This is an obvious idea so there must be some reason why it won't work. In scramjet propulsion a big problem is that the airstream is moving so fast it is difficult to achieve complete combustion in the short time the air is in the engine, even with the great amount of slowing used in scramjets. So why not just have the air circulate around and around to allow sufficient time for combustion? The space shuttle takes about 500 seconds to reach orbit. Let's say 200 seconds of this is during the altitude and velocity conditions when a scramjet might operate. Prior to that we could use the known airbreathing turbojet and ramjet methods. So if the air during the scramjet phase is made to circulate only for one second before being ejected we still only need to be carrying on board at any one time (1/200th)*(5 times more air mass than pure O2) = 1/40th oxidizer mass needed to be carried during this phase than a rocket. Keep in mind also during the earlier turbojet and ramjet phases we don't need to carry any oxidizer. Since the air is being circulated in a circle, ideally it is not being slowed down so should not create extreme heating. You now have one second to complete combustion compared to the times measured in milliseconds for usual scramjets. Am I missing something here?
Bob Clark