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re: thermal mass for large thermosyphon solar air heater
19 nov 2003
david delaney   wrote:

>>>i propose a heat store having two constituent heat-storing masses...
>>
>>your web site diagram
>>
http://geocities.com/davidmdelaney/thermal-mass/two-part-heat-store.html
>>
>>seems to have blocks and drums on the same level, which surprises me,
>>since you seem to like stratification. why not put the drums on top...
 
>...i was preoccupied with how the building inspector would view this wierd
>structure of concrete blocks, and hoped to get him to think of it as a
>"storage pile" rather than a non-code "wall" or "structure"...

it's still interesting to wonder which arrangement would store more heat.

>i was also preoccupied with minimization of entropy creation
>and preservation of stratification during energy transfers
>inside the heat store after dusk. there is less entropy
>creation with the stacks side by side.

i woulda said "more," altho thinking about entropy makes my brain hurt. you
predicted your original vertical stack would be hotter near the top, and
that seemed good to me, with rarely-used hotter cloudy-day heat stored near
the top and frequently-used cooler average-day heat stored near the bottom. 

i've often thought "drums on top of blocks" would allow the blocks to absorb
lots of heat from warm air on an average day, with a short time constant,
and allow that heat to transfer to the drums overnight, with a longer time
constant. it seemed to me this would work better with drums on top, since
warm air rises. it wouldn't work well with blocks on top. it might work well
with drums and blocks at the same level, but that would make the drums cooler,
so they wouldn't store as much cloudy day heat.

>cool air enters low in the concrete stack, is heated and
>rises through the concrete stack...

..."is heated"? i thought the heating took place in the absorber below...

>putting the drums higher would improve energy
>collection efficiency in two ways. 1) it would
>place more drum surface in the hotter part of the
>heat store during the day, exposing it to greater
>temperatures. 2) one of the scarce resources here
>is temperature swing in the concrete.

thinking of temperature swing as a scarce resource makes my brain hurt.

>we want the concrete temperature to cycle during an average
>day so as to maximize energy absorption. putting the drum higher
>would mean greater night time cooling of the concrete (and compression
>of its temperature gradient) in preparation for efficient
>energy collection on the following day.

sounds good. compression of its temperature gradient makes my brain hurt.
 
>although putting the drums higher would disimprove
>stratification and increase night time entropy
>creation in the heat store...

aarrrgh!

>it might well be worth while for improved energy collection.
>at dusk the concrete will be hotter than the drums even if the
>drums are higher than the concrete, because of the much more
>rapid absorption of heat by the concrete.  after dusk, while
>the concrete is hotter than the drums above it, and again due to
>the much more efficient exchange of energy between concrete and air
>as compared to drum and air, the temperature gradient from the top
>of the concrete to the top of the store will be fairly flat...

i'm not quite able to convince myself that the water at the top of the drum
would be about the same temp as the water at the bottom. seems to me there
could be lots of stratification in a long-term steady-state scenario. water
isn't a great insulator, about r2.75 per foot for downward heatflow at 104 f,
according to the 1998 schaum's outline on heat transfer, and 55 gallon drum
walls won't add much conductance, but warm water floats. even if it didn't,
page 352 and 9 of that book say water's thermal diffusivity alpha = 0.00554
ft^2/h, so if we make the top surface of a 70 f water tank 130 f, the water
temp x feet below the surface will rise to 100 f in 180x^2 hours, when erf()
= 0.5. water doesn't relax well. how long would it take to make tea, if we
heat 8 oz of water from 60 to to 200 f average in a 3" diameter pot by aiming
a blowtorch at the top surface, with no mixing or warm-water buoyancy or
active interference from the pot owner?

>the greatest air-drum temperature difference at
>the bottom of the drum. this will speed up
>transfer of energy from the concrete to drum, and
>result in cooler concrete in the morning, but will
>increase night-time entropy creation in the heat
>store compared to side-by-side stacks. 

i wonder what that means or why it matters.

>the concrete temporarily holds the highest temperature heat.
>we would like the drums to be at the end of the line of receivers
>of that heat, after the heat requirements of dhw and the house
>have been met.

i would think we'd like the drums to "be at the beginning
of the line of receivers," so they could store cloudy-day heat
at a higher temperature, and the lower temp leftover warm air
could heat the house on an average day.

>putting the drums above the concrete may produce only
>a small degradation of this goal however...

i'm not clear on this goal or why it's important.

>...since both dhw and house heat would be taken from high
>in the heat store and the resistance of the drums is so
>comparatively high.

nor why that matters...

>>or make a 4'x12'x8' tall "shelfbox" with 12 4'x8'x2" deep shelves on
>>4" centers in the lower 4' and 6 4'x8'x6" deep shelves on 8' centers in
>>the upper 4'. this would store 15,360 btu/f with 3,456 ft^2 of surface
>>and 38 ft^2 of "long side permeability," 
>
>i make it 12*32/6 + 6*32/2 = 64 + 96 = 160 ft^3.
>160 * 62.4 = 9984 btu/f,

oops. shoulda wrote 12 4'x12'x2" deep shelves, and so on.

...240x64 = 15,360.

>and 2*12*4*8 + 2*6*4*8 = 1152 ft^2 + edges.

and 2x4x12(12+6) = 1728 ft^2. oops.

>but i take your point. a pair of these might be used instead
>of a pair of concrete and drum stacks with twice the btu/f and
>about the same surface area and 2/3 the mass.

i was comparing this 4'x12'x8' tall stack
with one of your 5.2'x11.3'x7.6' stacks.

>but the internal interlayer duct area is a lot smaller (0 vs 13 ft^2).

what's an internal interlayer duct area and why does it matter?

>>...you'd need 216 ft of 30" round poly film duct (or vinyl or epdm,
>>at a higher cost) and 4' welded-wire fence at a cost of about $200. 
>
>i won't be swinging a hammer on this job. i have
>to think in terms of preparing and documenting a
>detailed design for fabrication by someone else,
>with all that that entails. i have to include the
>time to design shelves and containers (or purchase
>them) and document the assembly while also
>designing the rest of the house. i have to include
>time and materials to build the shelves and
>assemble and fill the containers. i gain greatly
>from a reduction of detail in the design.

your documentation labor could have lots of leverage, if we
build more than one of these or want to do further research. 

>i also have to think about simplicity and transparency of
>maintenance in the case that i am not around down the road.

ah yes. death. a discomforting certainty.

>that being said, i'm still interested. how do you seal the ends
>of the duct to make containers?

i'd raise the ends and attach them to something above the shelf water level.
israeli greenhouses have long 250 mm poly film water ducts on the ground
between rows of plants, with the ends raised ("max 0.5 m") and attached to
stakes. figure 4-49 on page 212 of joe hanan's greenhouses book (crc, 1998,
$120) shows this. i have an extra copy of that book, if anyone would like
to buy it cheaper.

>i would definitely feel uncomfortable about  6 mil poly, by the way.

well, you are ultra-conservative, reliability-wise. this poly film duct
lasts for a year or two when attached to a fan for air distribution inside
a greenhouse, with lots of uv and temp changes and vibration. it seems to me
it should last a long time on a shelf, on top of another layer of plastic 
film to smooth out wire fence bumps and guard against leaks. i'd try poly
film first, and replace it with something more expensive if there were leaks,
eg epdm, or those water-filled blue vinyl sausages used to hold down swimming
pool covers in wintertime.

>...one reason i did not think about shelf boxes, among other reasons, was
>that i had always seen them described with pumps, which are not needed here.

a little pump seems like a good idea, storing more heat, with the shelfbox
on the ground. do you worry about earthquakes? two little pumps could make
a shelfbox ultra-reliable (roughly squaring the mtbf), and a shelfbox might
operate fairly well with no pump, in a pinch...

>>1.  tc                        td
>>    |   rc =          rd =    |
>>    |1/(1.5x1961)  1/(1.5x323)|
>>    |----www----/ ----www-----|
>>    |            s            |
>>   --- cc=3411 btu/f         --- cd = 8276 btu/f
>>   ---                       ---     
>>    |                         |
>>    -                         -
>this model assumes the heat store loses heat neither
>wastefully nor usefully. but the withdrawals for dhw,
>space heat, and loss to the environment, are in fact
>substantial...

right. it just seemed like an interesting quick check
on the two mass and area ratios...

>...for a long string of average days, we want the daily
>sum of these losses to equal the daily gain. i suggest
>modeling the dusk-to-dawn heat store, lumping losses and
>useful withdrawals into a single resistance, rs,
>(resistance of the store) like this:
>                                                 
>            rc                   rd   
>        +--www------+-----------www--+
>        |           |                |
>    +   |        +  |             +  |    
>       ---          w                ---     
>   tc  --- cc    ts w  rs        td  --- cd
>        |           w                |      
>    -   |        -  |             -  |   
>       ---         ---              ---
>        -           -                -

interesting. i'd think i'd attach the lower part of rs
to some thevenin equivalent temperature, vs ground...
 
>>>the temperature of the concrete mass will descend below the temperature of
>>>the water mass if the night-time heat withdrawals and losses from the heat
>>>store are large enough. the water drums will become the main source of heat
>>>output only when the temperature of concrete is distinctly less than the
>>>temperature of the water.
>>
>>like, after a few cloudy days. wouldn't you rather have a stratified store
>>then? how do you get the heat out of this overhead store without fans?
>
>i claim it is stratified.

the version with drums on top might store more heat.

>i hope there will be sufficient convection across the ceiling of the house

http://geocities.com/davidmdelaney/flow-organiser/flow-organiser.html

>that either radiation or radiation and a 110w push-down ceiling fan
>outside the heat store in the house will be sufficient.

sounds like a plan. got any numbers? you might use less than 110 w.
why push-down? you might blow indoor air up into the attic through
a hole in the ceiling and let air fall down out of the attic along
the inside of exterior walls.

>>>the primary consideration in sizing the concrete block stack is the
>>>combination of the amount of energy that must be collected in one day and
>>>the temperature range of the air from which the energy must be collected.
>>>the desired one-day energy collection divided by the thermal mass of the
>>>concrete equals the rise in the average temperature of the concrete required
>>>to store that amount of energy. this required temperature rise must be less
>>>than the difference between the average temperature of the air from the air
>>>heater and the temperature of the concrete at the beginning of the day.

i'm still trying to figure out what that means and why it's important.
a few equations might help.

>>it might look like this on an average day, with rcc = 1.2 hours and rcd
>>= 17.1 hours and ta = 100 f for 6 hours per day and 70 f for 6 hours per
>>day, which makes...
>>
>>2.   ----------------------------ta
>>    |                         |  
>>    w                         w  
>>    w  1/(1.5x1961)           w  1/(1.5x323)
>>    w                         w
>>    |  tc                     |  td
>>   --- cc=3411 btu/f         --- cd=8276 btu/f
>>   ---                       ---     
>>    |                         |
>>    -                         -
>>
>>tcl = 70+(tcu-70)e^(-18h/1.2h) = 70 and tcu = 100+(70-100)e^(-6/1.2) = 99.8
>>and tdl = 70+(tdu-70)e^(-18/17.1) = 45.6+0.349tdu = 55.9+0.246tdl = 74.2 and
>>tdu = 81.8. wouldn't you rather have a stratified store, with drums on top?
>>how can we calculate its performance?
>
>i am bothered by the assumption of the radical day-night difference in ta.

i think of that as the temperature of the air inside the heat store, 100 f
for 6 hours on an average day when the sun is heating it, and 70 f for 18 h
when it supplies heat for the house. assuming a square wave simplifies calcs.
knowing the amount of sun on an average day and the outdoor temp and the
air-water heat store conductance and house heating requirement, we might
design the sunspace to produce an average of 100 f air over 6 hours. 

>...i have not yet reacquired the skills to solve more complicated
>rc nets, but i'm working on it.

this one is simpler than the one above. the rcs are independent.

>it still bothers me to hear the drums-on-top configuration
>described as better stratified. the average temp of the concrete
>is lower, and its temperature gradient is less, so its definitely
>cooler than the upper part of the store, and therefore will collect energy
>more efficiently. but i believe that the side-by-side configuration holds
>more exergy for the same amount of energy collected.

my head hurts again.

>the side by side stacks seem more likely to be
>well characterized by their average temperatures
>and simple assumptions about air film resistances.

agreed.

>the drum over concrete configuration
>(long-tc-small-area mass over short-tc-large-area
>mass) involves larger and more variable (over
>space) stack-air temperature differences, and a
>lack of intuitively reasonable assumptions about
>temperature differences. how much entropy is
>created? you could create less entropy when the
>drums are higher than the concrete by positioning
>the drums to one side of the concrete so that the
>air movement through the drums would be down. but
>this is not practical, since we need the
>horizontal space for the concrete and we want to
>use the concrete to support the drums. so we are
>stuck with a fairly chaotic and fairly high rate
>of entropy creation to transfer the heat upward to
>the cooler drums. how high a rate? does it matter?

my head is hurting again.

>it might be acceptable to simply be sure that the
>warmest part of the concrete will be no warmer
>than the coolest part of the drums on the last
>mornings of a long sequence of average days. we
>would assume that most of teh temperature swing
>takes place in the concrete and size it so that
>the swing required for an average day is not too
>great to prevent the collection after a long
>sequence of average days.

i can almost understand that...

keep up the good work.

nick




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