The purpose of recirculation fans is decrease the use of engine bleed air. If you didn't recirculate some of the air would have to use engine bleed air for all of your cabin air needs. That would increase fuel burn which drives up your costs. The recirculated air goes through HEPA filters to remove airborne particulates.
The recirc fans allow for less airflow from the air conditioning packs by recycling air from the cabin and cockpit (some aircraft may vary) and adding it to fresh pack being delivered by the pack. This increases the efficiency of the system by decreasing the demand of bleed air from the engines. Furhtermore, depending on the aircraft
*Note
The moisture is invisible so long as it remains at cabin temperature which is well above a temperature known as “dew point”. Dew point is simply the temperature that water vapor becomes visible at when the air is cooled. When the air is cooled in the devices that provide air conditioning for the aircraft, the invisible moisture exhaled by passengers and crew gets lowered to the dew point and becomes visible. Air conditioners can be designed to remove much visible vapor but not all of it. As soon as the visible water vaper gets circulated back into the cabin it is heated up past the dew point and then it becomes invisible again. The cycle repeats for the duration of the flight.
Dew point is a way to measure how much moisture is in the air. You often hear it referred to in weather broadcasts as a percentage of humidity which is derived from the difference between the air's temperature and the dew point (or moisture content) of that air.
An important piece of this is that the warmer the air is, the more water it can hold before being 100% saturated.
When you cool air to its dew point, the cooled air is 100% full of moisture and at this temperature the moisture becomes visible since the air is entirely saturated.
The air close to the outlets for the air conditioning is very cold and cools the cabin air it's meeting quickly down to that air's dew point. That cooled air warms back up as it continues into the cabin and this is why you see the vapor disappear: the air has warmed back above the dew point.
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