Off on a tangent, found that an Auburn U professor made a vane pump engine:
https://contest.techbriefs.com/2017/...portation/8456
Anyways back to the air motor, if you have fixed ports, there's basically a tradeoff between how well it works as a supercharger and how well it works as an air motor. If you use it as an air motor with internal expansion, your engine will lose efficiency at high load because the air motor has been turned into a useless vacuum pump. If it's used as a compressor, you lose efficiency at low load because it's needlessly compressing air.
If it's used like a hydraulic pump with no internal compression at all, it's basically like a Roots blower, with the advantage that variable displacement is easier to achieve.
I worked out the efficiency before at some point, using a Roots blower as an air motor is something like 40% efficient before mechanical losses and leakage. That's a bit better than the <10% I worked out for ITBs.