this "adiabatic" engine developed by Smokey Yunick and Ralph Johnson in 1984
Raises the enthapy of the system. Increases the energy going in, increase the energy for work.
I have a feeling that engine would go boom. Not only are you soaking the impeller in gas, the temps and pressure would auto ignite fuels way to easy.
The pic is literally depicting running fuel through a water-air heat exchanger and again through an air-air exchanger with exhaust gas. Hope nothing leaks