Calculating volume ratios using PV=nRT

[VincentG]

Here's the click bait version...Given ideal conditions(and I'll explain below why they are achievable) in a 300k to 600k Gamma cycle, compression and expansion work does not even start until the displacer swept volume is smaller than power piston swept volume. In other words, less than 1:1.

For this I am going to assume my theory in this thread is true. viewtopic.php?f=1&t=5561 Furthermore, I'm going to assume some other "ideals". That is mainly having enough heat sink capacity to reach near isothermal values as the power piston moves from high volume to low volume. The other ideal is that the gas inside the engine is reaching a high of 600 and a low of 300. This is definitely doable, even if the hot end needs to be a good bit higher to reach a true 300k delta.

We will be using PV=nRT to illustrate this given a known delta T, displacer and power piston displacement.

Displacer = 100cc
Power piston= 100cc

Lets start by calculating the moles of gas in our engine at 450k and power piston at MDC, or 150cc total volume. We get .004 mol.

Now when we figure the volume of .004 mol at 300k we get 100cc

So then at 600k we of course get 200cc.

What this suggests is that given our (not so far-fetched at low rpm) ideal constraints at a 1:1 swept volume ratio, an engine at operating temperature actually loses zero work to compression and expansion of the gas. So to gain efficiency, we must reduce the volume of the displacer even further.

What's really interesting to me, is that an LTD with a 60:1 volume ratio running on about a 10F delta is actually at about this zero point of compression and expansion.

Now, I'm sure there is a bunch of high level math that I am leaving out, but why not construct such an engine and do some testing on it? For my little LTD in this thread viewtopic.php?f=1&t=5570 , I've determined that for a delta of Tmin=50F and Tmax=250F, I need roughly 15cc of power piston displacement to get to this "zero point".

I am using chat GPT to help me work out a formula to quickly find this zero point, given basic temperature and displacement constraints.

[matt brown]

From Vincent's linked post...
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We'll start with the basic 300k-600k cycle.

Now for the hypothetical. Bob is our engine builder, and he lives on a planet that has an atmospheric condition of 450k at 14.7psi. This planet happens to have 300k ground water, and abundant geothermal hot springs of 600k.

Bob says, "Wow, I have free heating AND cooling available to influence my atmospheric conditions".

Bob builds a Gamma type engine, and lets its internal pressure equalize with his atmosphere while the power piston is in the middle of its stroke. In this way the engine at base temperature will have internal pressure>atm at TDC, and internal pressure<atm at BDC. In this way Bob has created a perfectly balanced compression and expansion ratio.
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Sq cycle.jpg (67.12 KiB) Viewed 12575 times

Bob has various engine options (and no electric bill). If 1-2 is 300k isothermal compression, point 3 could be 600k, and 3-4 could be 600k isothermal expansion. However, if adiabatic expansion, then 1-2-3 cycle with 3-1 expansion is possible (aka Green cycle). Another possibility is a 2-3-4 Lenoir cycle.

Returning to this thread, I'm a tad lost. When closed cycle, PV=nRT usually reduces to simply PV=T since the number of moles remains constant, and the gas constant R is irrelevant except for finite calcs (like energy). OK, so .004 moles per 100cc at STP, now what...

[VincentG]

Put simply, throw away the idea of adiabatic expansion and compression.

Consider the only time the gas temperature changes is when the power piston is dwelling at TDC and BDC.

Other than that, assume constant gas temperature with ideal heat input and removal.

[matt brown]

So are you scheming something similar this where the line is 1 bar...

forced work PV plot.png (31.14 KiB) Viewed 12568 times

[matt brown]

This is from a study gaming minimal Wneg similar Hall video and Tom's drumbeat.

[VincentG]

Yes the line indicates the original state of the gas. But in ideal operation it will never be near 1atm at 450k and 150cc again.

I imagine the pvt plot would look more like an elliptical donut with a hole in the center.

[VincentG]

Now what's really interesting if we assume this theory is that the higher the Tmax, the less moles of gas are in the engine.

So not only is there better heat transfer due to a higher gradient, but there is less gas to heat and cool in the first place.

And in practice, my engine seems to find this balance naturally. A snifter valve would actually hurt rather than help here. If anything, a very small but purposeful leak path(think orifice) should keep this balance. This would be needed for a diaphragm type engine that is absolutely air tight.

[matt brown]

If less moles when Tmax, is there some minor open cycle aspect ???

[VincentG]

No sorry Matt I meant for a different cycle... let's run a 300k to 900k cycle. Now the starting mass of gas is 1atm at 600k at 150cc.

And with a 300-900 cycle now we can reduce the displacer volume further still for even less internal gas.

[matt brown]

Geez...900k is off the charts, but gaming this stuff does offer insight into alternate possibilities.

I had another altered state event 2 nights ago when jumping between your and Tom's posts along with some of my graphics. Checking google, it appears I'm not the first guy with this 'new' twist on an old cycle. It always amazes me how you can look at stuff for years and never see something until you're in the right frame of mind, then it seems obvious...

[Tom Booth]

forced work PV plot.png (31.14 KiB) Viewed 12521 times

This is from a study gaming minimal Wneg similar Hall video and Tom's drumbeat.

Just FYI, I wonder about "atmospheric pressure" being a straight line in these diagrams, including the Hall video.

"Atmosphere" from the perspective of the engine itself is whatever the pressure happens to be on the immediate back end of the piston, which generally would be the small portion of "atmosphere" partially enclosed in the power cylinder and subject to at least some variation due to the movement of the piston itself within the same cylinder.

The atmosphere is shoved out, then, presumably returns, the air itself has some mass and therefore momentum and inertia. It seems reasonable to assume that if the pressure on the back of the piston were actually measured it would not be a straight line as depicted..

I would guess that "atmospheric" pressure (inside the power cylinder behind the piston) would at a minimum, increase somewhat, as the piston moved outward..

After that what happens, or what might happen gets a bit fuzzy.

If the gas inside the engine literally contracts, pulling the piston inward, then it might be expected that the outside pressure would be left behind and fall somewhat. Generally any object moving quickly through air will leave a partial vacuum behind it. But "compression" in a free piston engine, logically should be due to atmospheric pressure. With a flywheel pushing the piston things could be different.

Anyway, I speculate that in actuality, the localized atmospheric pressure (inside the cylinder that is, behind the piston) tends to "tilt" in such a way as to follow the curve of the PV diagram.

That is, the pressure behind the piston would actually be more like the green line:

Resize_20230915_023250_0046.jpg (48.92 KiB) Viewed 12522 times

Logically, to me anyway, the piston would reverse direction when the pressure reversed.

If true, this would tend to eliminate the so-called "forced work".entirely.

[VincentG]

Tom and Matt, are you referring to Andrew Hall's Stirling powered boat video?

[Tom Booth]

Tom and Matt, are you referring to Andrew Hall's Stirling powered boat video?

Well, no. At least I'm not

I started a discussion thread on the subject here a while back.

I assumed you had seen it due to your earlier comment about a "one stroke" engine. Or I think you said "return power stroke". I took it as a reference to Andrew Hall's demonstration since he uses that expression to describe a Stirling engine running without a flywheel.

Anyway, the first video in this thread:

viewtopic.php?f=1&t=5497

https://youtu.be/SHyke4hUNOs?si=PQ9gXANxcc4vhsjF


Actually he has several videos describing and/or demonstrating Stirling engines of various types running without a flywheel. He does not, however, support MY conclusions about adiabatic cooling necessarily. He pretty clearly attributes it to the displacer motion shifting the air to the cold side causing "contraction".

https://youtu.be/LjjvIl1BfbQ?si=3TANWQ152hG9QRgP

While this is true at low speed, there are a couple of problems

Heat transfers slowly and engines have high RPM. Sometimes extremely high, which seems to rule out conductive heat transfer (at high RPM).

Secondly, not all heat engines have displacers to shift the air between a hot and a cold side, thermoacoustic, free piston, thermal lag, laminar flow, hybrid, (metronome maybe?) etc.

So, IMO something else comes into play, particularly at higher RPM's and that "something" IMO is "adiabatic" heat internal thermal energy transfer through work output.

[VincentG]

Well I'd say he hit the nail on the head.

Keep in mind that I'm not suggesting there is no adiabatic expansion and compression in real operation at speed. For certain these other types of engines rely heavily on adiabats, and there is less time for heat transfer at high rpm.

What I am suggesting is that I'm trying to build an engine that attempts to keep to isothermal ideals. From my observations, the LTD with displacer dwell and full displacer contact is nearly there already. There are many improvements still to be made on the next version of a model LTD that is being made from the ground up.

[Tom Booth]

Well I'd say he hit the nail on the head.

Keep in mind that I'm not suggesting there is no adiabatic expansion and compression in real operation at speed. For certain these other types of engines rely heavily on adiabats, and there is less time for heat transfer at high rpm.

What I am suggesting is that I'm trying to build an engine that attempts to keep to isothermal ideals. From my observations, the LTD with displacer dwell and full displacer contact is nearly there already. There are many improvements still to be made on the next version of a model LTD that is being made from the ground up.

Well, I certainly do not in any way want to discourage your efforts. It is always worthwhile to try different things and test all possible theories, though so far I pretty much concur with what Goofy wrote in his post here: viewtopic.php?f=1&t=5550&p=19900&hilit=Adiabatic#p19900 I'm not trying to prove "adiabatic" vs. "isothermal" or anything like that really. Actually, there does not really seem to be a proper term to describe the actual consumption of heat or the actual conversion of heat into mechanical motion in all of thermodynamics theory.

Thermodynamics, according to Kelvin established itself on the foundation of caloric theory which treats "work" production from a heat engine as a kind of byproduct of the heat as a "fluid" flowing through the engine. In one side and out the other. ALL the thermodynamic "ideal" models are ultimately based on this assumption, that heat as a substance of some kind is conserved, so that after being "put into" an engine to cause expansion, it then has to be "removed" to cause contraction and that "work" is only a consequence of this addition and subtraction of heat.

Our goals are different it seems.

I'm trying to get to the bottom of, or answer the question about, what is the ultimate nature of heat. For that, I'm looking for the common denominator for ALL the various types of heat engines. What is actually essential?

The flywheel can be removed in some engines, so that is not essential Some engines don't need a regenerator, so that is not essential. Many engines run without a displacer, so that is not essential. Heck, you can even take out the piston and the gas itself will still expand and turn a pinwheel. Most controversial of all seems to be, do you need a cold "sink"?

I've tended to emphasize "adiabatic" mainly because, by definition it at least allows energy exchange through "work", so I've taken a crowbar to that crack in the armor of thermodynamics theory, but "adiabatic"" is not really adequate either..

The 2nd "Law" of thermodynamics says that "not ALL heat can be converted to work" but in actual practice, what it really means is no heat whatsoever can be converted to anything. Heat is indestructible and ultimately conserved. Heat that goes into a heat engine must also come out. No heat is "converted". No heat "disappears", Heat DOES work as it passes THROUGH the engine, it is not CONVERTED INTO work.

Tesla contested this idea of the 2nd Law put forward by Carnot and Kelvin. He claimed that heat was a form of energy, not a conserved fluid. He claimed that the heat going into a heat engine DOES NOT need to be removed, because it is removed as WORK. It is CONVERTED.

I'm just trying to figure out who was right, Carnot and Kelvin or Tesla. Isothermal AND Adiabatic are really BOTH in the Carnot/Kelvin camp, under the umbrella of the 2nd Law.

The idea that heat itself can literally "disappear" when "converted" into work is kind of hard to think about or imagine. How can you keep putting heat into an engine without any heat coming back out somewhere?? Impossible!!