alt.energy.renewable

daestrom wrote:
>
> "Morris Dovey" wrote in message
> news:4801B9BE.FDAC2F4E@iedu.com...
> > daestrom wrote:
> >
> >
> >
> > I'm still struggling with this thing, and have been trying to get
> > a hold on one corner of a software model. I've roughed some code
> > together that produces some numbers (which I'm sure don't reflect
> > the real world) but might be a start. At this stage I'd
> > appreciate a sanity check from anyone who knows more about this
> > stuff than I (which is probably just about everyone).
> >
> > I used a hot side temperature of 200F (this comes from an actual
> > measurement), a cold side temperature of 70F (a number out of the
> > air), and volume numbers derived from tubing size (4"ID) and
> > target stroke (18").
> >
> > My initial conditions:
> >
> > p1 = 101.325; /* Initial pressure kPa */
> > t1 = tmax; /* Initial air temperature K */
> > v1 = (vmin+vmax)/2; /* Initial air volume */
> > nR = p1 * v1 / t1; /* Gas Constant factors */
> >
>
> If this is supposed to be point 1 on the diagrams, then v1 should be vmin,
> not the average.

Just for grins, I added the code to see what things would look
like if I assumed constant volume with heating from startup to
point 1.

This is really point 0 (and at startup point v1 is really v0)
with the system at rest at the instant the full heat is turned
on. Interesting to me was that it took a full cycle to stabilize.

> If you want to figure out what nR is, then yes I'd use (vmin+vmax)/2 and the
> temperature of things before you start up (probably 70 F ??).

Yuppers. I'd never done any PVT calculations before and wasn't
sure that kPa, K, and cc were the units that were compatible with
values I'd found for R - and I figured that by taking this route
I could avoid having to count atoms to determine n. ;-)

It's a relief to know that I can get away with this approach.
:-)

> > Then I calculated the trip 1->2:
> >
> > v2 = vmax; /* Calculate expanded air volume */
> > t2 = t1; /* Constant temperature */
> > p2 = nR * t2 / v2; /* Ideal Gas Law */
> >
>
> Perfect...

Another sigh of relief. I figured that this /should/ follow from
PV = nRT, but I wasn't sure. There are times when there's just no
substitute for having a mentor.

> > Then 2->3:
> >
> > v3 = v2; /* Constant volume */
> > t3 = tmin; /* Minimum temperature */
> > p3 = nR * t3 / v3; /* Ideal Gas Law */
> >
>
> Also correct...
>
> > And 3->4:
> >
> > v4 = vmin; /* Min vol at high water level */
> > t4 = t3; /* Constant temperature */
> > p4 = nR * t4 / v4; /* Ideal Gas Law */
> >
> > Finally 4->1:
> >
> > v1 = v4; /* Constant volume */
> > t1 = tmax; /* Peak temperature */
> > p1 = nR * t1 / v1; /* Ideal Gas Law */
> >
> > The calculated results were:
> >
> > P(kPa) T(C) V(cc)
> > ------- ------- -------
> > 1: 139.322 93.33 4942.22
> > 2: 79.613 93.33 8648.89
> > 3: 63.923 21.11 8648.89
> > 4: 111.866 21.11 4942.22
> >
>
> Using a gas constant of 0.287 kJ/kg-K for air, and some unit conversions,
> these work out to about 0.00655 kilograms (6.5 grams) of air in the system.
> As they all are pretty close to the same value, as they should.
>
> But if the volume of the system when shutdown is (vmin+vmax)/2 and the
> temperature is 21 C, then the mass would be higher, about 8 grams. So
> either you lost some air, or the shutdown volume isn't the average of vmin
> and vmax. Oh well, it's not too important either way.

I'm not sure - some of the parameters are only WAGs, and need to
be replaced with actual measurements. On the first go-round I'm
satisfied just to not have any glaring errors in the method of
computation. Refinements will follow.

> > The diagrams at the link below is still distorted, and I'm hoping
> > to use this model to producing a somewhat more realistic plot
> > that can be compared to (distant future) real measurements.
> >
> > Constructive criticism and suggestions will be most welcome!
>
> Other than the way you describe v1 as (vmin+vmax)/2, I think you have it.

Thanks. I've modified the model to calculate intermediate points
- and I'm about to make changes to allow reasonably reconfiguring
tubing dimensions (both inside diameter and length). If I get
some time I'll try to figure out how to get my DesignCAD package
to plot the graph.

After that, I guess it'll be time to start learning about heat
transfer so I can deal with the heat exchanger inside the hot
head and evaluate design choices for the cold head.

Many thanks to all - most especially to daestrom and Bruce - for
the help and encouragement!

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