As I child, I was fascinated with jet engines. Today I am fascinated even more. Basically it is a very simple machine and therefore beautiful.
The compressor (either axial or centrifugal) compresses the air. In the combustion chamber the air is mixed with fuel and burned (actually the burning process continues all the way to outlet). As it burns, its temperature, and thus also the volume grows several times. Some of the energy contained in burning gases is used to drive the turbine (the turbine powers the compressor), and the rest of energy is used to speed the gas up in the outlet nozzle. The output nozzle directs the gas in one direction to enlarge the thrust efficiency.
To me, the whole cycle looks very similar to a diesel-engine cycle. Only it is continuous.
But dont think that, because its basic form is so simple, the jet engine is something anyone can build. There are many problems like materials that have to do with high temperatures and stress, stability of the burning flame issues, efficiency issues and, sure, a very difficult real-world mathematics involved. To increase efficiency, a real-word jet engine would have two or three coaxial compressor-turbine tandems.
Now, for a long time I was confused about the following thing: why in the world doesnt the burning gas exits at both ends of the engine? If in the burning process a high pressure is produced, then why doesnt the gas exhausts at the front end? Of course, as it often is the case, the answer is most obvious no high pressure is generated in the burning process.
The compressor compresses the air to the pressure (or a bit more) that is found in the combustion chamber. That is the role of the compressor to overcome the pressure difference and push the air inside. The air is at its highest pressure just at the exit of the compressor (i.e. at the combustion chamber entrance). From that point on, its pressure drops.
A coarse diagram of pressure, temperature and volume of the air (gas) as it is advancing through the engine.
However, the fuel is burned and the temperature of the gas is greatly increased in the combustion chamber, and thus also the volume of the gas. It means that from this point on either the speed of the gas must be higher as it passes to the outlet, or the cross-section surface must be larger (both things are true in the real-world jet engine).
This increase in the volume of the gas is how the power is gained. Not the increase in pressure. Although the pressure difference at the turbine is smaller than the pressure difference at the compressor, the turbine has larger cross-section and generates all the needed power to turn the compressor. In addition, some pressure is present also at the output of the turbine and is used to speed up the gas further in the outlet nozzle (and still, lot of energy is wasted in the form of hot exhaust).
Why do we need the compressor in the first place? Why cannot we simply burn some fuel in uncompressed air and get some energy from its volume increase? The answer is in thermodynamic There is no way to extract mechanical energy directly from a hot gas if the gas has the same pressure as its surrounding. In fact, the higher pressure difference the greater efficiency we can expect from such engine. (By the way, this is why a diesel engine has inherently greater efficiency than a gasoline engine.)
There are jet engines that work without a compressor. These are called ramjet. But they still need the pressure difference to do the mechanical work (that is, to speed up the exhaust gases). A ramjet uses inertion of high-speed incoming air to create the high pressure in its combustion chamber. It can work only when already moving at high speed. (Of course, a high-speed moving also can help a regular jet engine in the same manner).
Danijel Gorupec, 2006
General Electric aviation page
Rolls-royce home page
Pratt & Whitney home page