Transient development of friction-induced low-velocity detonations

Detonation velocities as low as 20% of the Chapman-Jouguet (C-J) values are observed in tubes with a dense array of obstacles. The present study attempts to investigate these low-velocity detonations (LVDs) through the use of a friction factor to account for the momentum losses due to the interactions with the flow obstacles. The present study investigates the asymptotic approach to the LVD solution from a transient solution of a detonation initiated via a strong blast wave. Pulsating detonations are obtained asymptotically even for cases when the activation energy is below the stability limit for the case without friction. The result indicates that friction tends to increase the effective activation energy and thus renders the detonation more unstable. Following the previous studies of Zeldovich, Gelfand et al., and so forth, it is found that the generalized C-J criterion can be used to obtain steady solutions for the detonation structure. However, below a certain velocity, the generalized C-J criterion breaks down. On the basis of the non-steady solution, a different criterion of zero particle velocity (absolute) at the chemical equilibrium plane can de used to continue the solution further to the low-velocity regime with very high friction. However, the non-steady analysis gives highly unstable pulsation detonations with no meaningful averages that can be ascribed to these steady-state LVD solutions for realistic values of the activation energy.