Analytical study of rotating detonation and engine operating conditions

In this paper, the mechanism of rotating detonation is analytically discussed using a two-dimensional sheet model. Two ratios are employed in this discussion: the ratio of the sonic point width to the detonation front width, and the ratio of the effective mixture injection area to the injection area. In the rotating detonation, the unconfined boundary can increase the width at the sonic point and decrease the detonation wave speed. Although the high detonation pressure hinders mixture injection, effectively preventing some injectors from functioning, the high pressure acting on the injection end wall produces thrust. Mass, momentum, energy, and angular momentum conservations are used to determine these ratios. The calculated results are in reasonable agreement with past experimental and numerical findings. The present model succeeds to clarify the features, parameter relationships, and overall mechanism of the rotating detonation analytically and to specify flow field of the rotating detonation under given boundary conditions, e.g., the velocity deficit and the effective injection area ratio. The specific impulse of a rotating detonation engine was lower than that of an ordinary rocket engine due to the lower combustion gas pressure when the combustion gas expanded to 1 atm. The thrust coefficient and the specific impulse of an air-breathing rotating detonation engine were shown to be lower than those of a ramjet engine, respectively, primarily because of the smaller airflow rate into the engine.