UPDATE 5/30/18:
The original circuit allowed voltage adjustment from 0-12V. The fan will shut off at around 9V or less, meaning only the last 1/4 turn or so of the potentiometer could be used for adjustment, below this the fan would just stop spinning. I have included a second schematic which uses a Zener diode, changing the voltage range to 9-12V and solving this problem.
Do you wish the fan was more powerful? Try using a 18V or 24V supply for increased maximum airflow (be careful going too high as this could damage or shorten the life of the fan).

Remix of Thing 2170098 (bladeless fan by StefanR), upgraded to include a power switch and airflow adjustment knob.

I customized the fan casing to fit the following components:

• Power Jack (DIGIKEY P/N 839-1291-ND, CONN PWR JACK 2.1X5.5MM)
• Fan (DIGIKEY P/N 1570-1083-ND, FAN AXIAL 40X20MM 12VDC)
• Potentiometer (DIGIKEY P/N 987-1738-ND, POT 500 OHM 1/10W)
• Switch (DIGIKEY P/N EG2463-ND, SWITCH TOGGLE SPDT 0.4VA 20V)
• Power Supply (DIGIKEY P/N 993-1232-ND, AC/DC WALL MOUNT ADAPTER 12V 3W)

Refer to the attached schematic/diagram for wiring instructions.
Refer to the original Thing for the other STL files necessary to complete the fan.

ASSEMBLY NOTES:
If you are having trouble getting the inner case into the outer case, put the inner case in a freezer for a little while to shrink it a bit, it should snap in easy after this!
M10 (metric) or 3/8 (imperial) nuts can be used on the bottom of the pedestal to give a little extra weight to the base and prevent the fan from tipping over.
I used small machine screws instead of self-tapping screws for attaching the outer case to the fan casing (just what I had lying around, worked great).
I used yellow poster putty as gasket material around the fan and between the fan casing and outer case (you will see some of this at the seams in the images).
The toggle switch is a light press fit, I would recommend using a small glob of super glue or epoxy to keep it secure.

GENERAL NOTES:
The potentiometer I used is 500Ω, higher resistance would also work since it is functioning as a voltage divider (rather than rheostat), so long as the supply can provide enough current. Higher resistance will improve the maximum output voltage, but it is a negligible difference. Total cost to purchase all parts from Digikey is ~$20, if you have spare electronics laying around you can cut cost down close to zero.