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water-wall greenhouses
7 nov 1998
living in a greenhouse isn't everyone's dream. not burglarproof, ugly,
some say, hard to see clearly outside through plastic films that need
replacing every 5-10 years. but very cheap, at $1/ft^2, erected from
scratch... too cold at night, too much sun during the day, and too much 
humidity, if it's full of plants evaporating about a pound of water
per square foot per day.

most philadelphia greenhouses have too much uninsulated glazing to stay
very warm using only the sun over an average january day, and they would
get very cold at night with no other heat source. ok for some plants,
if they don't freeze at night, but not so good for people. otoh, living
in a house inside a low-thermal-mass greenhouse might be nice, eg in a
mobile home or a stack of strawbales with some insulated mass to keep it
warm for a few cloudy days in a row.

a quarter- or half-cylindrical greenhouse with an insulated north wall
and 2 layers of 5 cent/ft^2 4-year plastic film with a us r-value of 1.2
and 80% solar transmission would collect about 800 btu/ft^2 of sun through
the south wall and 500 through the roof over an average 30 f january day
in phila (or 340 and 200 in seattle, on an average 40.5 f december day.)

it would lose about 24h(t-30)/r1.2 btu/ft^2 of glazing surface. suppose
a long greenhouse has an e-w orientation and a 16' radius and lots of
thermal mass and no heat-generating animals or evaporative heat loss or
air leaks. then, if the solar energy flowing in on an average day equals
the heat energy flowing out, for a 1 foot slice of this long greenhouse,
24h(t-30)25ft^2/r1.2 = 16ft^2x800+16ft^2x500, so t = 71.6 f, not counting
heat loss to the ground or through the north wall. one might raise the
daytime temperature by partitioning one end section of the greenhouse
with a layer of plastic film to make a low-thermal-mass sunspace with a
couple of passive plastic film one-way dampers in the partition to prevent
reverse thermosyphoning at night or on cloudy days.

a 2' thick x 16' high north water wall with good insulation outside might
be made in 4'x8' modules weighing about 2 tons each with 6 1x3 studs on
16" centers and 2 4'x8' 4" square galvanized welded-wire fence sides
(about 5 cents per square foot) and vertical 1x3 cap strips to hold the
fence on, and 2 wire fence troughs (with a newspaper shelf liner?) 32"
and 64" above the ground, with some 2' 1x3s above the troughs to space
the walls apart. each of the 9 16"x24"x32" tall compartments might contain
2 nested grainger 3u725 plastic drum liners (~13 cents each.)

this makes the greenhouse time constant rc = r1.2/25ft^2x2x16x64 = 98 h.
if the air and water wall temperatures were the same, eg 72 f at dusk,
after 24 cloudy hours, t = 30+(72-30)exp(-24/98) = 63 f. after 5 cloudy
days, t = 30+(72-30)exp(-120/98) = 42 f. cold...

but if sun shines on the water wall, it can be warmer than greenhouse air. 
the r-value of slowly moving air near the wall surface might be about 2/3.
if the wall has a temperature tw and absorbs 800 btu/ft^2 on an average day
when the air temperature is 71.6 f, 24h(tw-71.6)/r2/3 = 800, so tw = 93.8 f.
an extra layer of r1 glazing over the wall with 90% solar transmission might
make 24h(tw-71.6)/r1.7 = 730, so tw = 122.3 f. this is good, since warmer
thermal mass can store more heat for cloudy days, even though it does not
increase the average greenhouse air temperature.

with an extra layer of glazing over the water wall, we might have something
like this electrical analog:

                            tg = 71.6 (initially)
                            |
              r1.2/25ft^2   |   r1.7/16ft^2
    30 f --------www---------------www------------tw = 122.3 (initially)
           exterior glazing     ww glazing   |     
              resistance        resistance  ---   c = 2x16x64 
              = 0.048           = 0.104     ---     = 2048 btu/f
             \________ r = 0.152 ______/     |
                                             -

rc = 0.152 f-h/btu x 2048 btu/f = 311 hours for the water, so after 5
cloudy days we might have tw = 30+(122.3-30)exp(-120/311) = 92.8 f, with
a heatflow through the wall glazing of (92.8-30)/0.152 = 413 btu/h and a
greenhouse air temperature tg = 30+413x0.048 = 50 f. still too cold.

how about insulating the glazing at night? either partition the greenhouse 
with an e-w insulated wall, eg strawbales, and use a solar closet, or fill
the space between the layers of plastic film with bubbles at night, using
something like the system developed by richard nelson at thermatics in
montreal, and use an interior water wall. tiny cold bubbles are as good as
fiberglass insulation, say r20 at night for a 6" glazing cavity.

we might use a water wall with 2 extra layers of glazing as a cloudy day
heat source, and vary the foam height or duration or turn on a ventilation
fan or use some $12 automatic foundation vents with bimetallic springs to
control the greenhouse air temperature. if the wall is initially 122 f,
on the first cloudy day, a 1' wall slice would supply 24h(122-70)16ft^2/r2
= 10k btu, and a 1' greenhouse slice needs 24h(70-30)25ft^2/r20 = 240 btu
to stay warm with the foam in place, so we dump (yes, waste) about 9,750
btu of heat to the outdoors by venting warm air, which reduces the water
temp by 9,750/(2x16x64) = 5 f to 117. on the second day, the wall supplies
9k btu, we waste 8750, and the water cools to 113. after 5 cloudy days,
tw = 70+(122-70)exp(-120/311) = 105.

on an extremely cold day (99th percentile) in phila, the wall needs to
supply heat at a rate of (70-(-10))25ft^2/r20 = 100 btu/h or 100/16 =
6.25 btu/h per square foot of wall, which requires a minimum water temp
of 82.5 f after 5 cloudy days, or less, if some automatic foundation vents
or a 2 watt motorized damper open to let room air flow up vertically behind
the glazing from a hole near the bottom of the wall.

if 82.5 = 70+(122-70)exp(-120/rc), rc = -120 ln(12.5/52) = 171 hours 
= r2x64lb/ft^3t, where t is the wall thickness in feet, so the wall only 
needs to be 16" thick, or we might use fewer 2'-thick wall modules.

this "shunt-regulated thermal power supply" wastes a lot of solar heat,
but it's very inexpensive to build, and solar heat is free :-) and thermal
mass is good for natural summertime cooling, with night ventilation, and 
the water might be used for plants, and reclaimed as condensation from the
cold greenhouse glazing. a less-wasteful scheme with a lot less thermal
mass might have bubbles partially filling the waterwall glazing cavity
on cloudy days.

nick




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