# Air Collector - Black Heat Paint vs Selective Paint? - Page 5

Posted by Iain McClatchie on January 17, 2006, 7:14 am

Morris,

Very dark surfaces, like charcoal, have convolutions so that for light
to escape from the surface it must reflect off several surfaces.  So
if each individual surface has an absorptivity of, say, 90%, you get
an overall absorptivity of 1 - (1-90%)^n, where n is 5-10.  Accoustic
absorbing surfaces work this way as well.

Your curved vanes are accomplishing some of this convolution on
a macroscopic scale, with better permeability to air, which is good.
The overall effect is to increase the absorptivity coefficient.  There
is no change to the emissivity coefficient, nor any change to either
the absorptivity or emissivity aperture.

Why no change to emissivity aperture or coefficient? Emission
is, so far as I understand, omnidirectional.  You have more area,
but much of your emissions will be absorbed by the other vanes,
so there is no net gain of aperture.

Now this could be a very interesting benefit.  Look at the table
(which I'm sure you know about) at http://www.redrok.com/concept.htm

The best selective surface there, plated nickel oxide, has
absorptivity = 0.92
emissivity = 0.08
ratio = 11.0

Now note that there are surfaces with better emissivity than that.
Convolutions change one number but not the other, which gives the
possibility of changing the ratio, and thus the stagnation temperature,
and best of all... *doing it with a cheaper material than nickel
oxide*.

Specifically, polished aluminum is
absorptivity = 0.09
emissivity = 0.03
native ratio = 3.0
absorptivity, 10 reflections = 0.61
convoluted ratio = 20.3
Aluminum foil is
absorptivity = 0.15
emissivity = 0.05
absorptivity, 10 reflections = 0.80
convoluted ratio = 5.35
Aluminum sheet is
absorptivity = 0.80  (seems really high, suppose 0.3 instead)
emissivity = 0.12
absorptivity, 10 reflections = 0.97
convoluted ratio = 8.08
Chromium
absorptivity = 0.30?
emissivity = 0.10?
absorptivity, 10 reflections = 0.97
convoluted ratio = 9.7

I'm sure you have the idea by now.  You're looking for something
cheap, bright, tough, and moderately selective, say, emissivity
< 0.12, and absorptivity > 0.2.

One difficulty is that you must ensure actual reflection on the
way in, not merely scattering (off dirt).  That means your surfaces
have to stay clean, which is difficult.  Perhaps that means a
cover glass.

Another difficulty is that the convolutions require more material.

Posted by Morris Dovey on January 17, 2006, 3:42 pm

Iain McClatchie (in

Iain...

Thank you! Your response was/is *most* helpful.

| Very dark surfaces, like charcoal, have convolutions so that for
| light to escape from the surface it must reflect off several
| surfaces.  So if each individual surface has an absorptivity of,
| say, 90%, you get an overall absorptivity of 1 - (1-90%)^n, where n
| is 5-10.  Accoustic absorbing surfaces work this way as well.
|
| Your curved vanes are accomplishing some of this convolution on
| a macroscopic scale, with better permeability to air, which is good.
| The overall effect is to increase the absorptivity coefficient.
| There is no change to the emissivity coefficient, nor any change to
| either the absorptivity or emissivity aperture.

Yuppers - this is the observed behavior. I had a choice of bright
metal or powder-coated in my choice of colors. I opted for the
thinnest (opaque) black the factory could produce with the intention
of spraying the absorber vanes flat black (my first real goof in the
design since all of the coatings I could add actually /degraded/ the
absorber performance).

| Why no change to emissivity aperture or coefficient? Emission
| is, so far as I understand, omnidirectional.  You have more area,
| but much of your emissions will be absorbed by the other vanes,
| so there is no net gain of aperture.

Exactly so - this was my original "aha!". However, it would appear
that the emissivity aperture can be improved (reduced) by spacing the
vanes closer together. There're a couple of downsides to this: it
raises the panel costs and it'll impede airflow within the panel. At
the moment I'm inclined to say: "It'll cost what it costs," but it's
still bothersome. The airflow trade-off is a PIA and will need to be
determined experimentally: I'll build a pair of collectors and do the
analog of a binary search by altering the vane spacing of the least
efficient panel each trial until I can't observe improvement in
performance...

| Now this could be a very interesting benefit.

It has been - and is. :-)

[useful info quoted from http://www.redrok.com/concept.htm  snipped]

| I'm sure you have the idea by now.  You're looking for something
| cheap, bright, tough, and moderately selective, say, emissivity
| < 0.12, and absorptivity > 0.2.

I think I don't want 'bright' and I'm not sure I want 'selective'; but
I definitely want to minimize _losses_ resulting from emissivity and
maximize the other characteristics.

| One difficulty is that you must ensure actual reflection on the
| way in, not merely scattering (off dirt).  That means your surfaces
| have to stay clean, which is difficult.  Perhaps that means a
| cover glass.

To my amazement, dirt hasn't been a significant degrading influence.
The 6'x12' panel in my shop has sucked up a _lot_ of powder-fine
sawdust (although it isn't very visible to anyone outside) without
significant performance drop-off. I suspect that effective aperture
plays a much bigger role in this design than I'd imagined...

| Another difficulty is that the convolutions require more material.

I'm not sure about that. I don't think I want to attempt those
convolutions in the extrusion process because of die wear
considerations; but it may be possible to improve the surface with a
rolling process that'd net out with the same amount of material.

Iain, thank you again. You've been more help than you could even begin
to guess.

--
Morris Dovey
DeSoto Solar
DeSoto, Iowa USA
http://www.iedu.com/DeSoto

Posted by Iain McClatchie on January 17, 2006, 6:54 pm
Morris> However, it would appear that the emissivity aperture can
Morris> be improved (reduced) by spacing the vanes closer
Morris> together.

Can you elaborate on this?  Is the emission from a surface a bit
anisotropic?

I see a possible way to reduce emissivity slightly, detailed below,
but it has nothing to do with aperture.

Morris> I think I don't want 'bright' and I'm not sure I want
Morris> 'selective'

If you want to get high utilization of the solar energy crossing your
aperture, you'll need absorptivity > 0.2.

If you want to get high stagnation temperatures, you'll need a ratio
better than 3-5.  I haven't done any math on this, but if you want to
match the stagnation temperature of black chrome, you'll need an
emissivity < 0.10, since after reflections the best your absorptivity
could be is 1.0.

Since 0.2 > 0.1, you're looking for a surface that is at least
moderately selective.  However, you don't need super-high
selectivity.  It seems like the selectivity of aluminum or chrome
will do fine, and both are known to weather well and are widely
available.

Anything that's not a high cost highly selective surface, with an
emissivity < 0.10, is going to have an absorptivity < 0.30.  It's
also got to be highly reflective to make the multiple-bounce
trick work.  Any such surface will appear bright.  So, I stand by
my point: you're looking for something bright, not black.

Morris> I suspect that effective aperture plays a much bigger role
Morris> in this design than I'd imagined...

What's "effective aperture"?

I suspect your absorptivity/emissivity ratio is not dramatically
better than 3 yet, and you are not yet relying on multiple reflections.
My guess is that when you get multiple reflections actually working
in your favor, you will see a noticeable boost in performance.  Maybe
you don't need that boost if you're happy with what you see now.

Morris> it may be possible to improve the surface with a rolling
Morris> process that'd net out with the same amount of material.

You aren't going to get more than 2-3 reflections (average) with an
extruded surface, and there is no way you'll get the material
thickness down.  Rolled aluminum sheet, or chrome-plated steel
sheet, would appear to be your best bet.

I know you don't yet buy the idea of using a bright shiny surface to
capture sunlight.  Give it a try, please, and tell me if I'm wrong.

Oh, one other thing:  how to get 10 reflections.  It's a lot.
- Imagine a "V" pointed at the sun.  Imagine a ray of sunshine
coming straight in.  It's first reflection (most obviously), and
every reflection after (less obviously), will be turned by the
interior angle of the V.  If you want 10 reflections before that
ray goes out, you'll need an interior angle of 18 degrees.  That's
a depth 3.2 times the aperture opening.
- But you want to get 10 reflections even when the sun does not
come straight in.  Let's say it comes in (and subsequently
leaves) at a 45 degree angle.  Then you need 10 reflections to
turn it 90 degrees and an interior angle of 9 degrees.  That's a
depth 6.4 times the aperture opening.
- I guess, but haven't worked through the geometry, that your
curved vanes are nearly the same as the straight-sided V
above.  In particular, the vane length will have to be the same.
So if you have a vane every inch, then you'll need a six-inch
wide sheet of metal, curved through nearly 90 degrees.  The
resulting structure is 3.8 inches deep.

If the curved vanes are attached in any way where they lap over
one another, they'll be quite strong.  If they are soldered onto a
copper tube where they lap, you'll have an interesting liquid-
cooled absorber.

Final note: I think you can get your emissivity down further.
If you draw a V with a bunch of reflected light rays, you'll
notice that most of the reflections happen deep in the V.  So
that's where most of the absorption happens.  But most of the
emission happens at the outer part of the V.

If there is a temperature difference between these two surfaces
of the V, you will alter the absorption/emission ratio.  Since
emission goes as the 4th power of temperature, a difference of
even 30 F (say, 170 F vs 200 F) would change your relative point
emission by 20%.  You might see an overall 10% difference then,
which would lower an emissivity coefficient of 0.1 to 0.09.  This is
a small effect compared to the V thing, but it's still something.

If you draw air from outside in, you'll get some sort of
temperature delta.  It will be larger in a less conductive material
like chromed steel, and less in aluminum.

If you solder a copper tube to the back side of the vanes and
absorb the heat with water, you'll get a reverse temperature
gradient, and see more emission than you'd like.  I don't see a
way around this yet.  Perhaps having the tubing run
perpendicular to the vanes, as in a heat pipe CPU heatsink,
and midway through the vanes might help.  But this gets into
fin-tube construction, which is already expensive without adding
curves.

Posted by Iain McClatchie on January 17, 2006, 10:43 pm
#^%\$@%!! calculator.  Let's try that again.  I should have
known those depth numbers were way too good.

Assume V width is 2 inches.

Assume straight in, 10 reflections to turn 180 degrees, internal
angle 18 degrees, then depth = 6.3 inches.

Assume 45 degrees in and out, 10 reflections to turn 90 degrees,
internal angle 9 degrees, then depth = 12.7 inches.

That's more like it.

Now since the noon sun swings through 47 vertical degrees,
(half of that in the colder six months of the year) and the
United States is just 31 N - 47 N (another 16 degrees), and in
the three hours on either side of noon the sun swings up/down
perhaps another 20 degrees, you really only need to have a
"sweet spot" for this collector that's 50 degrees wide.

Furthermore, if your material actually has an absorbtivity of
30%, 8 reflections will do.  8 reflections turning 130 degrees
is an internal angle of 16 degrees, depth = 7.1 inches, which
is not so costly.

Finally, even if the panel is always mounted vertically, you can
bias the entry angle of the vanes to point up from the horizon
a bit.

I think I'm done now.

Posted by Morris Dovey on January 17, 2006, 10:56 pm
Iain McClatchie (in

| Morris> However, it would appear that the emissivity aperture can
| Morris> be improved (reduced) by spacing the vanes closer
| Morris> together.
|
| Can you elaborate on this?  Is the emission from a surface a bit
| anisotropic?
|
| I see a possible way to reduce emissivity slightly, detailed below,
| but it has nothing to do with aperture.

I'll try - keep in mind that I'm not a physics cat and that it's been
four decades since I took my last thermodynamics course. Consider me
"vocabulary impaired".

I'd like to inexpensively capture all energy that makes it past the
glazing. My objective is not to make the box (or any part of it) hot -
but rather to transfer as much of that energy to the air in the box as
quickly and efficiently as I can; and to facilitate the natural
convective flow of air through the box.

The aluminum vanes that constitute the absorber are fairly thin (only
a few thousandths of an inch thick) and seem to warm and cool quite
quickly as the incident energy varies in intensity. My gross
interpretation of this is that they're functioning well as both
absorbers and exchangers. That interpretation is reinforced by
observing that even in the brightest sun, the individual vanes are
nearly impossible to discern from the front of the panel. For the
photo on my web page, it was necessary to set the absorber in an
unpainted, unglazed panel and aim the camera up through the vanes to
see anything other than just a black area in the photo.

This has led me to consider the entire absorber area as an "input
aperture"; which eventually led to consideration of an "output
aperture" - and to consider the quality of both of these and how their
qualities might be optimized. Obviously, I'd like to maximize the
ability of the input aperture to accept energy - and minimize the
ability of the output aperture to provide a return path.

I think that spacing the vanes more closely will not have a
significant effect on the quality of the input aperture. I could be
wrong but don't think so.

I think that spacing the vanes more closely may "close the window" at
least somewhat on the return path - not so much for the reflected
energy which already seems adequately trapped - as for the re-radiated
energy. I could be wrong here, too, but in this case I'm not quite so
sure. Thus the urge to conduct the experiment.

|
| Morris> I think I don't want 'bright' and I'm not sure I want
| Morris> 'selective'
|
| If you want to get high utilization of the solar energy crossing
| your aperture, you'll need absorptivity > 0.2.

Ok. I'll buy that. What I'm attempting to do is catch what's pitched
at me, and to catch what I miss on the first (second, third, ...)
bounce. My hope is to have an effective absorbtivity that is the sum
of all of the "catches" and minimizes re-radiation back to the
outside.

| If you want to get high stagnation temperatures, you'll need a ratio
| better than 3-5.  I haven't done any math on this, but if you want
| to match the stagnation temperature of black chrome, you'll need an
| emissivity < 0.10, since after reflections the best your
| absorptivity could be is 1.0.
|
| Since 0.2 > 0.1, you're looking for a surface that is at least
| moderately selective.  However, you don't need super-high
| selectivity.  It seems like the selectivity of aluminum or chrome
| will do fine, and both are known to weather well and are widely
| available.

I have a problem here. I don't understand what you mean by
"stagnation" and "selectivity" - and my dictionary doesn't provide
definitions that make sense to me in the current context. I know that
I don't want to block the removal of heat from the panel and I know
that I don't want to exclude any of the incident energy from the
capture process. Would you please clarify?

| Anything that's not a high cost highly selective surface, with an
| emissivity < 0.10, is going to have an absorptivity < 0.30.  It's
| also got to be highly reflective to make the multiple-bounce
| trick work.  Any such surface will appear bright.  So, I stand by
| my point: you're looking for something bright, not black.

Aha! This I understand. But I don't really /want/ this stuff to
reflect. I want it to stick (be absorbed) without bouncing.
Unfortunately, in the real world some of it is going to bounce, no
matter what my preferences. What I decided was that I could live with
the reflectivity so long as there was a really poor quality exit path
(to the outside world).

| Morris> I suspect that effective aperture plays a much bigger role
| Morris> in this design than I'd imagined...
|
| What's "effective aperture"?

Good question. I wish I had a nice, crisp answer. In sloppy terms I
think that if emissivity is omnidirectional, then it will be reduced
with a closer vane spacing which may cause energy that might have been
unproductively radiated to be absorbed by a neighboring vane.

| I suspect your absorptivity/emissivity ratio is not dramatically
| better than 3 yet, and you are not yet relying on multiple
| reflections. My guess is that when you get multiple reflections
| actually working
| in your favor, you will see a noticeable boost in performance.
| Maybe you don't need that boost if you're happy with what you see
| now.

Somehow I suspect that I'll always be looking for "just a little
more," no matter how well it performs. :-)

| Morris> it may be possible to improve the surface with a rolling
| Morris> process that'd net out with the same amount of material.
|
| You aren't going to get more than 2-3 reflections (average) with an
| extruded surface, and there is no way you'll get the material
| thickness down.  Rolled aluminum sheet, or chrome-plated steel
| sheet, would appear to be your best bet.
|
| I know you don't yet buy the idea of using a bright shiny surface to
| capture sunlight.  Give it a try, please, and tell me if I'm wrong.
|
| Oh, one other thing:  how to get 10 reflections.  It's a lot.
|   - Imagine a "V" pointed at the sun.  Imagine a ray of sunshine
|     coming straight in.  It's first reflection (most obviously), and
|     every reflection after (less obviously), will be turned by the
|     interior angle of the V.  If you want 10 reflections before that
|     ray goes out, you'll need an interior angle of 18 degrees.
|     That's a depth 3.2 times the aperture opening.
|   - But you want to get 10 reflections even when the sun does not
|     come straight in.  Let's say it comes in (and subsequently
|     leaves) at a 45 degree angle.  Then you need 10 reflections to
|     turn it 90 degrees and an interior angle of 9 degrees.  That's a
|     depth 6.4 times the aperture opening.
|   - I guess, but haven't worked through the geometry, that your
|     curved vanes are nearly the same as the straight-sided V
|     above.  In particular, the vane length will have to be the same.
|     So if you have a vane every inch, then you'll need a six-inch
|     wide sheet of metal, curved through nearly 90 degrees.  The
|     resulting structure is 3.8 inches deep.
|
| If the curved vanes are attached in any way where they lap over
| one another, they'll be quite strong.  If they are soldered onto a
| copper tube where they lap, you'll have an interesting liquid-
| cooled absorber.

Indeed, but we're talking about serious cost increase here. Ultimately
the product must be inexpensive enough for ordinary people to purchase
as a practical means of buying down current heating costs without
having to mortgage the farm.

| Final note: I think you can get your emissivity down further.
| If you draw a V with a bunch of reflected light rays, you'll
| notice that most of the reflections happen deep in the V.  So
| that's where most of the absorption happens.  But most of the
| emission happens at the outer part of the V.

This is the effect I'm after, even though I'm not using the V
geometry.

| If there is a temperature difference between these two surfaces
| of the V, you will alter the absorption/emission ratio.  Since
| emission goes as the 4th power of temperature, a difference of
| even 30 F (say, 170 F vs 200 F) would change your relative point
| emission by 20%.  You might see an overall 10% difference then,
| which would lower an emissivity coefficient of 0.1 to 0.09.  This is
| a small effect compared to the V thing, but it's still something.

From where I am now, I don't think anything affordable is going to
produce an overall 10% difference. FWIW, it took a year to get the
maximum operating temperature down from 180F to 165F.

| If you draw air from outside in, you'll get some sort of
| temperature delta.  It will be larger in a less conductive material
| like chromed steel, and less in aluminum.
|
| If you solder a copper tube to the back side of the vanes and
| absorb the heat with water, you'll get a reverse temperature
| gradient, and see more emission than you'd like.  I don't see a
| way around this yet.  Perhaps having the tubing run
| perpendicular to the vanes, as in a heat pipe CPU heatsink,
| and midway through the vanes might help.  But this gets into
| fin-tube construction, which is already expensive without adding
| curves.

I did a bit of experimenting in this direction - and yes, the fin tube
isn't cheap.

Iain, thank you agin. You've give me much to think about and provided
some much-needed "handles" to hang onto.

--
Morris Dovey
DeSoto Solar
DeSoto, Iowa USA
http://www.iedu.com/DeSoto/solar.html

•
• Subject
• Author
• Date
 Re: Air Collector - Black Heat Paint vs Selective ... Iain McClatchie 01-17-2006
 Re: Air Collector - Black Heat Paint vs Selective ... Iain McClatchie 01-17-2006
 Re: Air Collector [long] Morris Dovey 01-17-2006
 Re: Air Collector [long] Iain McClatchie 01-18-2006
 Re: Air Collector [long] Morris Dovey 01-18-2006
 Re: Air Collector [long] Iain McClatchie 01-18-2006
 Re: Air Collector [long] Morris Dovey 01-19-2006