Neither methanol nor Water creates any Oxygen while burning.
My calculations from above are only talking evaporation into account. You were asking about if evaporation of methanol in the inlet increases air and with it oxygen density.
Answer is yes, it does.
Water is much similar except for two things. It's heat of evaporation is twice as large while its vapor density is lower due to the lower molecular weight of water vs methanol.
But let's assume vapor density is the same to keep things easy.
You could conclude water cools twice as much as methanol. That is the theory if all the water would evaporate. In your 40C airstream, it does not. That is the thing. The water's vapor pressure is MUCH higher than the vapor pressure of methanol. Water evaporates MUCH slower than methanol. Cooling power is joules of heat of evaporation per second.
Before digging out any equations a first approximation would be 10x slower. This is very crude since these are highly nonlinear phenomena that happen on a logarithmic scale. Once you hit a boiling point, things change again.
Just put some water over your finger and methanol. What feels cooler?
If you have a very hot environment such as a gas turbine with its 40:1 pressure ratio and 1000C air exiting the compressor, water injection works as theoretically predicted as all water evaporates. In a inlet tracks with 150C 20PSI air exiting the compressor and cooling down to 40C things are more complicated. Here rather less water will evaporate, some of the water evaporated in the compressor will even condensate again. Here methanol will do the majority of the cooling work, not the water.
In the cylinder things will get better as things get hotter, but still big droplets won't even fully evaporate during a entire combustion cycle.
Now water is not best, it is just different. In the cylinder it slows down flame propagation speed. Now if the distribution is not perfect within the cylinder, you still experience knock from the perimeter zones of the cylinder that contain less water.
Water and methanol work well to gether. They work on different temperature and time scales and act differently,
Here are some experimental data on the evaporation speed of a few solvents. Under the same conditions in this rotary evaporator, Methanol evaporates 8x as fast as water.
http://data.biotage.co.jp/products/t...ation_rate.pdf
The evaporation time of a droplet is about proportional to its diameter. A 200µm droplet takes 4x the time to evaporate than a 50µm droplet.
Air assisted nozzles create a finer mist than hydraulically driven nozzles. if the water mist is fine enough, it will also evaporate reasonably fast, at least until the air is saturated. But in the cylinder, the very fine residual water mist will help equilibrate in cylinder temperatures. it will also slow down flame development speed. This is where the extra timing requirement comes from. Methanol on the other hand burns faster than gasoline. a mix of methanol and water requires less extra timing. it is therefore easier to tune and can extract more power than water alone is most instances at the same boost level. You might achieve more power with water alone, but you need to add more boost. And there are limits in most setups.
In WW2 this was well optimised. water is the main agent, but methanol water mixes made more power with less tuning over a wieder AFR range.
As all planes except the FW190, it had a single throttle control lever, had manual fuel control. You had to adjust throttle, ignition timing and AFR yourself while manually open and close oil cooler covers and other stuff. When now folks start shooting at you, you did not want to fine-tune everything and watch EGR gauges while engaging war emergency power = water methanol injection. It only required little adjustments.
Pure methanol would require more adjustments and more of the stuff= weight = less time on big power = potential death.
also remember that those engines were running at very high pressure ratios. A P-47 Thunderbolt would run with up to 1.7 bar of manifold pressure at 30000 feet. Atmospheric pressure at this altitude is 0.3 bar. This corresponds to a pressure ratio of almost 6!!!!! At 0°C and a 75% efficiency you end up at turbo exit temperatures of 250°C. Pre-turbo water methanol injection had a huge effect. The water would literally boil while the air was compressed.
Richard L wrote that the WRC engines were driving the turbos at pressure ratios of 4 due to he inlet restrictors. This makes then very inefficient leading to very hot air temperatures. They used water injection to great effect. Water methanol would have even been better for power, but was not allowed.