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Effect of altitude on convective airflow

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Posted by Morris Dovey on March 1, 2008, 2:56 am
What is the effect of altitude on convective airflow? Can anyone
suggest methods of calculating boyancy for constant input at
varying altitude?


Morris Dovey
DeSoto Solar
DeSoto, Iowa USA

Posted by daestrom on March 2, 2008, 10:37 pm

Gets a bit tricky.  The first half is to notice that the driving head
between the hot 'riser' and the cold 'return' is easily calculated from the
ideal gas law.  Find the pressure at the base of each leg by   pressure =
height*density and density = <absolute-pressure> / nRT where T is in
absolute.  You'll notice from this that the *difference* between hot and
cold pressure at the base of each leg is....

dP = h *((P/nRThot) - (P/nRTcold))

The second half of this is that viscosity of air changes with density.  I
don't have a simple formula for that, I think you'll have to go with
empiricle data if you can find some.

And the third half of the issue is that since the density is lower at higher
altitudes, the amount of heat a given volume flow rate carries is less.

(and there's a 'forth half' in that lower density air is harder to get heat
into/out of at the top and bottom because it forms a different film on heat
transfer surfaces).

But the first one is the 'first order' effect, the other effects are minor
unless you're talking about a really significant change in pressure (say
from sea level to over a mile altitude).

Bottom line is, it's a nasty business and empircal measurements at a few
different altitudes might give you a real simple curve fit that is 'close


Posted by Morris Dovey on March 2, 2008, 10:28 pm
 daestrom wrote:

Thanks (I think <g>)

This past week a panel that'd performed extremely well at between
200 - 300 feet ASL produced a less spectacular airflow at between
5000 - 5100 feet ASL. In the mile-high neighborhood the airflow
is slower, and the discharge air is hotter.

I appreciate your response. It adds a bit of definition to the
"Well, duh!" response from my hot-air balloon pilot homemate, who
assured me that higher flights required more frequent "burns" to
keep her balloon at altitude.

Morris Dovey
DeSoto Solar
DeSoto, Iowa USA

Posted by Anthony Matonak on March 3, 2008, 12:52 am
 Morris Dovey wrote:

If you're sticking with an entirely passive design then perhaps
you would do well to add fans as an option. This would speed
the airflow and lower the discharge temperature which should
improve overall efficiency.


Posted by Morris Dovey on March 3, 2008, 4:58 am
 Anthony Matonak wrote:

Yes, I've been thinking about the fan option. My mile-high
observer reported that the glazing remained cool and that he
couldn't detect significant heat loss back through the glazing,
so my current thinking is that I need to take measurements to
nail down altitude dependencies.

It may be that the efficiency hit isn't large enough to justify
the costs associated with fans and control system. If so, then it
just becomes an altitude performance dependency - to be
considered when calculating panel area requirements and not
worried over otherwise.

Thank you for your help!

Morris Dovey
DeSoto Solar
DeSoto, Iowa USA

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