A HRV should reduce indoor humidity in hot humid summers?
The common rule of thumb is that HRVs (versus ERVs) do not change the moisture content of incoming air.
However in a 105F summer with RH 65%, the incoming air will be brought down to well below dew point in the heat exchanger. This should cause moisture to condense out, and deliver supply air with a lower humidity than the outdoor air. The excess moisture is taken away by the condensate drain.
That’s the theory anyway, but I couldn’t find any references to this in all my reading on HRVs. What’s the flaw in my theory?
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You are correct that condensation will occur in the HRV when/if the outdoor air is chilled below its dewpoint. HRVs have drains for this reason. However, the outdoor air will not be chilled below the temperature of the indoor air. In fact, it will always be a little bit warmer than the indoor air because of efficiency losses. Therefore, the air coming from the HRV will be a few degrees warmer than the indoor air, but at 100% relative humidity. So even though some moisture has been wrung out of the airstream, your indoor air will still be way too humid for comfort. In order to dehumidify the indoor air enough to be comfortable and healthy, you need to chill it down to a much lower dewpoint - below about 50 degrees F to get your indoor humidity down below 50%. But in fact you need to chill the air far lower than that if you want to also remove humidity from indoor sources. This is why most A/C systems chill the coils down to near 40F. The very cold coils wring out the moisture of the air contacting the coils, which is not all of the air passing through. The air leaving the coils is generally about 15 degrees cooler than the return air, but much drier in terms of total moisture. When that air mixes with the room air, the mixture approaches the design conditions.
I don't know if that's really the rule of thumb. The rule of thumb is that HRVs will be worse for indoor humidity in humid summers than ERVs, which is true. An HRV will condense some water and reduce the humidity of incoming air relative to the outdoor air, but it will still be much higher than the indoor humidity (in the scenario you described). An ERV will transfer more moisture from the incoming stream to the outgoing stream than an HRV will condense out.
Having used both in the same house in a mixed climate (cold and dry* winters, hot and humid summers, often muggy spring/fall), the ERV wins in every season. It might be a tie in the shoulder seasons.
*all cold air is dry
I should add that other scenarios are much worse for the HRV. For example, 90F and 65% is a dew point of 76.6F. At that point, your HRV is not condensing anything, assuming an internal temperature of around 72-75, because outgoing air temperature is going to be about 76-79.
HRVs do cause moisture to condense out of the air, which is why they need condensate drains. (ERVs do not need condensate drains.) But they are only around 80-92% efficient, so the incoming air when it's hot outside will always be warmer than the indoor air, so you are still increasing the relative humidity of the interior air.