Are there any ducted propeller or fans without a shaft in the centre?
Perhaps an aeronautic version of one of the Voith maritime systems? This one appears to be electrically powered. 
http://www.voith.com/en/products-services/power-transmission/voith-inline-thruster-voith-inline-propeller-11014.html (watch the "installation" video).
Also, this video explains the concept a bit (for maritime applications)

                
            
I suppose if you could arrange a lightweight frictionless magnetic ring bearing (possibly integrating electric drive), and/or peripheral drive linking system, it might be worth it if you needed to have two or three smaller fans beside each other, driven by a single core, rather than a singe large fan, in order to reduce fan/nacelle height. (imagine a B52 nacelle with one side shortened to just a fan cowling) I doubt that this would reduce overall drag, though, but I am intrigued by the concept of the greatest chord of the blades travelling the fastest.