I’m curious what your BOTEC was / if you think 130 is too high an estimate for the exhaust temp?
I don’t remember what calculation I did then, but here’s one with the same result. Model the single-hose air conditioner as removing air from the room, and replacing with a mix of air at two temperatures: TC (the temperature of cold air coming from the air conditioner), and TH (the temperature outdoors). If we assume that TC is constant and that the cold and hot air are introduced in roughly 1:1 proportions (i.e. the flow rate from the exhaust is roughly equal to the flow rate from the cooling outlet), then we should end up with an equilibrium average temperature of TC+TH2. If we model the switch to two-hose as just turning off the stream of hot air, then the equilibrium average temperature should drop to TC.
Some notes on this:
It’s talking about equilibrium temperature rather than power efficiency, because equilibrium temperature on a hot day was mostly what I cared about when using the air conditioner.
The assumption of roughly-equal flow rates seems to be at least the right order of magnitude based on seeing this air conditioner in operation, though I haven’t measured carefully. If anything, it seemed like the exhaust had higher throughput.
The assumption of constant TC is probably the most suspect part.
Ok, I think that ~50% estimate is probably wrong. Happy to bet about outcome (though I think someone with working knowledge of air conditioners will also be able to confirm). I’d bet that efficiency and Delta t will be linearly related and will both be reduced by a factor of about (exhaust—outdoor) / (exhaust—indoor) which will be much more than 50%.
… and will both be reduced by a factor of about (exhaust—outdoor) / (exhaust—indoor) which will be much more than 50%.
I assume you mean much less than 50%, i.e. (T_outside—T_inside) averaged over the room will be less than 50% greater with two hoses than with one?
I’m open to such a bet in principle, pending operational details. $1k at even odds?
Operationally, I’m picturing the general plan I sketched four comments upthread. (In particular note the three bulleted conditions starting with “The day being hot enough and the room large enough that the AC runs continuously...”; I’d consider it a null result if one of those conditions fails.) LMK if other conditions should be included.
Also, you’re welcome to come to the Air Conditioner Testing Party (on some hot day TBD). There’s a pool at the apartment complex, could swim a bit while the room equilibrates.
I studied the impact of infiltration because of clothes dryers when I was doing energy efficiency consulting. The nonobvious thing that is missing from this discussion is that the infiltration flow rate does not equal the flow rate of the hot air out the window. Basically absent the exhaust flow, there is an equilibrium of infiltration through the cracks in the building equaling the exfiltration through the cracks in the building. When you have a depressurization, this increases the infiltration but also decreases the exfiltration. If the exhaust flow is a small fraction of the initial infiltration, the net impact on infiltration is approximately half as much as the exhaust flow. The rule of thumb for infiltration is it produces about 0.3 air changes per hour, but it depends on the temperature difference to the outside and the wind (and the leakiness of the building). I would guess that if you did this in a house, the exhaust flow would be relatively small compared to the natural infiltration. So roughly the impact due to the infiltration is about half as much as the calculations indicate. But if you were in a tiny tight house, then the exhaust flow would overwhelm the natural infiltration and the increase in infiltration would be close to the exhaust flow.
Another factor is the dehumidification load on the air conditioner. This is a really big deal in the southeastern US, though it would be less of a deal in the Bay Area. Basically, if it is very humid outside, the additional infiltration air has to be de-humidified, and that can double how much heat the air conditioner needs to remove from the infiltration air. So this could counteract the benefit of the net infiltration being smaller than the exhaust flow.
The exhaust temperature of 130°F sounds high to me for regular air conditioner, but heat pumps designed to heat hot water and dry clothing to go even higher than that. So it is possible they increase it more than a regular air conditioner to increase the overall efficiency (because the fan energy is significantly larger with the hose as compared to a typical window unit). Still, I am confident that the reduction in efficiency of one hose versus two hose is less than 50% unless it is very hot and humid outside.
If the building is ending up around 70, that means I’m underestimating the exhaust quantity by about 2x. But then apparently the extra infiltration is only about half of the exhaust. So sounds like the errors cancel out and my initial estimate happens to be roughly right?
Tc does seem like a bad assumption. I tried instead assuming a constant difference between the intake and the cold output, and the result surprised me. (The rest of this comment assumes this model holds exactly, which it definitely doesn’t).
Let Tr be the temperature of the room (also intake temperature for a one-hose model). Then at equilibrium,
Tr=(Tc+Th)/2
Tr=((Tr−Δ)+Th)/2
2Tr=Tr+Th−Δ
Tr=Th−Δ
i.e. no loss in cooling power at all! (Energy efficiency and time to reach equilibrium would probably be much worse, though)
In the case of an underpowered (Δ=15) one-hose unit handling a heat wave (Th=100), you’d get Tr=85 and Tc=70—nice and cool in front of the unit but uncomfortably hot in the rest of the room, just as you observed. Adding a second hose would resolve this disparity in the wrong direction, making Tr=Tc=85. So if you disproportionately care about the area directly in front of the AC, adding the second hose could be actively harmful.
I don’t remember what calculation I did then, but here’s one with the same result. Model the single-hose air conditioner as removing air from the room, and replacing with a mix of air at two temperatures: TC (the temperature of cold air coming from the air conditioner), and TH (the temperature outdoors). If we assume that TC is constant and that the cold and hot air are introduced in roughly 1:1 proportions (i.e. the flow rate from the exhaust is roughly equal to the flow rate from the cooling outlet), then we should end up with an equilibrium average temperature of TC+TH2. If we model the switch to two-hose as just turning off the stream of hot air, then the equilibrium average temperature should drop to TC.
Some notes on this:
It’s talking about equilibrium temperature rather than power efficiency, because equilibrium temperature on a hot day was mostly what I cared about when using the air conditioner.
The assumption of roughly-equal flow rates seems to be at least the right order of magnitude based on seeing this air conditioner in operation, though I haven’t measured carefully. If anything, it seemed like the exhaust had higher throughput.
The assumption of constant TC is probably the most suspect part.
Ok, I think that ~50% estimate is probably wrong. Happy to bet about outcome (though I think someone with working knowledge of air conditioners will also be able to confirm). I’d bet that efficiency and Delta t will be linearly related and will both be reduced by a factor of about (exhaust—outdoor) / (exhaust—indoor) which will be much more than 50%.
I assume you mean much less than 50%, i.e. (T_outside—T_inside) averaged over the room will be less than 50% greater with two hoses than with one?
I’m open to such a bet in principle, pending operational details. $1k at even odds?
Operationally, I’m picturing the general plan I sketched four comments upthread. (In particular note the three bulleted conditions starting with “The day being hot enough and the room large enough that the AC runs continuously...”; I’d consider it a null result if one of those conditions fails.) LMK if other conditions should be included.
Also, you’re welcome to come to the Air Conditioner Testing Party (on some hot day TBD). There’s a pool at the apartment complex, could swim a bit while the room equilibrates.
I studied the impact of infiltration because of clothes dryers when I was doing energy efficiency consulting. The nonobvious thing that is missing from this discussion is that the infiltration flow rate does not equal the flow rate of the hot air out the window. Basically absent the exhaust flow, there is an equilibrium of infiltration through the cracks in the building equaling the exfiltration through the cracks in the building. When you have a depressurization, this increases the infiltration but also decreases the exfiltration. If the exhaust flow is a small fraction of the initial infiltration, the net impact on infiltration is approximately half as much as the exhaust flow. The rule of thumb for infiltration is it produces about 0.3 air changes per hour, but it depends on the temperature difference to the outside and the wind (and the leakiness of the building). I would guess that if you did this in a house, the exhaust flow would be relatively small compared to the natural infiltration. So roughly the impact due to the infiltration is about half as much as the calculations indicate. But if you were in a tiny tight house, then the exhaust flow would overwhelm the natural infiltration and the increase in infiltration would be close to the exhaust flow.
Another factor is the dehumidification load on the air conditioner. This is a really big deal in the southeastern US, though it would be less of a deal in the Bay Area. Basically, if it is very humid outside, the additional infiltration air has to be de-humidified, and that can double how much heat the air conditioner needs to remove from the infiltration air. So this could counteract the benefit of the net infiltration being smaller than the exhaust flow.
The exhaust temperature of 130°F sounds high to me for regular air conditioner, but heat pumps designed to heat hot water and dry clothing to go even higher than that. So it is possible they increase it more than a regular air conditioner to increase the overall efficiency (because the fan energy is significantly larger with the hose as compared to a typical window unit). Still, I am confident that the reduction in efficiency of one hose versus two hose is less than 50% unless it is very hot and humid outside.
Thanks! It’s amusing that we had this whole discussion and the one commenter who knew what they were talking about got just one upvote :)
It sounds very plausible that exhaust is small relative to natural infiltration and I believe you that (extra infiltration) = 50% (exhaust).
In the other direction, it looks like I was wrong about 130 degrees and we’re looking at more like 100 (alas, googling random forum comments is an imperfect methodology, though I do feel it’s plausible that John’s AC has unusually cold exhaust).
If the building is ending up around 70, that means I’m underestimating the exhaust quantity by about 2x. But then apparently the extra infiltration is only about half of the exhaust. So sounds like the errors cancel out and my initial estimate happens to be roughly right?
Tc does seem like a bad assumption. I tried instead assuming a constant difference between the intake and the cold output, and the result surprised me. (The rest of this comment assumes this model holds exactly, which it definitely doesn’t).
Let Tr be the temperature of the room (also intake temperature for a one-hose model). Then at equilibrium,
Tr=(Tc+Th)/2
Tr=((Tr−Δ)+Th)/2
2Tr=Tr+Th−Δ
Tr=Th−Δ
i.e. no loss in cooling power at all! (Energy efficiency and time to reach equilibrium would probably be much worse, though)
In the case of an underpowered (Δ=15) one-hose unit handling a heat wave (Th=100), you’d get Tr=85 and Tc=70—nice and cool in front of the unit but uncomfortably hot in the rest of the room, just as you observed. Adding a second hose would resolve this disparity in the wrong direction, making Tr=Tc=85. So if you disproportionately care about the area directly in front of the AC, adding the second hose could be actively harmful.