Subject: Re: Trombe wall efficiency

From: [email-masked] (Nick Pine)
Date: 20 Jun 1995 14:20:39 -0400

Will Stewart  <[email-masked], not!> wrote:
 
>>Oops. Let me do this again: this solar siding is about 16' high, and it has
>>a continuous 1 1/2" wide airspace at the top and the bottom, so a 1' wide
>>section would have cfm = 16.6 Av sqrt((Tu-Tl)h), where Av = 1.5/12 x 1'
>>and Tu-Tl is about U/cfm, and h = 16', and
>>
>>U = 300 Btu/hr x 16 ft^2 - (68F-32F) x 16 ft^2/R1  =  4200 Btu/hr,
>>    full sun received      loss thru single glazing
>
>why are you using 68F instead of an average?

Because, Will, like I said before, the air that is near the cold glazing is
mostly unwarmed house air, with a temp of 68F. This siding has two vertical
airflow passages, each 1 1/2" wide (Norman Saunders improves on this by having
one passage, divided by a diagonal porous absorber.) The unwarmed house air 
passes vertically up through the Southern passage, from South to North through
the shadecloth, and further up and North through the Northern passage, closer
to the house, and farther from the glazing.

But go ahead and use an average if you like. It doesn't make an enormous
difference. The average temp is 100F, which would make the 4200 above about
3200, and lower the solar collection efficiency from about 85% to 66%. Who
cares? Houses need siding anyhow, and the solar collection efficiency of
vinyl siding is about 0, only slightly worse than a conventional Trombe wall,
and it doesn't do much to keep the sun from heating up the house in the summer,
or provide any natural summertime ventilation, either.

>Is the height 16' or the square footage 16 ft**2(i.e., a 1' wide glazing)?

Yes. As I said, I was talking about a 16' high x 1' wide piece of siding.

>It's been a few years since I had fluid mechanics, so I'm having trouble
>following your CFM estimates. 

I have the benefit of never having taken a course in fluid mechanics :-)
You probably learned how to do this more painstakingly. I did, however,
read Bill Yanda's book, _The Food and Heat Producing Solar Greenhouse_,
which has that nice little solar chimney formula in the back, on page 189,
cfm = 16.6 Av sqrt((Tu-Tl)h), which roughly agrees with the formula in
the 1993 ASHRAE HOF book, cfm = 407 Av sqrt((Tu-Tl)/(459+T)h), where T
is the average temp, as I recall. The two formulas agree when T is 142F.

The only other thing you need to "know" :-) is that 1 Btu heats about 55 ft^3
of air 1 degree F, which for large values of 55, means that Tu-Tl = U/cfm.
Substitute all this in the above equation, do a little algebraical cranking,
and voila, cfm=k^(2/3), or as you might say, cfm=xk**(0.6666666666666667) :-)

>Don't forget they have to overcome the plastic damper, no matter how light.

They, the teeny air molecules? If this bugs you a lot, perhaps you could
use a small fan, or a more diaphanous damper, or a manual damper or a Grainger
motorized damper controlled by a thermostat, or some Zomeworks Skylids (tm). 

>What is the heat loss from the damper area?

Not much, comparatively speaking.

>What are the kinetic energy losses around the damper?

I don't know. I suppose you could write a thesis about that. Or look it up in
the ASHRAE HOF, or go build one... Or better, a hundred. Do you want to help,
or stand around displaying your erudition and throwing darts at this idea?
As I said before, some solar engineers recognize that it's often better to 
build something and measure it, than to calculate forever and ever.

>Are you only considering radiative losses?

Not even. Just R-value losses. Simple arithmetic.

>If not, are you assuming laminar flow on your convection losses at the
>glazing and on your heat gain at the shadecloth?

I assume that a still air film has an R-value of 1. And that the air in
the sunspace is still. (Is it? 66 cfm passing through 3" x 1' is 264 fpm,
which would make an air film R-value of about 1/(1+264/176) = 0.4. But
the plastic glazing is horizontally corrugated, so the air near the plastic 
is probably still (0 velocity, if laminar flow), but the plastic has more
than 1 ft^2 of area/ft^2 of glazing, because of the corrugations, etc.
Where do we stop? With some reasonable assumptions and simple models.)

And that the glazing has an R-value of 1 on the inside surface, 0 in the
middle, and 0 on the outside surface. To a first approximation, the heat that
comes in through the glazing has nowhere to go but into the air, and into the
house. If you want to refine this, see Duffie and Beckman's _Solar Engineering
of Thermal Processes_, 2nd edition, 1991, figure 6.4.4(b), page 261, which
says that the R-value of a single piece of glass varies from about 0.75 to
1.5 for an absorber plate temperature of 0 to 200C. I call that R1. Recall
Voltaire: "The best is the enemy of the good." Recall Keynes, "In the long
run, we are all dead." As I said, passive solar houses are so disastrously
ill-designed now that I don't think it pays to get too picky about the math,
in improving their design. A little arithmetic goes a long way, for now. 

>Won't the shadecloth at the top transfer less heat to the air and more to the
>glazing due to the smaller tempature differential?

Sure. Or maybe it will just run hotter than the shadecloth below. As I said,
to a first approximation, the solar heat that enters the glazing has nowhere
else to go, except into the house. BTW, you mispelled "temperature" :-)

Regards,

Nick

---

From: [email-masked] (Nick Pine)
Date: 21 Jun 1995 18:13:14 -0400

>>>why are you using 68F instead of an average?

Will, if you are still interested in discussing this further in private, vs.
these sort of public pontifications regarding things that I have already
(largely un-)learned, actually doing engineering for the last 25 years,
could you please send me the next iteration by email, [email-masked],
so we don't have to keep wasting bandwidth in this group? Or post your
email address again...

>>Like I said before, the air that is near the cold glazing is mostly
>>unwarmed house air, with a temp of 68F.
 
>Unless you have laminar flow, turbulent flow will result, lowering the
>boundary layer flow effect that gives the R1 value for still air on a
>surface.

Well _you_ could do a calculation with turbulent air, or air at the average
velocity of about 64cfm/(1.5"/12 x 1') = 512 fpm, which gives an R-value of
about 0.3. If you have a hypercube processor or Cray-2, and you want to go
do an aerodynamic study, the glazing has a corrugation pitch of 3" and a
corrugation height of about 0.6", and the corrugation sides are straight
slants with an angle of 45 degrees with respect to the overall surface.
There are 1" 10-32 screws every foot or so, along the horizontal seams, and
vertical 2 x 2 sleepers every 4'. And the shadecloth blocks 80% of the sun,
with what looks like a square grid with 50% open area, with holes that look
to be about 1/32" on a side. To me, this seems like over-refinement, for
various reasons, among them (1) that we are now wasting oil like crazy, and
(2) we are not doing much to save that with solar siding now, and (3)
we all have finite lives to live, especially those who live in Iraq...

>>...use an average if you like. It doesn't make an enormous difference.
>>The average temp is 100F, which would make the 4200 above about 3200,
>>and lower the solar collection efficiency from about 85% to 66%. Who cares?
 
>Engineers care partly because they have to satisfy their clients and
>they prefer to get as close to reality as possible.

Some clients would be very happy if warm air came out of their walls for a
change. In the winter :-) Some engineers wish to avoid the complications of
reality at as high a level as is reasonable, focusing on what really matters,
ignoring what can be ignored, happy with order of magnitude answers, almost,
consistent with building something that works  fairly  well, given constraints
(1), (2) and (3) above. Others are happy to do calculations forever, esp. if
they are being paid by the hour for that, and there is no danger that anything
will ever be built, that might not work :-)

>The disasters of the past have come back to bite us in the backsides,

Disasters? You mean this siding might catch on fire, or collapse?
I was in a Swiss rail disaster once. The train from Luzerne left 14
seconds late. Of course they made up for it, by the next stop.

>so the application of engineering calculations to build models can give
>us errors in the order of magnitudes if applied incorrectly.

Well (yawn) yes. But recall that this is a lot like wall warmers that
have been built since the 1881 patent by Morse... So there are unlikely
to be a lot of surprises. And the ones that pop up, like small water
leaks in driving rains, may be difficult to model mathematically :-)
It might be better to build one of these, rather than talk about it.

>My purpose is not to shoot down your thesis, but to provide a means
>for you to refine it and make it withstand similar questions in the future.

So you are helping me? :-) Fine, perhaps you will rework the numbers
while I go build one. I think this wall may have to withstand rain,
and heat, and cold, and wind, but not questions...

>Just consider this a friendly, egoless design review.

Perhaps there was talk like this in the time of the Spanish Inquisition... 

>Often, these calculations, along with empirical data, are used to
>identify payback periods.  If the capital equipment is very inexpensive
>and produces a fair amount of energy,

Or if you need siding on a house anyway? Yawn. Er, did you say something else?
This is like having a cogenerator in the basement instead of an oil burner.
People say, "Gee, 3 years is a long payback period." But the payback period
for an oil burner is "infinity years." It lasts for 20 years, maybe, and never
makes you a nickel, and then you buy a new one.

>then cost models are not as important.  However, if someone is planning to
>live off the grid, and makes just a few simple errors, then they could be
>out tens of thousands of dollars trying to correct the problem.

I doubt it. I put up my first wall-warmer with screws, so I could take
it apart if I wanted to fix it. I put a few slices in the foam seals,
in case I wanted to open some vents in the summer. So far, no fixes or
venting required. But screws are what you normally use to attach this stuff.
Hex head screws. You can take it all off in an hour or two if you like,
with an electric drill and a nut driver.

>Out of the three heat energy losses (conductive, convective, and
>radiative), why do you only consider conductive?

I don't. R-values are measured, and they include conductive, convective,
and radiative losses. Are you sure you're an expert?

>Since the air is moving, convective needs to be addressed.

Well then, perhaps you'd like to address it.

>And radiation losses must be considered if you are going to try to 
>calculation overall losses as well.

I disagree. At these low temps, R-values work fine. But if you'd like to go
calculate this to prove that to yourself, you might assume that the shadecloth
has an alpha of 1 and an epsilon of 1, for starters. This is all capable of
infinite elaboration... Polycarbonate does a fairly good job of blocking
longwave IR, I think. You can get a curve of transmission vs. wavelength
by calling Replex at (800) 726-5151, or Dynaglas at (408) 997-6100.

>>I assume that a still air film has an R-value of 1. And that the air
>>in the sunspace is still. (Is it? 66 cfm passing through 3" x 1' is
>>264 fpm, which would make an air film R-value of about 1/(1+264/176) =
>>0.4. But the plastic glazing is horizontally corrugated, so the air
>>near the plastic is probably still (0 velocity, if laminar flow), but
>>the plastic has more than 1 ft^2 of area/ft^2 of glazing, because of
>>the corrugations, etc.
>>
>>Where do we stop? With some reasonable assumptions and simple models.
>
>One way to refine your estimates is to build a device as you describe
>and then log the data.  That way, you can provide 'proof' of your assertions.

That would be dandy, if one required 'proof' :-)

This may happen in the fall, at a local college. Sometime after this
particular wall is built. Those measurements might be useful in tweaking
the system's performance, but more likely it will just keep a student and
a physics professor employed for a while, and then they will forget all
about it, perhaps having added a paper to our vast scientific literature,
thus meeting another pressing need of society. 

I also sent a copy of the drawing to Norman Saunders, PE, who seems to
have learned pretty well, over the years, what to ignore and what to
study in all this...

>Don't let my questions deter you, make it happen!

My Kentucky grandmother used to say, "If you can't help, don't hinder."

Feel free to help.

Nick