This idea suddenly came to me: what if an expansion engine is used instead of a TXV in a phase change system? I see that it would improve cooling capacity and efficiency as the energy that turns the engine must come from somewhere, and based on what I understand, as the liquid evaporates into a gas in the engine and then expands, it would absorb heat. Surely enough, there must be some reason why it won't work, as there is no phase change system that uses an expansion engine to recover some energy. I'd like a really detailed explanation why it won't work.
I am unclear on exactly what you mean by an expansion engine but if you were to use the liquid refrigerant to drive some sort of piston engine, all you would accomplish is the engine getting cold instead of the evaporator. The energy driving the engine would be coming from the compressor. A txv is used to regulate the refrigerant flow into the evaporator, most of the evaporation occurs in the evaporator (hence the name). I could be completely wrong about this, or misinterpreted your post, but I can see no way that running some sort of mechanical engine with the refrigerant will boost the cooling capacity.