I imagine you have made some autocaskade/cascade systems. When you build two-stage systems you have to think a bit different. And R744 (CO2) is really different from the usual refridgerants. I'm sorry but i'm not used to working with psi (i live in europe). R744 has a critical point of 73,6bar (31.1 °C). In other words to make a traditional system with condensing, and subcooling you must have a pressure below 57bar(20°C).
This is how a typical transkritical 2-stage R744 the system is buildt. As you can see the pressure in the middle pressure reciever is quite lower than the gas cooler pressure.
This system solution does not requier external cooling. and will give a good cooling capasity with low mass-flow. And therefor a low compressore displacement. Sub cooling before the evaporator vent is not neseserry in so small builds. You recomand having a suctiongass-heat exchanger on the low pressure compressor. Leting the middle pressure liquid heat exchange with the suction gass from the evaporator. This will superheat the gass before the compressor and subcool the liquid before the evaporator. And then secure your low pressure compressor from "liquid-hammering" (destry the compressor).
EDIT: Usually you have a 2 times larger dispacement on the low pressure compressor i R744 systems.
The valve between the gas cooler and the middle pressure reciever is important if you plan on running transcritical. If you don't have it you'll have a low evaporator performance.
I do not recomend building a sub-critcal system with R744 if you dont heat exchange the condensation with another refridgeration loop (cascade)
A solution for subcritical R744 is something like this:
This is a good way of doing things but requier a lot of automation + oil return systems.
Hope this helps.






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