The Carnot efficiency problem

[Goofy]

In my (simple) mind, it´s the pressure that´s doing the work, not the heat as so. The heat supply is causing the pressure to rise so you
can use it to preform mechanical work on a piston.
Then the pressure falls during the stroke from TDC to BDC and. When the pressure falls the temperature falls,
as known in the p*v/t = m*R/M equation.
And you are left with LESS heat. It is not "flown through" to the cold side.
It is easier (for me at least), to visualize the process as: Energy in form of heat, is converted to pressure, who is converted to mechanical work.
This way one can better understand why the heat had "disappeared" and not carried away in a cold sink.
It doesn't matter to me, if the process is isothermal or adiabatic, these are theoretical terms for ideal gasses/processes, who not occurs as so in praxis/nature.
The same is for the term Carnot efficiency. It´s only a theory who claims, that the efficiency of an engine ONLY depends on deltaT.
And (as Tom point´s out) that´s further more down to 0 Kelvin, regardless of what temperature you started with ? ? ?

If one would construct an engine only from these premise, you will end up with not trying anything practical, because in theory it´s a VERY bad idea. You will "loose" almost every Joule you have.

In theory, theory and praxis are the same. In praxis they are not . . .

I hope more people in this forum will do some practical experiments with their small Stirling engines. I should not be so difficult to
isolate the cold side of the engine and see if there is something to Tom´s experience.

- And you don´t need high precession thermocouple's to do this. Look for the tendencies, not the "correct" temperature.

But have anyone in here done that ?

Yes, I have my self ;-)

The Stirling cycle is a closed one. Everything are to be isolated from the environment . . .

And don´t just try to "push" more heat in to the engine, than it can convert to pressure and thereby work.
Think on, when water boils (in ambient pressure), you can´t raise the temperature in the water, no matter how much heat you are supplying.

[MikeB]

Goofy - the problem is this:
If for a moment, we ignore the "work done" on/by the piston, then what keeps the motor running? The simple answer is the alternating change in pressure of the working gas. What causes that change in pressure? The smaller reason is change of volume from the piston, but the larger reason (in most motors at least) is change of temperature due to moving the working fluid from hot area to cold.
If the cold end isn't colder than the hot end the pressure will never change, and the piston will never move.
Therefore, if the cold end doesn't remove heat from the working fluid, the cold end will heat up over time until equilibrium is reached...

Conversely, if we assume that cold end does nothing, then the only way for the motor to keep running, is if the work done by the piston removes exactly 100% of the energy that the hot end puts in.

[Goofy]

Mike, repeating the paradigm " if the cold end doesn't remove heat from the working fluid" simply doesn't make any sense.
The heat is not "removed" it is converted to pressure, who pushes the piston. Therefore the heat is not to be found anymore or pile up somewhere.
It is pressure who moves the piston and then drops, not the piston that moves (by flywheel ?) and then by larger volume creates a pressure drop.

Chicken or egg came first ?

[MikeB]

Goofy, What is the point of the displacer? Is it needed?

[Tom Booth]

(...)

I hope more people in this forum will do some practical experiments with their small Stirling engines. I should not be so difficult to
isolate the cold side of the engine and see if there is something to Tom´s experience.

(...)
But have anyone in here done that ?

Yes, I have my self ;-)

That's great to hear. Thanks!

From what you say, generally, it sounds like you've been able to replicate the same or similar results that I've seen, in particular you have said:

It is easier (for me at least), to visualize the process as: Energy in form of heat, is converted to pressure, who is converted to mechanical work.
This way one can better understand why the heat had "disappeared" and not carried away in a cold sink.

I would say momentum plays a role, but aside from some minor details in how to "think about it" your conclusion is the same. The heat disappears or is converted, ultimately to work, rather than being carried through to the sink.

It doesn't matter to me, if the process is isothermal or adiabatic, these are theoretical terms for ideal gasses/processes, who not occurs as so in praxis/nature.

Agreed, and well said.

[Goofy]

"Goofy, What is the point of the displacer? Is it needed?"

In a Stirling engine, yes. But as you write " (in most motors at least)"

The Carnot equation includes all heat engines. Also steam and diesel.
As a Marine Engineer, I have been knocked on my head with these formula's for so many years, whiteout getting a proper explanation.
Academia clings to the theories regardless of your questions.

But I´m a hands-on guy, so I give my respect to Tom for keep on bringing these so called "facts" in play !

Forgive me for copy/past this liner, but it says a lot of my thoughts on this discussion :

“It is a capital mistake to theorize before one has data. Insensibly one begins to twist facts to suit theories, instead of theories to fit facts.”

Sherlock Holmes to Dr. Watson, in A Scandal in Bohemia (A.C. Doyle, 1891)

I

[Tom Booth]

Goofy, What is the point of the displacer? Is it needed?

Two questions really.

The function is in the name. A displacer by definition "To move or shift from the usual place or position"

https://www.thefreedictionary.com/displacer

So what's the point and is it needed.

Apparently it isn't needed in thermal lag, thermo-acoustic, or lamina flow type engines or some "free piston" or "hybrid" engines.

Is it needed?

What does it actually do?

It seems multi-functional.

It moves (displaces) the working fluid. Generally it also insulates. It has some timing function, it acts as a kind of "heat valve" to control heat input and presumably heat output though that last "function" is what is at issue.

If the displacer is only actually required as a heat INPUT valve it is nevertheless difficult to discard as also apparently acting as a kind of heat "exhaust" valve whether it actually serves that purpose or not.

When moving off the hot plate to let in the heat, the displacer has to go somewhere, and then upon returning to "close the valve" it appears that the other valve is left "open".

I've tried to answer this question experimentally by permanently closing the heat outlet "valve" by stuffing it up with insulation.

I've checked the cold side in various ways to see if there is actually any heat being let through the "open" or "stuffed up" valve.

I have a few ideas for possibly more conclusive experimental methods for eliminating the "heat outlet valve" to see if it is actually required or not.

I've used engines with the "heat outlet" side made of acrylic, covered with aerogel.

Maybe heat could be let into a heat impenetrable engine using an infrared heater rather than a displacer, coat the interior with silicon carbide and zap it with microwaves.

As Goofy points out, we need more data, more experiments.

It is a theory: No heat outlet is required

How can that theory be tested.

Or the reciprocal theory: A heat outlet IS required. Previously it seems, that assumption has never been tested because it has never been challenged.

With all my attempts at "stuffing up" the heat outlet, the idea that it is required remains an unproven and unverified assumption.

I've done nearly everything I could think of and the available data so far indicates a heat outlet is not required.

Insulating the sink has no or very little effect on engine performance, sometimes performance is improved!

Thermo measurements at this heat "exhaust valve" show almost no indication of any "heat rejection" sometimes it appears that there may even be some very slight COOLING, or so little heat being "let out" that it is within the margin of error of the measuring device.

[Fool]

I would like to, please, ask for an experiment:

Tom, could you try the following, if interested:

Turn an LTD Engine upsidedown. Stack some blocks, books, or build a stand. Heat the piston crank side, potentially use ambient or hot pad, and cool the flat side, potentially use ambient or water ice.

After getting a baseline of how it runs. Insulate the flat side, block of foam, should be easy. Try heating and cooling the piston crank side. Record observations.

Also you may like insulting the piston side for additional observations.

You have a real dilemma in that a Stirling Engine runs faster when one side is insulated. I'm just wondering if it might be sucking cold air in through the piston and displacer gland. The fact that the displacer is barely coming off the hot side indicates that very little heat is entering the engine. It is very surprising how little energy these little engines need.

I'm thinking that the ice on top caused moisture to condense on the cylinder and piston. Maybe freezing too.

Goofy, love your comments. I would like to point out that PV/T=mR/M are state points on a PV diagram. Heat and Work aren't in that equation.

Heat and Work are dependent on the path (integral) that is taken. Adiabatic and Isothermal are just two different paths. They are extreme, perfect, and reversible paths all other paths will have some irreversiblity and be less efficient. Carnot is about one potential and perfect path and it is for a full cycle. Single processes should not be compared to it. Adding up, carefully, all the single processes is one way to prove the Carnot limit. Real engines rarely get half that limit. Mostly because Carnot ignored heat losses, irreversible paths, and friction. It is a maximum. Real efficiency depends on way more degrading engineering factors.

It is similar to the equation of a circle r=✓(x^2+y^2) all real circles will be less perfect. Backed by mathematics not fantasy. Real circles are effected by many degrading engineering factors, but less than for heat engines.

[Goofy]

@Fool
" I would like to point out that PV/T=mR/M are state points on a PV diagram. Heat and Work aren't in that equation."
Just to point out :

p : Pascal
V : M3 (cubic meter)
T: Kelvin
m: kilogram
R : 8314 Joule/Kelvin*kilomol (gas-constant)
M : Molar weight in kilogram/kilomol (for air its app. 29 gram/mol)

So heat surely are in this equation. All it actually tell you is, that p*V/T is a constant for a specific gas.

A Stirling engine is a closed system with a fixed amount of gas inside, so m is constant, R is constant and M is constant.

So here pressure, volume and temperature always relates to each other on a fixed set of rules.
But it it very hard to tell which is where and when in a sterling engine, as it depends on cam-angles and stroke-lengths.
If with a magnetic connected displacer, it gets even worse to figure out, as seen in Tom´s slomo video.

So it will be hard to calculate these values and plot them in a pV diagram. You will have to measure them in realtime.

Hmm, but where to put the probes ?
If we put a thermocoupler probe inside the middle of a thick base copper or aluminium plate. I have Just drilled a ø4mm hole from the side of a 8mm thick plate.

So I know the temperatur of "heat in". Of cause it´s also nice to know the amount of kilojoules going in . . .

But it can be really messy to point out the exact p, V and T in a running Stirling engine

Have a nice weekend !

[Tom Booth]

I would like to, please, ask for an experiment:

Tom, could you try the following,

(...)

I'm thinking that the ice on top caused moisture to condense on the cylinder and piston. ...

Condensation is certainly possible and can be something of a problem when running a Stirling engine "on ice" (on EITHER side) for any length of time.

Condensation would be depositing additional heat. Simultaneous evaporation would take heat away, but in some cases there is more condensation than evaporation and the spinning flywheel can also apparently accelerate the process by keeping the air moving.

I thought it might be possible to take advantage of the heat in from condensation and out with evaporation by having an engine with a raised top so the distilled water accumulating on the HOT (ambient) plate could run down to the cold side and evaporate to help bring additional cooling to the cold side.

The condensation on the ambient (Hot) side I have also, previously seen freezing, but I have only recorded this with some degree of certainty in connection with a "control" engine sitting idle on a cup of ice. In a running engine where the flywheel is constantly "pulling" more warm moist air across the top of the engine, I have not confirmed ice formation or freezing in the cylinder actually recorded on video, but have certainly suspected that a number of times when the engine seemed to suddenly "freeze up" while running on ice (or rather running on ambient heat using ice as the "sink")

I put SINK in "air quotes" to denote my skepticism. I might say "so-called sink".

I have come to view it as a kind of "cold presence" or partial absence or reduction of heat contribution. Ice is still, apparently, contributing heat to the engine by my alleged or suspected or theorized "heat pump" action of the engine.

Good insulation, theoretically, would contribute or supply LESS heat than ice as it could, in theory, contribute no heat at all if the insulation were "perfect". As the Eskimos know, ice is actually a very good insulator. That seems to be it's contribution. It is not so much a "sink" as it is an effective form of insulation so the engine does not have to work as hard to keep itself cold.

Condensation around the cylinder after 4 continuous hours running on ice (top of engine insulated):

https://youtu.be/GLzTxVzMjIQ


Condensation on top of the engine after 12 continuous hours running on the same cup of ice (with no top/ambient side insulation):

https://youtu.be/-7zntz8kwIk


By comparison, after 10 hours of just sitting on ice this experimental "control" engine apparently became "cold saturated" and would not start.

https://youtu.be/41d6kIHLK7M

A few more hours sitting idle on top of the cup of ice, but no insulation on top (I had removed the top insulation to warm up the engine on the "hot" side with ambient heat to see if it might then start up) the control engine piston apparently became frozen in the cylinder.

https://youtu.be/fnxC8hymFLU


What is notable, I think is that the "control" did not accumulate any visible condensation.

With the running engine however, I found myself mopping up the accumulated condensation with a paper towel from time to time.

What I think is also notable is that the ice took an additional five hours to completely melt when used to run the engine and melted that much sooner just sitting under the idle "control" engine.

For example, melt time on a cup of ice :

Running engine 33 hours
Idle control engine. 28 hours

Considering that the running engine was apparently keeping the warm ambient air circulating and apparently absorbing more heat of condensation than the idle engine this is the opposite of what might be expected.

I have not done many experiments with the ice on top, in contact with the engine but under insulation, but should.

As I previously related, the one time I tried that the engine ran well for only a few minutes before "freezing up". But by the time I got the insulation off, I could not confirm that any actual ice had formed in the cylinder, but the engine seemed to be cold saturated and would no longer run until I had gotten it warmed up again. The engine in that case seemed to freeze or "jam up" very abruptly. I could not identify any actual mechanical cause. The engine did not appear to be damaged in any way and ran normally once it warmed up again.

Much of this is speculation or guesswork unfortunately. "It seemed like" or "apparently" are phrases I use often because I don't know for sure. Obviously more testing would be necessary before making any final conclusions.

That ice, generally, takes measurably longer to melt when used used to "power" the engine (by ambient heat) is pretty well established IMO as I ran this experiment several times using different quantities of ice and the results seemed to be consistent. The ice always melted faster when just sitting under an idle, inoperative engine, and stayed frozen longer under a running engine.

I can do more experiments when I have time, but your directions seem rather vague along the lines of: try different things...

These are some of my observations from previous experiments which maybe might help spark some ideas on how to proceed with some additional experiments.

I'm not sure what your objective is in running an engine "upside down".

[Tom Booth]

Something kind of interesting I just noticed while rewatching those old videos:

Aside from the condensation being especially heavy directly under and in line with the rotating flywheel, there is a general light condensation all over the top of the engine.

However, this light haze of condensation stops forming an almost perfect circle at the line where the working fluid inside the engine is no longer in direct contact with the top metal plate.

Resize_20230804_060953_3597.jpg (82.96 KiB) Viewed 7475 times

This only becomes visible in the video when the light hits the top of the engine just right making this haze of condensation visible.

I guess this makes sense as the displacer is agitating the air inside the engine and "bringing up" the cold from the ice down under the engine. Presumably also carrying ambient heat down? But if that is the case, why should the ice melt more slowly?

Anyway I just noticed that and thought it was interesting, though not sure what to make of it.

The condensation is only above the gas in the engine, not at the perimeter outside of that.

IMO I think at this point that it is another indication of some kind of active cooling by the working fluid in contact with the top of the engine.

[Tom Booth]

From my observations, the reason that the cold is "pulled up" causing condensation but the heat is not "pulled down" to melt the ice faster is, well, first of all hot air rises, but I think also or mostly:

When the displacer drives the air up to the top this happens to uncover the top plate to introduce ambient heat to initiate the power (expansion) stroke. So as the cold air is pushed up to the top plate it is expanded and cooled.(expansion and simultaneous work output)

Readings, apparently indicate that the working fluid gets colder than the heat exchanger plate at this time, judging from this chart:

Temperature_vs_angle.jpg (61.48 KiB) Viewed 7470 times

Admittedly this graph is rather old from Wikipedia and of unknown origin, contributed by an anonymous editor. Not even sure if it is real readings or just a computer "simulation" so I have over used it and consider it weak support for my theories, but, if it is accurate and applicable to this kind of little LTD engine, it could help to explain the condensation pattern.

By the time the working fluid is pushed back down to the ice it has already been "refrigerated" cooled by expansion and work expenditure. So it (the working fluid) does not carry much, if any ambient heat back down to the ice, rather, the heat is used up during this expansion/power stroke that draws heat away from the top ambient plate in the process.

Basically the ambient heat is being pulled down and "consumed" or utilized for mechanical work output.

Therefore, the hot ambient top side of the engine is continuously cooled, causing condensation, but the cold ice side underneath remains cold, allowing the ice to stay frozen longer. (Longer than if the heat were allowed to pass through the engine without being "consumed" in the process.

[MikeB]

Tom, It seems to me that a very simple experiment is possible, and hopefully useful, which is to de-couple the displacer from the piston of a suitable engine - probably by connecting a second flywheel.
My question was meant to be somewhat rhetorical, and based round logical thought experiments but physical experiments have their place too!

My thinking is that you would probably need to spin the flywheel of the displacer to get the engine running, but if the cold-sink is not actually doing anything, then the engine will continue to run if that flywheel is stopped.

[Tom Booth]

...
My question was meant to be somewhat rhetorical, and based round logical thought experiments but physical experiments have their place too!

LOL...

My thinking is that you would probably need to spin the flywheel of the displacer to get the engine running, but if the cold-sink is not actually doing anything, then the engine will continue to run if that flywheel is stopped.

LOL...

The displacer and "cold sink" are not the same thing, and have different functions.

The displacer, as I said previously, has multiple possible, probable, theoretical or assumed functions.

The issue or problem is to sort out which apparent functions are actually essential and which are only apparent.

An essential function of the displacer is to isolate the heat source from the working fluid until needed. Another essential function is timing the heat input event so it takes place at the most advantageous moment, just before TDC.

Another essential function is to discontinue this heat input so the heat can be fully utilized allowing the working fluid to give up its energy, cool and "contract" so the piston can return for the start of another cycle.

An essential function of the cold "sink" apparently, is to NOT supply heat or to supply less heat. Basically you don't want the "less hot" side fouling up the carefully controlled and timed heat input, that might act as a pre-ignition or reduce efficiency.

The cold side is essentially NULL. It does not or should not be a participant in the process introducing heat when it isn't needed. Or drawing heat away when it is needed.

I must emphasize : theoretically. These are my opinions or tentative conclusions based on my observations and experiments. I'm open to hearing some better explanation.

You can't however just toss out the displacer and expect the engine to run with no controlled or properly timed heat input.

If you are going to disable or remove the displacer you would have to replace the displacers essential function(s) as a regulating "heat valve" in some way.

For example; a pulsed infrared heating element inside the displacer chamber. This could be controlled by an electrical contact on the flywheel to turn the heat input on and off.

Or having some material that generated heat from microwaves inside the chamber, then zapping that material with pulses of microwaves similarly timed.

Obviously the engine would not run without controlling the heat input.

That would be like having the spark plug on an IC engine constantly firing or some hot carbon ember causing the engine to misfire.

The displacer controls the "ignition", but since there is no physical air/fuel involved there is no need to "exhaust" any combustion materials.

The unused heat, if any, can just be returned to the hot side, which may be another function of the displacer.

So, as a "thought experiment" tossing out the displacer or simply disabling it to demonstrate that the engine won't run without it proves or would prove absolutely nothing.

[Tom Booth]

It is, I think, worth reading Carnot's unpublished notes as he struggled with these same questions and issues.

When a hypothesis no longer suffices to explain phenomena, it should be abandoned.

This is the case with the hypothesis which regards caloric as matter, as a subtile fluid.

The experimental facts tending to destroy this theory are as follows :

(1) The development of heat by percussio or
the friction of bodies (experiments of Rumford,
friction of wheels on their spindles, on the axles, experiments to be made).

Here the elevation of temperature takes place at the same time in the body rubbing and the body rubbed. Moreover, they do not change perceptibly in form or nature