Calculating volume ratios using PV=nRT

[Tom Booth]

All in all you have a dynamic system where changes are taking place very rapidly and what you actually have at any one time is a swirling mixture of hot and cold gas.

The best you can say to describe this chaotic situation is that "on average" this or that or the other thing.

So what you said I said, or how you interpreted it, was not entirely wrong. There was some truth to it, Yes, some gas molecules would be giving off heat and cooling while simultaneously other gas molecules would be heating up. "On average" what's really going on is mostly guesswork.

[VincentG]

A running engine is in a dynamic condition, but a dynamic condition can be characterized by a sequence of static conditions. Similar to a motion picture being a series of still images. If you can figure out how to manipulate the static sequences, it may be possible to create the desired dynamic. Wishful thinking maybe, but it seems the most effective way to approach these engines.

The first step is reducing the number of variables at any one moment. So dwelling the displacer when the volume is changing the most(expansion and contraction stroke) and moving the displacer when the volume is most static(TDC and BDC) is a good start.

The best engines require the least amount of ignition advance. In the case of my LTD, quite a lot of advance was needed to heat and cool the gas in time for max torque, even at low rpm. Increasing the size of the power piston to introduce a real compression phase just before TDC will aid in quickly raising the gas temperature far quicker than the hot plate alone can manage. Hopefully this will reduce the advance of the displacer required for peak torque, and so increase the effective power stroke(s) of the engine.

Any further temperature gain(and loss) from what I believe Martini was suggesting, would just be icing on the cake.

[matt brown]

Yes, I did say that since heat is added and heat of compression combined with that, the combined heat could drive the working fluid to a temperature above the hot side heat source temperature and that this could cause a "heat pump" effect where heat could transfer from the working fluid back into the heat source.

But then, yes, with expansion/cooling 90° Before BDC the DISPLACER moves to the hot side, (which exposes the cold side) so you have a compounding of the cooling so the working fluid could become colder than the "sink" so as to draw heat out from the cold side, which for an instant, causing the engine to function as a heat pump.

It is an interesting conundrum anyway.

Xlnt wording, tho many will still be wondering WTF. Sorry, I botched my hipshot recap, but I've been working 6 day weeks for over 6 mns, so living in a daze at times.

I found this during my gamma deep dive over the summer from idealized modeling. As a long time alpha fanboy, this stuck me as another gamma/beta issue that's casually missed. I've never seen anyone mention this until you did which is very insightful !!! I agree, it's likely minor, but I often wonder how many of these minor unknown/uncertainties compound into larger known/certainties.

[matt brown]

A running engine is in a dynamic condition, but a dynamic condition can be characterized by a sequence of static conditions. Similar to a motion picture being a series of still images. If you can figure out how to manipulate the static sequences, it may be possible to create the desired dynamic. Wishful thinking maybe, but it seems the most effective way to approach these engines.

A smooth pitch like a slick tech ad for a new fangled gadget - lol. This may fail to identify many problems and solutions directly, but is the preferred approach to such (problems & solutions).

The first step is reducing the number of variables at any one moment.

Oz kindly shares a look behind the curtain (classic modeling).

So dwelling the displacer when the volume is changing the most(expansion and contraction stroke) and moving the displacer when the volume is most static(TDC and BDC) is a good start.

...Increasing the size of the power piston to introduce a real compression phase just before TDC will aid in quickly raising the gas temperature far quicker than the hot plate alone can manage.

If the temp rises prior heating then less heat will be available for input (less temp differential everything else equal). In theory, Wneg during compression is constant whether condensed near TDC or spread out across compression stroke. This sounds like an Otto cycle with input from a displacer (chamber) similar to Tom's hot potato, but where the hot potato matrix is replaced by a displacer and heating moved to extreme end of heater (abutment plate).

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[VincentG]

Oz kindly shares a look behind the curtain (classic modeling).

Jeez Matt don't blow my cover..

If the temp rises prior heating then less heat will be available for input (less temp differential everything else equal). In theory, Wneg during compression is constant whether condensed near TDC or spread out across compression stroke. 

Yes, but while I'm freeze framing, there's a thermal lag regardless of process. So the aim is to align peak compression temperature and heater input just at the right time at or just after tdc like otto. And just like ICE, more advance may make more power, but the same power with less advance and better efficiency(smaller engine/less fuel) is more ideal.

I'd say my LTD peaked at around 30 degrees displacer advance BTDC. I'm pretty happy with that for an effectively non-compression engine. Reducing displacer volume(and bringing back compression) should reduce that advance even further.

[Tom Booth]

... If you can figure out how to manipulate the static sequences, it may be possible to create the desired dynamic....

I can't say that I exactly "believe in" so-called "entropy" but I sometimes look at a heat engine as a kind of "negative entropy" generator.

That's king of a very broad generalization or compass, kind of the opposite of looking at the sequence of events frame by frame.

What we have to work with at the start is the chaotic random motion of gas particles animated by "heat". Let's say kinetic energy or just motion but the point is, being disorganized it is at maximum entropy and essentially useless every particle has an opposing particle moving in the opposite direction so all forces involved in these particle movements cancel each other out.

Adding more HEAT without reducing "entropy" is a waste of energy. The particles move faster but still cancel as the faster movements still cancel. Likewise with cooling.

So, the goal is not so much to heat and cool as to bring some degree of order out of the general chaos.

One way of doing that is to convert "pressure" into velocity by releasing pressure through an orifice or nozzle. The random motion of particles represented by "pressure" becomes a more unified, "laminar" laser-like motion through a narrow "venturi".

Another method of organization or "negative entropy" is to corral hot particles and/or cold particles. A chamber full of disorganized hot particles with a lot of random motion by itself is as useless as a chamber full of cold particles with little motion of any kind.

Division into hot and cold is only one kind of "negative entropy" or method of organizing particles. Velocity has been largely ignored or neglected, but I tend to think it plays a role in at least some engines, such as the "laminar flow", where hot air expands through a nozzle of sorts and drives the piston, not so much by generalized "pressure" in the power cylinder, but I imagine more in the order of a concentrated stream of particles, like a fire hose. If that is the case then the "pressure" is localized at the surface of the piston head rather than the power cylinder generally, which might actually be a partial vacuum throughout except where the air stream is actually impacting the piston surface.

Are there other means or methods for generating "negative entropy" as yet unidentified?

[VincentG]

One way of doing that is to convert "pressure" into velocity by releasing pressure through an orifice or nozzle. The random motion of particles represented by "pressure" becomes a more unified, "laminar" laser-like motion through a narrow "venturi".

I've thought about this a bit. Putting entropy aside, some of the fastest running model Gama's have a very small port between pp and displacer. ICE runs best with a port much smaller than cylinder and theoretically much less gas is "flowing" in a Stirling. So maybe my engine would benefit from such an orifice aimed to increase air velocity at the piston face.

My reservation is the additional cooling effect this could have on the gas, and less chance for a good isothermal expansion stroke. It would make more sense with your adiabatic model. I won't rule it out, easy enough to add on later.

As for the entropy thing, that's really way over my head. But if one were to make that a goal, maybe entropy reduction, rather than "negative entropy"(I'm assuming you mean a lack of entropy here) would be a good first step. Either way that's way outside the realm of this thread and my admittedly very basic attempt to model this "Stirling" cycle.

[VincentG]

Adding more HEAT without reducing "entropy" is a waste of energy. The particles move faster but still cancel as the faster movements still cancel. Likewise with cooling.

You got me thinking Tom. Maybe a way to reduce entropy is to decrease the amount of gas, while increasing the working range of said gas. That's the basis of what I'm gaming with this thread. But that goes along with increased delta T.

I was running the numbers on the same 4(pp) to 1(dp) cycle, and figured I'd try a 300k-700k cycle, and a 200k-600k cycle, all with the same 100cc pp. The results were not what I expected. The 300-700k cycle started with less gas than the 300-600k cycle, and saw less overall compression and more overall pressure gain, as expected.

But the 200k-600k cycle, while starting with more gas than the 300-600k cycle, had far less overall compression and far greater overall pressure gain. I'm going to plot the curves of all the cycles on excel, but it was something like only a 5psi compression gain at TDC full cold, and a 45psi! pressure gain at TDC full hot.

That lead to a deep dive into the gas constant used in PV=nRT to try and find the cause of this. It seems it's just that, a "constant", so I'm not sure where the extreme gains are coming from(Though I easily could have missed something). Especially since there is said to be more energy gained from 600k to 700k, as opposed to 200k to 300k. But maybe I'm wrong in saying that.

Regardless, it now seems to me that the importance of lowering the gas temperature(however you'd like) cannot be overstated.

[Tom Booth]

Cold gas has lower "entropy". Meaning it is more "orderly".

So heating a cold gas gives more opportunity for "expansion", though possibly not the right term exactly.

Think of it this way. If you have a new deck of cards, it comes pre-sorted into suits and all in order from duces to ace or ace to king or whatever.

"Heating" is introducing disorder, like shuffling the deck of cards.

So, "heating" or shuffling a "cold" deck of cards creates much more "entropy" than re-shuffling a deck that has already been "heated".

The amount of "disorder" that can be generated by shuffling the deck again and again becomes less and less as more and more "heat" is introduced.

At least that is an explanation I read recently somewhere while browsing.

Cold enough the gas becomes liquid, then solid, which is very ordered, like a crystal. So that is why phase change packs such a punch. (According to this entropy concept).

[VincentG]

In any event, doing more work with less gas is the target for me.

I see it as a simple series of questions.

Can we delay the start of real compression work till 50-30 degrees BTDC- I think so, quite easily.

Can we hit a 2 to 1 effective compression ratio just before TDC, while keeping near the cold sink temperature- I think so.

Can we heat this mass of air to near the hot sink temperature as the piston sweeps through TDC- I think so.

If those events can take place, there is far more pressure gain available with an atmospheric engine than current models allow for, even if real world results are half of expected.

I've been working on engines for 20 years now, and when I got the timing right on my LTD, it clearly(to me) went from being a "toy" to something that had real potential.

Take a look at the Essex hot air engine for a small atmospheric Beta that started to get things right as I see it. It was not a toy, it did real work.

[VincentG]

The cold space was at the far end, with the hot space closer to the power piston which makes more sense from a gas flow perspective. As a result of that, the displacer could have effective advance BTDC of the power piston, which a more modern Beta design does not allow. What it lacked was modern materials and thermal separation from the cold end.


https://youtu.be/rN1cLc17U6I?si=IqbjtxiTF813oVQQ