[serialk11r]

Sorry okay I'm thinking about it more, so the vane pump has a displacement, and a compression ratio. You need the displacement to always be positive or else the pump will attempt to pump air away from the engine, consuming power.

What needs to vary is the inlet location. For maximum compression, you want to let air in where the vanes are furthest from the center of the rotor, close off the inlet where maximum inter-vane volume occurs, and open the exhaust near minimum chamber volume. To make it into a turbine with maximum expansion ratio, you want the exhaust port open from maximum volume all the way until the volume is nearly zero, then open the inlet briefly.

This is not easy to accomplish mechanically, since you have to change the port shape :/ You can change it in discrete steps but not continuously, so if you want to flip it from compressor to turbine mode without moving the rotor or housing around you can have valves to swap flow between intake and exhaust ports then open up a bypass built into the housing surface to make the displacement negative. That creates some fabrication challenges.