A modified Lotka–Volterra oscillating chemical scheme for detonation simulation

Abstract

Modified Lotka–Volterra chemical schemes were developed with the goal of performing numerical simulation of detonation driven by single- and multi-stage heat release profiles. An initiation reaction was added to the original Lotka–Volterra model to create an induction zone, which is an important characteristic of combustion process. The kinetics parameters of the reaction rates were adjusted, so that up to eight peaks of heat release could be generated in the steady detonation reaction zone. The structure of steady detonations driven by modified Lotka–Volterra models were examined in detail. Interestingly, the stability criteria typically employed to characterize detonations, i.e., the reduced activation energy and the χ parameter, do not seem to be applicable for Lotka–Volterra schemes exhibiting multi-stage heat release profiles. The applicability of these multi-step chemical models to unsteady detonation simulation was verified through preliminary results obtained for one- and two-dimensional numerical simulations. Under super-critical detonation initiation by a point-energy source, some Lotka–Volterra schemes led to an unusual behavior with large velocity oscillations at large over-drive but a rather steady propagation at near Chapman–Jouguet velocity. Two-dimensional cellular detonation driven by Lotka–Volterra scheme with two stages of heat release and a high activation energy of the initiation step demonstrates some features which are characteristic of a double cellular structure. The present work constitutes a first step toward the understanding of the features and dynamics of detonation driven by Lotka–Volterra schemes as further work is needed to fully grasp the complex responses induced by multiple stages of heat release on detonation dynamics.