How do Tower fans work?

I, too, was quite intrigued by my tower fan at home. Inside it, there's a cylinder/drum with vanes on it. So it looks like it should work like the reverse of a centrifugal pump or impeller mechanism:

What amazes me is this:

An impeller will propel air out from the inside of the drum to the outer circumference of the drum. However, my tower fan does not do this. It actually creates suction on it's slatted sides, and pushes out air from the output slats on the other side. I can't understand how one side sucks and the other blows when it is just a rotating drum with vanes. The vanes should move air either all outward of the drum or all inward. How can the same vanes cause suction on one side and blowing on the other?

My theory is the shape of the casing plays a big role. On the suction sides, the drum is exposed to the static outside air. Then the casing narrows around the drum surface, sealing that half of the rotating drum. Finally the narrowed casing opens to the output vent, where the air blows out of. The casing once more hugs the drum and opens back out into the suction side.

What I think is happening is this:

The air speed is slow on the suction side, so when the impeller spins, the faster moving air in the impeller vanes is at a lower pressure than the static air (Bernoulli's Principle). Thus you get suction as static air is sucked into the fast moving impeller.

Then the casing narrows and hugs the impeller - no more air can be sucked in, but the air is being flung outward by 'centrifugal force' i.e. its inertia. The casing prevents this air from being flung out until it hits the output vanes - then it shoots out and this is the fan blowing. The casing immediately hugs the drum again to seal off this output vane, before opening up to the suction half of the drum.

From what I've read the air is pulled into the core of the cylinder and forced out the top and or bottom into the housing the out the vents.

I don't understand why the air isn't sucked right back into the core rather than out the vents

i.e. instead of converting kinetic energy to static pressure (like an impeller pump), it converts the static pressure of stationary air to kinetic energy.

I'm sure I don't have a complete understanding of what's going on, and I'd like to ask a fluids professor, but this'll start you off anyway. I'll check back here in case anyone came up with brighter ideas, and post a link if you end up finding out the answer elsewhere.