displacer cylinder size and proportions

Discussion on Stirling or "hot air" engines (all types)
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Joined: Wed Jan 27, 2016 5:18 am

displacer cylinder size and proportions

Post by samandress » Wed Jan 27, 2016 6:41 pm

Hello all, i've turned my hands to allot of things over the years, now i've caught the stirling bug,
symptoms include only eating foods that come in unusually shaped cans....

I do actually have an engineering background but my experience of thermodynamics mostly taught me that theory merely emulates reality,
and so i've been trying to gather data on proportions, rules of thumb and proven running models.

i think i've got a pretty well rounded set of rules and guides governing each part
but one key aspect where information seems to be either lacking or contradictory.

in terms of the width / height ratio of displacer cylinder and its total volume,
there is no ideal size or proportion, but instead the two variables must be chosen to make the engine
fit for its chosen purpose or more accurately its heat source.

trouble is those factors are naturally a compromise with each effecting the other and the actual solution that
could only reasonably be determined experimentally, hence i have come here for the wisdom of more experienced builders,

take for example an engine designed to be powered by a single small candle, (Gamma)
i have seen two different designs for this one purpose,
1) a 30mm diameter cylinder roughly 3 times as long as it is wide (a rule i have heard once or twice)
this has the advantage of keeping the hot area very hot all the way across as the energy output of the flame is on a smaller target
but with the disadvantage of making it easy for the heat to short around the cylinder
most models i've seen like this require a water jacket to keep running
this design also requires a relatively long stroke

2) i've seen "square" engines that are actually wider than they are tall, often seen as the "coffee cup" engines
made to run from a candle the high heat is will be dissipated across the hot heat exchanger therefore giving a lower temperature
but also a greater contact area of gas to hot metal
the dissipated heat will also mean less issues of thermal shorting through the cylinder wall
pumping losses will likely be less? and the rpm higher

So the rule of cylinder length being 3 times its width only seems to apply to high temperature engines (mostly to prevent thermal shorting).
and for LTD engines the displacer cylinder is very flat (mostly to reduce pumping losses).
so depending on temperature difference there would logically be a plot between a height to diameter ratio of 1:10 going to 3:1
obviously there are no charts about where you can read of a ratio for hand heat, candle heat, gas burner etc.
i think such ratios could only be determined experimentally,
so i was wondering if the experience of the forum has any rules or guides as to how to determine the ratio you choose for a given application?

Now when it comes to the total volume of the displacer cylinder, the optimal level should be determined not by the temperature difference but
by the power (Watts) that are available from the heat source,
i.e. whether you had 1 candle or 5 the peak temperature would be the same but the power would be boosted
Are there any rules or guides on determining the volume that is appropriate to the power of the heat source?

Sorry for the essay but this seems a vital aspect that has received little attention,
and it could only be useful for everyone to be able to design their displacer cylinder for the heat source they intend.

- Sam

Ian S C
Posts: 2221
Joined: Thu Dec 02, 2010 5:15 am
Location: New Zealand

Re: displacer cylinder size and proportions

Post by Ian S C » Thu Jan 28, 2016 3:04 am

Sam, my main experience is with atmospheric, high temperature motors, and with these the long displacer (3 x the dia) is the normal, and a ratio of 1.5 : 1 swept volume between the displacer, and the power piston (that ratio goes right back to Stirling at the beginning of the 19th century, and before).
Engines such as the Coffee Cup motor are designed to run on the hear from a coffee cup, not a candle, these motors can have a displacer dia ratio of 20 : 1 to the power piston dia. A good LTD motor will do between 100 and 200 rpm with very little power.
There used to be some charts on a web site some where (lost it), one for high temp, and the other for low temp motors. They had diameters, and strokes of displacers, and power cylinders.
The main thing governing the power out put of these motors (other than temperature), is the quality of engineering that goes into it when it is built, that includes choosing the right materials for heat conduction, coefficient of friction.
Ian S C

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