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I thought you guys might find this amusing. As I continue my deep dive into gammas, I'm finding a lot of stuff that I've never seen mentioned. Today's tidbit comes from a parametric study on total displacer volume vs displacer swept volume vs power piston swept volume. To simplify stuff, I'll refer to the displacer volumes as simply DP and power piston volume as PP. No doubt, we've all seen gammas like this and wondered how efficient this gamma could be with all that "dead volume" in the heater.


Yep, even typical NASA grade gamma has a relatively massive heater volume. I decided to check this out by comparing various volumes. I took my favorite 300-600k cycle and considered DP vol 2x PP vol where 100% of DP vol was swept. Next, I considered same vols, but where only the UPPER 1/2 of DP vol was swept, only to discover you never want to do this. Then, I considered same vols, but where only the LOWER 1/2 of DP vol was swept, and was surprised that this wasn't anything like previous upper 1/2 mess. So, I continued exploring this option by expanding PP vol, but this was inconclusive, since the 2:1 DP:PP vol was also the 2:1 thermal ratio at first, but now these were out of sync (a future study). Anyways, here's what I have for now...


I stripped out the actual values I used to minimize the clutter, but here's 3 samples that compare interestingly. All 3 cycles (ABC) have the same 2:1 thermal cycle (300-600k) AND 2:1 swept vol DP:PP. The only "major" difference is the ratio of hot:cold space in displacer "cylinder" and the effect this has on other values. The windows have the key info, but the most important is that all 3 cycles have the same ratio of regen gas mass to PP gas mass, so there's no difference between these 3 cycles with output vs regen efficiency (each unit of output requires the same amount of regen). So, despite Tom's endless harping on the impossibility of isothermal heating, cycle C has a constant massive hot reservoir to draw from (vs cycle A which at times has none) and at no cost to efficiency.


I opted to use a "square" cycle where the pressure after expansion equals the pressure after compression.




A cycle like this where pt 4 is lower than pt 2 indicates a cycle where Vr>Tr and free piston DP is not possible.



This is an xlnt example of free piston PV where output is only achieved via high Tr and mega bar charge pressure (aka NASA type).

In your spreadsheet diagram, do the purple sections indicate dead-space?

This effect should be even greater at higher temperatures no? It seems that the hot space dead volume, being higher pressure AND containing far less gass molecules, keeps to itself so to speak and does not impact efficiency as it is calculated.

Is that the basic mechanism here?

matt brown wrote: ↑Fri Aug 11, 2023 12:42 am
(...). Today's tidbit comes from a parametric study on total displacer volume vs displacer swept volume vs power piston swept volume. To simplify stuff, I'll refer to the displacer volumes as simply DP and power piston volume as PP. ...

Have you been using this convention all along, or in previous posts?

I might need to re-read some of your posts because I'm sure I took DP and PP as simply displacer piston and power piston.

This could also be ambiguous displacer Pressure power piston Pressure. Without this explanation, I'm sure I would never have taken DP and PP as Volumes. (Unless that was explicitly stated as DP volume etc )

Dv, PV maybe might be less ambiguous Vs Dp, Pp ?

Anyway, I'll have to reread, reinterpret previous posts if you've been using this consistently, but I don't know that either.

matt brown wrote: ↑Fri Aug 11, 2023 12:42 am (...)
So, despite Tom's endless harping on the impossibility of isothermal heating, ...

I'm simply going by what I have read and have seen reaffirmed hundreds if not literally thousands of times in thermodynamics literature, textbooks, online resources etc. Often it is stated as part of the very definition of "isothermal".

One quick example from the first page of Google search results.

https://www.jagranjosh.com/articles/iso ... ractically.

So the fact that an isothermal process is not possible or practical in a real engine does not originate with me, it's just a widely recognized fact. You are certainly free to try and challenge that but on my own threads, I'm discussing Real engines and Real experiments and trying to research how Stirling engines REALLY operate in the real world, so when you constantly come into such a discussion about an ACTUAL experiment and actual observable results you may not like or agree with, using these arguments based on isothermal processes, I really have no option other than to point out that such isothermal processes or cycles are not real.

You and others are constantly "harping on" these idealized processes.

That isothermal processes in an engine are not possible or practical is not a consequence of "Tom's endless harping", ITS IN ALL THE TEXTBOOKS.

matt brown wrote: ↑Fri Aug 11, 2023 12:42 am (...)
...Today's tidbit comes from a parametric study on total displacer volume vs displacer swept volume vs power piston swept volume. ...

I'm not entirely clear what the distinction is between "total displacer volume" and "displacer swept volume".

In a typical LTD there is no difference.

Your picture appears to show an Alpha.

In a typical Alpha the regenerator and connective piping are between the hot cylinder and cold cylinder, so, to which cylinder or piston volume does this essentially shared space actually belong?

Should the "heater head" be included with the displacer volume exclusively?

In reality all of the "volumes" are interconnected.

You say: "cycle C has a constant massive hot reservoir to draw from".

What do you mean by "reservoir to draw from".?

The bright red colored area, I would assume to be the hot gas in the heater head pipes. This gas is already expanded hot gas so I'm not sure in what sense this could be "drawn from".

The narrow purple bit on the side I assume is a regenerator.

I'm not trying to contest or refute whatever you are presenting here as I don't yet understand what it is you are saying enough to have any opinion about it one way or the other.

Probably I'd have nothing to say on this topic if not for your dig: "So, despite Tom's endless harping on the impossibility of isothermal heating, cycle C has a constant massive hot reservoir to draw from (vs cycle A which at times has none) and at no cost to efficiency."

This appears to be another effort at refuting Tom Booth and or countering my experiments/conclusions/statements/opinions or whatever

For example I recognize that air being compressible, "dead air space" is generally recognized as detrimental, potentially or inevitably resulting in lower efficiency.

In an extreme case, the gas might simply be compressed, or "compress itself" rather than move the piston in the cylinder. In that case there would be zero power output, zero work, and only a pressure fluctuation, if the engine were forced to move, as in an attempted but failed startup.

I've experienced this "dead air" phenomenon when working with pneumatics, pressure switches.

On some bathtubs for example with water jets, a pressure switch is used to avoid having an electric switch near a bath, for obvious reasons, you don't want to mix electricity and water so a pneumatic switch is used.

Press a button, which is really like a plunger, similar to a syringe.

Pushing this button/plunger, pushes air through a rigid tube to actuate the actual electrical switch.

If the tube is too long, too much "dead air space" the switch will not work because the air is simply compressed in the tube and nothing happens at the electrical end of the tube.

If a greater distance is necessary sometimes a thinner tube can be used to reduce the volume of air.

The compressibility of air is real, and too much "dead air space" can have real consequences.

For this compressibility to show up in the math, you would actually have to include some "compressibility factor" into the math, otherwise, obviously, it isn't going to show up in the math.

Matt, the “A-B-C” graph shows both pistons topped out so I’m guessing you’re dispensing with the usual 90 degree linkage and are assuming full displacer travel, then full power piston travel, and so on. So in the position shown, the displacer is about to move the air to the hot side and then the power piston will stroke, but that seems to be out of phase with some of the description. That’s possibly some dyslexia on my part; but I’m sorta with Tom about some of your wording and abbreviations being a bit difficult to decipher. Swept volume ratio by itself isn’t that meaningful, you have to add swept volume and dead space together compared to power stroke volume to get the compression ratio, then that’s what determines (or is determined by) the temperature ratio. I’m pretty sure you know all that, but you seem to gloss over dead space as some triviality to be addressed another day. Anyway, I’m still looking for the relevance here; it seems it would take infinite dead space, and thus no power, to get fully isothermal heating. I’m still waiting for that”Ahah!” moment to see what you’re getting at though.

Bumpkin

VincentG wrote: ↑Fri Aug 11, 2023 4:18 am This effect should be even greater at higher temperatures no? It seems that the hot space dead volume, being higher pressure AND containing far less gass molecules, keeps to itself so to speak and does not impact efficiency as it is calculated.

Is that the basic mechanism here?

Vincent nailed it, the hot space "keeps to itself" !!! Awesome wording that escaped me, but this does appear to be what's happening where the red space blinds us like Al Gore and his gold bars.


https://vimeo.com/132709990

I was rushing to get that post all up before being timed out, then my connection crashed before I could make some edits.

This is from a parametric study I'm doing where the focus is on volumes. This is not an actual engine, but only a comparison on the process values as they relate to displacer and power piston volumes. Consider this a solar1 style gamma (vs LTD) where there's 2 cylinders connected by a small transfer tube. Forget typical 90 deg phasing and focus on the processes at hand. So, yeah, I'm tinkerbell with a magic wand that can control all mechanical motions.

The purple regen and the blue transfer tube will be considered zero volume, since I only was concerned about the main volumes. Consider all 3 have 100cc PP cyl and all 3 PP sweep 100cc. Next, consider all 3 have a DP that sweeps 200cc. Now, the weird part: A has 200cc DPcyl, B has 400cc DPcyl, C has 800cc DPcyl.

The swept volume ratio (in cc) between DP and PP remains 2:1 (200cc:100cc) but the swept volume ratio within each DP cyl varies. All 3 have 200cc cold space in DPcyl, but hot space in each DPcyl varies: A=200cc, B=400cc, C=800cc. So, DP in A sweeps 100% DPcyl, but DP in B sweeps 50% DPcyl, and DP in C sweeps 25% DPcyl. Interestingly, this A=100%, B=50%, C=25% swept ratio in respective DP cyl just happens to be the pressure swing between pictured start state and prior expansion (after "first" regen when DP reaches BDC).

The red in graphic sucks us in like a bug to a light in the darkness, but this is deceiving. Yes, there's thermal issues at hand, but pressure drives the engine and the pressure is (assumed) uniform thruout engine. Again, the 2:1 DP:PP swept volume ratio coincides the 2:1 thermal ratio (300-600k) so I'll continue gaming this to see where it goes. But the main takeaway is that I'm not seeing any efficiency loss when DP sweeps less than 100% of DPcyl as long as this partial sweep is the "lower" region of DPcyl. As long as the cycle includes DP reaching BDC of DPcyl, everything appears similar. The biggest difference is that A transfers 1/2 its gas from DPcyl to DPcyl vs B transfers 1/3 vs C transfers 1/5, so C will have less relative output. However, all 3 appear to have the same 2:1 ratio of regen gas (in DPcyl) to working gas (in PPcyl). I need to verify this from another angle, but for now, I think it's just another 2:1 ratio coinciding the 2:1 thermal ratio.

What does this mean ??? Well, we can can have a large heater at no efficiency cost which allows a better heat "buffer" due to greater (continual) hot gas mass AND greater surface area for heating.

I'm also looking into similar cold space "dead volume" and think that it's also overblown. What this really proves is that mechanical issues are paramount and any out-of-phase mech is a loser.

Tom Booth wrote: ↑Fri Aug 11, 2023 5:02 am

matt brown wrote: ↑Fri Aug 11, 2023 12:42 am
(...). Today's tidbit comes from a parametric study on total displacer volume vs displacer swept volume vs power piston swept volume. To simplify stuff, I'll refer to the displacer volumes as simply DP and power piston volume as PP. ...

Have you been using this convention all along, or in previous posts?

I might need to re-read some of your posts because I'm sure I took DP and PP as simply displacer piston and power piston.

This could also be ambiguous displacer Pressure power piston Pressure. Without this explanation, I'm sure I would never have taken DP and PP as Volumes. (Unless that was explicitly stated as DP volume etc )

Dv, PV maybe might be less ambiguous Vs Dp, Pp ?

Anyway, I'll have to reread, reinterpret previous posts if you've been using this consistently, but I don't know that either.

It was due to posting time constraint which I hope recent post clarified.

Tom Booth wrote: ↑Fri Aug 11, 2023 5:45 am

matt brown wrote: ↑Fri Aug 11, 2023 12:42 am (...)
So, despite Tom's endless harping on the impossibility of isothermal heating, ...

I'm simply going by what I have read and have seen reaffirmed hundreds if not literally thousands of times in thermodynamics literature, textbooks, online resources etc. Often it is stated as part of the very definition of "isothermal".

Indeed, isothermal is dreadfully slow, but thermo is loaded with constraints. I'm always looking for wiggle room, and when I saw some with the gamma, I started a new chase...

Here's 2 comparisons from my hot space:cold space study. Note PVT values with "m" (abstract gas mass) included, but I removed some 'cold space' displacer values to reduce clutter. Anyway, PVTm values ignore regen and transfer tube volumes AND hot and cold space clearance volumes. I kept a few constants (1) 300-600k cycle (2) 6m gas mass (3) 2:1 DP:PP swept volume (4) 6 bar after initial regen (stg 2)

Why Tom thinks such a mech is impossible is beyond me, since it's nothing more than the "double dwell" idea that he and Vincent floated months ago. My pitch is simply adding some appropriate calcs to inspire where guys could go AFTER solving dwell issue.

And Tom, note that there's no "heat" directly producing PP work. To paraphrase Al Gore...ummm, I sure would like to get my hands on some of that red hot high pressure gas. The whole temperature thing is overblown and apparently only Vincent gets it.

Matt, I'm a bit confused here. Something I've been harping on from time to time is to consider the "neutral" state of a Stirling engine. I would consider graphic B4 to be the neutral state(3 bar, displacer and power piston in middle position). It seems you are counting the power piston volume as cold space here, but I'm not so sure this is accurate.

Graphic A2 shows the peak pressure state the engine will see as 6 bar.

Conversely, A4 shows the minimum pressure state the engine will see as 2 bar, where one might expect less.

I think it would be more realistic to count the power piston volume as half hot space and half cold space at graphic B4.

But then to my way of thinking, a balanced Stirling engine with 3 bar at position B4 will only reach 5.62 bar at position A2. Thats 3 bar x 1.25(pp back to TDC) x 1.5(from B4 neutral state of 450k to 600k)= 5.62bar.

matt brown wrote: ↑Sun Aug 13, 2023 7:35 pm (...)

Why Tom thinks such a mech is impossible is beyond me, (...)

As far as I know, this is something new you just now put forward, so how you think that I think it's impossible is beyond me.