Unified dynamics of hydrogen–oxygen–diluent detonations in narrow confinements

Abstract

The present work addresses the interesting question that whether universal relationships can be obtained for characterizing the dynamics of hydrogen–oxygen–diluent detonations in narrow channels and as well in small circular tubes. Theoretically, we first demonstrate the success of adopting the effective induction zone length, which accounts for the leading shock velocity deficits resulting from wall losses, in unifying the quasi-one-dimensional (quasi-1D) detonation dynamics, predicted by the first principles models. These theoretically unified quasi-steady dynamics, irrespective of the geometry dimensions as well as the mixture compositions, are found to be in very good agreement with the large scores of already published detonation experiments in narrow confinements. Moreover, the experimentally unified dynamics of detonations at the macro-scale excellently follow the geometrically expected scaling of 2:1 between the 3D circular tube diameter and the 2D thin channel width results. Such excellent agreement of scaling between theory and experiments not only confirms the negligible role of small-scale cellular structures in the macro-scale propagation mechanism of weakly unstable detonations, but also permits the successful establishment of the universal correlation for characterizing the dynamics of hydrogen detonations in narrow channels and tubes.