I wonder if it's possible to make an efficient turbine engine that uses only hot compressed air to move but only that, meaning there is no ignition involved. To put it simple can we use compressors like turbo or superchargers to make a small turbine engine that will be able to move (not lift) 100+ kilos at high speed, well lets say around 40km/h (25 m/h)? I've studied it a bit and to actually know i need to make it but before that i thought to ask people that know certainly more than i do. Also if you can think of a way to do it i'd love to hear it cause iv'e thought of something but it might not work (i guess that's the fun of it tho doing tests and rebuilding and stuff). Ok, in addition to all that let's say that power for this comes from batteries and it's meant to work for short periods of time.
Well, ships have been using turbine engines powered by super-heated water since the late 19th century. But you still have to have an energy source to heat the steam. And it's no good for a "jet" engine since the whole point is thrust by accelerating air through the engine, where the turbine and compressor are there just to keep the cycle going. It would only work for a turbo-prop or turbo-shaft where the turbine's job is to produce torque for doing the work.
Theoretically, you could have a turboprop powered with a steam turbine, or some other heated gas, but you still have to have an energy source. Maybe some kind of weird and wonderful battery powered water heater, or a tiny nuclear reactor? Then you also need a huge supply of water or other fluid or gas to heat up.
It is possible however to have a closed system that recycles the water used for the steam. You then have pretty much a small nuclear power plant or nuclear sub. It's theoretically possible though, to have a nuclear powered turboprop that could fly for months. If it works for subs and aircraft carriers, why not, if you could make the whole thing light enough.
Actually, none of that stuff is really new. There were nuclear powered aircraft concepts in the 50s, that weren't really practical.
The thing about turbine engines powered by kerosene is that it's still the most efficient way to convert potential energy to kinetic energy in a light weight and trouble free package. 50 years from now? Who knows.
The idea falls foul of the law of thermodynamics.
The chief problem is that you seem to convert electricity (from the battery) via thermal energy (heat) to mechanical energy. This cannot be efficient. The amount of thermal energy that you can convert back to other forms of energy is limited by the [Carnot efficiency](https://www.e-education.psu.edu/egee102/node/19420.
As @jamesqf points out in the comments, you can skip the whole thermal step and just have an electrically driven propeller. By not heating the air, you avoid the inefficiency.
Now turbine engines running on kerosene are also limited by this same Carnot efficiency. I just told you it's bad, but why then do planes still burn kerosene? It turns out that kerosene has a much higher energy density than batteries. This means the plane can be much lighter at take-off, which compensates for the thermal inefficiency.
@jamesqf gave the correct answer in his comment. Let me elaborate on why it would be inefficient.
Typical turbofan engine energy path is like this
chemical energy (fuel) -> thermal energy (burning fuel) -> mechanical energy (low pressure turbine shaft rotating = fan blades rotating) -> mechanical energy (large volume of air accelerated out the back of the nozzle).
So 3 different conversion steps. Each step is not 100% efficient. You lose a decent amount of energy at every step. So the more steps there are the worse. Your proposed situation is something like:
chemical energy (batteries) -> electrical energy -> thermal energy (heating the air) -> mechanical energy (low pressure turbine shaft rotating = fan blades rotating) -> mechanical energy (large volume of air accelerated out the back of the nozzle).
This has more conversion steps than a typical jet engine. It will be less efficient. The alternative path proposed by @jamesqf is
chemical energy (batteries) -> electrical energy -> mechanical energy (propeller rotating) -> mechanical energy (large volume of air accelerated past the propeller).
Do you see how this has one less conversion step? you just go straight from electrical to mechanical energy with no thermal step in between. Less conversion steps is better.
A turbojet with 'no ignition involved' is in principle possible, and it has been put into practice in the 1950s, in working prototypes of nuclear powered propulsion units.
As I understand it you want to have a compressor creating compressed air that exits in a high-speed jet, thus causing thrust, but you want the jet to be comprised only of air, not of combustion products.
That describes the air that is accelerated by the fan in a fanjet engine, which provides a substantial portion of the total thrust in such an engine.
Or if you prefer, rather than powering the fan by a turbine, you could power the fan or compressor by a piston engine. The "motorjet" concept (see https://en.wikipedia.org/wiki/Motorjet ) used in the The Caproni Campini N.1 -- ( see https://en.wikipedia.org/wiki/Caproni_Campini_N.1 ) might seem to approximate this idea, but in the "motorjet" concept the compressed air IS mixed with fuel and ignited after compression, to provide more thrust than would be provided simply by allowing the compressed air to exit the nozzle without ignition.
There was at least one piston-driven "jet" engine concept in which the air was NOT ignited after compression -- see for example the Coanda-1910 (see https://en.wikipedia.org/wiki/Coand%C4%83-1910 ). This plane apparently never flew, but a similar engine was used to drive a snow sledge. That seems to be a good match to what you are envisioning.