On a Control Problem for a Linear System with Measurements of a Part of Phase Coordinates

We consider a three-dimensional unsteady flow with a rotating detonation wave arising in an annular gap of an axially symmetric engine 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°, 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. 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 multiparameter calculations and visualization of flows. The calculations were carried out on the Lomonosov supercomputer at Moscow State University.