I have a question about Heat recovery ventilators.
I have a home with with 10″ of dense pack cellulose in the walls and 14″ in the celling.
I am looking to install a h.r.v. I have a very open floor plan and would like to use only one vent in and one vent out. Drawing air from the upstairs bedroom and putting new air into the living room downstairs. Air would travel through the stair well at the other end of the house . Calculations say I need about 100 cfm. Is there any problem moving this amount of air through only one duct?
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Probably no, but you should go by the manufacturer's installation instructions.
100cfm seems like a quite lot of ventilation for a bedroom- how many people are sleeping in there at any one time?
Two pairs of Lunos Nexxt would get you to above 100cfm (53cfm per pair), without ducts, which may be easier to pull off in a retrofit, but more expensive. ($1500 per pair,$3K for two pair vs. ~$700-900 plus ducts and vent terminators for a 100cfm+ ducted HRV.) The air both enters and leaves each unit of the pair, with the direction changing every minute or so. That actively ventilates and exhausts the air from any room that has a half-pair. The pairs balance by having one exhaust while the other pulls air in, inducing very little pressure difference between indoors & outdoors that would drive air infiltration through other paths.
With ducted systems 100cfm isn't a big deal to design, but the diameter of the duct needs to be sufficient for the HRV to be able to deliver that flow at the ducts' "equivalent length". I would expect that to all be spelled out in the installation instructions.
Ducted HRVs typically have just one intake, one exhaust penetrating the exterior walls, but there are limitations to how close or far apart they can be placed. It's generally true that they need to be placed on the same side of the house, to guarantee that wind currents don't un-balance the flow and it's better if they're reasonably close to each other, just not "too close" per the manufacturer's minimum separation specifications.
The distribution path the air takes is dictated by the duct & register designs. If you only want one exhaust register located in the bedroom and only one supply register located in the living room the HRV can be located somewhere else entirely (and usually is). There's usually some amount of vane tweaking and measuring with a manometer to ensure that it's sufficiently well balanced that it doesn't pressurize or depressurize the house, or the individual rooms.
A more typical one-supply one-exhaust register configuration is to put the supply register in a master bedroom, which is usually occupied around 8 hours or more at a time, and the exhaust register in a bathroom, where excess humidity and odors can be removed without passing through other rooms.
I found another post of yours and looks like you're in Maine?
How big is your house? How many people live there?
How many bathrooms and what is the ventilation setup in those, bath fans?