You don't just turn the fan around?
Mitch are you joking? I did have a working group leader at the shop that tried to tell me that would work.
If not joking I guess I need to explain it like I have to others in the past.
You need to understand that a fan or propeller is for all practical purposes a very short screw that moves air by "threading" itself into the air.
Now think of the air as a nut and the fan blade as a very short piece of all-thread. If while holding the nut still and you un-thread the the all thread from the nut and turn it 180º and now try screwing it in the nut and you turn it the same direction as before the nut will move in the same direction. It does not matter which end of the threaded rod faces the nut turning clockwise will move the nut in the same direction.
Now as I'm sure OIH would tell you turning fan around will make some difference as the curve of the fan, if run facing the wrong way, will cause a loss of air flow but it will still be moving in the same direction.
And if anyone has one of those spring loaded reversible fans be very careful to get all blades set for the same direction of air flow. One blade set the wrong way will cause over heating on a warm day. Seen that one first hand!