moving on to the original question (as the usual suspects have digressed yet again)
Looking at the physical properties of the gases involved...
Carbon dioxide which the bees exhale is about 1.66 times as dense as air.
This means that given no fanning and normal respiration, the exhaled carbon dioxide will sink to the floor of the hive and spill out, either though the standard entrance, or the mesh floor. Air will flow in to replace it.
As most hives have the standard entrance at the bottom, whether or not they have an OMF floor or not, I would expect that the displacement would cause a good deal of circulation and exchange of air would occur naturally even without the bees fanning.
I haven't done any experiments with a beehive, but I know from brewing experience that opening a porthole on an industrial fermenter, if you place a candle below the porthole when opening it the CO2 will quickly spill out and extinguish the candle, so the tendency for CO2 to displace out is quite significant.