A convective-diffusive reaction zone structure model for turbulent detonations

The present study examines one-dimensional models for the turbulent reaction zone structure of unstable detonations. Simulations of direct initiation are performed with the postulated reaction zone models and the results are compared with experimental measurements of the critical initiation energy in methane-oxygen-nitrogen detonations. First, it is shown that the assumption of inviscid detonations with homogeneous chemistry leads to over-predictions of the initiation energy by several orders of magnitude. This suggests that turbulent transport in the reaction zone plays an important role. One-dimensional models addressing these effects were investigated. The first model assumed homogeneous chemistry and introduced mass, momentum and energy transport in the governing equations, modeled by the gradient mechanism. In order to recover the correct initiation requirements, the transport terms need to be artificially augmented such that the diffusive time scales are comparable to the convective time scales. In the second model considered, the transport terms are neglected and only the effective activation energy in the one-step Arrhenius model is changed. It is found that the effective activation energy required to capture the correct initiation limits is lower than derived from homogenous ignition chemistry by a factor of ∼5. Detonations with such low activation energies are stable, which correlates well with the global stability of turbulent detonations to external perturbations.