Efficiency is not great, but with no moving parts this design is accessible to early-stage technological development.
https://www.youtube.com/watch?v=bWvv8Y4qhOA&t=20s
The valveless pulsejet in the video would be disqualified from Safehold because it used a spark plug, but the key thing is that it's only needed once for startup. A matchlock-like system would presumably work.

