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 - Picking Corn - by Rick Nikolich. It was the day before Christmas shutdown at work and I asked our lead engineering expert Scott Andrzejewski what he was going to do over the holidays. He said that he had some corn that he still needed to pick with an antique one-row New Idea corn picker. Scott has a nice farm about an hour north of Lansing in St. Johns, MI. He wanted to get the rest of his corn in by the next day (Christmas Eve). We had about an inch of new snow on the ground and single digit temperatures. So in the bac
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