I have read with interest the comments so far and some have merit, as many people have thought about this principle for a long time.
I have thought for some time about the idea of combining the hotair engine (open cycle) and a boiler, probably a flash generator.
The main idea behind the hotair engine is to get as much heat across the steel wall of the displacer cylinder as possible to expand the compressed air.
Steam has a large quantity of heat latent in it so it seems to me that if a quantity of air is compressed in a cylinder and steam is admitted via a valve, that latent heat will disipate in the air causing it to expand.
So instead of using the expansive properties of steam we use its latent heat to expand the air, much in the way an IC engine works; but remember, the IC engine only uses a fraction of the heat available from combustion to expand the air, the rest is dumped into the exhaust and cooling system. It could, if it works, be an economical way to use fuel.
If I am talking a lot of hotair, I’m sure someone will set me straight.
Mark