Engine Pressurization

[VincentG]

Ok thank you. Yea these engines are a strange beast. Seemingly simple but so complex and all aspects are related to some degree I agree that the gas can be heated and cooled that rapidly as well, with a good heat exchanger and some thought put into airflow management.

A good test would be to power an LTD model with an electric motor for some time at normal operating rpm. Then record the temperature difference of the top and bottom sinks. I think the effects of compression and expansion on gas temperature are insignificant compared to the heat source relative to ambient temps.

[stephenz]

Regarding time scale stuff, I just launched a quick CFD analysis:
- a pipe of 20mm ID, 100 mm long
- a single iron mesh of 0.2mm thickness and perforated with 0.4mm holes, on a 0.5mm pitch, located in the middle of the pipe (50mm away from either end), the initial temperature of the mesh is 293K
- helium enters the pipe on one end with volumetric flow rate of ~ 100cfm and a temperature of 600K (picked up that number from the volume displaced by a 70mm OD piston in a 50mm stroke)
- this is without pressurization, i.e. 1atm
- this is a type dependent analysis with time step of 1E-5s

The idea is to see how fast the mesh temperature is rising during the transfer (i.e. from the displacer cylinder to the piston cylinder), i.e. at what time scale, and by how much the gas temperature is dropping.
This type of simulation could be used to figure out how many of these meshes would be needed to increase the reduce the temperature of the gas by a targeted amount.

The simulation will run for a few hours.
edit: attached what the mesh temperature looks like after 4.2ms. (temperature rise of close to 50K+ in ~4ms)
edit: attached what the mesh temperature looks like after 6.2ms. (temperature rise of close to 70K+ in ~6ms)

Mesh-Temp-at-4.2ms.png

Mesh-Temp-at-6.2ms.png

[Tom Booth]

A Stirling engine is completely sealed, regardless of how many apparent "expansion chambers" and "compression chambers" or "spaces" or whatever, it's still just one volume of gas.

So when the displacer moves and the air heats up and expands it will push the piston at that time regardless of what path it takes through what chambers or ports or pipes or regenerators or whatever.

There may be less lag, as the path is more direct and with a 90° advance, you could be absolutely right. The gas might expand before the piston reaches TDC and push the piston backwards.

However, if that did happen, you might have to make a timing adjustment and reduce the advance from 90° to maybe 45° or something.

Not sure what I am missing here, I would really like to understand though.

Just to be clear my comment is about the image you posted here, where you are blocking the pathway joining the power piston to the compression space and instead you are joining it to the expansion space.
download/file.php?id=2385

The change you made will make the piston compress gas in the heater (and expansion space) rather than the cooler (and expansion space).
This to me will just make the crank spin in the other direction.

In actuality there are no separate and distinct expansion and compression spaces. There is just one interconnected volume of gas that is alternately compressed/heated and then at another TIME expanded/cooled. The actual air or working fluid between all these so-called spaces is contiguous/undivided.

A regenerator is hardly a barrier to air pressure changes. It is basically an open door between so-called 'expansion space" and "compression space".

There is little resistance to movement of the displacer because there is practically equal pressure all around it at all times which cancels out.

[stephenz]

I agree but by trying to compress the fluid while it is on this of the displacer (i.e. close to the heater) you are defeating the purpose of compressing the gas while it is getting cooled, and expanding while it's getting heated. Of course because none of these steps are actually distinct there is always going some gas that gets compressed or expanded while it's on the wrong side of the displacer, but doing what you showed I think you are just compressing a small volume of cooled gas, and expanding a small volume of heated gas.

If you're going to try this, hacking a LTD engine is probably the easiest, I'd like to see what results you get.

[stephenz]

First 10ms of the simulation are complete, I'll save it as an animation shortly.

At 3000 RPM, you're looking at a cycle that lasts 50 ms, assuming each step was 1/4 of the cycle, you'd be looking at a maximum transfer time of 12.5 ms.

But in 10ms the mesh went from 300K to over 400K, heat is transferring pretty fast.

I'll keep it going a little.

[Tom Booth]

First 10ms of the simulation are complete, I'll save it as an animation shortly.

At 3000 RPM, you're looking at a cycle that lasts 50 ms, assuming each step was 1/4 of the cycle, you'd be looking at a maximum transfer time of 12.5 ms.

But in 10ms the mesh went from 300K to over 400K, heat is transferring pretty fast.

I'll keep it going a little.

A few things just to start with.

Your simulation is based on a flow of helium moving at 100 cfm????

Just for comparison sake, helium is I believe about 5 times more heat conducting than air.

My 10 horsepower shop compressor can move air at 100 cfm. But a model Stirling?

But OK, I did say absolutely impossible so carry on, however I did have in mind a typical model Stirling with ordinary air running on a propane torch.

Logically, in any case I would think that the hotter the engine is heated, the hotter the working fluid gets every 1/2 cycle, the other half spent cooling it back down

A propane torch burns at about 2000°C I believe.

So the air is heated up to, how near to 2000°C maybe?

Then cooled back down to room temperature in less than a second, then back up to 2000°C before that second is over?? No actually how many times a second is this supposed to happen?


https://youtu.be/YlqzdtC7V-0

[stephenz]

These are just rough first approximations to show you the temperature response of the regenerator (and gas) as they exchange heat in the regenerator.

Flow rate is actually very easy to estimate.
The engine is sealed and the piston is physically displacing xxx cm3 per stroke.
If you know the RPM, then you know the volumetric flow rate.

3000 RPM -> 50 Hz -> 0.02 s / cycle -> 0.005s per step (assuming 4 steps per cycle of equal length)
200 cm3 -> 0.2 L

0.2L / 0.005s = 40 L/s -> 0.04 m3/s -> 85 cfm
I rounded it up to 100 CFM as input to the analysis (0.047 m3/s).
Notes:
- In reality not the entire displaced volume would flow through the regenerator, but only the displaced volume minus dead volume would flow through it, so the 200 cm3 above is greater than in reality
- the 5ms is probably underestimated here: the 4 steps of the cycles are not independent, and the overlaps will generate some transfer of gas outside of this window
- the 5ms also assumes constant flow rate which is wrong, there will be acceleration and deceleration causing the flow rate not to be constant

I agree with you that it seems like a high number, but it's well in line with the design I was working on. The piston I designed years ago is 70mm diameter, 50mm stroke (about 200 cm3), the engine I am working on that will use for of those on a swashplate drive.

Anyway, the higher the RPM and piston displacement the higher the flowrate. That's why pages ago I mentioned not to underestimate the pressure drop, as the higher the flow rate, the higher the pressure drop. You really want a regenerator with the least flow restriction. Undersizing the generator is obviously bad as usable energy would go straight to the cooler, hence directly reducing efficiency. But oversizing it is also bad as it increases both flow pressure drop and dead volume.

edit: as for helium, I'm just selfish for running Helium in the simulation because that's what I would use in the engine I will build. If you'd like me to run that same simulation with air, higher or lower gas temperature and lower/higher flow rate, let me know. I'll run it overnight.

[VincentG]

Looking forward to the animation.

Tom, to be sure, the air is not reaching even close to 2000c. At that temp your engine would be a molten pile of metal. I'd be surprised if air temperature is reaching over 500 degrees between the heat lost to natural air cooling, the poor conductivity of the metal plate, and the less than ideal flat internal surface of the hot plate.

If you play around with the thermal camera its pretty amazing how hard it actually is to transfer heat through a sink as intended, then add the loss from the metal to air interface and it becomes a real handicap.

[stephenz]

I am keeping it running until 100 ms, we'll get a better feel for the logarithmic response.
At 37ms the regenerator is well above 500 K already.

After that I'll run another one with maybe 5-10 of those meshes in series.

[Tom Booth]

...If you'd like me to run that same simulation with air, higher or lower gas temperature and lower/higher flow rate, let me know. I'll run it overnight.

You may if you like, but I can pretty much guarantee, whatever the results, it isn't likely to alter my conclusions.

Back in 2012 on this forum I had a crazy idea that expansion work might be cooling the engine below the temperature of the ambient "sink". If the engine runs better the greater the ∆T and ambient is warmer than what the engine is cooling itself by work expansion, then insulating the cold side, to prevent infiltration from the surrounding ambient heat would allow tbe engine to run more efficiently. Partly based on the fact that a Stirling engine can operate as a Cryocooler, without modification.

The response was, if the cold side were insulated, the engine would certainly stop running as it needs to dump the excess heat each cycle.

So, I pretty much put that idea to the side, until about ten years later I got a model Stirling engine to play with and just out of curiosity I carried out that experiment and covered the cold plate of the engine with insulation, fully expecting it would quickly grind to a halt from overheating.

Well it didn't stop. It didn't overheat. It actually ran at a little bit higher RPM.

My point is, any computer simulation is limited and not necessarily representative of actual reality. My conclusions are based on experiments. I tend to believe what I see and observe. A computer simulation is not going to persuade me that what I see with my own eyes is wrong.

[stephenz]

You may if you like, but I can pretty much guarantee, whatever the results, it isn't likely to alter my conclusions.

Back in 2012 on this forum I had a crazy idea that expansion work might be cooling the engine below the temperature of the ambient "sink". If the engine runs better the greater the ∆T and ambient is warmer than what the engine is cooling itself by work expansion, then insulating the cold side, to prevent infiltration from the surrounding ambient heat would allow tbe engine to run more efficiently. Partly based on the fact that a Stirling engine can operate as a Cryocooler, without modification.

The response was, if the cold side were insulated, the engine would certainly stop running as it needs to dump the excess heat each cycle.

So, I pretty much put that idea to the side, until about ten years later I got a model Stirling engine to play with and just out of curiosity I carried out that experiment and covered the cold plate of the engine with insulation, fully expecting it would quickly grind to a halt from overheating.

Well it didn't stop. It didn't overheat. It actually ran at a little bit higher RPM.

My point is, any computer simulation is limited and not necessarily representative of actual reality. My conclusions are based on experiments. I tend to believe what I see and observe. A computer simulation is not going to persuade me that what I see with my own eyes is wrong.

I don't question your observations but in my humble opinion there must be another explanation. Without oversimplifying things, Stirling engines run off the temperature delta between heater and cooler. Everyone has played with LTD's and see them stop once the temperature difference between the 2 plates isn't sufficient enough anymore. In the case of an LTD running off a hot cup of coffee, then engine stops because the coffee cools down and the cold plate eventually warms up. In the case of a HTD running off a candle, even if the candle doesn't stop burning, the engine will stop once the cold cylinder gets warm enough.

Insulating the cold plate of a LTD stirling engine is not as easy as it may sound:
1. The insulation process doesn't change the temperature of the cold plate. It was cold (colder than hot plate) before you insulated it, then it will remain cold until the losses from the stirling engine warm it up.
2. if the temperature of your insulation itself was cool, it likely added capacity to your cold plates. Most thermal insulators have high specific heat (heat capacity).
3. LTD's work on very, very small amount of power, which means it will take time for the cold plate to warm up.

I think what you may have thought was the product of the insulating properties of the material, shielding the cold plate from the environment, was in fact what kept your engine going because you simply added some thermal capacities to your cold plate, effectively allowing the engine the run longer and probably faster.

An (LTD) engine's RPM is based on the temperature difference. The greater the difference the higher the RPM. If you observed higher RPM, then surely the temperature difference was greater. I would suspect the greater temperature difference is the reason why it last longer.

[Tom Booth]

You may if you like, but I can pretty much guarantee, whatever the results, it isn't likely to alter my conclusions.

Back in 2012 on this forum I had a crazy idea that expansion work might be cooling the engine below the temperature of the ambient "sink". If the engine runs better the greater the ∆T and ambient is warmer than what the engine is cooling itself by work expansion, then insulating the cold side, to prevent infiltration from the surrounding ambient heat would allow tbe engine to run more efficiently. Partly based on the fact that a Stirling engine can operate as a Cryocooler, without modification.

The response was, if the cold side were insulated, the engine would certainly stop running as it needs to dump the excess heat each cycle.

So, I pretty much put that idea to the side, until about ten years later I got a model Stirling engine to play with and just out of curiosity I carried out that experiment and covered the cold plate of the engine with insulation, fully expecting it would quickly grind to a halt from overheating.

Well it didn't stop. It didn't overheat. It actually ran at a little bit higher RPM.

My point is, any computer simulation is limited and not necessarily representative of actual reality. My conclusions are based on experiments. I tend to believe what I see and observe. A computer simulation is not going to persuade me that what I see with my own eyes is wrong.

I don't question your observations but in my humble opinion there must be another explanation. Without oversimplifying things, Stirling engines run off the temperature delta between heater and cooler. Everyone has played with LTD's and see them stop once the temperature difference between the 2 plates isn't sufficient enough anymore. In the case of an LTD running off a hot cup of coffee, then engine stops because the coffee cools down and the cold plate eventually warms up. In the case of a HTD running off a candle, even if the candle doesn't stop burning, the engine will stop once the cold cylinder gets warm enough.

Insulating the cold plate of a LTD stirling engine is not as easy as it may sound:
1. The insulation process doesn't change the temperature of the cold plate. It was cold (colder than hot plate) before you insulated it, then it will remain cold until the losses from the stirling engine warm it up.
2. if the temperature of your insulation itself was cool, it likely added capacity to your cold plates. Most thermal insulators have high specific heat (heat capacity).
3. LTD's work on very, very small amount of power, which means it will take time for the cold plate to warm up.

I think what you may have thought was the product of the insulating properties of the material, shielding the cold plate from the environment, was in fact what kept your engine going because you simply added some thermal capacities to your cold plate, effectively allowing the engine the run longer and probably faster.

An (LTD) engine's RPM is based on the temperature difference. The greater the difference the higher the RPM. If you observed higher RPM, then surely the temperature difference was greater. I would suspect the greater temperature difference is the reason why it last longer.

I've pretty much heard all these "explanations" before and have had endless debates on such topics, but, just for example, it is still difficult for me to understand how or why styrofoam can keep my cup of coffee hot, and insulate the heat of the coffee from my hand holding the cup, but the same styrofoam helps my Stirling engine stay cool, readily conducting the heat away, better than no insulation at all

[matt brown]

...
Note that if ANY displacer is truely a 'displacer' than the gas flows around the displacer. So, in my mind, the only way for gas to flow thru this regenerator is for the 'displacer' to act as a positive displacement piston...

The air is still flowing freely around the displacer, so the displacer is not acting as a piston compressing or expanding anything, it is just moving within a close fitting but open ended sleeve or tube, but there is usually still a slight clearance between the displacer and sleeve so there is no friction, other than some air drag perhaps. Most of the air is forced through the regenerator but it is still basically acting as a displacer, IMO.

Except that the regenerator is integrated into the sleeve rather than isolated in a separate tube.

gamma regen Tom.png (69.46 KiB) Viewed 4372 times

OK guys, here's your daily laugh...I never noticed that there's 2 types of displacers (1) a float displacer like in LTD with a wide annular clearance where an internal regenerator might be located (similar Robert's orig.) and (2) a piston displacer like above with no annular clearance (except to nix friction) where an external regenerator is located. Yeah, both are valid displacers since (in theory) pressure is uniform on top & bottom. I don't know how I missed that, but this clearly shows how entrenched I am in alphas when scheming Stirling.

Nevertheless, Tom's point on working piston driven by cold gas is xlnt and why I favor alpha. I reread this thread and noticed something that appears to have slipped past you guys. Take a look at above gamma and as a starting point, consider the 4 distinct Stirling events and avoid phasing particulars. When the displacer moves the gas from hot space, thru regen into cold space, if this was an idealized event sequence, then the cold space would be Tlow with the piston at TDC, whereby an expanding piston would lower gas temp below Tlow, like stephenz zig-zag regen diagram. Remember, I'm pitching this as an idealized event sequence here, but it's clearly there. The question is whether this is more or less of an issue with 'normal' phasing.

So, stephenz, why Stirling? Have you studied Ericsson?

[Tom Booth]

Not sure what you think "slipped past you guys"

That engine arrangement is basically the same as many (well, maybe not many but some, the NASA engine also) others. The giant LTD under discussion on the other thread for example:

Resize_20230520_042814_4902.jpg (81.36 KiB) Viewed 4360 times

The big LTD just turned vertical and the power piston slid over to center. The displacer widened and flattened. (Heater and cooler sandwiched around the regenerator is unusual).

Functionally identical with an LTD gamma with a regenerative displacer (regenerator incorporated into the displacer itself).

What do you mean, about "ideal" vs "normal" phasing?

Anyway in both (horizontal in your post and vertical big LTD) the displacer is inside a sleeve or tube with the (stationary) regenerator surrounding the sleeve.

[Tom Booth]

I agree but by trying to compress the fluid while it is on this of the displacer (i.e. close to the heater) you are defeating the purpose of compressing the gas while it is getting cooled, and expanding while it's getting heated. Of course because none of these steps are actually distinct there is always going some gas that gets compressed or expanded while it's on the wrong side of the displacer, but doing what you showed I think you are just compressing a small volume of cooled gas, and expanding a small volume of heated gas.

If you're going to try this, hacking a LTD engine is probably the easiest, I'd like to see what results you get.

The sequence of events is the same in any of these different configurations.

Heat addition takes place during the compression stroke.

The academic "idealizations" that allegedly involve isothermal cooling during compression are some dreamt up, completely impossible fantasy that does not, and cannot exist in reality.

This heating during compression is no different than the spark advance in an internal combustion engine. The displacer begins to shift the working fluid over to the hot side well in advance (90° ahead of) full compression at TDC.

So, we are supposed to believe there is any significant isothermal cooling (a "quasistatic process" which takes an "infinite" amount of time) in the 1/50th or whatever of a second that it takes to execute the so called "compression". Which "compression" is actually (IMHO) contraction of the working fluid after its energy(heat) has been spent as a result of expansion work.

The REAL (as opposed to "Ideal"/imaginary) cycle, IMO, effects "cooling" primarily by expansion work.

By "expansion work" I mean the working fluid is heated at TDC (BEFORE, during and after TDC that is, but generally around TDC but mostly before) which results in rapid expansion and simultaneous work output (power stroke). Work output takes place during the power stroke. Cooling primarily, almost exclusively takes place as a result (conservation of energy) energy is used to drive the engine, the expenditure of energy results in rapid(instantaneous) cooling. Part way through the power stroke all the heat has already been used up but the momentum of the piston carries the expansion further causing an additional and sudden temperature and pressure drop that snaps the piston back to TDC due to a rather sudden cooling and contraction of the working fluid at the end of the power stroke.

It is utterly impossible for there to be "heat rejection" during this contraction/compression which is a result of the working fluid's sudden drop in temperature at the very extremity of the power stroke as the working fluid has already become colder than anything else. It already used up all its heat with expansion work, then it was mechanically expanded and cooled even further by the momentum of the piston "stretching" the working fluid like a rubber band beyond it's natural limit, after already using up all the heat-energy that was supplied to it just before TDC.

The so-called "compression" is really a kind of "snapping back" of a stretched elastic gas.

Contrary to all the academic claptrap, heat addition takes place from BDC to near TDC when the working fluid is cold and contracting and able to accept heat (during "compression").