd 2009) and cannot be treated as perturbations. Analysis of unstable detonations revealed that although the structure is highly transient, it recovers qualita-tively a quasi-one-dimensional average structure analogous to the ZND structure, with an average sonic surface (Gamezo et al 1999;Radulescu et al 2007b;Reynaud et al 2017;Maxwell et al 2017). It thus appears that, with the appropriate kinetic description for the averaged fluid state and speed dictated by an effective rate of energy release, the ZND model with its extensions may be an appropriate framework to model real detonations at the macro-scale.…”

Diffusion and mixing effects in hot jet initiation and propagation of hydrogen detonations

“…Large-scale vortices involved in the highly unstable shear layers dominate the formation of the turbulent flow and the rapid turbulent mixing between the unburned jet and burned product. Maxwell et al (2017) also showed that for planar detonation propagation in a thin channel, turbulent mixing rates can significantly influence the observed cell patterns and detonation structure. Therefore, to account for diffusion and mixing effects, rather than the commonly known classification of weakly unstable and highly unstable detonations, it should be more appropriate to quantify to which extent the unburned reactant is still present behind the shock front under a specific condition.…”

Mechanism of detonation stabilization in a supersonic model combustor

“…Maxwell et al . (2017) have reported that the triple point is a location of high temperature and pressure due to shock compression from multiple waves as well as a source of enhanced turbulent mixing. These triple points can give rise to slip lines further developing into shear layers that are susceptible to the Kelvin–Helmholtz (KH) instability (Massa, Austin & Jackson 2007), hence acting to enhance the turbulent mixing between the unburned pockets and burned gases (Gamezo, Ogawa & Oran 2007; Oran & Gamezo 2007).…”