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Stirling Cycle - Page 2

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Posted by daestrom on April 15, 2008, 10:08 pm

Of course, now we have to work through the T-S diagram too :-(


Posted by Morris Dovey on April 15, 2008, 11:29 pm
daestrom wrote:

Ok (why not?) Do you know of any good links to entropy
calculation methods?

Morris Dovey
DeSoto Solar
DeSoto, Iowa USA

Posted by daestrom on April 16, 2008, 10:49 pm

(somehow, I just knew that would come back to haunt me.... <grin>)

Absolute entropy is a bit nebulous, and in this sort of thing, unnecessary.
It is the *change* in entropy that is important to this sort of stuff.  And
that isn't too bad if you know some other parameters of the gas.

For an ideal gas (close enough for air under these circumstances)...

S2 - S1 = M*cv*ln(T2/T1) + M*R*ln(V2/V1)


S2 - S1 = M*cp*ln(T2/T1) - M*R*ln(P2/P1)

Where cv is the specific heat for constant volume, or cp is the specific
heat for constant pressure.  Either formula works out to the same
mathematically for ideal gasses because of the definitions for cv and cp and
their relationship. (of course, the T2 and T1 must be on an absolute scale).
So you can pick a somewhat arbitrary reference point and call S at that
point 'zero'.  Then work out the difference between that reference point and
your first operating point to find S1.  A lot of tables and such do exactly
this and use STP as the reference point.  Of course, if you happen to go
below zero, just keep track of sign and carry on merrily.

Also keep in mind that the area under the curve in a T-S diagram is the
amount of heat added/rejected.  In the 'ideal' Stirling cycle, the area
under the curve from 4-1 is exactly equal to the area under the curve 2-3,
so they 'cancel' out.  This is the regenerator.

This leaves you with the area under 1-2 as the heat added, the area under
3-4 as the heat rejected.  Obviously the  ideal work out would simply be
(Q1-2) - (Q3-4).  Also, on the P-V diagram, the work out is area under 1-2
minus the area under 3-4.  So if you can integrate the curves, that's a good
check of the work.


Posted by Morris Dovey on April 17, 2008, 12:37 am
 daestrom wrote:

I don't mean for it to actually /haunt/ you, but suggestions are
always welcome. When I realized that development could proceed
much faster if I learned enough to /engineer/ a solution (as
opposed to endless "cut-and-try") I expected that I had a fair
amount of learning effort ahead of me.

Well, it's been nearly a half century since I was a math student
- and my calc/diffEq skills are thoroughly rusted - but I think I
can do close enough numerical approximations on the computer once
I internalize the relationships.

Now I'm going to go sit in the corner for a while and see if I
can get a firm hold on what you've provided...

Thanks again!

Morris Dovey
DeSoto Solar
DeSoto, Iowa USA

Posted by allilinin on April 15, 2008, 10:30 am
very active group - have been watching it for a while
solar air heat exchangers are new to most of the people in this
group ;
regardless , some are very experienced in fluid mechanics and
thermodynamics .

good luck !

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