Author Topic: Stirling Engine Thermodynamic design notes  (Read 4927 times)

Offline tvoght

  • Full Member
  • ****
  • Posts: 932
  • Indiana
Stirling Engine Thermodynamic design notes
« on: August 29, 2014, 12:49:37 AM »
I said I'd start a thread to discuss the simple thermodynamic analysis I did
in the design of the "Gamma1-VPA" engine.

Link to the build thread:
http://www.modelenginemaker.com/index.php?topic=4006.0

I made several false starts on a writeup before realizing I had no idea
how or where to start.

If you haven't read anything on the thermodynamics of Stirling engines, you
could do much worse than to follow this link to Ohio University (long a hotbed
of Stirling engine research).

http://www.ohio.edu/mechanical/stirling/me422.html

In particular, the link to Isothermal Analysis on that page outlines the
type of analysis I did.

http://www.ohio.edu/mechanical/stirling/isothermal/isothermal.html

I really made a breakthrough in understanding when I bought the book
Mechanical Efficiency of Heat Engines by James R. Senft.

http://books.google.com/books/about/Mechanical_efficiency_of_heat_engines.html?id=2SqxYs59wDUC

It's not a particularly cheap book, but anyone wanting a reasonably technical
yet understandable-by-hobbyists text on Stirling engines might consider it.

Without a lot of explanation, I'll show some of the graphs I came up with in
my simulations.

Below is an indicator diagram. It's a graph of internal pressure of the engine
versus internal volume.  Remember that theoretically, the engine always
contains the same mass of gas, while the volume varies with the sweep of the
power piston.



In that kind of graph, the area enclosed in red represents the "Indicated Work"
done by the simulated engine during one cycle. The units of work would be in
Newton-meters.

Next is a key graph that shows how I chose the Swept Volume Ratio of the engine.
Imagine an indicator diagram as shown above was evaluated at each different value
of Swept Volume Ratio along the bottom axis. The red line shows indicated work,
and the green line shows Shaft work, which is the Indicated Work minus
"Forced Work" which is the work returned by the flywheel during certain parts
of the cycle when the differential pressure on the piston opposes the flywheel.



You can see a clear peak on the green Shaft Work line which allowed me to
pick a Swept Volume Ratio for the design.

By the way, Swept Volume Ratio is the volume swept by the power piston divided
by the volume swept by the displacer.

That's all I'm going to say in this post. There is a great deal that has been
left unsaid.

I hope this is enough to provoke some questions or comments from those interested.

Regards,
--Tim

Offline AussieJimG

  • Full Member
  • ****
  • Posts: 450
  • Bywong, NSW, Australia
Re: Stirling Engine Thermodynamic design notes
« Reply #1 on: August 29, 2014, 07:58:07 AM »
Thanks Tim, this thread might tell me more about thermodynamics than I want to know but I am certainly interested in Stirling Engines.

Thermo was one of those mysterious subjects inflicted on we poor electronics students at Uni and which few of us understood.

I think most of us tried (and failed) to construct electronic analogs (yes, it was in the days of analogs) of the concepts. If only we had succeeded ...

So I will follow to see if I am any smarter fifty years later.

Jim

Offline Maryak

  • Global Moderator
  • Full Member
  • *****
  • Posts: 1818
  • Aldinga Beach South Australia
Re: Stirling Engine Thermodynamic design notes
« Reply #2 on: August 29, 2014, 08:22:46 AM »
Yeah,

That damn zeroth law gets you every time  ;D

Best Regards
Bob
Если вы у Тетушки были яйца, она была бы Дядюшкой

Offline tvoght

  • Full Member
  • ****
  • Posts: 932
  • Indiana
Re: Stirling Engine Thermodynamic design notes
« Reply #3 on: August 29, 2014, 12:27:13 PM »
Thanks for commenting Jim and Bob.

My knowledge of thermo is painfully limited. The Isothermal analysis I tried to do revolves mostly around the Ideal Gas Law:

PV = nRT

and that's something that I remember being covered in high-school physics (though any real understanding was missing then, I was given
a silly mnemonic to memorize the equation). Given a reason to want to understand it, it makes somewhat more sense now.

Here's another graph that's sort of fun to look at. It shows cycle work versus the two parameters of phase angle and Swept Volume Ratio.
It didn't have much practical use in my design (the numbers are easier to pick out of a list), but like I said, sort of interesting to look at.




I'll note that all the graphs I have shown were made assuming the
temperature inside the hot cap was 500K and the temperature inside the cooler
was 350K (so hot, about 227C, and cool about 77C).

Changing the hot/cold temperature ratio gives a different optimum Swept Volume Ratio, with lower temperature ratios requiring a lower
Swept Volume Ratio. Think of the LTD Stirlings with a very large displacer relative to the power piston.

--Tim


Offline MMan

  • Full Member
  • ****
  • Posts: 89
  • Hampshire, UK.
Re: Stirling Engine Thermodynamic design notes
« Reply #4 on: August 29, 2014, 01:33:39 PM »
Spent a couple of hours on the Ohio site. Fascinating, not sure I understand it any more now than I did. At least I know what the analysis looks like for when I want to run a potential design over it.

Mman.

Offline tvoght

  • Full Member
  • ****
  • Posts: 932
  • Indiana
Re: Stirling Engine Thermodynamic design notes
« Reply #5 on: August 29, 2014, 02:39:42 PM »
MMan,
To any would-be designer of Stirling engines, this stuff is good to understand to some extent (mostly because as you said, it's interesting).
For me, there was a need to know that I had at least a viable design before going to all the trouble of a build.

Having done it, the only design parameters I derived from the analysis were a Swept Volume Ratio and a phase angle.

I'd know the next time that a well-built engine with a a Swept Volume Ratio of one-half and a phase angle somewhere near 90 degrees
would probably run well at the temperatures achievable with an alcohol lamp and air cooling.

I'd know that, but it probably wouldn't keep me from doing a simulation, because I've already got the software in place.

The analysis was a fun part of the project. That's why I wanted to share a bit of it.

--Tim

Offline philjoe5

  • Full Member
  • ****
  • Posts: 1012
Re: Stirling Engine Thermodynamic design notes
« Reply #6 on: August 29, 2014, 03:49:21 PM »
Tim,
This is quite interesting to me.  At one time in my life loooooong ago, I taught thermo to chemistry students.  I wish I had heard of and had access to a Stirling engine, or had access to a working steam engine at the time.  It would have made the subject so much more real to me and the students.  Thanks for posting

Cheers,
Phil
If you pick up a starving dog and make him prosperous, he will not bite you. This is the principal difference between a dog and a man.  - Mark Twain

Offline tvoght

  • Full Member
  • ****
  • Posts: 932
  • Indiana
Re: Stirling Engine Thermodynamic design notes
« Reply #7 on: August 30, 2014, 03:54:05 PM »
Thanks for commenting Phil, and now that you mention it, it probably was in chemistry class where I first heard of the Ideal Gas Law.

It's true in my case that until I got interested in Stirling engines,  the thermodynamic behavior of ideal gases was hardly interesting to me
at all.

Now I think about it all the time.

--Tim

Offline tvoght

  • Full Member
  • ****
  • Posts: 932
  • Indiana
Re: Stirling Engine Thermodynamic design notes
« Reply #8 on: August 30, 2014, 05:44:29 PM »
It might be interesting to look at the indicator (or P-V) diagram with a little
more attention to detail,



I've drawn in vertical black lines to show that the point of maximum volume
is when the power piston is at Bottom Dead Center (BCD) and at a minimum at
Top Dead Center.

The Blue line represents "Buffer Pressure" which is in this case atmospheric
pressure. Senft points out that a practical engine running will through (however
small) leakage past the piston quickly equalize to have an average internal
pressure equal to the Buffer Pressure.

I've added numbers to the "oval" indicator line to point out key details in the cycle.
Imagine that the engine has come to speed and the average internal pressure
is equal to atmospheric -the blue line-.

Starting at "1", Bottom Dead Center, the piston starts moving inward. since the
engine pressure is less than atmospheric, the piston is being "pushed" in by
atmospheric pressure. This is consistent with the momentum of the flywheel.
At "2", the situation changes. The engine pressure is now higher than atmospheric
but the piston is still moving inward, so in the portion of the cycle between
"2" and "3", the piston opposes the flyweel. Between "2" and "3", the
flywheel is putting compression work back into the engine. Senft calls this
Forced Work. In terms of accounting for work at the shaft, The portion between
"1" and "2" was adding work to the flywheel, while betwen "2" and "3" work is
being taken from the flywheel.

At "3", the piston reverses and starts its trip outward. Since internal pressure
is higher than atmospheric, the piston is adding work to the flywheel. Finally,
between "4" and "1" the flywheel has to supply work until the piston reverses
at "1".

The concept of Forced Work is important here because if an engine was designed
with only attention to Indicated Work, the end result might be an engine in
which Forced Work was higher than Indicated Work. That would result in a
negative Shaft Work, and an engine that would not run.

Regards,
--Tim

Offline Roger B

  • Global Moderator
  • Full Member
  • *****
  • Posts: 4458
  • Switzerland
Re: Stirling Engine Thermodynamic design notes
« Reply #9 on: August 31, 2014, 08:53:48 AM »
In a previous edition of the German magazine 'Maschinen im Modellbau' one of the writers had produced an indicator for his hot air engine giving a display on an oscilloscope. If I remember correctly he used a diaphragm transducer for the pressure and a snail cam obscuring a light beam for the rotation. Maybe another German speaking member remembers more or has a copy of the magazine.
Best regards

Roger

Offline tvoght

  • Full Member
  • ****
  • Posts: 932
  • Indiana
Re: Stirling Engine Thermodynamic design notes
« Reply #10 on: August 31, 2014, 01:55:13 PM »
Thanks for the info, Roger. I would be interested to hear if anyone knows more about the article you mention.

I said in the build log that I have given consideration to doing something similar. I have already identified a pressure transducer that would
work in the cylinder head. I had a somewhat different idea for shaft position sensing, and a plan to use computer data acquisition instead
of an oscilloscope. I take it the German writer was using the snail cam to modulate light intensity and thus get an analog voltage piston position signal. Very clever.

It would be very interesting indeed to compare measured results to the simulated graphs.

--TIm

Offline Roger B

  • Global Moderator
  • Full Member
  • *****
  • Posts: 4458
  • Switzerland
Re: Stirling Engine Thermodynamic design notes
« Reply #11 on: September 04, 2014, 08:00:28 AM »
A work colleague has a copy of the magazine. It is available electronically from the publisher.

http://www.vth.de/maschinen-im-modellbau/ausgabe1/4837-maschinen-im-modellbau-12014/

I have a scan of the article, which I obviously cannot post on here, but if you pm me a suitable email address I will send it to you (it is not possible to add attachments to forum pms).
Best regards

Roger

Offline tvoght

  • Full Member
  • ****
  • Posts: 932
  • Indiana
Re: Stirling Engine Thermodynamic design notes
« Reply #12 on: September 04, 2014, 06:04:21 PM »
As we sometimes say in my neighborhood, Roger: "You da man".

--Tim


Offline Roger B

  • Global Moderator
  • Full Member
  • *****
  • Posts: 4458
  • Switzerland
Re: Stirling Engine Thermodynamic design notes
« Reply #13 on: September 04, 2014, 06:43:20 PM »
Glad to help, there's often someone somewhere who has already done half the work if only you can find then.
Best regards

Roger