Another Stirling gamma anomaly under the radar

[Fool]

I'm having brain atrophy. I'm too asleep to pour through all the numbers. Sorry. What I do notice is that some of the expansion is at constant Th and some is at constant Tc. And some is being expanded and regenerated. From that, it doesn't appear very Carnot challenging. Could be my stubbornness.

Can't comment on the Hall video. Again brain atrophy and onslaught of magic numbers. Sorry. Need sleep. Zzzzzzz

I'm trying. Thanks for your help here.

[matt brown]

Here's the graphic again so we're on the same page LOL

A 300-450k.png (25.45 KiB) Viewed 3233 times

Let's consider vol A first where I show 100cc in DP1 becomes 80cc in PP2. Here's my logic, the 100cc in DP1 will reduce to 66cc in PP2 due to 450-300k regen whereupon "slight" expansion in both DP and PP drops from 1.5 bar to 1.25 bar. During this pressure drop, any gas in DP and PP is expanding, whereby by PP2 vol A has expanded from 66cc to 80cc. After vol A is at PP2, I consider it an independent vol that expands to 200cc by PP5.

As vols ABCD past thru regen, each vol initially decreases volume by 1/3 but then continues expanding in PP at the same rate as DP gas (graphic sums this 1-2, 2-3, 3-4, 4-5). If we consider vols ABCD as a singular 400cc volume, then a 1.5 to .5 bar expansion would end in 1200cc. Offhand we know that 1/3 of this 400-1200cc 450k isothermal input never occurs here since the gas is leaving the DP, plus we know that a large amount on ABCD input in DP goes to regen. So, the actual source input in DP for vols ABCD that actually "does anything" is quite small vs total DP input (despite massive vol E).

As gas flows into PP, the gas expands at the same rate as the DP gas without any back-and-forth mass redistribution due to equal pressure in DP vs PP. Now, if we consider the proportional relationship of isothermal expansions, once the gas is in PP then all sink ABCD input is producing expansion vs most DP source ABCD input is 'lost' to regen. I'll let you think on this before throwing more at you.

[matt brown]

I've been bogged down chasing heat and work values for this cycle via ratio analysis. The gas flow in previous graphic is correct, but the heat vs work issue is elusive due to source input for each volume during transfer from DP to PP.

However, in prior post I callout:

"The Pmin values are after displacer reciprocates just prior compression. I added the 800cc PP as a lofty extreme, but a sharp eye will catch that DP and PP pressures are 'quickly' converging."

Kinda funny how I tagged this yet missed THIS...

300-450k compression.png (18.51 KiB) Viewed 2833 times

Here's the compression process when viewed 'backwards' (right to left) which is illuminating. If expansion was carried to 5, then indeed, P after expansion is nearly P prior compression, so a lot of the expansion work from 4-5 will be given up to compression whether sub ambient P per graphic or over ambient P (unshown multi bar charge).

Note short table above DP where I list P expansion real vs P compression bogus and P compression real. I may be choking on heat vs work values, but comparing PP expansion vs compression simplifies my chase. Since this is a 300-450k cycle, then compression via Carnot would be 2/3 of expansion or the P compression bogus line which doesn't happen. Nope, the P compression real line is what happens where MEP during compression exceeds Carnot values. Due to the displacer, the expansion ratio does NOT equal the compression ratio, but the idea is to have a low expansion ratio (with high MEP) and high compression ratio (with low MEP). So...despite sink input "backflow" during expansion, this bugger appears to have (slightly) worst eff than standard Carnot, but this is inconclusive without knowing actual DP source input.

[Fool]

I understand what you are doing here. Kudos. Modeling an engine by finite elements with each element having a set mass of gas. Excellent. It seems like it might avoid problems with set volumes. It might even allow ultimately mixing of the gas, and flow modeling. Excellent. Separating hot processes from cold process, expansion and compression. Excellent. Showing what happens as intermediate stages in expansion. Excellent.

Your processes show how expansion has three competing events. In the hot zone expansion is at Th constant temperature. In the cold zone expansion is at Tc constant temperature. In the regenerator expansion is 'between' with heat loss and expansion happening simultaneously, (as Happy Quinn says.) 'not good'. The complexity of these engines always seems to amaze me.

If your point is that all the expansion needs to be in the hot zone, and all the compression needs to be in the cold zone, and the regenerator volume needs to open for heat transfer, and close for volume change. I get your point.

P.S., I didn't even see the pressures at the bottom, and that they differed from those at the top. Brain dee-ead. LOL.


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[sarimshaikh]

I really like your blog. Great article. It's most evident, people should learn before they are able to weeklymagpro

[matt brown]

Thanks for the nod !!!

Your processes show how expansion has three competing events. In the hot zone expansion is at Th constant temperature. In the cold zone expansion is at Tc constant temperature. In the regenerator expansion is 'between' with heat loss and expansion happening simultaneously, (as Happy Quinn says.) 'not good'. The complexity of these engines always seems to amaze me.

Your 'not good' is what always made me avoid gamma and beta until my gamma deep dive started last summer. Vincent got me into this and keeps feeding me tidbits like his Essex head banger.

If your point is that all the expansion needs to be in the hot zone, and all the compression needs to be in the cold zone, and the regenerator volume needs to open for heat transfer, and close for volume change. I get your point.

As a long time alpha fanboy, simple logic is to keep all expansion in the hot 'space' and all compression in the cold 'space'. However, regen is a wildcard and I've been forced to review some long held concepts (mine and others). While trying to chase down heat vs work on that last cycle, I had another altered state experience which led to this the next morning...

mono T gas flow.png (26.97 KiB) Viewed 2367 times

Jeez, why not cut to the chase and rework regen completely ??? This is a work in progress and only one way of several I already know to game this. I recycled various values from past graphics to keep my head straight, but used a 300-600k cycle to simplify displacer reversal values. I checked my values thru an online calculator with a watchful eye on m values. Anyways, some may notice something right away here...that source input equals sink input (ambient backflow). But the hidden gem is that this sink input exceeds work of compression (at least for this cycle). Anyone who wants to know the exact values can spend a few minutes with a good online calculator.

The basic scheme is 1:2 'cold space' expansion where this expansion rate matches the 'hot space' expansion rate, so both hot and cold volumes are expanding together with each sucking in their own input...hot from source vs cold from sink. In this graphic, an independent (positive displacement) piston separates these 2 volumes while the purple regen displacer is driven by who knows what (no biggie). When Vincent makes it this far, he's probably already noticed that these 2 pistons could be 1 double-diameter piston a la Ericsson. Don't sweat the heater location and function, since this is only meant to relate gas flow values.

So there you are Fool, definitely a Super-Carnot cycle if we overlook the ambient input.

Sorry for the fuzzy graphic, but I had to shrink it quite a bit to make 1 graphic. Now, can we stop bickering about Carnot and save the ice cubes for a long tall cold one !

P.S., I didn't even see the pressures at the bottom, and that they differed from those at the top. Brain dee-ead. LOL.

I'm feelin' more braindead everyday, how did I miss the 'obvious'...

PS - graphic values closely follow previous cycles in this thread, so this is shown with 'ambient' compression. No issue with online calculator which will simply consider everything running in a vacuum (aka no buffer pressure).

[matt brown]

BTW at frame 6 the PP cylinder is 1 bar 1600cc (24m) while the DP cylinder is .5 bar 1600cc (12m). The pros and cons of interconnecting these 2 spaces can go from amusing to confusing depending whether ambient buffer or vacuum. Anyone who looks at this closely will see what I mean.

[Fool]

I get the benefit of a hot expansion piston. PP and DP are both hot, AKA Essex. And in that, the hot is pushed into the cold during compression through the regenerator. Seems excellent to me.

I'm wondering about having a very large displacer volume, so much so, that the expansion is done at almost constant pressure? There would only be a slight difference between cold PP and hot PP. Right?

It seems to me that is what is happening for the little pancake displacer LTD that we discuss here. Very little compression.

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[VincentG]

My favorite part is that cold compression graphic. The power piston has a 50% volume reduction but only ~25% air mass reduction, illuminating just how far we may be able to increase PP to DP ratio, and just how small transfer ports can be.

Matt, it would be nice if you added notes to indicate just how cold the gas wants to get when it's expanding into the cold space (before backflow heat from sink).

[Fool]

Good points.

I think he is assuming constant temperature expansion and compression.

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[matt brown]

I think he is assuming constant temperature expansion and compression.

Indeed isothermal and all the other Schmidt stuff. To recap

duplex gas flow.png (24.77 KiB) Viewed 2295 times

Did anyone notice upper half is Essex ???

Essex upper half of duplex.png (8.11 KiB) Viewed 2295 times

The volume change in Essex is a nobrainer wherein heat and work are easy to follow. However, this duplex scheme is a tad out there since this 800-1600cc expansion entails 'dual' sweeps with a total 1600cc 'swept' volume, not 800cc. This is where the 2 expansions come from and why the 'first' 800cc sweep is driven by DP source input while the 'second' 800cc sweep is driven by PP sink input (ambient backflow).

This scheme is gaming the rather obscure fact that 2 different temperature volumes have the same isothermal Q and W values when both have the same pressure/ratio and volume/ratio. 100cc of 300k and 600k gas have the same isothermal Q and W inputs and outputs when the same pressure since 600k gas has 2x "everything" per mole than 300k gas, but the 600k gas has only 1/2 the moles per volume vs the 300k gas (I'm avoiding specific vs relative volume to nix confusion).

duplex values.png (10.67 KiB) Viewed 2295 times

Essex values yield typical Carnot=.50 inline 300-600k cycle. My premise for this duplex scheme is that 2x Qin = 2x Wout during expansion and that 1x Win = 1x Qout during compression. In this manner, the duplex has Carnot=.50 just like the Essex, but if we remove the 'free' ambient input then Carnot=1.0 per last pair of rows.

I still have some doubts about this scheme (not to mention actual mech req'd) so consider it a work in progress. But wait, there's more, a variation that I expect Vincent saw...

Ericsson duplex.png (12.32 KiB) Viewed 2295 times

the old double-diameter piston (a la Ericsson) that allows a wider range of gaming values. More later...

[matt brown]

Here's the simple version of this duplex scheme devoid of most notation

duplex unbundled.png (7.9 KiB) Viewed 2159 times

duplex bundled.png (7.09 KiB) Viewed 2159 times

The 1st graphic is the "unbundled" duplex where the upper half is an Essex with Carnot=.50 and the lower half is an isothermal "gas spring".

The 2nd graphic is the "bundled" duplex where something has changed despite identical PVT values. Can anyone spot this fuzzy difference ???

[Fool]

The two pistons are solidly connected in the second bundle?

[matt brown]

The two pistons are solidly connected in the second bundle?

That's not "fuzzy", but this is...

compression detail.png (9.45 KiB) Viewed 2025 times

Check out this side-by-side graphic of compression phase where internal PVT values are the same for both, but external "unbundled" PVT values are altered via "bundled" cylinders. We're used to simple single-acting pistons where the pressure differential between each piston's faces yields a simple integral. However, when combined, things quickly becomes more complex. With that said, have another look...

[Fool]

I'm stumped. Sorry.