Here is a very simple and easy bullet point way of explaining exactly how does a modern airliner jet engine function and work.
1. Large amounts of air is sucked in from the front rotating fan blades.
2. The air is then compressed in the first compressor stage to a higher pressure.
3. In the later, fuel is mixed with this compressed air and ignited to create high temperature gas.
4. The hot gases then pass through turbines to extract power sufficient enough to run its compressor and other accessories.
5. The gas is then allowed to expand and pass through at a very high velocity which then produces enough THRUST to move the aircraft forward.
6. Modern turbo-fans also pass air through a by-pass to create further additional thrust.
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