Hi Russ,
I guess the point here is the question of whether or not the idea presented in the OP is physically possible. To be fair, let’s address the issues surrounding the problem of feasibility.
That sounds nice except that we already know it isn't true. Cooling towers are an extrordinarily well-researched device and we already know that if you spray water in the top of a cooling tower, air will flow up, out of the cooling tower.
Very good point. Had to research this just a bit. From Wikipedia:
Natural draft, which utilizes buoyancy via a tall chimney. Warm, moist air naturally rises due to the density differential to the dry, cooler outside air. Warm moist air is less dense than drier air at the same temperature and pressure. This moist air buoyancy produces a current of air through the tower.
A cooling tower is trying to cool hot water which produces moist warm air. Heat from the water is actually sufficient to warm the air, hence this is not applicable. We need to do an energy balance which is applicable.
But it gets worse. Air at higher altitude is already cooler than air at lower altitude, and yet it is less dense. Why? Because of the altitude!
Not sure what the point here is. The same applies to all air both inside and outside the tower. So if the tower pressure at the top is the same as the pressure outside the tower at the top, then the pressure at the bottom of the tower, if the air is denser, will be at a higher pressure.
But it still gets worse. Since air at higher altitude is cooler than air at lower altitude, evaporation is less efficient and may even be impossible.
True. But how high are the towers? I don’t suppose they are proposing the towers be built more than a few thousand feet high, so I don’t see why this should matter. Air pressure is still going to be 13 psia, give or take, at the top of the tower.
But it still gets worse. Since air at higher altitude is cooler than air at lower altitude, evaporation is less efficient and may even be impossible.
Very good point. As mentioned earlier, we need to do an energy balance on this to determine the feasibility. Draw a control volume around a differential, horizontal layer of air at the top of the tower. Into this control volume, we find dry, atmospheric air and liquid water entering. There’s no reason to assume they are at different pressures or temperatures, though that could be changed also to try and improve the efficiency. Exiting this control volume is the mixture of air and water vapor. The question then is, is the air entering the CV higher or lower in density than the air leaving.
For this CV, the first law reduces to the sum of the enthalpy for the water and air in equating to the enthalpy of the air/water vapor mixture leaving.
This turns into a long, boring problem…
I did some quick calcs using a database I have which indicate a rise in density of something like 3 to 7 percent, indicating the concept is feasible. Granted, I didn’t do all the math here, but I’m not inclined right now. If you do it, I’d be interested in what you come up with.