Numerical Simulation of Deflagration to Detonation Transition in a Straight Duct: Effects of Energy Release and Detonation Stability (Advances in Applied Mathematics and Mechanics, 2021)
Numerical simulation based on the Euler equation and one-step reaction model is carried out to investigate the process of deflagration to detonation transition (DDT) occurring in a straight duct. The numerical method used includes a high resolution fifth-order weighted essentially non-oscillatory (WENO) scheme for spatial discretization, coupled with a third order total variation diminishing Runge-Kutta time stepping method. In particular, effect of energy release on the DDT process is studied. The model parameters used are the heat release at $q=50, 30, 25, 20, 15, 10$ and $5$, the specific heat ratio at $1.2$, and the activation temperature at $Ti=15$, respectively. For all the cases, the initial energy in the spark is about the same compared to the detonation energy at the Chapman-Jouguet (CJ) state. It is found from the simulation that the DDT occurrence strongly depends on the magnitude of the energy release. The run-up distance of DDT occurrence decreases with the increase of the energy release for $q$=50~20, and increases with the increase of the energy release for $q$=20~5. This phenomenon is found to be in agreement with the analysis of mathematical stability theory. It is suggested that the factors to strengthen the DDT would make the detonation more stable, and vice versa. Finally, it is concluded from the simulations that the interaction of the shock wave and the flame front is the main reason for leading to DDT.