The Effect of Boundaries on the Velocity Deficit and the Limit of Gaseous Detonations

Abstract

Effects of boundaries on the gaseous detonation velocity and on detonability limits are examined. A generalized Kármán-Pohlhausen procedure is employed to obtain a system of quasi one-dimensional equations which include the boundary effects correctly. The equations differ from the usual quasi one-dimensional equations used by Zeldovich, Fay and others. The use of the latter equations is avoided because they incorporate the transport effects only qualitatively. A new Chapman-Jouguet condition which is exact in a Zeldovich-Neu- mann-Döring sense is derived through a singularity consideration of the governing equations. The result takes the boundary effect into consideration and degenerates to the classical form in the limit of infinite tube diameter.The boundary effects are calculated by introducing the Oseen-Kármán-Millan approximation into the boundary layer equations. The analyses lead to the following results which have not been revealed by existing theories:(a) The propagation velocity deficit ΔD is a double-valued function of the heat of combustion and of the tube diameter; one value is small, the other is appreciable (corresponding, respectively, to the ‘almost’ C-J detonation and to the ‘slow’ detonation).(b) There exists no eigenvalue ΔD if either of the two parameters lies below a certain critical value (the con-centration limit and the diameter/pressure limit).

These features are illustrated by a calculation for ozone-decomposition detonations, and good agreement is obtained with the existing experiments.