The threads on combining a turbocharger with a pulsejet gave me this idea.
It's halfway between a turbocharged engine and a jet engine in that while the air/fuel mix in pumped into a cylinder equipped with intake and exhaust valves to be burned, there are no pistons and the whole force of combustion is used to spin the exhaust turbine. Any power extracted for work would come from the turbine shaft.
The point being to achieve high air pressure for combustion without needing all the complex compressor stages that make normal gas turbines so expensive and hard to make.
The valves would be timed to allow combustion to be total for maximum efficiency rather than the compromise that conventional piston engines must use. Likewise with exhaust.
In the animation below I gave it two alternating combustion chambers to smooth out the power pulses.
To further clarify, aside from the simplicity, the advantage is that even though the intake/compression/ignition/exhaust cycle is intermittent like in a piston engine, it's timed according to what is best for the fuel burn rather than needing the movement of a piston.
The fuel and air isn't ignited until it's perfectly mixed, the exhaust valve doesn't open until everything is burned, and the next cycle doesn't begin until all of the exhaust has exited and the incoming air has scavenged every bit of it from the chamber.