Thermal quenching and re-ignition of mixed pockets of reactants and products in gas explosions

An approximate solution of the problem of quenching and re-ignition of products/reactants pockets mixed by turbulence is presented. The approach is based on the analysis of thermal regimes of the pocket, but not on the concept of flame stretch. Critical conditions for quenching and re-ignition of the mixed pockets are obtained in a simplified analytical model, and applied to the problem of the sharp difference between the cases of weak and strong flame acceleration in gas explosions. The critical conditions of the mixed eddies in the turbulent flow are shown to depend on the size of the mixed eddies, mixture properties and turbulence intensity. The critical Karlovitz number, Ka, for thermal quenching is shown to increase with the ratio of densities between reactants and products, σ, and with the overall reaction order, n, and to decrease with the Zeldovich number β (dimensionless activation energy) and Lewis number, Le. For the smallest mixed pockets, which are about the size of the laminar flame thickness, the critical Ka-number defines the boundary of the domain of broken flamelets and distributed reaction zones. This number is shown to be of the same order of magnitude as that found from experiments and from direct numerical simulations. The critical conditions for thermal quenching of the largest pockets that can be mixed by turbulence are shown to be independent of the turbulent intensity and could be expressed as a function of σ on β, n, and Le. The mixture properties, thus, may prescribe certain types of flame behavior in turbulent flows. The corresponding critical conditions are linked to the sharp boundary between the cases of weak and strong flame acceleration, which was not satisfactorily explained in previous studies. These critical conditions are shown to have similar critical σ-values and general trends as the experimental data.