Numerical Investigation of Deflagration to Detonation Transitions

Transitions from deflagration to detonations are studied. A model consisting of the Navier-Stokes equation and a one-step reaction equation is used. Arrhenius kinetics are utilized, and the diffusive parameters of the problem are chosen so that the smallest scale of the problem can be resolved on the chosen grid. It is shown that for certain parameter regimes the transition can be described by three phases. First, an ordinary flame accelerates and a shock wave of increasing strength is produced ahead of and separated from the flame. In this phase, the shock wave "preconditions" the unburnt media. The pressure in the fluid between the flame and the shock wave increases with time. In the second phase, a "convected explosion" in the compressed state occurs, which is responsible for the transition to an overdriven detonation. In this phase peak pressures substantially larger than the Zeldovich Neumann Döring (ZND) pressure are obtained. Third, a relaxation to an ordinary Chapman-Jouget (CJ) detonation occurs. The convected explosion is driven by a gradient in the source term in the reaction equation. One-dimensional calculations show that the extension of the gradient required for a transition to occur is reduced if the strength of the shock wave is increased. The transition process is very sensitive to perturbations, and examples of this are shown by numerical experiments. It is also shown that the maximum separation between the shock wave and the flame zone increases with increasing activation temperature.