A simple formulation to model deflagrative burning behind a detonation front was proposed to determine the dynamics near criticality for stoichiometric hydrogen–oxygen mixture. Two different combustion mechanisms, auto-ignition and deflagrative burning, were separately activated based on local temperature. When the temperature was below the crossover temperature of the chain-branching reaction \(T_{\text{ B }}\) , deflagration was selected. Conversely, an auto-ignition source term was utilized when the local temperature was above \(T_{\text{ B }}\) . This study examined the significance of deflagrative burning on the quenching limit for gaseous detonation in a layer of stoichiometric hydrogen–oxygen semi-confined by nitrogen. With the inclusion of the deflagrative burning model, the propagation limit was significantly extended and the dynamics of a marginal detonation, i.e., higher velocity deficit compared to that given by Zel’dovich, von Neumann, and Döring model with curvature, was reproduced. The proper mass flux for deflagrative burning to reproduce the quenching limit ranged from one to two times the laminar value at post-shock state relevant to the lowest velocity at the near-limit condition, i.e., near the end of the cell. The contribution of deflagrative burning became more important near the limit (peaks of 30%, with a mean of 15%), whereas it was negligible at the supercritical condition far away from the limit. Therefore, the pivotal role of deflagrative burning in reproducing the dynamics of detonation near the limit was highlighted. In addition, the present finding reinforces the detonation paradox that inviscid simulations predict a different trend from that observed in experiment, as in Radulescu (Combust. Flame 195:151-162, 2018).
