Artisi, I was thinking that it would be best to keep the air away from the impeller eye. With 100% water entering the pump, the impeller will always be able to get a grip and send the water on through. By injecting the air a little downstream of the eye, the air must go along with the water flow, away from the eye, so it can’t cause the pump to become air bound.
However, it would be good to know whether the air can be injected into the water just upstream of the pump. At present, I am not able to run even this simple experiment. If you would like to try it, here are some suggestions.
I would use 100% new water in the pump. That is, don’t recirculate the water for this experiment. Instead, use a constant source of new water. The dissolved air in recirculated water would cause a problem. I have a way to deal with it, but it is best to avoid it for now.
The water entering the pump should be at a slight pressure, say 1 or 2 psig. This can be achieved with a head tank, or maybe a booster pump to supply the main pump. Of course, the inlet piping should run straight into the pump suction for at least a few feet, no bends near the pump suction.
The water should be given a swirl before it enters the pump, in the direction of the impeller rotation. Install an air injector in the pump inlet piping, just upstream of the pump suction. I would make it like a reverse pitot tube, with the outlet of the injector at the center of the water stream, pointing in the direction of flow.
The important point here is to get the injected air into the center of the water stream. If the air were evenly distributed in the water before the mixture enters the pump, the pump would probably become air bound. The air should be divided into small bubbles as it leaves the injector and enters the water.
The impeller can be open or closed, but the bigger the pump, the better. Use the biggest pump you can find and run it at the lowest speed you can manage, although it probably should be at least 600 rpm to start with, or whatever the lowest speed is on your pump curve, so you can determine the flow at that speed. This gets complicated though, because the injection of air will affect the flow to some extent.
For every 100 gallons per minute of water flow, inject about 3 cubic feet of free air per minute. You will need a blower for this, which will handle that much air at the required static pressure. This static pressure will be the sum of two pressures: the water pressure at the outlet of the pitot tube injector, and the pressure drop from the outlet of the blower to the outlet of the injector.
I hope this is enough to go on. The main question is whether the pump will move the air/water mixture in a steady flow without any problems. If it does, then the mixture leaving the pump will be at a higher pressure, and the compressed air can be separated for use.
In that case, the next important question is the temperature of the compressed air. It should be close to that of the water. If it is very much higher, then something is wrong with the concept, or maybe the test setup.
If these conditions have been met, then what is the efficiency of this compressor? But that can be determined later. Please let us know if you get any results.