To EdStainless, you are right on the heat balance. However, when using the conventional definition of
saturation, as long as the outlet air temperature is sufficiently high no air "saturation" is expected. Saturation, in this case, is meant to say that the air is at its
water dew point.
Let's make an exercise on air at atmospheric pressure.
When cooling the air from 800 K down to 500 K the amount of water evaporated would be about 160 g/kg bone-dry air. If the cooled air leaves at 400 K, the amount of water evaporated would be about 200 g/kg. In either case the air isn't "saturated".
The mole fractions of water in the leaving gas mix would be 0.21 and 0.25, respectively. The
dew points would be 62 and 65 deg C, respectively. These are the temperatures for (the leaving)
air saturation to take place.
In practice, the amount of evaporated water is a function of the contacting residence time and the contacting efficiency between water and hot air.
Time is needed for water droplets to evaporate. This factor and the air flow rate, among others, would help to determine the configuration of the quenching column.