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Most fans (small and large) have inner hubs (see image left). Would there be a gain in efficiency by removing that center hub, thus creating more blade space?

You could fix the blades to an outer ring (see image right - yes awesome paint.net skills) and put the components necessary for rotation in the outer frame.

Are there fans that work this way? Would they work at least comparably?

Are there reasons beyond airflow efficiency that this wouldn't work like the engine design being not worth it, using more electricity, etc.?

Fan rework

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For a large and/or high speed fan, there are several mechanical disadvantages, for example

  • The outer ring is highly stressed and therefore heavy. It may also need a heavy containment system to avoid collateral damage if it breaks. For example in a large turbofan jet engine, a mechanical failure caused by a crack near the hub of the fan usually only releases one fan blade. A crack in the outer rim would be likely to destroy the complete fan.

  • The blades fixed to the rim are compressed radially, instead of being in tension when fixed to the hub. That means they have to be designed to resist buckling which might compromise their aerodynamic shape.

  • With no central hub, you need a bearing the would support the entire rim of the fan, which would be large (and complex) compared with supporting a central shaft.

A fan adds energy to the air mainly by increasing its tangential (whirling) velocity, not its axial velocity. (If the objective is the increase the air pressure, the tangential velocity is reduced by static vanes behind the fan and converted into a pressure increase). Therefore even if the hub blocks say 10% of the total area of the fan, additional airflow through that 10% would create a much smaller increase in useful work than 10% because the tangential velocity of the air is lowest at the hub. (Note, even if the hub radius is as large as 1/3 of the outer radius, the hub only blocks 1/9 of the total area, not 1/3 of it.)

So the advantages of "increasing the effective area" are less than the disadvantages. For example the thickest part of the blades would have to be at the outer radius, where they would obstruct the air flow in the most efficient part of the annulus, not at the hub where they only affect least efficient part of the annulus area.

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Fans like the one on the right exist. These where first invented as rim-driven thrusters (rim driven is your search term, not centerless) for marine applications. The rim is the rotor of the electric motor driving the fans, the shroud around the rim contains the stator.

With the amount of research I'm willing to do right now, I found no definitive statement on efficiency relative to hub mounted motors. In theory, not mounting the motor in the airstream could lower pressure losses, leading to higher efficiency. However rimless fans require close integration of motor and fan.

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Well, a couple of points come to mind:

  1. the motor behind has a similar shape or "blocking area" so will not change the efficiency very much

  2. the angular acceleration given by the blades to the fluid moving through will be so small compared to the blade section farther out from the centre

  3. the blades have to be fixed and that hub provides a secure fixing point that is stronger and easier to machine or at least produce in a mold.

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There is another factor here that is not being discussed.

Primarily in turbo fan gas turbine engines the central hub is also a mount for the 'spinner' or 'cone'. This allows the incoming fan drawn air to be inducted in such a way as to created a convergent air flow increasing air velocity in to the fan.

This process more than makes up for any induction losses by lost blade space at the central hub.

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