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

*> I've managed to convince gnuplot to plot the data I posted, and*

*> managed to do (most of) a plot window capture using xvpick. The*

*> result is at*

*> http://www.iedu.com/DeSoto/Stirling/fm_plot.gif *

*> Note that the (vertical) pressure scale runs from 80 - 160 kPa*

*> and the (horizontal) volume scale runs from ~ 7.5 - 11 L.*

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

daestrom

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

daestrom wrote:

*> *

*> > I've managed to convince gnuplot to plot the data I posted, and*

*> > managed to do (most of) a plot window capture using xvpick. The*

*> > result is at*

*> >*

*> > http://www.iedu.com/DeSoto/Stirling/fm_plot.gif *

*> >*

*> > Note that the (vertical) pressure scale runs from 80 - 160 kPa*

*> > and the (horizontal) volume scale runs from ~ 7.5 - 11 L.*

*> >*

*> *

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

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

calculation methods?

--

Morris Dovey

DeSoto Solar

DeSoto, Iowa USA

http://www.iedu.com/DeSoto/

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

*> daestrom wrote:*

*>>*

*>> > I've managed to convince gnuplot to plot the data I posted, and*

*>> > managed to do (most of) a plot window capture using xvpick. The*

*>> > result is at*

*>> >*

*>> > http://www.iedu.com/DeSoto/Stirling/fm_plot.gif *

*>> >*

*>> > Note that the (vertical) pressure scale runs from 80 - 160 kPa*

*>> > and the (horizontal) volume scale runs from ~ 7.5 - 11 L.*

*>> >*

*>>*

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

*> Ok (why not?) Do you know of any good links to entropy*

*> calculation methods?*

(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)

-or-

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.

daestrom

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

daestrom wrote:

*> *

*> > daestrom wrote:*

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

*> >*

*> > Ok (why not?) Do you know of any good links to entropy*

*> > calculation methods?*

*> *

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

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.

*> 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)*

*> *

*> -or-*

*> *

*> 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.*

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

http://www.iedu.com/DeSoto/

Posted by *allilinin* on April 15, 2008, 10:30 am

*> This is an attempt by the blind to lead the blind. Without any*

*> good educational qualifications, I'm trying to post a*

*> how-it-works web page to explain to other people (also lacking*

*> currency in thermodynamics) exactly why/how the fluidyne engine*

*> I've been working on is able to operate.*

try

http://tech.groups.yahoo.com/group/SolarHeat/

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 !

Martin

alchemyarch.net

*> I'd be grateful if anyone who is up to snuff would take a few*

*> minutes to look over what I put together and point out errors and*

*> suggest improvements. I'd be especially grateful for that input*

*> from anyone who teaches (or has tought) this stuff to newbies, as*

*> well as suggestions that'd help remove the element of "magic"*

*> from the picture.*

*> The web page is at*

*> http://www.iedu.com/DeSoto/Stirling/StirlingCycle.html *

*> ...and my e-mail address is valid. Thanks!*

*> --*

*> Morris Dovey*

*> DeSoto Solar*

*> DeSoto, Iowa USAhttp://www.iedu.com/DeSoto/ *

> I've managed to convince gnuplot to plot the data I posted, and> managed to do (most of) a plot window capture using xvpick. The> result is at> http://www.iedu.com/DeSoto/Stirling/fm_plot.gif> Note that the (vertical) pressure scale runs from 80 - 160 kPa> and the (horizontal) volume scale runs from ~ 7.5 - 11 L.