N. Pine, Pine Associates Ltd., 821 Collegeville Rd., P. Bashus, Physics
Dept., Ursinus College,
Collegeville, PA 19426, USA Collegeville, PA 19426, USA
(610) 489-0545 nick@ece.vill.edu (610) 409-3000 pbashus@acad.ursinus.edu
ABSTRACT
A "solar closet" is an insulated box filled with sealed containers of
water, with a solar air heater attached to one insulated side. In a
simplified solar space- and water-heating technique, a low-thermal-mass
isolated sunspace heats a house on an average winter day, with an
average amount of sun. A higher-temperature, compact, high-thermal-mass
sauna behind the sunspace provides domestic hot water and space heat for
the house during cloudy weather.
KEYWORDS
Passive, solar, space, water, house, heating.
CONVENTIONAL SOLAR HOUSES
Many solar houses are expensive and low-performing. Active systems can
perform well, but they tend to be expensive and complicated. "Trombe
walls," invented in 1881 (US Patent No. 246,626), by Edward Morse of
Salem, Massachusetts, are still being used in today's passive solar
houses. However, because they are so poorly insulated, Trombe walls
perform poorly on cloudy days... A person might well build a typical
passive solar house, and end up with a house that costs more than a
neighbor's, while only using 30% less oil for heating. Some passive
solar houses take 20 years to pay for their passive features, versus
non-solar houses. A direct-gain passive solar house typically has a very
large uninsulated window in a living area, with a masonry floor in front
of that, to store solar heat. This works well in sunny climates, with
few cloudy days in a row.
However, cloudy-day performance becomes more important as we approach
90-100% solar heating. Sunny-day heating is taken for granted; domestic
water heating becomes more important. With the end of solar tax credits,
dollars saved per dollar invested and annual backup heating fuel bills
become more important. Solar houses now need to stand on their own
economic feet, as do superinsulated houses. They can be combined…
Typical solar houses have limitations: masonry floors and walls are not
good "heat batteries." Water is less expensive than masonry, and stores
about three times more heat by volume, with a lower thermal resistance.
We cannot cover masonry floors with rugs on a sunny day. Perhaps they
should be covered at night... A direct gain house has an optimal solar
glazing/heat load ratio: too little glazing gives too little solar gain,
and too much glazing allows too much cloudy-day heat loss. A direct gain
house gets exponentially colder with each cloudy day, barring a backup
heating system. A higher temperature, more compact, better-insulated
heat store that is maintained at a temperature of, say 54oC vs. 20oC,
will have a longer discharge lifetime and can provide controllable heat
for a house during longer strings of cloudy days. In a direct gain
house, we have to live inside the heat store, so we cannot charge it up
to a high temperature during sunny weather.
SOLAR CLOSETS
Solar allen roth closets solve the problem above, as well as the
"optimal solar glazing area" dilemma. A simple solar closet is an
insulated cube, with some sealed containers of water inside and a
passive solar air heater attached to one insulated side. How much water
and how much insulation? A cube with about half water and half
insulation by volume will maximize its natural (RC) time constant,
prolonging the discharge lifetime of this heat battery.
We arrived at this conclusion by differentiating the formula for the RC
time constant. However, the use of calculus seems overdone in solar
heating. Many practical solar heating systems can be designed with
arithmetic and, at most, algebra or computer tools. Voltaire (1764)
said, "The best is the enemy of the good." He meant that it is better to
do calculations on the back of an envelope and go build something than
to spend one's life on earth designing better and better systems without
ever building one. This includes the pursuit of better materials as well
as mathematical and physical models. The energy crisis is not over yet,
and very few houses are 100% solar heated. Let's take a step backwards
in our sophistication and let builders and architects design simple,
high-performance, passive solar houses, home solar panels, using simple
assumptions and arithmetic, just as they do simple beam design calculations.
Consider a 1 m cubical solar closet (Fig. 1A) sitting outdoors on an
average 0oC December day near Philadelphia, Pennsylvania, USA. The south
wall of the closet, i.e., the solar air heater, receives about 3
kWh/m2/day of solar heat, i.e. Ein = 3 kWh/day, more if there is snow on
the ground or a white surface or a shallow frozen reflecting pool in
front...
Say the closet has 10 cm of insulation with a metric R-value of 4 m2
oC/W, and it contains an 80 cm cube of water in 1 or 2 liter plastic
soda bottles or rectangular 3 liter olive oil cans, with some spaces for
warm air to flow around the cans. The cans have about 14 times the
glazed area. During an average 6 hour December day, the closet loses
heat through the R0.1 single-pane glazing of the air heater, and during
all other times it is well-insulated, and the air and water temperatures
inside the closet and the air heater are all the same, Tw, then the heat
flow out of the closet on an average day is
Eout = 6 hr (Tw-0) 1 m2/R0.1 south (equatorial) wall, day
+18 hr (Tw-0) 1 m2/R4 south wall, night
+24 hr (Tw-0) 5 m2/R4 other walls
(Tw-0)(60 + 4.5 + 30)
(Tw-0) 94.5, (1)
so if Ein = Eout, then Tw = 0 + 3k/94.5 = 31.7oC. (2)
Note that the solar closet is acting like a stagnated solar collector,
with some thermal mass inside just keeping itself warm, not a whole
attached house. This is a "naturally-trickle-charged heat battery," with
a solar collection efficiency of 0. How long will it take to discharge
to 20oC inside?
When the sun is not shining, the cube has a thermal resistance of about
R4/6 m2, and a capacitance of about 0.5 m3 x 1 kWh/m3C, so its time
constant is RC = 500 hours or about 20 days. Taking logarithms, we find
the time t in the equation 20oC = 0oC + (31.7 - 0) exp(-t/20) (3)
is 9.6 days. Not bad for a solar house, but this is more like an aquarium...
A)
B)
Fig. 1 - A 1 meter solar closet (A) and a larger system (B) showing airflow.
An 2 m cube containing 18 - 200 liter drums full of water with a 9:1
drum/glazing area ratio (bigger closets can use bigger containers), and
20 cm of insulation would work better, with a time to cool to 20oC of 33
days. A 4 m solar closet with R16 insulation would take 5 months (156
days) to cool to 20oC, at a constant 0oC outside with no sun, using
these simple assumptions. As a rule of thumb, the time constant in weeks
of a solar closet is roughly its dimension in meters, squared.
The passive air heater absorber above might be a thin, black-painted
sheet of metal with some holes in it, as in the Conserval air heater,
with cooler air moving south from the lower part of the closet (Fig.
1B), up through an airspace between the glazing and the absorber,
sideways from south to north, through the absorber plate, into an
airspace behind the absorber, and back into the top of the closet via a
hole in the insulated south wall. As an alternative the absorber might
be black window screen or 80%-absorbing, black, porous, greenhouse
shadecloth, costing about $2/m2, perhaps behind some green shadecloth,
for aesthetics. The glazing might be 0.05 cm thick single-layer, clear,
flat, non-fibrous, semi-rigid polycarbonate plastic, costing about
$10/m2. The top of the air heater needs a passive plastic film air
damper to prevent reverse airflow at night. We might control airflow by
using an inexpensive automatic damper (e.g., the $11 FV-1B automatic
foundation vent made by Leslie-Locke of Atlanta, GA) with a bimetallic
spring to open some louvers to let air flow when the air is above an
adjustable soft threshold temperature, as in a spacecraft cooler. Two
opposed springs might make a differential thermostat. Another way to
prevent reverse airflow at night is to put the containers of water above
the air heater, as in igloos, or the attic warmstores of Norman
Saunders, P. E.
As an alternative, a small fan with a backdraft damper would move air
faster, raising heat flow rates and lowering air film thermal
resistances for the absorber and water container walls, thus increasing
solar collection efficiency. Figure 1 of ASHRAE (1993) shows thermal
conductivity U (=1/R) of surfaces increasing linearly with air velocity.
However, solar collection efficiency is not important here, since almost
all the heat losses from the solar closet end up in the house. A fan
would allow shrinking duct widths required for natural airflow, which
Baer (1979) estimates as 1/15 of the collector area.
How do we turn a solar closet into a house? Building the house around
the solar closet allows the closet to have less insulation or operate at
a higher temperature, since most of the Allen roth closet walls can be
inside the house, exposed to 20oC air versus 0oC air, with no wind. The
air heater wall should be inside a sunspace, to keep it warmer during
the day, when losses are greatest.
SUNSPACES
A low-thermal-mass sunspace can heat the house on an average winter day.
Transparent "solar siding" with an air gap and insulation behind it can
make a very thin sunspace. Houses need siding anyway, and corrugated
clear polycarbonate plastic sheets cost about $10/m2 and last many
years. We might use a commercial plastic film greenhouse for a sunspace,
or a steep equatorial-facing transparent roof over an insulated ceiling,
blowing down warm air to the house from this low-thermal-mass solar
attic with a fan.
Size the sunspace to keep the house at 20oC on an winter average day.
The solar closet would merely keep itself warm, leaking most of its
"waste heat" to the house, not to the outdoors, lying in wait, lurking,
ready to provide heat for the house at night, or during a string of
cloudy days. It could be in the airpath of a hot air heating system,
with a bypass damper that allows heat to flow out of the closet as
needed, or a motorized air damper near the top of the closet, controlled
by a thermostat or a setback thermostat could open the damper from the
closet to the house. Reversing the spring in the foundation vent
mentioned above would allow its louvers to open to let warm air into the
house as the house cools. An open attic warmstore, e.g., a vaulted stone
ceiling or concrete dome with foam on the outside might use a ceiling
fan controlled by a thermostat to blow warm air down into the house as
needed.
AN EXAMPLE
Suppose our new passive solar house is in Philadelphia, where the
average temperature is about 0oC and about 3 kWh/m2/day falls on the
south wall of a house on an average day in December, with some sun. NREL
(Marion and Wilcox, 1994) give this data for many U.S. locations.
NREL/NOAA also supply hourly solar weather data on CD-ROM
(orders@ncdc.noaa.gov). Suppose our well insulated house is 10 m x 10 m
square, and two stories tall (Fig. 2), with about 300 m2 of walls and
ceiling, with an average R-value of 6 and a heat capacity equivalent to
10 kg of water/m2, with no air infiltration or internal heat generation.
A)
B)
Fig. 2 - Solar closet house, side (A)
and plan views (B)
Using "Ohm's law for heatflow," 24 kWh/day will keep the house 20oC
inside when it's 0oC outside, about the same as a gallon of oil, burned
inefficiently. A square meter of glazing attached to the
low-thermal-mass wall of this house would gain about 3 kWh and lose
about 6 hr (20oC - 0oC)/R0.1 = 1.2 kWh, for a net gain of 1.8 kWh. Our
house would thus need 24 kWh/1.8 kWh/m2 = 13.3 m2 (~2 m x 7 m) of
sunspace glazing to keep it warm on an average December day, with some
sun. Sun-warmed air would flow into the house from the sunspace during
the day through holes at the top and the bottom, with dampers, and this
low-thermal-mass sunspace would get icy cold at night, unlike a Trombe
wall. The house would stay reasonably warm at night with the thermal
mass of its walls and floors, i.e.,
20oC - 18 hr x 1 kW/ (300 x 10) Wh/oC = 14oC. (4)
If the sunspace were a greenhouse, it might have an automatic damper to
allow warm air to flow from the house as needed to keep the plants just
above freezing.
To keep the house warm for say, 5 days without sun, we need to store 120
kWh. A 200-liter drum of 54oC water stores about (54oC - 24oC) 200
liters = 6 kWh of usable space heating energy, so the closet needs 120
kWh / 6kWh = 20 drums full of water inside. These could be stacked up
vertically in a rectangular array 2 m high x 3 m wide x 1 m deep, with
R3 insulation all round. Let's check the drum water temperature: after a
long string of average days in December, with an average amount of sun,
the steady-state water temperature Tw would be such that
Ein = 2 m x 3 m x 3 kWh/m2 /day = 18 kWh / day, and (5)
Eout = 6 hr (Tw - 20) 6 m2/R0.1 south wall, day
+18 hr (Tw - 0) 6 m2/R3 south wall, night
+24 hr (Tw - 20) 18 m2/R3 other walls
= (360 + 36 + 144) Tw - 7.2k - 2.88k. (6)
So if Ein = Eout then Tw = 28.08 kWh / 540 = 52.0oC. (7)
A)
B)
Fig. 3 - Preliminary experimental data (A); Fin tube water heating with
a solar closet (B)
We have built and tested a small outdoor structure. Figure 3A shows some
results, using a sunspace-to-room motorized damper for daytime
temperature control. The numbers and annotations are readable in the
full-size version of Figure 3A (115 KB).
ENHANCEMENTS
A conventional electric water heater might work well on the floor above,
with a larger solar closet, in a warm water connection loop with about 5
m of fin-tube mounted near the closet ceiling. Natural water convection
flow could provide sufficient hot water for a typical home, using a
standard water heater. The tank might need larger input and drain
fittings to make this work well. Assuming convective water flow is not a
limiting factor, how much air-water heat exchange area is needed inside
a solar closet for water heating? One meter of copper fin-tube baseboard
pipe provides about 600 W to a 20oC room, if the moving water inside is
at 80oC. So each meter of fin-tube passes approximately 600/(80-20) or
10 W/oC water-air temperature difference. How would our water heater
work using fin-tube pipe?
Suppose the closet air temperature is 54oC and the hot water consumption
of the house consists of 5 showers a day, each lasting 10 minutes, at 10
liters/min using 44oC water heated from 14oC. Each shower uses 100
liters of hot water. How much fin-tube would we need to support this
daily average heat transfer rate? If the fin-tube is X meters long, then
RC = 500 liters x 1 Wh/literoC / 10X W/oC = 50/X hr, and (8)
44 = 54 - (54 - 14) exp(-24 hr x X/50), so (9)
X = 2.9 m.
This fin-tube "solar collector" can be small, because it works 24 hours
a day. Figure 3B shows a system for heating water with a fin-tube
air-water heat exchanger near the ceiling and a conventional insulated
water heater on the floor above. If hot water circulates through the
heater tank from the closet, the heating element should seldom turn on.
Given a room that is 54oC for 24 hours a day, one might well add some
floorspace to make a sauna, perhaps with a small woodstove, or make a
place to dry clothes, with a closet-sunspace damper controlled by a
humidistat and a differential thermostat to let sunspace air into the
solar closet, if it is warmer.
The water in the solar closet might be wastewater in concrete septic
tanks or EPDM-rubber-lined plywood tanks with lids. Sewage treatment
rates double every time the temperature increases 10oC. Metcalf and Eddy
(1991) describe thermophilic anaerobic digestion as occurring at
temperatures of 49oC to 57oC, where thermophilic bacteria work much
faster than mesophilic bacteria. U.S. Patent No. 3,933,628 describes an
anaerobic digester for a 100,000 cow feedlot, using EPDM-rubber-lined
trenches to produce 200k m3 of methane per day. The inventor suggests a
temperature range of 32oC to 46oC, but to avoid temperature shock, the
process should have a daily temperature variation of at most +/- 1oC. A
3m cube of water cooling 1oC loses ~30kWh, comparable with the daily
house heating load of our example.
REFERENCES
ASHRAE (1993) In: 1993 ASHRAE Handbook of Fundamentals, I-P Edition
(Robert A. Parsons, ed.) p. 22.1. Approximate relationship: U = 1.5 +
v/5, for smooth surfaces, and U = 2 + v/2 for rougher surfaces, e.g.
stucco, where U is in Btu/hrft2oF and v is in miles per hour.
Baer, Steve (1979) In: Sunspots, pp. 62-66. Cloudburst Press, Seattle.
Marion, William & Stephen Wilcox (1994) Solar Radiation Data Manual for
Flat-Plate and Concentrating Collectors. National Renewable Energy
Laboratory, Golden, Colorado.
Metcalf & Eddy, Inc. (1991) In: Wastewater Engineering (George
Tchobanoglous, et al., ed.) p. 834. McGraw-Hill Publishing Company, Sydney.
Voltaire (1764) In: Dictionnaire Philosophique, "Le mieux est l'ennemi
du bien" (art dramatique.)
ACKNOWLEDGEMENTS
The authors wish to thank Steve Baer, Lynn Baumeister, Debbie Malone,
Howard Reichmuth, P.E., Norman Saunders, P.E., Carol Warrington, and
Malcolm Wells for their encouragement. William Beckman, Ph.D., William
Rosenthal, Ph.D., and William Shurcliff, Ph.D., have also been helpful.
[permaculture] Solar thermal expert Nick Pine & his "solar closet" design for space heating, also Trombe wall, a must read,
Lawrence F. London, Jr., 12/17/2011