You need to look at this in terms of the total energy. The problem with simply injecting water is that you'll use more energy to compress (and heat) the air than you'll get back from the expansion of the steam, unless you add additional energy from somewhere.
Energy can be neither created (except in an atomic reaction where matter is converted to energy) nor destroyed, only changed from one form to another. Water injection adds power to engines because it takes some of the heat energy from combustion that would otherwise go out the exhaust and uses it to convert water to steam, increasing cylinder pressure.
Converting water to steam requires that the water absorb energy from somewhere. In your example, the energy needed to convert water to steam would come from the heat generated by compressing air in the cylinder, which in turn comes from the energy needed to rotate the crankshaft and push the piston up the cylinder, which in turn has to come from somewhere.
If there's nothing to add energy to the water, even though the cylinder may be hot enough to vaporize it, there'll be a net loss of energy in the form of heat passing to the cylinder wall and heat created by friction between moving parts. This energy can be added either internally, like a gas or diesel engine, or externally, like a steam engine.
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Today's Featured Article - Grain Threshing in the Early 40's - by Jerry D. Coleman. How many of you can sit there and say that you have plowed with a mule? Well I would say not many, but maybe a few. This story is about the day my Grandfather Brown (true name) decided along with my parents to purchase a new Ford tractor. It wasn't really new except to us. The year was about 1967 and my father found a good used Ford 601 tractor to use on the farm instead of "Bob", our old mule. Now my grandfather had had this mule since the mid 40's and he was getting some age on him. S
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