I was just curious because the air is very compressed in the engine and some things do run on compressed air. And what if the engine was powered all by electricity?
A typical modern turbofan engine produces about 85% of its thrust from bypass flow, i.e. "compressed air", that never goes through the actual jet core.
However, as others have mentioned, in order to get the compressors spinning and sucking air in to begin with, you still need an energy source of some kind to turn them and, for lack of a better alternative, current designs still rely on jet core flow to turn both sets of turbines and, by extension, their associated compressors.
Where would you get the compressed air from? Jet engines "contain" compressed air because the engine itself compresses it using the energy from burning fuel. Asking if you could power the engine by that compressed air is like asking if you could power a car engine by the rotation of the gearbox: it's confusing cause and effect.
The engine is compressing air to more efficiently burn fuel. If you remove the fuel, there is no reason to compress the air. Other systems that run off of the engine bleed air only do so because it is a convenient source. The 787 uses a bleedless model that runs off of electric power instead of engine bleed air.
Electric airplanes are certainly an option, but a propeller is a better option than a turbine engine. You could however keep the duct around the prop.
In modern aircraft's jet engines (both turbojets and turbofans), compressed air is used:
- For starting the engine, spooling it up until the shut-off valve is opened and the fuel starts to enter and burn in the combustion chamber;
- For running auxiliary systems, like de-icing and pressurizing equipments;
This is not true for some newer engines like the General Electric's GEnx that use an electric starter or little jet engines (including APUs) and sometimes turboshafts (turboprops).
In aviation it's common to refers to the systems running/producing compressed air as 'pneumatic' systems or 'bleed-air'.
This, for instance, is the part of the overhead panel of a Boeing 737 used to manage pneumatic systems (taken from http://www.b737.org.uk/pneumatics.htm):
No. Air is compressed because we have jetful to run the compressor in the first place. No fuel, no compressed air (or very very few, from to drag induced by windmilling the engine).
Have a look at https://en.wikipedia.org/wiki/Jet_engine for more informations
A plane with compressed air tanks would also not be possible, as it requires A LOT of air to move an aircraft