Water injection has been used in both reciprocating and turbine aircraft engines. When used in a turbine engine, the effects are similar, except that normally preventing detonation is not the primary goal. Water is normally injected either at the compressor inlet or in the diffuser just before the combustion chambers. Adding water increases the mass being accelerated out of the engine, increasing thrust, but it also serves to cool the turbines. Since temperature is normally the limiting factor in turbine engine performance at low altitudes, the cooling effect allows the engine to be run at higher RPM with more fuel injected and more thrust created without overheating. The drawback of the system is that injecting water quenches the flame in the combustion chambers somewhat, as there is no way to cool the engine parts without cooling the flame accidentally. This leads to unburned fuel out the exhaust and a characteristic trail of black smoke.
The above is from wiki regarding water injection.
As a side note very fast planes like the MiG-25 used intake sprays that put alcohol into the air intake to cool down the air going into the engine so more thrust could be generated out the back. So much alcohol was used by the aircraft its nickname was restaurant...
A jet should work like this: "suck, squeeze, bang, blow" ... Suck and Squeeze should be the compressor, Bang the combustion chambers, Blow the turbine. I don't know if this is correct, but it is all I know about it.
Two things govern everything: first, the flow rate of the fluid accelerated through the engine (more fluid in unit of time, more thrust) and, second, the temperature of the engine (heat not good for the thrust).
Not bad but not right in some areas... first of all Heat IS thrust... the hotter the better, but too hot damages components in the engine so heat is limited to reduce chances of damage... if the engine parts could take it you would make it as hot as you could for a turbojet. A turbo fan moves volume air for thrust so it does not need to be so hot.
Anyway think of a turbojet engine as being a tube that starts out wide... gets a bit narrow in the middle and opens out again at the rear. Put a shaft down the centre and mount blades on the shaft.\
At the front the blades suck air into the engine.
Where the tube narrows the air is naturally compressed... as well as being pushed through by the air coming after it through the intake.
then the air is blasted out the rear as thrust.
the part where the tube narrows is called the hot section... that is where fuel is added and burned to generate even more heat and pressure and in the rear more fuel can be sprayed into the exhaust and ignited... the latter is called the after burner or reheat.
the shaft from the hot section is connected to the front blades so if you increased the fuel added in the hot section the natural result is the blades in the hot section and the front blades spin faster.
that is basically a turbojet engine.
A turbo fan engine has another tube around the outside so the front blades suck air into both tubes, the air going through the core is heated and fuel is added but at the rear the cold air going around the outside hasn't been heated yet and has had no fuel burned in it so it is dense heavy air that is oxygen rich so when it reaches the after burner or reheat section it can generate a lot more thrust because it has a lot more mass and is able to burn more fuel because it is still oxygen rich.
A high bypass turbofan like on a jet airliner has a huge front fan and a small narrow turbojet to the rear... the turbojet is just there to turn the big turbofan and most of the thrust the engine generates comes from the big cold fan. As most of the air comes from the cold fan air rather than from the hot turbojet it is called a high bypass turbofan. It can generate a lot of thrust by moving lots of heavy cold air, but is no good if you want to go supersonic.
Keep going in that direction and a turboprop like the engines used on the Bear use a turbojet to turn a large propeller in the front of the engine and it is the propeller that generates the thrust... very efficient for low level flying and of course only capable of subsonic flight. When the propeller blades break the speed of sound they create sound waves instead of pressure waves and lose efficiency.
in the opposite direction if you take the shaft and blades out of a turbojet engine you have a ramjet engine where air coming in is naturally compressed by the narrowing tube... fuel is added and burned and comes out the rear as thrust.
very simple and very light... many ramjet powered weapons like the KUB (SA-6 SAM), the Kh-31, and various anti ship missiles like Onyx and Brahmos use the column of empty space down the core of the weapon for a solid rocket booster to get the weapon in motion. Once in flight the solid rocket motor component is dropped, the intake opened to the air flow and the ramjet started... the speed of the ramjet is limited only by its ability to slow the air coming in to subsonic speed so fuel can be burned and then accelerating that air to high speed out the exhaust as thrust.
The Scramjet, or supersonic combustion ramjet is basically the same hollow tube but designed so that the fuel can be burned at supersonic speed... this is the holy grail because as long as you can control the temperatures the scramjet as no upper flight speed limit.
High bypass turbofans and turboprops are subsonic only. Turbojets and turbofans peak at about mach 2.8... any faster and the rotational speeds of the blades rip themselves apart... the SR-71 can fly at mach 3.5 for long periods because it uses bypass air as a ramjet with the main turbojet engines doing very little in the way of moving the aircraft through the air.
A ramjet is good to mach 7-mach 9 or so, but scramjets can be used to orbital speeds... though they can't be used as scramjets in space if you take some liquid oxygen you could supply fuel and oxygen and use it as a rocket for propulsion.
The water injection in front of combustion chambers should do two things: first, drops down the engine temperature, so increases thrust and, second, the water increases also the volume of the fluid (air + water) through the engine and also this should increase the thrust.
Dropping engine temperature just protects it from damage when used at very high thrust settings at low altitude where the air is very thick and could cause damage to the intake by heating it too much.