Stirling Engine Thermodynamics

[Tom Booth]

No Tom, you got me wrong. What I mean is for you to simply draw ANY closed cycle compression cycle on a piece of paper without cooling somewhere...

(1) isobaric compression requires cooling
(2) isothermal compression requires cooling

(3) adiabatic compression has no cooling but will require cooling (process) somewhere in cycle, otherwise it's a gas spring

I can doodle up lots of cycles with adiabatic compression (3, 4, 5 legged, whatever) but all these cycles will require a cooling process to return to start state. What I see you to be suggesting is something like a 3 leg cycle with adiabatic compression & expansion which meet at the 'tail' (aka BDC) on a PV plot and heat is supply at the 'head'. To avoid gas spring (and have any measure of Wpos>Wneg) expansion would have to exceed compression, somehow. How any heat would enter this cycle is what I'm wondering, even when allowing for 'irregular' volumetrics due to phasing. My point is that PV plots never lie in theory, but realities are always mere approximations. So again, show me some closed cycle compression cycle PV plot 'theory' with no cooling...

All early steam & HAE were open cycle. Watt's condenser closed steam, but HAE like Cayley, Stirling, Ericsson, etc continued with open cycle into obscurity. After Otto proved the advantage of compression cycles, open ICE & closed ECE became the favored formats. ICE have evolved a long way since Otto due to compression process, but ECE have remained bogged down by their closed cycle. Even Dean Kamen hasn't solved the ECE riddle...

Strange or as incomprehensible as it may seem, when atmospheric pressure drives the piston back inward, that is work being done on the gas. That work being done on the gas by atmospheric pressure puts energy into the gas increasing it's temperature. So in that way, heat is generated in the working fluid by adiabatic compression as a result of work being done on the gas.

To avoid gas spring...

Why do you feel it is necessary to avoid gas spring?

You basically have an oscillation. The piston bouncing between two air springs. The hot compressed gas on one side and atmospheric pressure on the other.

"Adiabatic bounce"

https://youtu.be/vT6n7VVBvqw

[matt brown]

I do believe, however, or I have come to, or been led to the understanding, through information such as in this video:

https://youtu.be/PMKPZuCj9a0

that as long as the piston is moving outward and the gas expanding, as far as the gas or working fluid is concerned, the piston is a "moving target" so that when a gas molecule collides with the piston, moving away from it, the gas looses energy to the piston, does "work" on the piston and cools down as a consequence. The greater the cooling, the more "free" so to speak, power can be returned by atmospheric pressure. Atmosphere then does work on the gas, increasing the temperature, adding to the heat that would result from simple compression (or reducing the volume, putting the gas into a smaller space) alone. As a result of doing work during expansion/cooling, the greater the cooling, the greater the payback in work accomplished by atmospheric pressure, adding energy to the system. So for that reason, I don't think it is a simple matter of positive work out during expansion and negative work during compression When the gas is compressed by atmospheric pressure pushing the piston inward, that is not taking energy out of the system, it is adding energy to the system.

Tom, this is all true, but there's something you overlooked...the conventional Wneg of compression from a flywheel has been removed, but the same Wneg has been 'stolen' from the 'system' during the expansion process, so it doesn't change Wnet. It's like a low tech bounce gas or were crankcase pressure changes nothing in efficiency (but might have some other benefit/s).

[matt brown]

Using atmospheric pressure to compress working gas will limit working gas pressure to some partial pressure. I think a better mental model would be 'replacing' paltry 1 atm that Mother Nature supplies with large 10 atm storage tank, and then 'replacing' partial pressure working gas with something substantial. Either way, the results remain similar where backside pressure on piston during expansion robs expansion work, proportionally. Interestingly, Watts advantage with condenser during early steam with very low piston pressures was simply reducing piston back pressure from 1 atm to (ideally) vacuum which gave efficiency a free ride.

[Tom Booth]

Not sure where you're going with that, but I think another path for heat to enter the system is during "compression", which in a sense is really contraction of the cold expanded gas.

The gas is coldest between BDC, full expansion and much of the way back to TDC, increasing in velocity as it travels.

Opposite to what is generally supposed, (that heat is "rejected" during compression), at this point the gas is cold and contracting, and also taking in heat.

Since it has become cold enough to contract how could it do otherwise than take in heat from the warmer surroundings, while also receiving work from atmosphere. The piston has weight and velocity that are converted back into heat at TDC.

The amount of heat taken in from the fire or whatever heating the engine is very minimal. The displacer moves to introduce heat when the gas is already hot and compressed. The heat is there mostly just to bounce off of. Most likely IMO, the real substantial heat is taken in when the gas is cold when expanded and during compression.

[VincentG]

Fascinating stuff for sure. I'm curious where you stand Matt, do you believe you have a complete understanding of the Stirling cycle in practice? I am completely impartial to how exactly the cycle works. I feel our only rational move is to tweak the cycle to get max power. It's unfortunate that other young men are not pouring effort into this work instead of call of duty. The solution is out there, just look at the Beacon 10.

Dead space is still the enemy here, that is to say, any volume of gas not contained in only one side of the displacer chamber at a time.

If we had our way, the working gas would be fully shuttled from cold side to hot side and then instantaneously heated to drive the working cylinder. Then the gas would move to cold side, maintaining temperature in transit, then instantly cooled to allow the atmospheric stroke. Or even more ideal, this temperature change would occur with no displacer at all, and the pressure change would act upon the working cylinder at 10-40 degrees BTDC (and BBDC on the return stroke), just as in an ICE. I still think that a low compression ratio is best, but I'll save that for testing.

[Tom Booth]

In a way, I think that the hotter the engine working gas gets during the compression "bounce" the colder it can become during expansion. It's sort of bouncing between two extremes.

I don't think it is necessarily all atmospheric pressure that drives the piston inward though. Apparently the gas or working fluid itself is literally contracting and pulling the piston back in, like a rubber band that has been stretched. So, in a sense I think the gas or working fluid continues to do "work" pulling the piston inward, which continues to reduce the temperature and pressure.

Look at the real PV diagram above, generated from actual readings from a running engine Pressure continues to drop during compression.

After crossing the 0 line (atmospheric pressure) the volume decreases while pressure also decreases.

Well, the gas was shifted over to the cold side by the displacer, but the expanded gas is colder than the cold heat exchanger. It could not possibly loose heat to the "sink" as it is colder than the "sink". The gas is contracting and doing work dragging the piston along behind it so continues to loose energy and the pressure continues to drop even while the volume is decreasing.

Then about midway through the contraction, the pressure starts increasing, but still has a long way to go before getting back up to atmospheric pressure, which it doesn't do until nearly all the way back at TDC again.

[Tom Booth]

The solution is out there, just look at the Beacon 10.

It seems the Beacon 10 website went offline about 10 years ago. And apparently it's remains have been scrubbed from the internet archive as well.

Seems, half a dozen similar "solutions" have either vanished or have been bought out or bought off or something.

If these off grid Stirling generators don't work or are not practical or whatever, tell me why the oil industry is using them on their pipelines out in the middle of nowhere.

[Tom Booth]

...
Dead space is still the enemy here, that is to say, any volume of gas not contained in only one side of the displacer chamber at a time.

If we had our way, the working gas would be fully shuttled from cold side to hot side and then instantaneously heated to drive the working cylinder. Then the gas would move to cold side, maintaining temperature in transit, then instantly cooled to allow the atmospheric stroke. Or even more ideal, this temperature change would occur with no displacer at all, and the pressure change would act upon the working cylinder at 10-40 degrees BTDC (and BBDC on the return stroke), just as in an ICE. I still think that a low compression ratio is best, but I'll save that for testing.

Don't suppose you've stumbled across my new heat engine "Ringbom"-ish type design with no cold side.

It doesn't exactly have a displacer. It has a form of a displacer, but doesn't function as a displacer.

A sketch of the idea, as a conversion from an IC engine or a compressor.

Resize_20221206_063014_4498.jpg (133.95 KiB) Viewed 3425 times

Explanation of how it would operate on this thread:

viewtopic.php?f=1&t=5481

Basically, the cold side of the displacer chamber no longer exists, but is replaced by an air spring, separated from the hot side by a diaphragm.

There is basically no "dead air space". As the working fluid only leaves the power cylinder rather briefly near TDC to be heated and expanded.

The "displacer" only moves enough to make room for the compressed air long enough for it to be heated, then it is returned to the power cylinder as it expands.

This is my main ongoing project at the moment.

It depends on the idea that a cold "sink" is entirely unnecessary.

[VincentG]

Some food for thought.....

• It is well known that Stirling engines operate much better on helium

• The thermal conductivity of air and helium is .026 and .15 W/mK respectively

• Gay-Lussacs law states that all gases expand similarly with temperaure

• Heat gained during the compression of gas is nearly instantaneous

My only conclusion is that the Stirling engine makes more power on helium strictly due its higher thermal conductivity(and perhaps a bit less pumping loss from its lower density). Therefore, the speed of heat transfer through sinks on either end is of paramount importance to power output.

More food for thought.....

• The thermal conductivity of copper and diamond is 400 and 1000 W/mK respectively

Perhaps a diamond encrusted internal heat sink would be an improvement. Also, what if readily available diamond dust was added to the working gas and allowed to swirl around in the displacer cylinder. It may have huge effects on the thermal conductivity of the working gas. Unfortunately a filter element would be needed to keep it out of the working cylinder, unless it was a diaphragm type.

[VincentG]

Don't suppose you've stumbled across my new heat engine "Ringbom"-ish type design with no cold side.

Interesting...I had attempted to make an open cycle engine of similar theory. I understand the concept but I don't see that working closed cycle with no cold side. Please prove me wrong though. In my case I had a 2 stroke piston port engine with a hot tube theaded into the spark plug hole. Just like a hot bulb gas engine. When superheating the bulb, the engine spun more willingly than with a cold tube, but i believe a timed valve is needed to make it work. Or now that I think about it again, maybe it just needed much less compression!

If you are not familiar with them, look into a piston port 2 stroke engine(like from a chainsaw) and see if that can help you with your design.

[Tom Booth]

Don't suppose you've stumbled across my new heat engine "Ringbom"-ish type design with no cold side.

Interesting...I had attempted to make an open cycle engine of similar theory. I understand the concept but I don't see that working closed cycle with no cold side. Please prove me wrong though. In my case I had a 2 stroke piston port engine with a hot tube theaded into the spark plug hole. Just like a hot bulb gas engine. When superheating the bulb, the engine spun more willingly than with a cold tube, but i believe a timed valve is needed to make it work. Or now that I think about it again, maybe it just needed much less compression!

If you are not familiar with them, look into a piston port 2 stroke engine(like from a chainsaw) and see if that can help you with your design.

I've been a small engine mechanic since, before graduating high school, so am very familiar with chain saw engines.

In this case, I don't think ports are needed.

The theory is very very simple. Pull the starter chord as usual. As the piston nears TDC the build up in pressure causes the displacer to move off the hot heat exchanger.

The compressed air flows into the hot chamber at TDC (more or less) the heated gas expands driving the piston.

The crankcase pressure from the pistons power stroke helps to return the displacer driving the remaining hot air into the power cylinder.

The expansion of the gas, doing work driving the piston causes the air to cool and contract, allowing the cycle to repeat.

The air spring can be made adjustable to provide the necessary resistance so the displacer only moves at the optimal time for heat delivery.

The only problem with this scheme is the notion that the "Carnot limit" and/or 2nd Law dictates heat needs to be rejected to some "cold reservoir" somewhere, which my experiments indicate is bogus nonsense.

The heat is 100% converted to power output on the expansion stroke. That the piston returns is inevitable as a matter of homeostasis or return to equilibrium.

The blast of heat creates an imbalance that drives the piston out, but then it is overextended and comes back.

This whole Carnot limit nonsense is apparently just that. A bunch of nonsense based on some silly outmoded idea of heat as some kind of fluid that seeks out a lower (colder) level to run down into.

Heat does not power a heat engine as a result of trying to get to some cold "reservoir". You aren't intercepting a "flow", your, as someone here said recently, organizing random kinetic energy, setting up an oscillation. A cold "sink" (or reservoir) for heat to flow into has nothing to do with any reality.

[matt brown]

Don't suppose you've stumbled across my new heat engine "Ringbom"-ish type design with no cold side.

Interesting...I had attempted to make an open cycle engine of similar theory. I understand the concept but I don't see that working closed cycle with no cold side. Please prove me wrong though. In my case I had a 2 stroke piston port engine with a hot tube theaded into the spark plug hole. Just like a hot bulb gas engine. When superheating the bulb, the engine spun more willingly than with a cold tube, but i believe a timed valve is needed to make it work. Or now that I think about it again, maybe it just needed much less compression!

If you are not familiar with them, look into a piston port 2 stroke engine(like from a chainsaw) and see if that can help you with your design.

I think I posted this Pinwheel scheme here somewhere before. Really, little more than a carefully ported vane motor with hot & cold reservoirs. Interestingly, it lends itself for both Otto or Atkinson cycles; you know, each to his own persuasion. Recently, in one of those invention challenges, some guy pitched this AND attempted to patent it (eyes roll). Nevertheless, this is the type of ECE guys should be chasing...fast adiabatic compression & expansion with plenty of heating & cooling time due to reservoirs. So yeah, Vincent, I love your engine project....I have a soft spot for Otto schemes....no bogus isothermal dreams and no regenerator mumbo-jumbo.

However, the Stirling cycle (in theory) is capable of much lower temperature ratios than Otto (before including 'Stirling' tinkertoys) AND a Stirling cycle will always have greater efficiency than an Otto cycle within the same temperature extremes. The Stirling cycle gets both it's higher relative power (think per rpm) and higher efficiency (than Otto) due to (ideally) source & expansion are at the highest energy level of cycle while sink & compression are at the lowest energy level of the cycle. Unfortunately, both isothermal & regeneration processes bog this cycle down. AND, that's even before one considers how to construct an actual engine that follows this vaulted cycle (phasing issues, pressure drop across regen, etc)

Since you're new to this, I'd suggest researching "thermal lag" engines, since your engine has some similarities. You might also google Peter Tailer thermal lag patent (he's the guy who kicked off this buzz decades ago).

[matt brown]

Some food for thought.....

• It is well known that Stirling engines operate much better on helium

• The thermal conductivity of air and helium is .026 and .15 W/mK respectively

• Gay-Lussacs law states that all gases expand similarly with temperature

• Heat gained during the compression of gas is nearly instantaneous

My only conclusion is that the Stirling engine makes more power on helium strictly due its higher thermal conductivity(and perhaps a bit less pumping loss from its lower density). Therefore, the speed of heat transfer through sinks on either end is of paramount importance to power output.

In theory, the main difference between gases in Stirling cycle is that heat transfer rate will provide faster cycle rate (rpm). In practice, heat transfer rate of helium proves far superior to air, but something else rears its ugly head in practice. Air is a diatomic gas while helium is a monatomic gas. Sooooo, assuming a 'real' Stirling engine with a real regenerator, and once you learn that monatomic helium holds less heat than diatomic air, then any regenerator less than 100% efficiency will 'tax' an air system more than a helium system. Think of it this way...if the tax man wants 20% to go thru regen (meaning regen=.80) then 20% of 15 (helium) is less than 20% of 25 (air). BTW another interesting Stirling buzz word is 'load' (sometimes preceded by regen) which simply denotes the ratio of source heat to regen heat. Back in the day, I was sometimes called the loadmaster, since I spent so much time chasing this bugger down. Then, once I had the simple reduction, it became known as my endless drumbeat. Yep, all I did was quantify (in simple terms) what everyone else had chosen to ignore (in simple terms). It remains on Zig Herzog's Stirling pages as "beyond what can be gleaned from practically any book on thermodynamics, remains the fact..."

[matt brown]

Vincent - my favorite working gas is argon. Maybe it lacks the heat transfer rate of helium, but no diffusion issues while safe, cheap, and available at welding supply shops. Another bonus to monatomic working gases is that they nix the moisture issue inherent with air due to oxygen content. The effect of moisture in air is only now gaining serious study (google that when you need a fresh rabbit hole). I had a brainfart a few weeks ago which led me to many hours on air compressor sites, just checking on where they're at on this. Overall, they consider it a limited cost vs air quality issue, and totally ignored some interesting thermodynamics.

Industry can be really weird, and this air-moisture-compressor issue made me remember a past encounter. 35 yrs ago, i worked in an industrial complex where one small shop dominated the desalinator business on small fishing boats thruout Southern Calif. The owner (a cool Kiwi) was just getting into reverse osmosis and thought they would displace thermal desalinators. Back then, reverse osmosis was pricey to install and operate, however, it was more efficient to operate vs thermal method. At that time, all these guys saw was a simple ratio of fuel to yield, whereby each lb. of diesel saves how many lbs. of water tankage, thus freeing up tonnage for more cargo (fish). I don't recall the actual specs, but back then reverse osmosis was rather crude, so req'd higher pressure than today AND the 'yield' was lower than today. Back then, you'd pressurize something like 50 gallons of seawater to get 1 gallon of fresh water, but that ratio escaped these guys. No, all these guys saw was fuel:fresh water. So, these early systems pressurized 50 units of saltwater for 1 unit of fresh water then simply dumped the 'brine' overboard. When I saw the massive high pressure pump and setup, I cringed. Yep, putting 50 units of energy into saltwater, collecting 1 unit of fresh water, then dumping 49 units of energy overboard with the brine. And so I pitched this Kiwi with a simple scheme to lower initial cost, operational cost, AND drastically improve system efficiency...use a back-back input-output pump where the discharged brine energy transfers to the seawater feed pump. Unfortunately, this poor guy was so overworked he didn't get it, but said he'd pay for prototype and patent if applicable and we'd split the proceeds. I trusted the guy, but didn't take the offer, somehow convinced that I was missing some technical tidbit. A few years later, this became the standard setup...

So, these early systems had guys transfixed on more tangible 'features' than the fact that their new toy was using 50 gals of diesel when it could easily use 1 gal of diesel for the same work.

[Tom Booth]

....Therefore, the speed of heat transfer through sinks on either end is of paramount importance to power output.

I would, of course agree as far as the hot end.

At the cold end? Not so much.

Of course heat input needs to be intermittent, allowing time for the heat to be "used up" before the next blast, but removing heat quickly to a "sink", to my mind, at this point is akin to quickly leaking the gasoline out of your cars gas tank.

Heat is the fuel for a heat engine, it gets used up by conversion to power output. You don't want any "leaks" intentional or unintentional.

The whole Carnot theorem postulates that a heat engine absolutely needs a gigantic gaping hole draining away the "fuel" which is absolutely preposterous.

It makes sense on the surface. Take a soda bottle and leave it in the sun for a while, it will swell and build up pressure. Then take it out of the sun and put it in the freezer, it will gradually loose the pressure and eventually shrink.

But if that was how a heat engine actually operated, by conducting heat in and out, it would take ten minutes to complete a cycle.

Heat conversion to work, or kinetic energy transfer as "work" input or output is instantaneous. Like one billiard ball smacking into another, the motion is transfered from one to the other instantaneously. Heat transfer is slow as molasses.

So, with heat conversion to work output, there is no need to remove the heat to a sink, infact it's impossible, as it has already gone out as work.

Well, only such and such percentage of the heat can be converted, the rest of the unconverted "waste heat" has to be removed, as determined by the Carnot efficiency limit formula: Efficiency = TH−TC/TH

Baloney.