I haven't seen any checks on this, but I suspect the Dyson can probably move more air than a regular fan. It probably isn't more raw energy-efficient, but it can be more comfort energy-efficient (more comfort for the same energy), because their principle makes sense -- if you use a regular fan, you air speed is going to be dictated by the blade speed, while the amount of air depends on the area. With the dyson, they can get a much greater area, which dictates confort, with the same air speed, because they've distributed the stream along this circle, and it picks up more air as it goes (and loses speed).
My point is, it may be poorly executed, but in principle it sounds nice, not even taking into account you don't actually have an exposed blade to worry about. It's not a scam.
If a ring of air magically propels a lot more air around it, do you think a fan of the same diameter might just compel the same air molecules to follow suit?
> if you use a regular fan, you air speed is going to be dictated by the blade speed
On the Dyson air speed IS dictated by blade speed. They have a damn fan at the base pushing air through the system and they use that air to accelerate some more air around it. Again, I am not going to waste my time doing any math. My educated guess is that the efficiency, when compared to a properly designed fan of the same diameter is atrocious.
One other point, air speed coming out of a fan is not solely dependent on blade speed. Blade shape, diameter, angle of attack, duct length and even airfoil come into play.
You also have centrifugal, fans which operate under slightly different principles and can deliver airflow at greater pressure than axial fans.
More importantly, if you are trying to cool something air speed isn't always the most important criteria. The volume of air moved per unit time is extremely important. It has to be matched to the thermodynamics of the heat exchange that will happen with whatever it is you want to cool Delivering air faster and with greater volume than necessary is a waste of energy.
My point is, it may be poorly executed, but in principle it sounds nice, not even taking into account you don't actually have an exposed blade to worry about. It's not a scam.