Dynamics of detonations with a constant mean flow divergence
  An exponential horn geometry is introduced in order to establish cellular detonations with a constant mean lateral mass divergence, propagating at quasi-steady speeds below the Chapman-Jouguet value. Experiments and simulations demonstrated that such quasi-steady state detonations can be realized, hence permitting to obtain the relations between the detonation speed and mean lateral flow divergence for cellular detonations in an unambiguous manner. The experimentally obtained speed ($D$) dependencies on divergence ($K$) were compared with the predictions for steady detonations with lateral flow divergence obtained with the real thermo-chemical data of the mixtures. For the 2C$_2$H$_2$+5O$_2$+21Ar system, reasonable agreement was found between the experiments and steady wave prediction, particularly for the critical divergence leading to failure. Observations of the reaction zone structure in these detonations indicated that all the gas reacted very close to the front, as the transverse waves were reactive. The experiments obtained in the much more unstable detonations in C$_3$H$_8$+5O$_2$ showed significant differences between the experimentally derived $D(K)$ curve and the prediction of steady wave propagation. The latter was found to significantly under-predict the detonability of cellular detonations. The transverse waves in this mixture were found to be non-reactive, hence permitting to shed off non-reacted pockets, which burn via turbulent flames on their surface. It is believed that the large differences between experiment and the inviscid model in this class of cellular structures is due to the importance of diffusive processes in the burn-out of the non-reacted pockets. 
Matei Ioan Radulescu and Bijan Borzou
physics.flu-dyn