Theoretical study of the propagation of non-ideal detonations.

摘要

The propagation of non-ideal detonations arising from friction, heat transfer and reactions steps involving a competition between exothermic and endothermic reactions (pathological detonations) has been studied theoretically by including source terms in the 1-D conservation equations of momentum and energy. To predict the steady-state non-ideal detonation velocity, the detailed structure of the detonation has been considered. The Generalized C-J Criterion has been used to seek a singularity-free solution from the whole spectrum of possible solutions to the differential equations for the structure.; For pathological detonations, the steady-state analysis predicts a detonation velocity in excess of the ideal C-J value in the H2 --Cl2 mixture, in agreement with experimental observations. Unsteady pathological detonation calculations with a simplified two-rate law model have also been carried out. The resulting asymptotically stable detonations are found to be in agreement with the steady-state predictions.; For non-ideal detonations due to friction, the Generalized C-J criterion is found to break down for very low detonation velocities. An alternative criterion based on matching the detonation wave with the back boundary condition is used instead. A continuous spectrum of steady-state solutions has been found for detonation velocities ranging from the ideal C-J value down to that of a sonic wave. For activation energies above some critical value, multiple steady-state solutions have been found for a given friction factor, and various detonation regimes have been defined.; An unsteady analysis of the transient development of non-ideal detonations due to friction has been carried out to determine whether the solutions from the steady-state analysis can be approached asymptotically. Friction and heat transfer are found to increase the instability of the detonation wave. Oscillatory and even chaotic detonations were observed for values of the activation energies corresponding to stable detonations in absence of source terms (ideal detonation). Moreover, the transient analysis has revealed that in the case of multiple steady-state solutions, only that with the highest detonation velocity could be approached asymptotically. The transient results of detonation with friction and heat transfer have been found to be in qualitative agreement with the experimental gaseous detonations propagating in porous media and in obstacle fields.