Request advice, volume ratios of components, displacer, cylinder, etc

[spinningmagnets]

I'm hoping to gather the common thoughts on optimum diameter-to-length ratios and also volume ratios between the big three components on a Gamma. Power cylinder (bore/stroke), displacer cylinder, and displacer.

For instance, a low-temp-differential Gamma (LTD) displacer-cylinder has a wide diameter, and a short stroke, but most of the youtubes show a gamma with a 1:2 ratio of the displacer cylinder. [ex: if the bore is six inches, the length is 12]

I'm not concerned about making the power-piston and power-cylinder. Or the cold end, which should be easy. But I'll probably use the old stand-by stainless steel cup for the hot end, simply because stainless is hard to do anything to, so I'll get something that almost ready to go. I can cut a cylinder shorter with a thin abrasive disk, but the cold end should be so much easier to build to match the hot end, the entire project will be scaled to the stainless steel hot end. Something like this:

A

StainlessCup1.png (419.12 KiB) Viewed 5221 times

So, once I find a good candidate, the diameter of the hot end will be set. I must then...

1. Choose a hot-end length
2. Make a cold-end out of aluminum to match the hot end (symmetrical)
3. Determine the volume ratio of displacer to displacer-cylinder [If D-cylinder is 12 inches long, would displacer be 8 inches long?]
4. Once the displacer and D-cylinder volume plus bore/stroke is determined, what is the optimum power-cylinder volume ratio to displacer gas volume? 20-1?
5. Once the power-cylinder volume determined, what is the optimum bore/stroke ratio? wide and short, roughly equal? or long and thin?

Thanks in advance for any suggestions. Normally I would just reverse-engineer a Stirling from the web, but...which one?

[Tom Booth]

You probably are not interested in some radical design, but I had also picked up some of those Stainless utensils holders from Big Lots locally thinking about going something like this:

Compress_20240702_225128_8803.jpg (24.04 KiB) Viewed 5199 times

A kind of Alpha/Gamma I guess?

Trying to do away with the cold side altogether.

If you go through those utensil holders you can sometimes find one that fits inside the other., or make them fit. Or use that for the displacer piston and something else on the outside.

As far as specific ratio issues, My rule of thumb is to just build it first. Leave the piston connecting rod off. Work the displacer manually and see how far the piston travels "free piston".

Make the power piston throw a little more than that. A little more than what it travels "free piston" that is.

I got that advice from an old timer on the forum a long time ago.

[VincentG]

A forum member from years ago, Ian S C, had a lot of hands on practical tips for classical Stirling engine building. I'd recommend a dig through his posts.

[spinningmagnets]

Thanks Tom Booth and VincentG!

[spinningmagnets]

Per "Ian S C" in New Zealand...search.php?st=0&sk=t&sd=d&sr=posts&author_id=1424

Displacer should be near three times longer than its diameter, with the warm walls of the displacer acting as a mild regenerator

Working gas volume in displacer-cylinder (minus volume of displacer) should be near 1.5 times the power cylinder volume (piston diameter x stroke) and this was what was used By Robert Stirling back in 1816. The Robinson SE has a real regenerator and the displacer has B/S of 1:1. The air-gap between the walls of the D-cylinder and the displacer should be roughly 1mm-2mm.

He prefers the power-piston to have a diameter that is equal to, or larger than the stroke. B/S is wide/short

The power-cylinder is preferred to be cast iron (or steel). Piston should be cast iron, with no piston seals since they add too much friction.

To keep the power-piston seals cool enough to survive, you might add a disc of insulation to the crown, and then add another metal portion. This is called a "Heylandt Crown" (viewtopic.php?p=11249#p11249) "...the Heylandt Crown on the hot piston, it should be a hollow item , made of stainless (best), or mild steel, light weight and without leaks... I made the Heylandt Crown on the hot piston of my ALPHA motor about two and a half times the diameter high, this allows the hot cap to be fairly long, thus keeping the heated area as far as possible from the fitted piston end, so that the hot piston is not too hot while the top of the hot cap runs at red heat..."

For a similarly-sized engine and the same heat input, an Alpha is about twice as powerful compared to a Gamma or Beta.

"...a good cylinder for a motor is the internal cylinder of a automotive shock absorber, these are about 400 mm long, with a bore of 25 mm to 40 mm...Brake cylinders and pistons are worth looking at..."

[matt brown]

Ian was a legend. It appears your text is a mix of alpha and gamma comments, but it appears you're going with a gamma design (smart move). To improve focus, let's add some numbers and start with volume. Going with Ian's ratios, let's consider PP=100cc and DP=150cc (swept volumes) and let's ignore dead volume for now. Thus, total volume = 250cc and PP=100cc results in an ideal compression ratio where 250/150 = 1.66 when events are distinct (vs typical out-of-phase). Here's a PV plot that I hope isn't too confusing. I couldn't change the scales, so consider volume axis values are 150cc vs 1.5 m^3 and 250cc vs 2.5 m^3 (and kJ work values are bogus due to massive m^3 volumes).

100cc gamma A 300-500k.png (93.46 KiB) Viewed 5139 times

This 300-500k cycle has a thermal ratio = 1.66 which is the same as Ian's volume ratio = 1.66 with points 2 and 4 on the same isobar. When the volume ratio equals the thermal ratio then ambient compression is most effective, whereby this "5 kPa" isobar could be ambient pressure. Also note that this isobar nearly bisects the work area where the compression cold stroke nearly equals the expansion hot stroke.

[spinningmagnets]

Thanks, Matt. I appreciate you taking the time to post that. It is very helpful to me!

[matt brown]

Now, let's venture from ideal towards real, but slowly. One can bitch and moan about design values such as heat rate and sink values, but the volume ratio will be the major reality since it's fixed by design. So, consider this 250cc design still has ideal everything including distinct motion, except for the thermal ratio. To reduce text, I'll use my favorite notation where Vr=volume ratio and Tr=thermal ratio. Here's 4 PV plots similar original PV, but where I removed the red adiabats for clarity yet kept the green isotherms. Note caption under each graphic.

gamma A 300-500k.png (49.72 KiB) Viewed 5115 times

gamma B 300-600k.png (49.54 KiB) Viewed 5115 times

gamma C 400-600k.png (49.33 KiB) Viewed 5115 times

gamma D 400-500k.png (49.44 KiB) Viewed 5115 times

gamma A is the original 300-500k cycle where Tr=Vr thus Tr/Vr=1
gamma B is 300-600k cycle where Tr/Vr = 2/1.66 = 1.20
gamma C is 400-600k cycle where Tr/Vr = 1.5/1.66 = .90
gamma D is 400-500k cycle where Tr/Vr = 1.25/1.66 = .75

Assuming gamma A is the ideal goal, the question is real vs ideal values where the major variation will be heat source and sink values when Vr is constant. Gamma B retains ideal 300k sink, but shows 600k source variation. However, any reality check on source value increase should also include sink value increase, thus gamma C shows +100k both source and sink above gamma A. Meanwhile, gamma D is the "converse" of B where D shows A source but with C sink.

I don't want to beat you to death with too many numbers, but compare point 4 and its potential ambient isobar across these 4 PV plots to gauge ambient compression potential. Interestingly, gamma D has most of its output from its "cold stroke" which likely is typical LTD model hallmark.

So, the actual source and sink values are quite flexible within Ian's 1.5 DP/PP volume ratio (lots of wiggle room). Also note relative output for these 4 gamma versions despite finite bogus value on PV plots where

A = C
B = 1.5 A or C
D = .5 A or C

[matt brown]

Let's review where we are...going with Ian's DP/PP = 1.66 appears xlnt and the only real issue this has is the infamous "sq cube" scale rule which is when linear dimensions double then surface area squares, but volume cubes. This tends to favor a smaller design over a larger design, but there's still plenty of wiggle room with low end designs. So, we have to keep an eye on relative dimensions somewhat, but at least this basic 1.66 volume ratio will pose minimal operational issues within a low end range of thermal ratios.

Moving along to Ian's next suggestion is the bore stroke ratio. Assuming you're going with a typical gamma slider-crank configuration, then there's no "thermal" issues with cold side PP except that bore>stroke increases TDC and BDC dwell. For common alpha, this dwell enhances heating and cooling, but gamma gains nothing here...directly. However, gamma gains a similar advantage indirectly from this PP 'dwell' due to displacer motion.

I'm not much of a gamma guy (I'm an alpha guy), so I'd go with whatever Ian suggests for bore/stroke ratio (many hover around stroke = .75 bore). The major gamma issue is low torque since Pmax for gamma is TDC, and there's not much dP (pressure swing) for any engine within ambient range. Another obscure issue is DP stroke which often appears more a matter of convenience than design parameter. Some details are loosely related and other details are closely related. As an alpha guy, I tend to favor a stroke/bore equal the thermal ratio and DP=PP stroke. IOW within this 1.66 volume ratio and 1.66 thermal ratio, I favor PP stroke 1.66 PP bore (trading work loss for torque gain akin alpha-gamma scheme).

[matt brown]

So, the actual source and sink values are quite flexible within Ian's 1.5 DP/PP volume ratio (lots of wiggle room). Also note relative output for these 4 gamma versions despite finite bogus value on PV plots where

yikes. make that Ian's 1.66 DP/PP volume ratio

this is what happens when you're racing the clock to avoid timeout - hopefully no other errors...

[spinningmagnets]

Thanks again, Matt! Lots of good info to study.

[matt brown]

Jeez, I've gotta eat some crow here...

Between site issues of timeout and no edit, posting anything technical can be tricky. Everything here so far is fine except some of the volume ratio buzz. Here's a little table with some basic values, but I forgot to include that volume is in cc.

volume ratios.png (10.83 KiB) Viewed 5076 times

Note that I've listed 2 volume ratios where I denote them as "layman Vr" vs "thermo Vr" and how these are derived. Ian's DP/PP = 1.5 is the common layman flavor, but "reduces" to 1.66 thermo flavor when calculated via Vmax/Vmin which is the compression ratio. This confusion is rampant in design discussions and likely why Ian choose safe values where both volume ratio methods are similar. Nevertheless, it's interesting to look at a table like this with 'matching' thermal ratios. Last line entry represents typical LTD despite massive 4L DP volume.

I'm trying to minimize notation and confusion, but I might have to jump to Vr for common DP/PP and Cr for compression ratio. Won't matter much at these ratios, but always good to be as precise as possible.

[matt brown]

Here's a few more issues to mull over and notice how I'm being rather vague just so you get the general ideas and avoid any premature commitment. Another DP issue for common slider-crank gamma is that all DP motion is lost work. This is far different than PP where piston momentum passes in and out of flywheel or ambient pressure. IOW typical gamma DP is always a driven member and taxing output, so low DP weight is crucial for any ambient engine scheme. However, this work loss is not merely due to DP weight, but compounded by the rpm in 2 ways (1) simple cycle rate in rpm (2) relative DP speed where DP with 2x stroke will have 2x piston speed and tax output more than 2x shorter stroke (won’t bore you with calcs). This DP work loss explains why some guys have explored various rotary DP schemes.

Another obvious issue is regen which some dismiss while others rave about it. The basic issue is that an ideal Stirling cycle recycles more heat than it converts to work. Therefore, nixing regen may not effect output, but it will drastically (1) lower efficiency (2) require more heating (3) require more cooling. Thus, nixing regen will require a "substantially" larger heater and cooler. Yet, regen favors a slow rpm with isothermal expansion and compression and disfavors a fast rpm with adiabatic expansion and compression (akin Otto cycle).

An often obscure reality is that we can't simply choose the cycle rate (rpm) as if picking candy. Nope, the cycle rate will be determined by the MEP (mean effective pressure). So, when constrained by 1 bar charge pressure (cold) and a fixed low volume ratio, MEP will vary little regardless of source potential while ambient compression taxes output by lowering MEP (note E in MEP is "effective"). The obvious way to increase output is via increasing charge pressure, but this nixes most ambient compression schemes unless engine includes megabar buffer pressure within crankcase or bogus isolated LP reservoir - LOL

[matt brown]

Another obvious issue is regen which some dismiss while others rave about it. The basic issue is that an ideal Stirling cycle recycles more heat than it converts to work. Therefore, nixing regen may not effect output, but it will drastically (1) lower efficiency (2) require more heating (3) require more cooling. Thus, nixing regen will require a "substantially" larger heater and cooler. Yet, regen favors a slow rpm with isothermal expansion and compression and disfavors a fast rpm with adiabatic expansion and compression (akin Otto cycle).

Here's another graphic to drop in the pot...

regen vs Vr.png (91.3 KiB) Viewed 5035 times

This one is a bit of a headbanger with all those pretty colors, but I'll clarify everything. This graphic shows the effect of various regen eff BUT only for a specific thermal cycle which isn't listed on this graphic. I have the original paper that I poached this from, but couldn't locate it easily. However, the horizontal red line at top is when regen = 1.0 and an ideal 300-750k cycle with perfect regen would have eff = .60 so these are close thermal cycle values.

There's 2 main takeaways here

(1) notice effect of "compression" ratio (henceforth Cr) which is the horizontal scale where ideal 1.0 regen doesn't effect thermal efficiency (thus top red line is constant) however anything less than 1.0 regen is greatly effected by the actual Cr. This is simply due that for a Stirling cycle with constant temperature isothermal processes, the more work per each cycle (rpm) increases the relative work output vs constant regen loss per each cycle. So, for any given thermal cycle with less than ideal regen (including no regen) a larger Cr increases the thermal efficiency as if by magic. The problem with this simple reduction is that common SE mechs tap out around Cr=2.

(2) notice regen effect on thermal efficiency where the orange line is no regen. Assuming this Ian study with Cr=1.66 and this 300-750k graphic, ideal 1.0 regen = ~.60 eff, but with no regen (orange line) this drops to less than .15 eff. So, this Ian engine with Cr=1.66 may have the same output with regen or not, but lacking regen expect (1) thermal efficiency will drop by ~3/4 when 300-750k cycle (2) heater and cooler will require 4x increase vs ideal regen

The bugaboo here is what's known in the trade as regen "load"...the ratio of ideal source input to ideal regen heat. Like nearly everything thermo, this is a variable that most SE gurus consider a wildcard. I've spent years studying this bugger and how it plays out, simply reducing my study to "the Stirling cycle is a top heavy cycle".

[spinningmagnets]

https://www.stirlingengineforum.com/vie ... 2118#p2118

Doing research ahead of time is always good, and...at the same time, I place a high value on real-world experiments that will expose issues that weren't thought of during the planning stage. Here's a simple gamma from 1904 with a record of production