Stirlingengineforum.com

This is a fantastic lecture that maybe gives this topic TOO thorough a treatment.

It is very heavy in mathematics, but the pi/2 resonant frequency at 90° offset jumps out from time to time.

About 50 minutes in there are a couple of good demonstrations.

https://youtu.be/Y_DmzZcQR7A

What is interesting to me is that this 90° resonance phase shift is so precise, has such a very strong effect and such wide application in many different systems.

I came across this i interesting statement:

the best coupling of energy into the system happens when the driving force is exactly 90 degrees out of phase with the amplitude (so force is in phase with the velocity)

https://physics.stackexchange.com/quest ... -resonance

I can't say that I understand exactly what is meant by that, but...

The piston is at maximum velocity when midway between BDC and TDC or vice versa. Which is the point at which the displacer changes direction. 90° from where the piston reverses it's direction at TDC and BDC.

What is kind of counterintuitive is that the "driving force" is in the opposite direction.

When the displacer lifts to drive the piston out with the addition of heat for expansion the piston is at maximum velocity traveling in for compression.

Yet, if you swing a pendulum, as the pendulum swings left, you will intuitively move your hand to the right, opposite to the direction of motion of the pendulum, and this increases the amplitude of the pendulum swing.

If the force were applied directly to the weighted end of the pendulum this would not happen. The pendulum would be slowed down or stopped by the opposing force.

So, this seems to apply where there is a "springiness" or compression involved, or indirect force applied.

That is; there is a spring between the driving force and the object.

The spring absorbs the velocity and sends it back in the opposite direction.

Most of the above demonstrations involve fome kind of spring attached between the driver and the driven mass.

In a Stirling engine air, or the "working fluid" is both the driver (expanding hot gas) and the "spring" in the form of an air spring, simultaneously.

Maybe I'm out in left field somewhere, just thinking out loud.

But if you are pushing someone on a swing, you don't start pushing at 90° when the swing is moving towards you at maximum velocity.

You wait until the swing finishes and starts to reverse direction and then push.

But what if you had to push on a big spring attached to the back of the swing? You would want to start pushing earlier to let the spring absorb the momentum of the swing, then your push would have more power.

When the swing was at full velocity, you would just begin to start putting resistance on the approaching spring.

Basically, I think, if you are pushing against a spring, you really don't need to move or shove the spring. Mostly you would just offer resistance and wait until the spring was fully compressed. Then at that point your effort would have a great effect, though only pushing a small distance. As you push, the spring also expands, so the forces are additive.

If you started pushing the spring earlier or later, you would just be pushing against a loose, uncompressed spring and no real force would be applied to the approaching mass.

https://thiscondensedlife.wordpress.com ... resonance/

It means that the maximum pressure should be at the maximum piston velocity, or halfway between top and bottom dead center. Similar to the graphic provided only more centered.

It seems to me that if the maximum is constant for the entire stroke, and the minimum for the entire return stroke, that would maximize work out per cycle. That is what the ideal Stirling Cycle tries to accomplish. Except it is for the maximum temperature.

It seems as if all the links you have supplied are talking about harmonic resonance. They are a mass, spring dampener system. Most of our Stirling Engine are very stiff and lightweight. That leads to high resonance frequency. So the only thing, spring, mass, would be the internal gas itself resonating.

Perhaps that is what happens in acoustical Stirlings, or even Jam Jar Pulse Jets. They resonate at a frequency dependent on several things such as: volume orifice, laminar connecting tube size and length.

In crankshaft engines the hottest and highest pressure is produced in a slow sinusoidal process, so the beginning is slow. Middle fast. Ending slow.

Also, Senft's lost motion link would both delay the onset of the pressure increase, and delay it's removal.

The ideal cycle has the displacer motion during either top or bottom. Essentially in phase.

Fool wrote: ↑Fri Jun 07, 2024 12:38 am ...
The ideal cycle has the displacer motion during either top or bottom. Essentially in phase.

I still have not found who came up with the supposed or so-called "ideal Stirling cycle", but IMO it is clearly wrong.

There is no such thing in Robert Stirlings patents. In ALL REAL actually functional Stirling engines the displacer leads the piston by 90°

I'm interested in reality. How these engines work in actuality, not some hypothetical nonsense some unknown Wikipedia editor put up as the supposed "ideal" Stirling cycle.

Does anyone know where the often touted "Ideal" Stirling cycle PV diagram actually originated? Because IMO it appears to be spurious. i.e. did not originate with the actual inventor of the Stirling engine, Robert Stirling or his brother, and is not a true or accurate model or representation of how a functional Stirling engine REALLY works.

Needles to say, sometimes, (I might even say often), inventors arrive at a working machine through trial and error that may or may not be based on some accurate or inaccurate underlying principle the inventor may or may not have been fully aware of at the time.

As far as I know no one has ever linked or associated Stirling engines with the resonant frequency of a spring mass type system which just happens to fall at 2/pi radians or 90° which just coincidentally happens to correspond exactly with the traditional Stirling displacer advance. So I don't really see the point "Fool" in throwing all this old theory that everybody already knows and is familiar with against the board.

This is an exploration into, (as far as I know), uncharted territory. A new theory.

Aside from your post being largely incoherent, off topic and vaguely confrontational your reference to, and use of my diagram is also misleading and wrong.

You say:

It means that the maximum pressure should be at the maximum piston velocity, or halfway between top and bottom dead center. Similar to the graphic provided only more centered.

This makes no sense and my graphic you have reproduced above is not in any way related to this topic at all.

Further, pressure and velocity are inversely proportional, meaning that when the velocity increases, the pressure decreases.

So no, "it" whatever "it" you might be referring to, does not and cannot mean anything of the sort.

A potentially helpful link in understanding all this: (probably more to follow soon)

https://www.quora.com/Why-is-there-a-ph ... nce-occurs

...we can see where this 90-degree phase shift comes from - it is where you put the most energy into the system.

If we want to do a lot of work on an oscillator, when should we exert force on it? The answer is when it is moving quickly. Work is force times displacement. If the oscillator isn't moving, we have zero displacement and don't do any work. When the mass is moving quickly, pulling on the spring does a lot of work on the mass"

(... Math does not c/p accurately...)

"The force should be proportional to the velocity to maximize work done in a cycle. That is where the phase difference come from. Because the force reaches a given phase before the position, we say that the force leads the position, and is in phase with the velocity.

What all this seems to boil down to IMO is that on the return stroke of the piston, the atmospheric or buffer pressure is converted into VELOCITY.

(Traditional engine thermo, PV diagrams etc. generally do not address piston/engine velocity.)

By adding heat 90° before TDC the working fluid acting as a gas spring can absorb the maximum amount of energy from the pistons velocity/momentum.

In this way, by using an advance corresponding to 90° (maximum piston velocity) the concentration of "heat of compression" and the added heat, the input from the buffer or atmospheric pressure (converted to velocity) can all combine to reach a "critical mass" so to speak at TDC.

I think this relates to, confirms, compliments, and makes more understandable my earlier "aligning heat vectors" thesis.

viewtopic.php?t=5556

Another way of describing this might be that what Matt Brown refers to as "work neg" during the return stroke, rather than being lost or subtracted from "work pos" is stored in the working fluid as gas spring pressure and returned as a positive driving force at and/or after TDC contributing to the expansion/power stroke.

In other words, if the working fluid is considered to be a spring of sorts, the returning piston is very much like a heavy ball being dropped onto a spring. The gravitational potential energy is conserved (in a hot air engine, atmospheric/buffer pressure rather than gpe of course) in the spring and returned, the heavy ball is thrown back up in the opposite direction. The energy is not lost.

Under no-load conditions the addition of a very small amount of heat gives the gas "spring" a little extra boost to compensate for friction and maintain the oscillation.

Under load, doing external work, additional heat added compensates for the additional work output.

In this earlier "heat vectors" theory though:

I was thinking that the displacer advance was merely compensatory for the time delay for heat to transfer from the heat exchanger plate into the working fluid.

Further experimentation by myself and others seems to indicate that such a time delay for heat transport is negligible, or virtually non-existent.

This new theory is, I think, a much better and probably true explanation for why the 90° advance is necessary, or at least HIGHLY advantageous.

It is to capture, convert and reuse the VELOCITY of the return stroke so as to direct all that energy back into the power stroke.

The velocity is at a maximum 90° BTDC so it makes sense that if you want to capture that energy you need to start at that point of maximum velocity.

Pushing a swing from the ground. Do you push when at it's fastest, the middle point? No. But that is the 90° point. Most people push right after top dead center, and after motion has stopped, reversed. That is the 0° point. It is when the swing is moving slowest and away from the pusher.

Have you ever done a run through? That is pushing for the whole stroke, from 0° to 180°. The change in swing amplitude is highest per single stroke with such a maneuver. Steam engine valve timing could be adjusted from the cab using a Johnson, to go into this mode. It can be adjusted back to small taps when just at top dead center. Applying a maximum temperature for the entire stroke, Th, is the best that can be done in a heat engine. Senfts lost motion link is an attempt to mimic that process more than just a crank driven displacer. I've seen attempts to use bevel gears to effect similar motions. It seems impossible to do in an IC engine.

There are reasons to study ideal concepts. One is that they describe a maximum target garnering improvements. The ideal models are not a limit. They are a goal. Nature is the limit, the models just describe nature. If someone breaks out of that model, using proper scientific testing, the model will change, not the nature.

For real engines, PV/indicator diagrams must be measured. I put one in my last post so that people could see that maximum pressure was reached at about the 45° point, and maximum temperature at past the 135° point. Until why there is that discrepancy is learned, the idealized harmonic resonance in a spring, mass, damper, driven system, will not be understood as to why it is about as unconnected as can be.

Why are the temperature, pressure, and piston velocity, peaks in that indicator diagram at three difference crank positions?

It has to do with kinematics, not resonance. It has nothing to do with aerodynamic flutter either, another 90° lead phenomenon. It's just coincidental. Unless you want to try pushing a swing at the 90° point, don't get mowed down by the swinger suddenly spreading their legs (Safety concern).

In heat engines gas pressure and atmospheric pressure are always pushing in opposing directions for the entire stroke. Account for that in your analysis. It is always a run through for both, although ether could be called a pushed back fight. The outside is a constant temperature and pressure. The inside is not and makes analysis complicated. Indicator diagrams are the only tool we have to study that gas action. Please use them in your analysis of real engines. Please also use dynamometers, volt and amp meters, thermometers, IR cameras, etc...

I found the resonance links very interesting. Please keep posting these kinds of threads. Thank you.

Fool wrote: ↑Fri Jun 07, 2024 5:38 pm
..Th, is the best that can be done in a heat engine..

That's like saying a fire piston can't generate any temperature above ambient

Or a heat pump for that matter.

Supposing there is anything to this 90° advance / driven oscillator concept, I'm thinking it may have application for Ringbom engines.

Formerly I had been thinking that an advantage of the Ringbom would be that without a direct connection to a crankshaft the timing of a Ringbom could be easily moved away from the 90° sinusoidal timing closer to IC engine-like timing nearer to TDC.

I may need to reconsider that plan.

At least it warrants some experimenting.

Ringbom engines are said to be "fussy" or difficult as far as getting the timing in sink.

Maybe the 90° thing, if really necessary, could serve as a guide to adjusting the timing of a Ringbom engine.

Fool wrote:Applying a maximum temperature for the entire stroke, Th, is the best that can be done in a heat engine.

Applying work to increase temperature in an adiabatic cycle is a zero net work cycle. Just as much goes in as comes back out. The effort is cancelled. Like pushing a wagon up a hill and letting it roll back.

Fool wrote: ↑Mon Jun 10, 2024 6:23 am

Fool wrote:Applying a maximum temperature for the entire stroke, Th, is the best that can be done in a heat engine.

Applying work to increase temperature in an adiabatic cycle is a zero net work cycle. Just as much goes in as comes back out. The effort is cancelled. Like pushing a wagon up a hill and letting it roll back.

That's your opinion.

I call it moving useless heat to a situation where it becomes useful. Low grade heat is useless. Compressing it to bring it up to a higher temperature at TDC where it can be used in the power stroke and converted to work makes it more useful

Again. There is no heat in adiabatic compression. You are only taking the work energy and storing it as internal energy, during a single stroke. Loss of work energy, stored as internal energy, indicated by temperature. Less work to output.

No free lunch. No heat/no energy to output as work.

If you have cooling for half the stroke you will have used less work for compression, thus have more to output for the cycle. Of course, that is the Carnot Cycle.

PV diagram needed.