Propellers in some form are really the only option.
It is currently the only efficient way to generate thrust with air as a medium.
Even jet engines are in some sense just a very elaborate system of propellers.
The reason for the turbine is to create an environment to efficiently burn fuel ( suck, squeeze, bang, blow ) to generate as much thrust as possible.
Hence, in an electric aircraft this is irrelevant.
You might be interested in the Airbus E-Fan , which uses ducted propellers increase efficiency.
However, it is still 'just' a propeller with an electric motor in the middle.
aviation.stackexchange.com/users/790/Thunderstrike
You may choose whatever propulsion you prefer, but need to accept the consequences.
An electrical turbine is easy to build, but will need a lot of power for heating the core flow.
Instead of burners you will need to install heater elements, which will necessitate a longer flow path and more volume between compressor and turbine, but by and large
the electric turbine engine will look much like a fuel-burning one.
You can also remove all the turbo machinery and only drive the fan with a big electric motor.
But that would have lower efficiency than turning a propeller instead, so only when your flight speed will cause supersonic propeller tips might an electrically powered fan be a better alternative.
Therefore, at speeds below Mach 0.7 propellers will give you more thrust per kW of power, and their efficiency is best at low speeds .
The much lower energy density of electric storage will demand flight at low speed, or your flight time will be very short.
Therefore, propellers are the best, but by no means the only solution.
A potentially even more efficient method might be ionic thrusters where a high voltage is used to ionize and accelerate air in order to produce thrust.
Designs using ionic thrusters would use the whole airframe for thrust creation and would need to be run at tens of thousands of Volts, but their potential efficiency surpasses even that of low-speed propellers - in theory.
The linked article, however, is an embarrassment to MIT.
A 1 kW jet engine that produces only 2 N thrust has to fly very fast (500 m/s, to be precise) while the 110 N cited for the ionic thruster at the same power mean that it could not had moved faster than 9 m/s.
aviation.stackexchange.com/users/1961/Peter Kämpf
You do not have hot combustion gases in an electrically powered engine.
The only gas available to you is the air around you, and some form of propeller is the most logical way to accelerate that air.
The nozzle you're imagining can be used to turn a large, slow stream of air into a faster but smaller air stream.
This can't provide thrust by itself as it isn't a powered engine part.
aviation.stackexchange.com/users/1956/MSalters
Ducted fans rather than external propellers increase the performance at high speeds, so gets round most of the problems.
You aren't really going to want to carry fuel AND batteries, so some sort of ducted fan is the best solution for a high speed aircraft.
While they do look somewhat like Jet engines, they are basically just prop engines in a tube, so they can better control the air-flow, which at high velocities, can cause issues for exposed props.
aviation.stackexchange.com/users/8669/Drenzul
For your requirement to use a battery for silent takeoff and landing, electrically driven propellors (or ducted fans) would certainly be good enough.
The requirement you mentioned for 350 mph to 550 mph is really only for cruise, which presumably would use a turbofan (or possibly turboprop) - and recharge the battery at the same time.
So I would guess what you want is a fairly high performance ducted fan which can be driven by either electric motor for silence or by a conventional turbine at cruise - a bit like a turboprop.
The question is then how do you arrange for an exchange between the two power sources.
(I assume two sets of engines wouldn't be possible, though perhaps they could be?)
(Edited to add...
your electric motors still need full power to takeoff.
So why not run the motor all of the time, and use an auxiliary turbine engine to provide the electrical power at cruise?
Not unlike a hybrid car.)
aviation.stackexchange.com/users/8417/Andy
The main difference between air and water is that the second cannot be compressed, while the first can and when you do, you heat it up loosing a cospicuous amount of energy.
The more you compress it and the more time you wait before releasing it, the more energy you loose.
A propeller also compresses the air: this is necessary to accelerate it, but it allows to achieve high air velocities with the minimum amount of compression.
It is also a very simple and light design, moreover one of the motivation to have an internal water compressor is the possibility to filter it, which is not required with air.
aviation.stackexchange.com/users/2345/DarioP
This is for an electric airplane (so no fuels for combustion):   Are propellers the only option?   Is there a turbine-jet possible with only air intake, electrically compress, and  a turbine and nozzle and get equal or more thrust than a propeller like a water-jet but then with air?
For an electric airplane are propellers the only option for propulsion?
aviation.stackexchange.com
<aircraft-performance><propeller><turbine><electric-engine>
aviation.stackexchange.com/questions/15163
aviation.stackexchange.com/users/8664/Arturo
Propellers are an option for an electric plane. Other options include ionic thrusters and ducted fans. There is some disagreement here. Some think that some form of propellor is the only viable option whereas others cite alternatives. Whichever form of propulsion you choose, there may be consequences. An electrical turbine, while easy to build, would require a lot of power. Other alternatives include ionic thrusters and ducted fans.
Some form of propellor is the only viable option. Any form of propulsion may have consequences. Although easy to build, an electrical turbine would need a lot of power. Alternatives include ionic thrusters and ducted fans.