In WW-II and shortly thereafter, piston powered aircraft peaked in power, performance and complexity wise. Power went up to over 4000 bhp for large multi-row radial engines. Only to be defeated by the jet, which was developed by (among others) Germany's Dr. Hans von Ohain and separately in the UK by Sir Frank Whittle. Its principles are based on the "Aeolipile" of the ancient Greek scientist Hero and other great thinkers like Leonardo da Vinci and the laws of Isaac Newton.
Compared to a piston, the gas turbine has less parts and the moving parts rotate in only one direction without stopping and accelerating as the pistons normally do in an engine. Thus, a running gas turbine is basically free of the vibrations normally found in piston models, which translates in much longer service life (TBO) and higher reliability.
But piston engines of this power class (over 4000 bhp) are so complex that the only way to go was to continue the development of the gas turbine in spite of all difficulties along the way. It is also able to extract more energy from a given amount of fuel than a piston engine.
Gas turbines operate on almost the same principle as piston Aero engines. They intake air, compress it, spray fuel in the hot compressed air which vaporises, ignites and then burns continuously (this is different from a piston), the hot exhaust expands quickly and exists the combustion chambers driving a turbine which in turns rotates the compressor.
When the hot exhaust finally leaves the engine it still contains enough kinetic energy to produce a forward thrust (Newton) propelling the aircraft along at high speeds. Inside the engine, only a small portion of air taken in is used for the combustion of fuel the remainder is used for cooling and other applications like cabin pressurization and air conditioning.
Thus the process of fuel combustion goes through almost the same sequence as for a piston engine, with the main difference that power is produced continually whereas with a piston it is intermittent.
Both piston and jet aircraft work on air to accelerate it, the piston or turboprop with a propeller which gives a small acceleration to a large amount of air and the pure jet gives a large acceleration to a small amount of air.
In a gas turbine combustion is at almost constant pressure with a volume increase, whereas high peak pressures common in piston engines are avoided. Making it possible to use low octane fuels. It becomes possible to use less robust components, but to ensure long live of the engine components special alloys are used to handle the higher gas temperatures.
For an turbine engine to produce any power air is compressed, increasing its pressure energy, and then by combustion of fuel heat energy is added. The cycle in which this is taking place is called the Brayton cycle. Named after George Brayton who did analysis on steam engine performance in the United States way back in the previous centuries.
During the work cycle of a turbine, an air mass will take in and give out heat to produce changes in pressure, temperature and velocity of that air mass. These changes are conform Boyle's and Charles laws: and this law says that the product of pressure and volume of an air mass is proportional to the absolute temperature of the air: P x V = T.
The above says that when a mass of air will heat up and cool off this will result in changes in pressure, velocity and temperature of that mass of air. As heat is form of energy, variations in temperature gives an idea of the work done in the engine. And this will occur in three main areas of a gas turbine engine:
As mass air flow is continuous, the gas volume changes only as gas velocity changes.
Also, the gas turbine is a heat engine, the greater the heat the more the gases expand and the more efficient the engine is. This is limited only to what the alloys of the engine can withstand. Cooling air is used to increase temperatures (and efficiency) beyond that of the materials the combustion chambers are made of.
This cooling air forms thin layers of air over the components thus isolating them from the heat and keeping them within designed limits.