Rotating detonation waves in annular gap with variable stagnation pressure

Abstract

We consider a three-dimensional unsteady flow with one, two, or four rotating detonation waves arising in an annular gap of an axially symmetric device between two parallel planes perpendicular to its symmetry axis. The corresponding problem is formulated and studied. It is assumed that there is a reservoir with quiescent homogeneous propane–air combustible mixture with given stagnation parameters; the mixture flows from the reservoir into the annular gap through its external cylindrical surface toward the symmetry axis, and the parameters of the mixture are determined by the pressure in the reservoir and the static pressure in the gap. The detonation products flow out from the gap into a space bounded on one side by an impermeable wall that is an extension of a side of the gap. Through a hole on the other side of the gap and through a conical output section with a half-opening angle of $$45^{\circ }$$ , the gas flows out from the engine into the external space. We formulate a model of detonation initiation by energy supply in which the direction of rotation of the detonation wave is defined by the position of the energy-release zone of the initiator with respect to the solid wall situated in a plane passing through the symmetry axis. After a while, this solid wall disappears (burns out). We obtain and analyze unsteady shock-wave structures that arise during the formation of a steady rotating detonation. We measure and compare thrust characteristics for different numbers of detonation waves. It was shown that the thrust weakly depends on the number of waves while the specific impulse increases with increasing number of waves. The study of rotating detonation at various values of the stagnation pressure was conducted. The calculation results show that at a stagnation pressure less than the critical value, the realization of rotating detonation is impossible. It is established that, depending on the stagnation pressure, qualitatively different shock-wave structures can be observed. The analysis is carried out within single-stage combustion kinetics by the numerical method based on the Godunov scheme with the use of an original software system developed for multi-parameter calculations and visualization of flows. The calculations were carried out on the Lomonosov supercomputer at Moscow State University.