Analytical and numerical study of the expansion effect on the velocity deficit of rotating detonation waves

Abstract

In this work, a quasi-one-dimensional ZND model of detonation considering the expansion process perpendicular to the detonation propagation direction is extended to the rotating detonation engine (RDE) to investigate the influence of expansion on the detonation waves in RDEs. This model is first used in more general cases of one-dimensional detonation waves, coupled with the one- and two-step kinetic models for stoichiometric hydrogen-air mixtures. The expansion has an effect on reducing the detonation propagation speed and can be attributed to two factors: the extra work during expansion and the lost heat released behind the sonic point. The one that plays the more important role depends on the kinetic model. Finally, a set of numerical simulations of RDEs are performed for comparison with the theoretical model. The results show that the expansion process in RDEs reduces the speed of the detonation wave by approximately 5%, which is an important factor for the detonation velocity deficit in two-dimensional simulations.