Spent some time trying to figure out about how much working force this engine could create on the piston. Unfortunately the results are pretty depressing. The only way this engine would work is if you could get about a 100˚C temp difference each revolution of the displacer. Lets face it…it would be nearly impossible to heat/cool air that drastically with only heat sinks 300 times a minute. This has made me think of different ways to increase the efficiency.
I can think of a few ways, but all seem relatively impossible as well. If you could pressurize the core of the motor you would also increase the working pressure available. I think I figured earlier that an 11.1˚C change in temperature would require the engine core to be pressurized to about 800 psi to generate around 30psi of working force for the piston. 800 psi seems unrealistic. In order to pressurize the core of the motor a redesign would be needed.
In this case you could use a pair of pressurized cores that have the displacer set at 180˚ offsets to each other so one chamber would be positive pressure and the other would have negative pressure. One combined piston would be used where the two engine chambers would be connected on opposite sides.
While thinking of a pressurized system I also thought about a system operating under a vacuum. If you were able to build the engine that could sustain a 100 mbar pressure, could you use steam at that point? Water would boil at around 25˚C under those conditions. Would it condensate quick enough? Would it just boil until it reached a pressure of equilibrium and stop?