The results of a systematic study of the structures and flow regimes with an oblique detonation wave (ODW) in an annular ramjet straight-flow detonation chamber (DC) of a new type have been presented. In the combustor with a new design, detonation burning of the reacting mixture is organized by using a compression body shaped as a continuous monofilar spiral with a constant pitch angle. Numerical simulations are performed for a supersonic flow of a stoichiometric hydrogen–air mixture with Mach number M0=3 and 5 at the combustor entrance. A mathematical model of the reacting flow in the combustor is developed in a two-dimensional (2D) unsteady formulation. The flow dynamics for the two different operation start types of DC and the final structure of the steady flow in the combustor are numerically studied. Various geometric parameters of the DC are considered (length, radius, and spiral pitch angle). A bifurcation of the steady flow structures with respect to the initial conditions of combustor start is detected for some combinations of the DC geometric parameters.