Stirlingengineforum.com

For a summation, by way of an illustration, IMO the way a Stirling engine ACTUALLY works, tossing all the "ideal" models into the dustbin:

Imagine a cannon with a very long barrel and the cannon ball attached a bungy chord.

After ignition, the ball is jettisoned down (up) the cylinder by the expanding gas. When the gas is done expanding the momentum of the cannon ball keeps it going until the bungy chord is stretched.

Finally the ball is pulled back down the barrel back to where it started where another charge can be ignited and the process repeated.

Air, or a gas is elastic, like this bungy chord that "stretches" and then "pulls" the piston back.

There is no role played by any "cold side" in this scenario.

In the cannonball illustration, gravity plays a roll in helping "pull" the ball back. In a Stirling engine the role of "gravity" is played by atmospheric pressure.

The cannon ball is jettisoned out against gravity which helps bring it back down.

A piston in an engine is jettisoned out against atmospheric pressure which then pushes it back.

That theory can easily be tested by running the engine as a heat pump.

VincentG wrote: ↑Sat May 20, 2023 8:12 am That theory can easily be tested by running the engine as a heat pump.

The engine is basically already acting as a heat pump. But in a direction opposite to what is usually believed to be the direction of the flow of heat.

Take the cannon with the extended barrel.

Supposing that the cannonball were mechanically driven up and down.

When pulled up, the gas inside the barrel is expanded/cooled and heat may then be absorbed into this expanded cooled gas.

When the cannon ball is subsequently driven back inward, the gas is compressed/heated, including the extra heat it absorbed while expanded. Now heat can move out, but this movement is confined to the small area at the base (or combustion chamber).

Heat is being taken in frome the barrel's upper extremities and "pumped" out at the base.

If this action is continued, the barrel will get colder and colder and the base will get hotter and hotter.

If the heat accumulating at the base is removed, by a water cooling jacket, you have a Cryocooler.

If additional heat is supplied at the base, you are back to having a heat engine, however this does not completely eliminate the heat pumping effect of the expansion and contraction that is trying to move heat towards what is now the heat source for the heat engine.

matt brown wrote: ↑Fri May 19, 2023 7:52 pm
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?

It's really hard to ignore phasing, which was the reason why I expect the temperature profile in the regerenator to be different in the cold to hot way, vs hot to cold way. A perfectly symmetric (from the point of view of phasing) should not yield this hysteresis. Another way to look at this: ignore the displacer completely as we know that due to phasing issues if you consider power piston TDC and BDC the displacer will be in a position that is not ideal: perfect power piston position yields less than ideal displacer position. As such, during compression and expansion, some gas will not be in the volume in which we wish it were. In other words some of the gas in the heater will get compressed when we'd wish no compression would ever occur in the heater/expansion space. And vice versa. There have been efforts into valving, fully independent linear pistons, etc. and as far as I know the pure lack of practicalities in those techniques are the reason why we won't see them implemented. If I was to spend a meaningful amount of time into researching a way to address phasing issue it would be on a 4-stroke concept.


No, I haven't studied Ericsson's. The bug for stirling engines comes from my thermodynamics professor back in engineering school.

One additional important point is the additional cooling effect during the power stroke due to the work output.

I posted some references to this early on in the "Stirling engine thermodynamics" thread:

viewtopic.php?f=1&t=478#p1225

To be clear, I don't discount the cooling effect from work. But at best that should bring the gas temp back to "ambient" levels. Any cooling beyond that I imagine would be done by the cold sink and by expansion. My only point, that these model engines don't have compression or expansion ratios high enough to make an impact here. A well designed engine must surely benefit from such effect, and when powered by electric motor would show some heat pumping action.

At the end of the day I'm after the truth of what makes these things tick. So the only way for us to get answers is by experimenting with our theories.

Here's the temperature response of the steel mesh exposed to a flow of helium at 600K.
Mesh size: 20mm OD
Hole size: 0.4mm
Thickness: 0.2mm
Flow Rate: 0.05 m3/s
Gas temperature: 600K

I will redo this with more meshes to see a meaningful impact on the gas temperature exiting the stack.

https://file.io/ts2hFEvc4tpK

The next simulation is more representative of a single stroke, with ramps up and down.This way I'll have a better idea of the final temperatures for the gas and mesh.
Have you guys every try to run basic calorimetry analysis to size your regenerators (or coolers/heaters for that matter)?

Thanks for that analysis Stephen. Could you possible post the final temp of the hottest section of mesh? Its hard to gleem from the color alone.

One interesting thing comes to mind. Tom, you often speak of the direct transfer of energy that the hot gas exerts on the piston. I don't discount that, but I don't think it a significant contributor to net results. But in this case, the air flowing through a mesh at those cycle times must be enough to excite the mesh into some level of vibration. That is enough to create its own heat and or accept heat from the air in the form of vibration. I would bet that the same test duplicated in real life would have much different results. I could be way off here but I know just from using the shop blow gun as a mechanic, things can get extremely hot just by blowing air through them. This is sort of how the rice steam engine works i imagine.

VincentG wrote: ↑Sat May 20, 2023 4:32 pm To be clear, I don't discount the cooling effect from work. But at best that should bring the gas temp back to "ambient" levels. Any cooling beyond that I imagine would be done by the cold sink and by expansion. My only point, that these model engines don't have compression or expansion ratios high enough to make an impact here. A well designed engine must surely benefit from such effect, and when powered by electric motor would show some heat pumping action.

At the end of the day I'm after the truth of what makes these things tick. So the only way for us to get answers is by experimenting with our theories.

Yes, glad you are open minded and willing to experiment, that is a good attitude.

My rationale, as far as "I don't discount the cooling effect from work. But at best that should bring the gas temp back to "ambient" levels." I ask why could it not? Why could the engine not cool "itself" so to speak, below ambient? It is, after all, inherently a kind of heat pump and there is a power source.

Also, it is not entirely without precedent. Heat driven heat pumps exist, and though uncommon, are, I believe, in use today, Generally, variations on the thermally driven Vuilleumier heat pump. More often than not, I believe most of these engines (Vuilleumier heat pumps that is) use a small external motor to drive the displacers for simplicity though, I believe some incorporate an additional small pressure actuated piston, that works similar to the Ringbom principle.

But there are reasons for concluding that a Stirling engine already cools the working fluid below ambient. The strongest evidence, I think, short of actual internal temperature readings, is that a thermal lag, or thermal-acoustic engine can operate quite normally without a flywheel. If the temperature were not dropping below ambient (outside atmosphere) then I would suspect that the piston would only travel outward a distance and stop without a flywheel to drive it back in. It is driven back in by atmospheric pressure, presumably, but how is that possible unless the engines internal pressure drops below atmospheric pressure, and if the working fluid is below atmospheric pressure I would argue that it is also below ambient temperature as the two are actually synonymous. In a gas, the temperature and pressure are both manifestations of the same molecular motion..

Unfortunately, finding a thermometer that is responsive enough to take accurate temperature readings of a gas at millisecond intevals is difficult.

https://youtu.be/HUWt3YrxoB4

As far as the pressure dropping below atmospheric pressure, there is no question about that. Is it possible to have such a drop in pressure below atmosphere, which is measurable, without a corresponding drop in temperature below ambient?

In the case of the engine in the above video, the "cold sink" is ambient. There is no external work, so logically expansion due to momentum of the piston is already cooling below ambient. I can only assume the addition of an external work load would produce additional cooling.

Just to make sure you read my one thought right, I was distinctly trying to separate the work(and cooling) the air does by impacting the piston, from the cooling of further expansion towards BDC.

Again, I don't discount even the former. But if true, I'd think that would be incredibly hard to prove in concrete terms at least in anything other than really high level research labs.

VincentG wrote: ↑Sat May 20, 2023 8:32 pm
.... Tom, you often speak of the direct transfer of energy that the hot gas exerts on the piston. I don't discount that, but I don't think it a significant contributor to net results. ...

Well, there is a chamber filled with air at 1bar (atmospheric pressure more or less), or whatever pressure, and we could imagine this as tiny atoms zipping past each other or rubber balls rather tightly packed.

If the latter, expansion on one side will mostly transfer to the other more or less instantaneously, but I think this would also be true at any point.

So if gas is pushed through a regenerator from left to right into a hot space, to some degree, when it expands it will have to expand back the way it came, through the regenerator, so however you slice it, or imagine the air molecules, with the usual arrangement there will be hysteresis loses because some hot expanding gas will move into the cold regenerator and cold space and contract, having an indirect effect, if not a direct one.

Anyway I think trying an arrangement that gives the heated gas a direct path to the piston, without cooling elements in the path is probably worth a try for comparison.

VincentG wrote: ↑Sat May 20, 2023 8:32 pm Thanks for that analysis Stephen. Could you possible post the final temp of the hottest section of mesh? Its hard to gleem from the color alone.

That first simulation assumed that 0.05m3/s for a total of 0.1s, that's a heck of a long time. But the idea was to make sure I would capture at what time the mesh would get passed a certain temperature threshold, i.e. to understand how fast the mesh thermal response was.

at 0.1s when the simulation ends the average temperature of the mess is just a few degrees below the gas temperature. but 0.1seconds would mean a much slower RPM (600 RPM) and as such, at that speed the displaced volume would be much less, i.e. the boundary condition on the flow rate is also 5 times greater than reality, so higher convection, etc.

following simulations will be more realistic, by just simulating a single stroke with ramps up and down

It seems you picked a good starting point for regenerator size then. I think 600rpm is realistic for a LTD style engine as well.

stephenz wrote: ↑Sat May 20, 2023 10:56 am
If I was to spend a meaningful amount of time into researching a way to address phasing issue it would be on a 4-stroke concept.

Hmmm, this made me realize I botched a recent post. As a gamma (but similar for beta) I assume your 4 strokes are,
and as always, considered as distinct ideal events with 300-600k cycle and regen:

(1) displacer TDC-BDC where TDC hot space (clearance volume) is minimal, but BDC space is noticeable, this event ends with Pmax thruout engine, 600k in hot space, and 300k in cold space

(2) piston TDC-BDC expansion lowers P thruout engine and further lowers T thruout cold space (and piston cylinder)

(3) displacer BDC-TDC ???

(4) piston BDC-TDC compression increases P thruout engine

If correct, then note that during expansion (2) T is <300k unless heated by "ambient" 300k which would add to Wpos. Of course, as an isolated event, an isothermal expansion following by an isothermal compression is a zero sum game, just like a matching pairs of adiabatic processes. The question is what happens during (3) ???

With just a single working 'oscillating' piston at a constant temperature, the only Wnet is via PV=mRT where that little "m" represents dP due to a change in density. This akin MEP (mean effective pressure) in the ICE world. Since piston cylinder volume is part of the cold space, and this cold space is ideally considered a constant temperature, a little quiet reflection should illuminate MEP limitations. Yep, since high compression appears impossible, the only way to achieve large pressure swings is with multi bar buffer pressures.

As a sidebar, note that the above sequence is 4 'clean' 180 deg strokes, and no alpha ever had it this easy.