Water Injection
There's a degree of confusion crept in on the thread. Water injection can be with or without methanol added.
First of all, there is no value using water to cool a jet engine. You can't carry enough of it and it would be counter-productive anyway to have super-heated steam chasing around the airframe rapidly corroding everything in sight.
The value comes in cooling the inflow air, thereby increasing its density, which means a greater burn can be sustained, which generates more power.
The difference in temperature between in and out can be used to measure thermal efficiency; the greater the temperature difference front and rear, the higher the efficiency. So at sea level - and relatively high inlet temperatures therefore - water cooling the air means it's at a temperature of several thousand feet higher, but with the density advantage of the lower level. Result = bigger bang (or in fact, higher volume of jet efflux available for generating thrust).
Methanol adds an anti-freeze effect to the water, so enabling even lower inlet temperatures to be achieved and with obvious advantageous consequences over straight water. However, it's also highly combustible, so adds to the fuel and burning properties as well.
It doesn't matter whether it's a high or low by-pass jet, turbojet or turboprop; the principles are the same. However the water/meth is usually (but not always) sprayed into the compressor stages. Clearly on a high bypass, that means NOT the big fan at the front, but the teeny-weeny stages that actually form the front-end of the hot core that drive the fan.
I am not aware of any physical, engineering or other reason why water-meth shouldn't be used on any jet or piston engine, provided it's not used where it would cause the engine to burn out or over-power. It's a perfectly valid way of overcoming the Weight-Altitude-Temperature (WAT) limit.