Another Stirling gamma anomaly under the radar

[matt brown]

Hmmm, the devil is in the details...

compression detail_2.png (18.01 KiB) Viewed 2207 times

Consider 'unbundled' cylinders as A vs 'bundled' cylinders as B. Per graphic, A has constant 1 bar ambient pressure under P1 with upper volume A akin Essex. This "cold stroke" is not a free lunch and required for Essex to achieve Carnot=.50 from a 300-600k cycle. This Wpos during "compression" merely offsets SOME of the Wneg during expansion from 1 bar ambient back pressure. Without resorting to boring math, this minor Wpos during compression "fills in the integral" of Essex Wpos during expansion from 2 to 1 bar, whereby Essex expansion is similar to constant 2 bar expansion fighting constant 1 bar ambient back pressure. Most guys overlook that common single-acting pistons have a declining pressure during expansion that is opposed by a constant back pressure !!!

Returning to the graphic, the lower volume A has a constant 1 bar back pressure over P2. However, by removing P2 in B, the initial back pressure on the lower volume is reduced from 1 bar in A to .5 bar in B. And by B-4, the back pressure on the lower volume remains reduced by 2 (equal A-4) but the driving pressure on the upper volume has increased by 2 (vs A-4). Thus, upper volume B produces more Wpos during compression than upper volume A while lower volume B requires less Wneg than lower volume A.

[Fool]

Okay, I think I'm getting it. You have a two area piston. Back driving a larger piston with 1 bar, produces up to 2 bars of back drive internally.

Wouldn't that completely eliminate any forward drive by your 2 bar max pressure?

.

[matt brown]

The note in previous graphic
"B removes the constant 1 bar pressure under P1 via removing P2 whereby work increases."

should read
"B removes the constant 1 bar pressure over P2 via removing P2 whereby work increases."

I agree, confusing as hell vs common ECE. The gamma anomaly that this thread is named after is a moving target. I still can't clearly describe it except that some PVT ratios I'm familiar with gaming ECE have occasional SE "irregularities" that defy logic. No biggie, until I was chasing values on that Ian-Hall model, I gained some "irregular" insight. I'm staying with this low pressure/ambient scheme until I have it figured out, then I'll compare it to "vacuum" model and multi-bar charge variants.

duplex bundled.png (7.09 KiB) Viewed 2067 times

Fool wrote "Wouldn't that completely eliminate any forward drive by your 2 bar max pressure?"

I assume you mean during expansion. In above graphic, both volumes have equal pressure during expansion, but lower piston has 2x area of upper piston. Allowing for unshown clearance volume at bottom of cold volume frame 1, I'd relate both faces of upper piston as cross-canceling due to equal pressure. However, the unequal pressure during compression does not have this simple cross-canceling relationship. Oddly, during compression, upper volume pressure is always 1/2 lower volume pressure.

I'll stop here before I step on my tail since I just spotted something else about these pistons. Thanks for the feedback.

[Fool]

I think you just caught what I was trying to say, even though I said it poorly. I'll leave you alone. Suffice it to say I meant it a little differently. Sorry.

[VincentG]

Not sure I get the point Matt. Are you trying to game the benefits of Essex hot piston expansion and the ambient heat backflow of cold connected Gamma? Wouldn't the area above the larger piston need to drop below 1 bar to get ambient backflow?

[matt brown]

duplex unbundled.png (7.9 KiB) Viewed 2007 times

Vincent - In this graphic, the top sequence is an Essex and the 3-4 "cold stroke" is required to achieve Carnot=.50 from this 300-600k cycle, it's not a free lunch. This Wpos from ambient pressure during compression only cross-cancels Wneg from ambient pressure during expansion. It's the well trodden issue where buffer pressure doesn't effect Wnet per cycle, but does effect Wpos per process.

Meanwhile, the lower volume here is an oscillating volume where heat in=work out during expansion, and work out=heat in during compression. My gimmick is noting that the constant 1 bar ambient pressure over the small piston in the lower sequence can be reduced by combining these 2 small pistons, whereby the pressure over the lower volume drops from 1 bar (ambient) to .5 bar, thus gaining a free lunch.

I need to fluff all these graphics to include piston numbers, etc.

[matt brown]

When the 2 bar 300k volume expands, it attempts cooling just like an air compressor feeding an air tool. As I mentioned earlier in this thread, any 2 bar 600k volume has the same heat in_heat out_work in_work out potential as an equal 2 bar 300k volume simply due that the 600k volume has 2x the gas mass of the 300k volume. Yep, this is always a head banger since our perception of 300k is less than 600k simply due to we're surrounded by 300k. This relative fact is up there with an infinite isothermal expansion having constant internal energy.

During 1-2 expansion above, both 2 bar volumes suck in the same quantity of heat and produce the same work, albeit 600k is a different animal than 300k. However, I'm starting to see some piston details that I missed during previous comms relating to "bundled" cylinders. As I said, a work in progress and Jeez, what a rabbit hole...

[matt brown]

duplex unbundled.png


Meanwhile, the lower volume here is an oscillating volume where heat in=work out during expansion, and work out=heat in during compression. My gimmick is noting that the constant 1 bar ambient pressure over the small piston in the lower sequence can be reduced by combining these 2 small pistons, whereby the pressure over the lower volume drops from 1 bar (ambient) to .5 bar, thus gaining a free lunch.

I just can't peck away without an occasional error [...]

"Meanwhile, the lower volume here is an oscillating volume where [heat in=work out during expansion, and work out=heat in during compression]."

should read...heat in=work out during expansion, and work in=heat out during compression

[matt brown]

Not sure I get the point Matt. Are you trying to game the benefits of Essex hot piston expansion and the ambient heat backflow of cold connected Gamma? Wouldn't the area above the larger piston need to drop below 1 bar to get ambient backflow?

During expansion, the 2 bar 300k volume doubles, whereby an adiabatic expansion would have pressure decrease by 2.64 and temperature decrease by 1.32 for air (diatomic). A sharp eye will catch this relationship dP=dV(dT) where d=delta.

Therefore, this meager 1:2 adiabatic expansion from 2 bar 300k would result in .7575 bar 227k. Meanwhile, the same 1:2 adiabatic expansion from 2 bar 600k would result in .7575 bar 455k.

[matt brown]

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).

Vincent - sorry for delayed response, could you clarify your

"The power piston has a 50% volume reduction but only ~25% air mass reduction"

is it somewhere in here?

300-450k compression.png (18.51 KiB) Viewed 1989 times

[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).

Vincent - sorry for delayed response, could you clarify your

"The power piston has a 50% volume reduction but only ~25% air mass reduction"

is it somewhere in here?


300-450k compression.png

Yup, moving from 2x zero point to Ian hall and looking at the power piston.

[matt brown]

Feast your Vulcan squinties on this...

Ian-Hall T drop_1.png (28.4 KiB) Viewed 1803 times

I fluffed the Ian-Hall graphic a tad

(1) PP volumes show adiabatic expansion T drop per segment as isolated volumes (no ambient sink input)

(2) DP left intact except to show adiabatic expansion T drop thruout DP (no source input)

Ian-Hall T drop_2.png (25.5 KiB) Viewed 1803 times

Here's a detail of how I did this. I took a conservative approach where I ignored the expansion in transit (purple volumes) and considered adiabatic expansion T drop after each volume was fully transferred. IOW volume A leaves DP at 100cc 450k and passes thru regen to become 66cc 300k, then expands to 80cc 300k. I ignore this 66-80ccc "transit" expansion since it's not a single volume. I've tried several unsuccessful math models to capture these transfer values, but already know these are minor differences.

Top graphic is a tad misleading, since DP values do NOT coincide PP values (both 'sets' never occur simultaneously) but I'm on track to chasing down work values. In my anomaly thread, I mention that 2 unique temperature volumes have the same heat in and work out during expansion when equal pressure and volume differential (expansion ratio). Therefore, we know that the 300k PP volume/s and 450k DP volume/s will have the same heat in and work out proportional to their volume. So...by frame 3 where DP=600cc and PP=200cc then DP source heat input is 3x PP sink heat input, and by frame 4 where DP=600cc ('unchanged') and PP=400cc then DP source heat input is now only 1.5x PP sink input.

Interestingly, by frame 5 PP sink heat input exceeds DP source heat input. Note that the adiabatic expansion T drop in DP (no source heat input) is 290k which is less that PP 300k. I expect this means that any further work of expansion will be lost to compression and suspected such a "cross-over" would appear. Just a hipshot that I'll get around to chasing down.

The takeaway here is that less input comes from source than commonly thought (450k isothermal vs 450-290k adiabatic) and more input comes from sink than common thought where DP vs PP heat in and work out will vary by DP vs PP volume per any given thermal cycle, just like Vincent suspects (wink-wink).

Hey Fool - how's that for creative RA - LOL

[Tom Booth]

duplex unbundled.png


Meanwhile, the lower volume here is an oscillating volume where heat in=work out during expansion, and work out=heat in during compression. My gimmick is noting that the constant 1 bar ambient pressure over the small piston in the lower sequence can be reduced by combining these 2 small pistons, whereby the pressure over the lower volume drops from 1 bar (ambient) to .5 bar, thus gaining a free lunch.

I just can't peck away without an occasional error [...]

"Meanwhile, the lower volume here is an oscillating volume where [heat in=work out during expansion, and work out=heat in during compression]."

should read...heat in=work out during expansion, and work in=heat out during compression

I thought you had it more or less right the first time.

If you have this heat backflow from the sink you guys have been talking about.

[matt brown]

I thought you had it more or less right the first time.

If you have this heat backflow from the sink you guys have been talking about.

I'll have to go back and check, but I thought my correction was right. Heck, this gamma chase is nuts, but it should settle several things. The odd thing about my technique is that it's extremely simple and devoid of math except for working the ideal gas law. If you favor conspiracy, it's hard to believe Uncle Sugar does know this already since it's not rocket science. On the other hand, they're fairly braindead.

My ECE interest in not Stirling, but when so, it's alpha. Vincent got me into my gamma deep dive, but the real thing that led me here is that Hall video with enough info (albeit fuzzy in freeze frame) that I focused on his engine (what I call the Ian-Hall model). Someone (staska?) mentioned a while back that anyone can make a working SE with these DP/PP ratios and 500C input, but dismissed it as lacking power. Hmmm, I assume he considers "higher" input = higher output.

[matt brown]

Here's a 300-360k "LTD" scheme for Vincent...

300-360k LTD.png (19.82 KiB) Viewed 1748 times

The gas flow here is similar upthread Ian-Hall model, but this is largely due that I opted to continue with my esoteric 6m gas volumes. I also continue with my same 1 bar Vmin Tlow used thruout this thread. So, by frame 5 the .4 bar pressure is lame and that's before the displacer reverses. So, a more realistic approach is to simply double all of these bar values, whereby (unshown) Vmin Tlow is 2 bar (aka 2 bar charge). Nevertheless, I suspect by frame 5 that gas flow is waaay past the "cross-over" point where any expansion work will be less than proportional compression work 'later' in cycle.

At a glance this looks just like the Ian-Hall model. No hanky-panky, I only resized graphic to capture that massive 1000cc PP in single frame without needing grandma's reading glasses to view. Like everything else these days, this is a work in progress. Once I figure out heat vs work for Ian-Hall model then I hope to have a little equation that I can apply to these other schemes. Until then, I'll let Carnot sleep...