Numerical simulation of the deflagration to detonation transition

The present work is focused on the numerical simulation of the deflagration to detonation transition. The Euler equations expressed for a time-dependent, compressible, and one-dimensional flow with finite-rate kinetics are solved with adaptive mesh refinement. Because of the problem stiffness, a time-step splitting method is used to couple the conservation equations and the chemical kinetics equations. The calculated length of the deflagration to detonation transition in H$_2$ – O$_2$ and CH$_4$ – O$_2$ mixtures in a confined domain and the time evolution of detonation are in good agreement with the theoretical values of constant volume explosions and Chapman–Jouguet conditions. The length of the transitional region is compared with experimental findings for a range of initial fuel concentrations, which shows that the model predicts the tendencies qualitatively well but yields significant quantitative deviations.