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Hey Fool, is this rigorous enough (note values carefully)




Vincent made some keen observations with his Essex engine that just needed an oldtimer to sort out. This graphic is my hipshot 300-600k cycle with double dwell, but rest assured I'm gaming this sucker big time. It reminds me of my ancient 'slingshot' alpha scheme that I never followed up with gamma versions.

Thanks to Vincent, I have another rabbit hole...

Follow me to find the rabbits lol.

.4 bar on the low end, can that be?

VincentG wrote: ↑Wed Jul 10, 2024 6:04 am Follow me to find the rabbits lol.

It's a long and winding road among many holes.

VincentG wrote: ↑Wed Jul 10, 2024 6:04 am .4 bar on the low end, can that be?

I doubt it since P values are inter-related to V values and I don't know actual Essex V values. I included the Essex "scale" to show what values would be via 1 bar charge when DP Vmin cold.

The PVT sequence under the cylinder is the main takeaway where the only Wneg is between the bottom and top "frames". There's definitely something going on here, but I only partially have figured it out. This evolved from comping hot vs cold gamma where certain values yielded logical results, yet other values appeared crazy.

in Trekkie buzz:

Chekov: "Captain, sensors detect an alien presence"
Kirk: "Spock, what is it ?"
Spock: "a subspace anomaly of unknown origin"
Kirk: "does it pose a threat ?"
Spock: "like the Thorian Web, Jim ?"
Kirk: "Scotty, give us all the power you've got"
Scotty: "I'm working on it..."

My small addition - it is beta hot end connected. Not gamma ?

Yes, hot beta. Ignore the double dwell, there is something else about this cycle...

Well talk about a textbook Stirling cycle.

VincentG wrote: ↑Thu Jul 11, 2024 7:37 am Well talk about a textbook Stirling cycle.

If you have a textbook anything like this, please share. To kick this can further down the road...


where TX represents unknown "textbook" hot PP beta vs EX represents my "Essex" hot PP beta. Both are 300-600k cycles with zero buffer pressure (aka vacuum). Furthermore, both are depicted as ideal everything with double dwells.

Although both are betas where DP and PP overlap, TX has an irregular motion DP vs PP which I'd characterize as DP leads PP by 270 deg (from PP at TDC). Meanwhile EX has a regular motion DP vs PP which I'd characterize as PP leads DP by 240 deg (from PP at TDC). Now, the fun part...TX has a 90deg dwell for DP and PP vs EX has a 60deg dwell for DP and PP.

TX has an obvious flaw where DP stroke exceeds PP stroke, but let's ignore that major caveat. Instead, let's focus on the similarities where both have the same Carnot efficiency from the same 300-600k thermal cycle, but EX produces more power from greater expansion (don't let the 2 red bar max fool ya). The main difference thermally between these 2 is TX process C vs EX processes C1-C2-C3. For EX, C2 process (180-240deg) could have DP 'run all the way over' to PP at BDC, whereby at 240deg, P=.66 bar vs .8 bar per graphic, but this would screw up the otherwise regular motion. However, if .66 bar at 240deg, then C3 work = 1neg and Carnot=.50 so .80 bar at 240deg looses a tad to Carnot. This difference is denoted by the question mark, but really just hair-splitting.

An interesting takeaway is that during C3 process, no backwork would yield Carnot=.66 yet the most ideal "tiny" .66 bar to 1 bar compression sinks cycle to Carnot=.50

If EX looks textbook, it's because an ideal 60deg dwell approaches the real far faster than any ideal 90deg dwell.

Oops, didn't mean the kinematics look text book. I mean the values are similar to what I was gaming as a perfectly ideal Stirling cycle here.

1 to 1 power piston to displacer volume
Displacer = 100cc
Power piston= 100cc
Buffer charge= .004 moles(150cc @14.7psi @450k)
Internal pressure TDC @300k= 14.7psi(zero point) No compression work.
Internal pressure TDC @600k= 30psi
Net hot stroke pressure= 15psi

Internal pressure BDC @600k= 14.4psi(zero point) No expansion work.
Internal pressure BDC @300k= 7.2psi
Net cold stroke pressure= -7.2psi

matt brown wrote: ↑Sun Jul 14, 2024 12:42 am

If you have a textbook anything like this, please share. To kick this can further down the road...

Just my all text book says hot end connected beta same pv as normal beta. Cause you can draw it anyway - power pistom from any side of displacer will see same pressure on expansion. Especialy if one imagine it as ringbom beta, where didplacer rides on power piston.

VincentG wrote: ↑Sun Jul 14, 2024 1:37 pm Oops, didn't mean the kinematics look text book. I mean the values are similar to what I was gaming as a perfectly ideal Stirling cycle here.

1 to 1 power piston to displacer volume
Displacer = 100cc
Power piston= 100cc
Buffer charge= .004 moles(150cc @14.7psi @450k)
Internal pressure TDC @300k= 14.7psi(zero point) No compression work.
Internal pressure TDC @600k= 30psi
Net hot stroke pressure= 15psi

Internal pressure BDC @600k= 14.4psi(zero point) No expansion work.
Internal pressure BDC @300k= 7.2psi
Net cold stroke pressure= -7.2psi

Nice values for simple DIY scheme but you made 1 minor error that we all have before..."buffer charge" should be charge P or charge mass (buffer is outside engine vs charge is inside engine). No worries, we get it. Most important is your rock solid .004 moles per 100cc at 300k which few guys know !!!

Hmmm ye olde "sq cycle" with Tr=Vr=Pr but where pts 1 and 3 are an ambient isobar

staska wrote: ↑Sun Jul 14, 2024 2:12 pm
Just my all text book says hot end connected beta same pv as normal beta. Cause you can draw it anyway - power piston from any side of displacer will see same pressure on expansion. Especially if one imagine it as ringbom beta, where displacer rides on power piston.

I'm a long time alpha guy when Stirling. Vincent got me into cold PP gamma last year and recently into hot PP beta via his Essex engine. The way I approach thermo takes me a long time to 'connect the dots'. For now, I will avoid ringbom (time constraint). I find the similarities vs dis-similarities among these engines very interesting and think Organ missed many details.

Matt is plotting a realistic representation of hot vs. cold Gamma(or Beta). A cold connected engine just can't compete in terms of power per total volume.

Any analysis that claims they are the same is significantly flawed, imo.

staska wrote: ↑Sun Jul 14, 2024 2:12 pm

matt brown wrote: ↑Sun Jul 14, 2024 12:42 am

If you have a textbook anything like this, please share. To kick this can further down the road...

Just my all text book says hot end connected beta same pv as normal beta. Cause you can draw it anyway - power pistom from any side of displacer will see same pressure on expansion. Especialy if one imagine it as ringbom beta, where didplacer rides on power piston.

Matt Brown wrote:Hey Fool, is this rigorous enough (note values carefully)

It's easy enough to follow. Leaves nothing to argue. Two thumbs up. Five star.

The benefit of the Essex is less dead space.

A hot piston has a hot expansion, cold gas rushes into the hot space through the regenerator.

Cold pistons expand the dead space in the cold space, and hot gas rushes into the cold space through the regenerator.

Hot pistons push the hot gas through the regenerator to be compressed in the cold space.

Hot expansion allows more work from the power stroke, while increasing the compression back work very little.

The drawback is increased temperature materials and seals. Possible higher friction. Maybe a very long piston could compensate.

Your cartoons engineering diagrams are very useful and depict the cycle well. It could use a PV diagram too. I like them.