The issue was that we were unable to get it running without compressed air. When we had a nice stream of compressed air running in the intake, it would fire right up, but it would die when the air was removed. We hypothesized that our tolerances on the engine weren't very accurate, and so decided to make a bigger one where the tolerances wouldn't matter as much. We scaled all the dimensions by two. With the new engine, we were able to get it running with compressed air just fine like the first engine. However, we had the same issue. When the compressed air was removed the engine would die. We now had a different theory. We wondered if the fuel wasn't mixing well when it was injected, and what the compressed air was doing was mixing the fuel really well. To remedy this, we took the fuel line and crimped it at one end and drilled small holes in it along its length to try to create more of an even distribution of fuel. This also didn't work, and the engine died when the compressed air was removed.
So, I am wondering if anyone here has suggestions for what we can do to get this engine running without needing to hold a compressor to it the whole time! Below is a link to a bunch of pictures of the engine: https://imgur.com/a/iCIfnIq
Any ideas are appreciated!
EDIT: We are using propane as fuel
EDIT 2: With compressed air, we are able to get it to pulse correctly. It is not just a continuous whoosh. We watched some videos of pulsejets, and we know the correct sound.