Hot Cold Ratios

[ElecTech]

New to the forum here.

I've built the Mizer LTD stirling and would like to build a Stirling stove fan as my next project. I have several CAD drawing versions and I'm about ready to begin cutting metal.

I'd like to start off discussing probably the most frequent mysterious burning question as to hot end/cold end ratios and what is realistic to modify hot end bores/length without altering volumes. I understand this could alter the temperature difference and effective power/rpm band expected. I also realize there is more physics involved to a running engine, but thought I would post to get other perspectives before I make a pretty chunk-o-metal that works no better for an engine or a pinwheel.

I have been doing some research around the web. Lots of reading technical reports, opinions, proven concepts and come up with a crude .XLS calculator(not allowed here) to gather relevant, although incomplete data to the factors that garner a running engine. I've adding in my mod's to see how it looks mathmatically....by comparison to known runners. Nothing proven beyond that.

The Kyko concept is the planned foundation and used as a template to my proposed variations with some mod's to base mount it as in something similar to other stove fans that used to be on the market. I do not plan on selling or doing production. Specifically the hot end of the Kyko makes it a bit too tall and top heavy. I'd like to make the hot end larger bore and shorter. In effect the displaced volume should be unchanged if possible. The point being trying to avoid negative effects. As if this "squating modification" were reasonable to take advantage of any positive effect such as lower temp ratio differences so the thing does not need 500 degrees to start running and broad enough to keep running.

In Kyko V2-4 I did increase the piston bore and played with the stroke to keep the hot/cold end projected displaced ratio near 1.5:1as recommended elsewhere as a general rule of thumb. That rule of thumb seems to get thrown out on proven running stirlings fan engines as the data shows. The Mizer does not really belong in the group since it is not a fan type. Just thought I would add it in to see the difference for low temp engines.

Not sure how anyone can use the data calculator and respond if further clarity is needed. I'll attach a pic instead. Thank you kindly in advance for your time to look at this and chime in. Dimensions are in inches and volume calc's are in cubic inches.

[Ian S C]

ElecTech, you'v got the 1 : 1.5 ratio right for the power piston to displacer vol. The displacer length to dia ratio should be about 3 : 1, ie., the length about 3 times the dia, both these ratios are those used by Robert Stirling, the one major divesion from this was the Robinson, with a short fat displacer, the displacer on that motor had a moving regenerator built into it. I suposethe best way of explaining the long displacer is keeping the hot end as far away from the cold end as possible, unfortunately or otherwise thats the way it is.
There is a photo of my one in my gallery. The displacer cylinder is about 40 mm/1 1/2" dia, the power piston is 30 mm/ 1 1/4" dia x 12.5 mm/ 1 1/2" stroke, its as you see it, no extra cooling other than the fact that the fan blows the cool ? air over the motor. Ian S C

[ElecTech]

Hello Ian, Thanks for responding.

I've seen that picture in my research of the somewhat rare stirling fan projects. I'm so glad to have you chime in. Nice work BTW!

Yes, I have read Stirlings ratio of 3:1 for the hot end. By my estimation provided the data of proven concepts seem to suggest the primary result will alter the temp differential; thereby the carnot cycle pressures and from there thing can all go arwy to the point of an engine that does not fit the application. I agree, the small diameter verses length of the hot end would obtain the wider temp differential and thereby pressure differential for the cycle. I've also read the shorter strokes help compensate for this to increase the running rpm. Possibly keeping the power band in the 700rpm torque range rather than going for it in higher rpm ranges to turn a fan. Tractor verses indy racer?

I was thinking about using a volvo 10" 5 bladed fan. I think many are aluminum so should not take too much power to turn as a loaded flywheel.

I'd like to plug in more numbers to my calculator. Your fan engine data was a bit incomplete and the i/m conversion skewed to put those variables to my calculator. (`12.5mm isn't = 1.5"). The displacer bore was 40mm, what was the stroke of the displacer? Piston bore and stroke to confirm?

Thanks again!

[Ian S C]

Sorry that should have been 1/2" stroke for the power piston, the displacer stroke is 3/4"/ 21 mm.
The larger the ratio the lower the heat diferential required, see the LTD motors, I think my one is about 20:1.
Yes I think your about right with the 700rpm, I'd say between 500rpm and 1000rpm. My stove top has a 3 blade fan, 12" dia, with easily adjustable pitch, it's all the flywheel that is required. I do find that a number of my motors will run without a flywheel, although there is vertually no torque, and the motor must run at high speed. Ian S C

[ElecTech]

Ian,

Using the 3:1 hot length:dia ratio I have used your numbers in my calculator with a few estimates. Here are the results. You can correct the estimates if need be.

My calculator puts the displacer length=(stroke -.03") shorter than the hot end length and the displacer diameter .03 smaller than the hot end bore. Not sure if you have already done these numbers and hope my calculator isn't off. Very surprised to see those numbers at 5.86:1 hot:cold ratio or near 391% above the the 1.5:1 rule of thumb.

[vamoose]

 ElecTech,
I think that there are potentially more aspects of these engines that could be tabulated in your calculator, for example, the surface area of the heat exchanger walls, the related gap to the displacer, the duration the gas spends passing through this gap (rpm related) and the volume of gas processed per cycle (relative to surface area).

The ratios of displacer size and other surface area considerations, have been settled upon over 'time and experience' for these engines, and without slotted or tubed heat exchangers or a proper regenerator, one is restricted to the surface area of a cylinder wall, its material composition and its potential rate of heat transfer in regards to its interaction with the working gas.

I would say that the ratios of these simple engine designs are a generic expression of a more sophisticated relationship, and to optimise thermal transfer you need to increase surface area and reduce the gap through which the gas passes without introducing excessive back-pressure.
Surface area for heat transfer is one of the keys, along with minimising heat exchanger gap size and reducing dead space, in my opinion. (and other stuff like balance and reducing friction and the list goes on).

You could consider making the throw of the power piston and connection rod adjustable, to try and optimise the rpm and power output of your engine.
vamoose

[Ian S C]

Another thing I should have mentioned, the long length of the traditional displacer may to a certain extent act as a regenerator, and if its made of stainless mesh, or steel wool, it is a regenerator in the same way as the standard Robinson motor. 'fraid I'm not that much into the finer points of the maths of these motors, I use the basics, then the rest is in hard metal, a working motor is the real proof that its right or wrong. The more you build, the more you refine the design, and discard the bits that aren't quite up to scratch. Ian S C

[ElecTech]

Vamoose, Ian,

You are correct about the missing finer details and precisley why I put in the caveat about incomplete data for my crude calculator. As to dead space, it appear to be a minimal aspect on these proven engine types I have looked into being so short coupled. No long run pipes, tubes or passages and the displacer cavity is often used efficiently with a .015 gap all around to both ends of the stroke.

I had read the length of the hot end gap is the effective regenerator area and thermal isolation. Hence my concern for making this lower profile may be upsetting the nature of temp differential. Considering the environmental factors atop a wood burning stove, the heat at the base verses ambient temp might not be wide enough differential to keep it running with any real power to turn the fan. I then moved on to compensating for these factors with bore and stroke to both hot and cold ends. The concept of variable stroke has been one of my thoughts, as well as a test bed hot end run by a motorized crank to see if there is a method to optimise the cold end bore and stroke to the environemental application intended. The Kyko and Moriya are burner type and designed thereby having intense localized heating vs. room temp differences of 1000degF+. I might be lucky to get 200-300degF differential?

I appreciate the brainstorming.

I'd presume you have seen this page before, but there is a link to a really nice worksheet by Jean-Pierre Van Dormael having more of the finer details but strange units to us noncomforming foot rulers!
Engine Theory

The worksheet was locked, but you can download an unlocker to play around with it.

[Ian S C]

The use of metric measurements for temperature, distance, volume, are worth getting to know, they are the universal language of the international scientific community, ie., USA, China. Europe, everywhere, except on one Mars trip by the USA where they mixed up miles and kilometres, and crashed the space craft onto the surface. Ian S C

[ElecTech]

Ouch! That hurt!

I've been using the coversions for years. It's just not native. It's like speaking another language where I have to convert it to comprehend, calculate - then unconvert it to comprehend again...

Well, mm aren't so bad. Working in (new to me) scientific exponential portions of a cubic meter is another story all together.

The ballpark from my data calculator would seem to point towards the 5:1 to 8:1 range for a stove top fan engine running between 400-500degF with the 200-300degF temp differential expected. Although it is still 400-500% over the projected 1.5:1 rule of thumb, it won't be running under the same burner conditions either.

Seems like a good place to start. The next dilemma will be deciding which end to alter to fine tune it. Piston bore and stoke or the associated parts effecting displaced hot end volume. Piston bore and stroke may be less parts to scale and easier access.

Back to my CAD drawings! Many Thanks!

[Hopper]

The old Stirlings seemed to use a 2:1 or 3:1 ratio between the hot end and cold end lengths respectively.
Before designing my own Gamma type engine recently I did survey of a good handful of currently available model Stirling plans and kits with a proven track record and most of them have closer to a 1:1 ration between length of the hot end and length of the cold end.
This may be due to the almost universal use of either stainless steel or glass for the hot end cylinder and aluminium fins on the cold end. The older models with a longer hot end tended to use all brass, or at least brass for the hot end and aluminium cold end fins (eg Kykyo if memory serves correctly.)

I also surveyed the swept volume of the displacer vs the power piston and the proven successful current models ranged from 1: 1.3 to 1:2.2, with most clustered right around the 1.5 mark.

If I can dig out the piece of paper I wrote it all down on I will post it.

From memory, the plans I surveyed included Bengs, Jan Ridders, Kykyo, Dr Senfts version of Kykyo called Moriya (?), and a few others.

[ElecTech]

Hi Hopper,

I am focusing on engine driven fans which do not appear to follow the basic volume ratio rules of thumb directly. These would still be considered Gamma engines although just set on a hot surface. Burner engines have a much broader temp differetial and much higher heat.

I think I can conclude from my data this would suggest lower temp and narrower the operation zone calls for deviating from the general 1.5:1 and not so far as the the 50:1 volumes for the LTD Mizer engines. Between Ian's and the Vulcan fan's 5:1 then the Myers near 8:1 as proven for the application - I think I can attempt something worth while to emulate. I'm really after functional, silent and long life. I'll see what the art-teest in me can do to make it pleasing to look at as well.

[Bumpkin]

My two cents on the stovetop ratio: In season, my stovetop typically runs about 25% hotter than room temp and will barely boil a teapot. The average might be higher, but that’s what's consistently available. Cut that difference in half to get heat in and out of a running engine, and the 1/8 ratio is what I settled on for my (still experimental) purposes. Bumpkin

[ElecTech]

Bumpkin,

Our stove is connected to the duct work and blows out around the insert. I run it just under 500degF and a portion of the radient heat is probably distributed through the cold air return (running the summer fan) once the main area is warm. I'd find it worthless if my stove would not radiat more than 25% above ambient. Most of the heat would be going out the chimney...well in all honesty it does anyways, but the point is to heat the house and recover as much efficiency as possible indoors in the process.

Checking my surface temps at the top plate will read 450 at the front edge and much higher closer to the damper. We use it for cooking when the power goes out. With rural living in mountain foothills, it often won't be back on for 10 days or more.

Besides the challenge of a fun build project, I am reasonably confident the stirling fan can cut down on using a generator to run the summer fan 24hrs a day. I could just buy a stirling fan, but where is the fun in that!

[ElecTech]

Success!

I know this is an old thread, but I wanted to update those that offered their input. Here are the pictures of the finished project.

I did find out that the brass rod has a high thermal conductivity, transferring heat to the top plate and lost differential temp. The fan would quit after about 10-15 minutes

If I can scrounge some ¼” titanium rods, TI has a TC of less than ¼ of brass but does not look as good. The grooves in the brass tie-rods prevent heat from traveling up the rods now. Ran it for about 90 minutes maintaining about 140deg temp differential. Whoohooo!



500rpm at 450 degrees.

Back view

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