Standing oblique detonation ram jets are also a thing. Instead of the detonation wave revolving around an annulus it occurs in a static position downstream of a really interesting series of C-D nozzles and fuel injectors. It uses the ram effect for oxygen intake and compression but undergoes a pre-burn through an upstream CD nozzle to accelerate the gas further to higher mach numbers. The gas then flows into another CD nozzle where more fuel is injected at the throat. This mixture then accelerates again and just downstream of the throat there's a ramp that causes a standing oblique shock wave. The rapid increase in heat and pressure crossing the boundary of the oblique shock causes the fuel rich hypersonic gas to detonate constantly.

Japan launched a small scale RDE into space on a sounding rocket. Iirc they ran it for a few seconds in a vacuum.