WARNING, found my soap box his morning...
That is a neat theory, but not possible. I have to track the temperatures and pressures for splitting water at work every time I run a plant. Inside the engine you are not in an oxygen free environment, so pyrolysis is not possible without chemical stripping. Pressure/vacuum is variable, but even in a gasoline engine where you might theoretically reach the magic 28 hg, all you need is roughly 2800f and depending on volume could finish around 4550f. If you are in a diesel, that vacuum is not going to be there, and if you glance at your boost gauge, you might have a bit of positive pressure there, raising that temperature a bit.
There is a chance that some of the water that hits the metal and gets super heated has a chance of getting to temp for a simple split by the infrared heat, but that small of an amount is never going to be noticed. At a molecular level there is far more variation of butanes and propanes traped within the diesel fuel than you could possibly generate.
Quite simply, if it were possible, all of us would be driving hydrogen trucks and cars. Science has been chasing this one for many years and the closest we've come is hydrogen fuel cells.
So the best you can theoretically achieve from the water is a touch of steam power, but like stated above that comes at the expense of volumetric loss of the cylinders area to allow for flame front expansion. I can't recall the lab that did the test on water injection and showed something like 99.5 % of all gains were able to be duplicated by the lower oxygen temperature, which followed the btu cooling capacity of the water mist in a perfect curb. Basically water mist= colder temp, which allowed for more oxygen into the chamber. That is when power increased in the engine. There was a ratio based on compression ratio, but it was very low. I found that lab work in a couple hours of searching the web on wmi advantages/disadvantages.
I don't want to mislead anyone, or get a backyard experiment person hurt, water can be fractured at lower temperatures under certain conditions, especially the absence of oxygen, but usually requires a tad more heat than is required to flash off the hydrogen, and since the separation can ignite the already hot enough hydrogen, all you need is oxygen- oops- it is now right next to that hydrogen molecule. And boom goes the dynamite, just as fast as it is produced it lights off. Why isn't it a viable fuel? More btu is required to make it happen than it produces- so a net loss occurs, please see E=mc2 for clarification. If you figure out how, you just became a multi millionaire, and will be claiming a certain peace and scientific prize soon.
This is why the power seeking group of wmi starts leaning towards Water Methonal iIjection instead of Water Mist Injection. Methonal is the extra power. Only thing is methonal is too high on the frational ratio chart of comparable fuels for diesels to take much of it without creating multiple flame fronts. Just a bit and the second flame front is close enough to not be noticed as a knock of the piston a the wrong time.
