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re: house cooling
14 may 2001
joelncaryn wrote:
>> ...opening your windows at night and closing them during the day
>> can buy you a couple extra weeks or months... before it becomes
>> necessary to switch on the heat pump/a.c...
let's automate this with a window fan and 2 modular "thermal extension
cords" with a grainger's $12.93 2e158 22 amp spdt line voltage thermostat
(+ 2/4 f heat/cool diff.) wired to a 38 cent split duplex ac outlet with
a 62 cent wallplate in a $1.61 3-gang electrical box (in courier font):
>--*--------------->
line cord | tx rl outlet active if tx < 70
(chopped >----------*---|--->
off a dead | 70 | cost: $15.54
appliance) --------------->
| ru outlet active if tx > 70
---x--->
the 2 identical cords could be plugged together like this:
---
| |rl --- controls cost: $31.08
120 vac ---|th | | |rl---fan
^ | |ru------|ta |
| --- | |ru---[optional window ac]
l ---
we could build a very slow computer with these "thermal neurons" and
light bulbs. they can do any digital function involving temperatures
and thresholds. for instance, here's a clock/ditherer, and a nand gate:
---
| |ru
120 vac ---|ta |
--- | |rl---
| |rl--- heater --- |
120 vac ---|tck| ck *--- heater c = ~(ab).
| |ru --- |
--- | |rl--- 1 00
120 vac ---|tb | 1 01
[we don't need heaters or | |ru 1 10
nand gates for this project...] --- 0 11
>basements have lots of thermal mass, and we can add more, eg 4" sewer
>pipes between the rafters. maybe we need two loops, 1 to cool the
>basement with outdoor air 1 to circulate house air through the basement
>as needed. this could become known as a thermal recirculation energy
>conservation system, aka "two loops le trec."
it would be simpler and almost as efficient to cool the basement while
cooling the house (vs separate fiercer cooling) by drawing cool outdoor
air in through a basement window using an upstairs window exhaust fan w,
with another fan b to circulate air between the basement and the house,
and a window air-conditioner ac as last resort.
here's one way to control them, given house temp th, outdoor temp ta,
and basement temp tb...
th ta tb | w b ac notes
------------------------------------------------------------------------
[>65] <76 - | on off off cool house & basement with outdoor air
>76 >76 <76 | off on off cool house with basement
>76 >76 >76 | off off on cool house with ac
we could implement this priority logic with 3 thermal neurons
---
|th |rl --- controls cost: $46.62
120 vac ---|76 | |ta |rl---w ---
^ | |ru------|76 | |tb |rl---b
| --- | |ru------|76 |
l --- | |ru---ac
---
located to sense house air, outdoor air, and basement air.
another in series [>65] at point l might limit the lower house temp...
---
|th |rl
120 vac ---|65 |
| |ru---...
---
nrel says july is the worst-case month for cooling in phila...
may june july august september
average daily min 52.7 61.8 67.2 66.3 58.7
average 24-hour 62.9 71.8 76.7 75.5 68.2
average daily max 73.1 81.7 86.1 84.6 77.6
suppose an average july day is 67.2 for 6 hours while we cool the house
and basement with outdoor air, then it's 76.7 for 12 hours, then 86.1
for 6 hours, ie an average of 79.8 for the 18 non-cooling hours.
we can keep the house arbitrarily near the daily min temp, given enough
thermal mass and thermal mass surface and airflow. say we use a $26.75
4300 cfm 166 watt grainger 4ch71 20" box fan in a window, and we have an
infinite thermal mass with infinite surface, ie no thermal resistance,
and we keep the house at temp t for 24 hours a day...
say the house has a heat conductance of 300 btu/h-f, and the windows are
shaded, so it gains 24h(76.7f-t)300btu/h-f btu/day of heat from outdoor
air, and frugal electrical usage of 300 kwh/month adds 1.4k btu/h or 34k
btu/day, and we exchange 6hx4300 cfm of 67.2 f air for t f house air, so
24(76.7-t)300+34k = 4300x6(t-67.2). t = (24gta+6ctm+e)/(24g+6c) = 70.3 f,
with ta = 76.7, g = 300, c = 4300, and e = 34k... 2 fans make t = 68.9.
grainger's $115 4c853 48" 21k cfm 86 w ceiling fan makes t = 68.0 f, ie
it can provide 24(76.7-68.0)300+34k = 97k btu of cooling with 6x86 wh of
electrical energy, for an eer of 187 or a cop of 55...
now let's suppose the real thermal mass is 2" of 2,000 ft^2 of masonry
basement floor and walls with 8k btu/f plus 2,000 ft^2 of 1/2" drywall with
1k btu/f plus 10k pounds or 1,250 gallons of clean water in 180 10'x4" pvc
capped sewer pipes in a 1,000 ft^2 basement ceiling with 3 in each 16"
rafter cavity. c = 19k btu/f, with about 1.5 btu/h-f-ft^2x6000ft^2
= 9k btu/h-f of slowly-moving airfilm conductance (=1/resistance.)
we might model cooling by discharging the mass at midnight through a
1/9k f-h/btu resistor into a 67.2 f 6x4300 = 25.8k btu/f capacitor.
c' = 25.8kx19k/(25.8k+19k) = 11k btu/f, with the 2 caps in series, and
rc' = 11k/9k = 1.2 hours. if the mass is tm at midnight, the air/mass
mixture would be tf = (67.2x25.8k+19ktm)/(25.8k+19k) = 38.70+0.4241tm
after a long time, or tf+(tm-tf)exp(-6h/1.2h) = 38.44+0.4280tm after
6 hours (almost the same, after 5 time constants.)
if the mass releases 19k(tm-(38.44+0.4280tm)) = 10.87ktm-730.4k btu,
18(79.8-t)300+34k = 10.87ktm-730.4k makes t = 221.4-2.013tm. with
a 4300 cfm basement-house fan, (79.8-t)300+1.4k = (t-tm)4300 makes
t = 0.9348tm+5.513, so tm = 73.2 and t = 74.0.
two window fans make c' = 13.89k btu/f and rc' = 1.54 hours and
tf = 49.12+0.2691tm, so the mass becomes tf+(tm-tf)exp(-6/1.54)
= 48.12+0.2786tm after 6 hours, releasing 19k(tm-(48.12-0.2786tm))
= 13.7ktm-914.3k btu, and 18(79.8-t)300+34k=13.7ktm-914.3k makes
t = 255.4-2.537tm = 0.9348tm+5.513, so tm = 72.0 and t = 72.8,
so a second window fan is probably not worth the difference.
however, we could improve performance by adding a differential
thermostat and another fan to circulate outdoor air through the
basement (without cooling the house) when the basement is warmer
than the outdoors. how much? a tmy2 simulation would tell...
and we might have less noise and fan power and more cooling by
evaporation and night-sky radiation if we used a shaded pond or
pumped water over the roof at night and collected it in a tank,
with a fan-coil unit inside the house, eg a $35 used 1984 dodge
omni radiator with its 12v fan.
nick
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