Constant volume compression/expansion-displacer chamber analysis-heat powered mechanical amplifier

[Tom Booth]

“As the gas is transferred at zero total volume change from the cold
space to the hot space the pressure rises. This pressure rise results in a
temperature increase in the gas due to adiabatic compression.
Therefore, at the end of the transfer process the mixed mean gas temperature
in the hot space will be higher than 900 K. Point 3 is calculated for all the
gas to be exactly 900 K. Adiabatic expansion then takes place. Then by the
same process as just described, the transfer of the expanded gas back into the
cold space results in a lower gas temperature than 300 K at the end of this
stroke. The computational process must be carried through for a few cycles
until this process repeats accurately enough. This effect will be discussed
further in Section 5.1.6.”

OK Martini is a big shot so I’m open to persuasion, but —

I’ve always thought the power piston compression/expansion is mostly prior to the displacer shift, so you can only transfer half of your available temperature difference before you run out of difference. The rest is already taken by the pressure change. So for instance for a 300K to 600K source/sink (100% difference) you would only want at most a 50% volume change engine. — But I dunno.

Bumpkin

I find it difficult to know exactly what the author has in mind. The section refers to an Otto cycle. Which is an internal combustion engine cycle (as far as I know always) the expansion and compression in an IC engine are decidedly "adiabatic". The ignition (heat addition" is "constant volume" at TDC.

So, it seems he is relating a Stirling cycle to an IC engine type compression/expansion heat addition scenario.

This does seem to relate to what has been discussed here lately as far as trying to make a Stirling engine more IC-like.

From my observations, in a gamma Stirling, the displacer lifts off the hot plate 90° ahead of the piston reaching TDC, so heat input (ignition-like event) and full compression take place, more or less simultaneously, allowing for a slight delay for the time necessary for heat to actually transfer from the exposed hot plate to the working fluid.

At TDC then, you have the combination of the heat input from the hot plate and the "heat of compression" peaking, more or less simultaneously at TDC.

That was the general idea I was pursuing in the "aligning heat vectors" thread I started recently: viewtopic.php?f=1&t=5556

I don't really know what type of Stirling the author of that paper has in mind.

There is that graph I've often posted showing the elevation in temperature in a Stirling engine above the temperature of the "heat exchanger", again, it's not entirely clear if that refers to the heat source hot plate or the internal regenerator, but I assume, the heat input heat exchanger, though thermally, in at least some configurations, there isn't much difference. Heat comes from the hot plate and/or regenerator. Either way, the combination of heat input just prior to full compression or heat concentration adds up to creating a temperature that exceeds the heat source temperature in either the hot heat exchanger or regenerator.

Similar to how the convergence of the crest of two waves results in a much larger wave, the "alignment of heat vectors" results in a higher peak temperature at TDC.

ezgif.com-optimize (1).gif (304.04 KiB) Viewed 6456 times

In the above quote, I assume he's talking about an Alpha when both pistons are moving and gas is being transfered through the regenerator from the cold to hot cylinder or vice versa.

Since one piston is going up and the other down the volume is sort of "constant" at times.

[Tom Booth]

After re-reading this thread, VincentG, especially your opening post at the start, I'm pretty convinced that I had no idea what you were proposing, and pretty obviously, I don't think anyone else did either, and possibly I still don't know but, I think basically the topic derailed after the first post.

Now, if I understand your proposal, you are, I think, suggesting doing away with any piston altogether?

To summarize in my own words; if you just had a displacer chamber and displacer and a heat source (and/or cold source) you could move the displacer causing pressure changes or just vibrations of the chamber walls.

The changing pressure swings or vibrations could then be used for generating electricity through the piezoelectric effect or similar technology as described in the link you provided at the start:

https://orbray.com/magazine_en/archives/1261

I have to confess I did not follow that link and your entire proposal or idea went completely over my head. After rereading the entire thread I'm pretty sure I'm not alone.

Image from your link:

SchemaPiezo.gif (108.39 KiB) Viewed 6096 times

This is such a radical departure from a conventional Stirling engine, whenever you mentioned your idea throughout the thread, my mind just drew a blank and glossed over because I had no idea what you were talking about.

[VincentG]

Yup that was the idea Tom. Either harness the vibration directly as in the animation above, or use the pressure swings to drive a speaker like linear generator at high frequencies.

[Tom Booth]

Yup that was the idea Tom. Either harness the vibration directly as in the animation above, or use the pressure swings to drive a speaker like linear generator at high frequencies.

OK,

Well now I understand what you meant:

The best we can do is use interrupted and partial bites of this energy. When powering a piston this is easier said than done. However in this configuration I believe that the most efficient use of this energy will be found at the highest cycle rate in which there is still a full(or maybe nearly full) pressure swing.

Power out is much greater than power in(displacer movement). The major benefit here is the potential to heat and cool a huge volume of air without the need for a large piston and cylinder.

Since you are not limited by the speed at which a physical piston can move up and down in a cylinder, friction, inertia, momentum,.. since there is no piston to move, ...

Thinking on this, It might be possible to have a completely, or nearly so, "solid state" hot air engine.

I was thinking something like a bimetal strip to actuate the displacer, or solenoid, like a door buzzer or perhaps some type of thermal diode:

https://www.circuitbread.com/ee-faq/wha ... rmal-diode

For the thermal diode, I'm not sure if there is some means by which these could be switched on and off rapidly.

There was a failed (apparently) Kickstarter "Stirling engine" I always thought was rather transparently stupid.

52bc8442a0c2ee76ac3bcbb157332573_original.jpg (77.28 KiB) Viewed 6043 times

Yeah right. Where's the piston? No way that could ever work.


https://www.kickstarter.com/projects/ep ... y-one-puck


I still doubt a cup of coffee sitting on a coaster could ever charge a cell phone or even light an LED, but... I'm a little less skeptical that something like that might be possible.

Would there be any advantage over a plain old TEG?

[VincentG]

I don't think a teg is efficient enough to be practical at large scale at the moment. That Kickstart project seems to be a scam but who knows. Why would they not disclose at least the basic operating principles? It may just be a standard teg.

I like the idea of a switch like you described to move the displacer.

The major benefit here is the potential to heat and cool a huge volume of air without the need for a large piston and cylinder.

I now realize that the major benefit is instead, heating a very small volume of air and applying the force over a large area without a piston and cylinder.

[VincentG]

I've completed construction of my new full epoxy displacer chamber intended for the continuation this thread viewtopic.php?f=1&t=5570 about max power from a model LTD. Unfortunately, I can't post pictures but I will update when I can.

Before I choose a power piston, I wanted to do some chamber pressure testing. The displacer chamber is 2.5" in diameter and .68" tall, internally. The displacer is also 2.5" in diameter, and .5" tall with 2 small pathways machined into the outer circumference for air flow, effectively displacing 14cc of gas.

Based on the ideal gas law, with a starting pressure of 14.7psi and a temperature of 373k(boiling water), there is .00049m of gas contained within. Moving the displacer to cover the hot end and expose the cold plate, who's temperature is 277k(40 degree f ice water), the internal pressure should theoretically lower to 7.73 in.HG.

In real world testing I was able to achieve 4 in.HG, which I am very happy with as it is far better than any previous attempt. The actual results are equivalent to the gas cooling down to 325k if actually heated to 373k. Realistically, the 50k reduction is likely split between the hot and cold temperatures.

The chamber is very air tight now, being o-ring sealed with machined mating surfaces, so I'll have to add a well sealed piston to measure gas volume expansion and contraction. It seems to breath much more air than the stock sunnytech displacer chamber despite being far lower in volume.

As promising as these results are, I think there is still room for improvement. More testing will follow.

[Tom Booth]

Where you say:

"the internal pressure should theoretically lower to 7.73 in.HG.

In real world testing I was able to achieve 4 in.HG,"

Do you mean BY 7.73 in. HG ?

If the pressure went down TO 4 in. HG that would be what ? Like 2 PSI ?

Even 7.73 inches of mercury would be like 1/4 atmosphere or under 4 PSI (relative to vacuum).

On the other hand, a heated, rarefied gas, cooled below ambient, would, I imagine, produce a partial vacuum.

Also, when you say:

"The actual results are equivalent to the gas cooling down to 325k if actually heated to 373k. Realistically, the 50k reduction is likely split between the hot and cold temperatures"

I'm not quite sure what you actually mean by "split between".

Supposing the working fluid temperature stayed below boiling, then a 50 k reduction would lower to a temperature below 325 k

[VincentG]

I should know by now not to miss important details like this.

The volume of the displacer chamber is 15cc. The swept volume of the displacer is 14cc. There is also around 2cc of gas in the test rig that is likely lowering actual performance. I need to get a fast response digital pressure gauge.

The chamber pressure was allowed to equalize to 1atm with the cold plate covered. Then it was sealed, and the displacer moved to cover the hot plate. Theoretically, it should have reached 7.73 inches of vacuum, but I achieved 4 inches of vacuum, or -2psi.

The actual results indicate a gas temperature differential of 50k, so I am missing 50k of available delta. For clarity, I attributed the full 50k to the gas not fully cooling from 373k, but realistically, the gas came 25k from either extreme.

That said, my theory is that the gas has a much easier time reaching the high temperature, and a harder time reaching the minimum temperature. The next round of improvements will take aim at this.

Note that the aim of these tests is purely to optimize the pressure swing of the displacer chamber at constant volume, with no regard for extracting power for the moment.

[VincentG]

I just updated the numbers in the gas calculator to reflect the 2cc of gas in the test rig. The theoretical vacuum is now 7.12in.HG, or -3.5psi. So my result of 4in.HG, or -2psi is even better than I first thought and represents a true delta temperature of 58k. It's so hard for me to be precise at these tiny volumes but still a good comparison I think.

[Tom Booth]

I think you mean 3.5 psi (absolute?)

No such thing as -3.5 psi

7.5 inches of mercury converts to 3.5 psi relative to vacuum not 0 psig.

If these numbers are correct, achieving a "partial vacuum" of that magnitude seems absolutely incredible.

I have to assume again, you must mean a pressure reduction of 2 PSI ?

That would be like 13 psig or 15 minus 2 psig

Is that -2 psig ? That is 2 below atmosphere?

[VincentG]

All numbers are a reference from 1atm. In other words if you read 4in.HG on an automotive vacuum guage, thats guage vacuum, not absolute.

So yes, -2psi means 12.7psi absolute. I generally like to write it as -2psi as it's easier to think about than saying 4in.HG of vacuum.

[Tom Booth]

OK thanks, that's what I thought. With psi, psig and all the other pressure scales things can get a bit confusing or ambiguous.

Also, thinking about the extreme vacuum produced in a situation involving steam, like those 55 gallon drum experiments, maybe a vacuum down to 2 or 3 psi absolute would not be entirely out of the question.

Also, I assume the numbers are theoretical based on "constant volume". If the piston moves in response to the "vacuum" then such a pressure drop would not actually register as the piston is drawn in.

[VincentG]

Yes, the numbers are based on constant volume. Once a piston is installed, I expect peak vacuum/pressure numbers to be greater at TDC and BDC accordingly.

I know the numbers will register, or the piston would not be drawn in or out at all.

I powered the displacer with my Dremel tool, and spun it to 2k rpm or so, and the pressure was still fluctuating. In this manner, I think the most power can be extracted from an atmospheric chamber at low temperatures, as rpm can far exceed what the engine could power itself to. This would fall under the "heat power mechanical amplifier" portion of this thread.

[Tom Booth]

Yes, the numbers are based on constant volume. Once a piston is installed, I expect peak vacuum/pressure numbers to be greater at TDC and BDC accordingly.
...

I suppose with an advance, that's possible.

What I was thinking though is that as heat is added, pressure builds, but when the piston moves (or is already moving in a running engine) the pressure is relieved so does not build up as much as it would without a piston, or if the piston were fixed or prevented from moving, or did not exist (constant volume).

Similarly as the working fluid cools, due to the displacer shifting air to the cold side, then the piston is drawn in, relieving the pressure of the "vacuum". With a moving piston there is not as much opportunity for a pressure difference to manifest measurably..

Like if I'm pushing a car I have to apply a lot of pressure to get it moving, but once it is in motion it is no longer possible to apply as great a pressure. The car begins to run ahead.

At least while running no load.

[VincentG]

Here I am spinning the displacer around 2krpm and still seeing great pressure fluctuations. The mechanical guage can't keep up but I believe the pressure is still reaching 2psi and 4in.HG. In this configuration the chamber would be used to power a free piston and linear generator.

https://youtu.be/wckqcHLoumU?si=EoQqoUoOJPc9aQEd