On a stabilization mechanism for low-velocity detonations

Abstract

We use numerical simulations of the reactive Euler equations to analyze the nonlinear stability of steady-state one-dimensional solutions for gaseous detonations in the presence of both momentum and heat losses. Our results point to a possible stabilization mechanism for the low velocity detonations in such systems. The mechanism stems from the existence of a one-parameter family of solutions found in Semenko et al. (2016). † However, to the best of our knowledge, no such direct comparison is available in the literature.

Heat and momentum losses in $${\text {H}}_{2}$$–$${\text {O}}_{2}$$–$${\text {N}}_{2}/{\textrm{Ar}}$$ detonations: on the existence of set-valued solutions with detailed thermochemistry

“…The colors represent the mixtures selected, using green, brown, and orange for the undiluted, nitrogen, and argon mixtures, respectively For E a,eff /R u T 0 → ∞, set-valued nor choking solutions are found, as the D-c f curves reach c f → 0 within the quasi-detonation regime. Stoichiometric H 2 -O 2 mixtures with high Ar dilution are thus good candidates for investigating the transition dynamics from the set-valued region to the quasi-detonation regime focusing on detailed kineticinduced effects; a natural extension of the work of Sow et al [24] is out of the scope of the present study.…”

“…Semenko et al [23] and Sow et al [24] used the set-valued solutions to explain the stabilization mechanism of quasisteady low-velocity detonations. The authors postulated that the presence of a set of stable solutions around a given friction coefficient c f at the choking regime could rationalize the experimental observations of Lyamin et al [25] and the rather long steady propagation at low velocities in Sow's transient solutions [24]. Perturbations to the system would not directly move the solution to the upper branch of the D-c f curve but cause slow continuous passages to the neighboring solutions within the set-valued region.…”

“…These solutions cover a continuum region of D-c f space and are thus called set-valued solutions. Sow et al [24] carried out unsteady 1-D simulations to investigate the long-time evolution using these set-valued solutions as initial conditions. The authors revealed interesting dynamics in which a transition to the upper high-velocity quasi-detonation regime takes place or the solution simply stabilizes into a neighboring point within the set-valued region; these results question the rigid convictions regarding the stability of the lower branch of the D-c f curves as the authors were able to sustain lowvelocity detonations for long periods of time.…”