Stirling Engine Thermodynamics

[Tom Booth]

I've been reading quite a bit about thermodynamics lately. Especially in regard to the fact that when a gas is "made to do work" it looses heat or gets cold.

This has been a hard concept for me to grasp, but apparently, when a gas does work of any kind, the heat energy in the gas is converted into "work" or the kinetic energy - such as moving a piston.

Now, formerly I had been under the impression that a Stirling engine functions by means of a temperature differential applied to it. One end of the displacer chamber is heated and the other end cooled - the air travels back and forth from one end of the chamber to the other and picks up or looses heat in that way...

But I'm becoming aware that there is also apparently something a little more subtle going on, that is, when the air in the chamber heats up and expands and then does work against the piston - the heat does not only travel to the "heat sink" at the cold end of the chamber but some of the heat is actually converted into work. In other words, what cools the hot expanding air back down is not so much, or not only coming into contact with the cold end of the chamber but heat is also lost on account of the gas being made to do work against the piston.

What I'm wondering is just how much heat is actually being absorbed in this way i.e converted into work as opposed to the heat being absorbed by the heat sink (the cold end of the chamber at ambient temperature).

If more heat is extracted as work than what actually reaches the heat sink, then theoretically, insulating the cold end of the displacer chamber against the external ambient temperatures would improve engine efficiency.

That is rather speculative, but I was also thinking that if what I have described above is true - i.e. that the heat is converted into work, then a Stirling Engine should operate cooler and be more efficient when under a heavy load doing some kind of actual work rather than just running without a load - not doing any work.

If heat is being converted into work then the more work the engine is made to perform the cooler it should run. Maybe the problem with many model Stirling engines overheating is that they are being run without a load of any kind and therefore the heat, rather than being transfered to the load on the engine to do work is just building up and causing the engine to overheat.

Perhaps this is already a known fact but for me it is something of a new realization and I'm wondering if anyone with more knowledge and experience in this area might be able to confirm or refute this supposition.

Thanks.

Tom

[Longboy]

.......the moving parts of the Stirling, such as the piston absorbs and releases heat. It is an "engine" and does work. Air at different temps generates a pressure differential that moves the mechanism, the basics of Stirling. Less heat input will not result in more work. Model Stirling nature is low torque output. An overheated Stirling will stall, there is no longer a sufficient heat differential to move the mechanism.

[Tom Booth]

...Less heat input will not result in more work.

I'm not suggesting less heat input at the hot end, just less heat input (from the atmosphere) at the cold end, where heat is not wanted.

Model Stirling nature is low torque output. An overheated Stirling will stall, there is no longer a sufficient heat differential to move the mechanism.

Regardless of the potential torque output, actual or theoretical, it seems to me that ANY work done, no matter how small or seemingly insignificant would have to result in cooler temperatures at the unheated end of the displacer where heat is not wanted resulting in greater efficiency and possibly a gradual increase in torque as the temperature differential increases.

In other words, by making a model (or any other) Stirling Engine do some work rather than just freewheeling, more heat would be converted into work and the temperature differential would increase proportionately to the amount of work being done.

It seems very difficult to find information on this subject and it is a rather obscure point, mostly discussed in relation to liquefying gases but I've found several references I can post here:

"Any gas, when compressed, rises in temperature. Conversely, if it is made to do work while expanding, the temperature will drop."

Refrigeration and air-conditioning By A.R. Trott, T Welch - pg 26

"The process" (of gas liquefaction) "has been considerably cheapened by the work of Kapitza. In the ordinary process air is highly compressed and cools itself by suddenly expanding. Kapitza saw that it would lose much more heat if it was made to do work while expanding, and designed a turbine to operate at liquid air temperatures to turn as much heat as possible into work.

Today the Soviet Union leads the world both in the theory and practice of gas liquefaction."

SCIENCE ADVANCES by J. B. S. Haldane pg 209

"The story then is one of triumph after triumph. Oxygen was liquefied by Olszewski in 1883, and two years later nitrogen and carbon monoxide. The list of lowest temperatures as they were reached, reads like the records of athletic achievements; in both the next step is always the harder to achieve than the one before. A new principle was applied to produce the cooling. If a gas under pressure, below the inversion temperature, is allowed to expand freely through a fine nozzle or if it is allowed to do mechanical work while expanding, it will cool, and may reach a temperature at which it liquefies. Thus we get two methods for liquefying the gases. One employs the Joule-Thomson effect, which allows the gas to expand suddenly and so produce the necessary cooling by the performance of internal work; the linde and Hampson processes depend upon this principle. The other processes employ the reversible expansion of the gas with the performance of external work; the Claude and Heylandt processes are of this nature."

Production and Measurement of Low Temperatures By K.R. Dixit No. 12 June 1938

"Another way to cool a gas is to have it do work adiabatically" (without heat transfer) "against a piston in an engine, and this has no temperature boundary like the Joule-Kelvin effect. Gas liquefaction using such engines is now common not only for helium, but also for air. These liquefaction plants are small and easily handled, so that every lab can have its own source of liquid air"

Helium -

http://mysite.du.edu/~jcalvert/phys/helium.htm

These references, (and many others I've come across) talk about producing extremely cold temperatures simply by making a gas expand and do work against a piston, cold enough to cause the gas to liquefy, which is certainly well below ambient temperatures, which leads me to believe that possibly the "cold" end of a displacer chamber in a Stirling Engine at ambient temperature is perhaps not cooling the air in the chamber at all but on the contrary actually heating it and reducing efficiency. If this is true then efficiency could be increased by insulating the cold end of the chamber against the heat intrusions from the external ambient air.

This seems hard to believe, but if the air is getting that cold as a result of performing work then perhaps it is true. That is, if the engine were given some actual work to do rather than just being allowed to run without any load. The more work performed, the more heat is converted into work rather than just building up.

[Longboy]

......Think in terms that a Stirling is not a compressor. Referencing liquification of gasseous elements to Stirling not valid here. It's not a mystery that dispelling energy does result in a cool down anyway. If you have a basic grip of thermodynamic principles........that heat travels to cold, increasing Stirling efficiencys by having a colder ambient power cyl. do more work will not grant you a "seems to me" pass. Its a givin that in modeling Stirlings that the hot side is insulated from the cold side, but heat will migrate to the cold side by working fluid and build materials conduction. Take the Senft fan engine, it is a verticle design and the heat rises into the model. Its power cylinder is very hot and it pulls a pretty good load driving the fan blades (work). There is enough heat differential to run and enough radiator to disperse exessive heat while being cooked by its burner. Chilling out the power side and having it pull more than its own flywheel will not give any efficiencys we wish to improve. You will run into a lack of torque here to even try a measured response to your premiss. My bets are with those thermodynamic principles. If two guys walked up to a model Stirling, one with a torch to the hot cylinder and the other with a bucket of ice for the power cylinder, guess where the smart money lies? I will be puttin' on the heat instead of standing in a puddle...........thats why they call them "heat" engines!

[Tom Booth]

......Think in terms that a Stirling is not a compressor.

Who said it was?

Referencing liquification of gasseous elements to Stirling not valid here.

"here" ?

Why not ?

It's not a mystery that dispelling energy does result in a cool down anyway.

So... are you saying I'm wrong by saying I'm right ?

If you have a basic grip of thermodynamic principles........that heat travels to cold, increasing Stirling efficiencys by having a colder ambient power cyl. do more work will not grant you a "seems to me" pass.

I said nothing in regard to a "colder ambient power cylinder". The temperature of the power cylinder is largely irrelevant.

Its a givin that in modeling Stirlings that the hot side is insulated from the cold side, but heat will migrate to the cold side by working fluid and build materials conduction. Take the Senft fan engine, it is a verticle design and the heat rises into the model. Its power cylinder is very hot and it pulls a pretty good load driving the fan blades (work). There is enough heat differential to run and enough radiator to disperse exessive heat while being cooked by its burner. Chilling out the power side and having it pull more than its own flywheel will not give any efficiencys we wish to improve. You will run into a lack of torque here to even try a measured response to your premiss.

Ummm... Your reference to the Senft fan engine that "pulls a pretty good load driving the fan blades (work)" would seem to prove my point. Unlike many model Stirling Engines I've seen, the Senft fan engine does have a load - THE FAN!

It is also pulling "more than its own flywheel". It appears that this engine uses the fan as a "flywheel".

You could certainly measure the difference by replacing the fan blade with a smooth flywheel of the same weight as the fan to reduce the work load (it will no longer be pushing air) on the engine while using an external electric fan to maintain the same air flow around the engine.

If the theory is correct, then the Senft engine should run hotter with the reduced load, though everything else would remain the same.

Or alternatively, you could add any kind of load to an engine that would otherwise be running without a load - such as a small permanent magnet motor used as a generator to power a light bulb. In that case the engine should run cooler with the additional load.

My bets are with those thermodynamic principles. If two guys walked up to a model Stirling, one with a torch to the hot cylinder and the other with a bucket of ice for the power cylinder, guess where the smart money lies? I will be puttin' on the heat instead of standing in a puddle...........thats why they call them "heat" engines!

I'm not sure why you keep saying "Chilling out the power side" or "bucket of ice for the power cylinder" etc.

The majority of the gas expansion and contraction is taking place within the displacer chamber. The gas in the displacer chamber is doing work against the piston reducing the temperature of the gas in the displacer chamber to one degree or another. Only a fraction of that gas, hot, cold or otherwise ever enters the power cylinder.

[jesterthought]

Hi Tom,
1. Insulating the cold end will not help (or we would all have been doing so).

As you say, model hot air engines sometimes slow down because the cold end gradually warms up, thereby reducing the temperature differential. If the cooling is by ambient air, the warmth of the “cold” end can be felt. Since it is above the temperature of the cooling medium, that medium cannot be heating it!

To insulate it would cause the cold end to heat more rapidly and slow the engine even sooner.

Expanding the working fluid enough to cool the cold end would require mechanical power for “heat pumping” (see 3. below). That would reduce the power of the engine – for example, by reducing the pressure on the piston.

2. The reason the cold end is warming is that we are putting heat into the engine. Engines are not yet 100% efficient, therefore the power out is less than the heat input, and most of the excess heat is rejected at the cold end – which must be cooled.

Heat is being fed to the cold end by the working fluid, internally, not from the atmosphere. Ambient air is still cooling it (although, sometimes, not quite enough).

In an engine delivering a net power, the working fluid is expanding from a high temperature (for a high pressure on the piston) to power the flywheel. It is compressed at a lower temperature (for a lower pressure), taking less power from the flywheel.

More heat also short-circuits the thermodynamic process by conduction through the structure, increasing the cooling required by the cold end.

3. Yes, Stirling engines are used for liquefying gasses, but not by heating them!

They are mechanically driven to “pump” heat from the cold end to the “hot end”, which must then be kept cool. This way, the cold end is made very cold. But the input is mechanical power, not heat.

In an air liquefier, air expands from a high pressure at near-ambient temperature, becoming very cold by doing some mechanical work on a piston, eg. Ambient air has to be compressed (which heats it and requires work) and then cooled back to near-ambient temperature, ready for the expansion. Compression requires the piston to do much more work on the air, so a net mechanical input is required.

Heat flows down only to ambient. It takes power to cool the working fluid below that temperature (despite the heat being released from it).

Jester.

[Longboy]

......Think in terms that a Stirling is not a compressor.

Who said it was?...............That would be you refferencing outta a HVAC manual to form your theory.

Referencing liquification of gasseous elements to Stirling not valid here.

"here" ?

Why not ?..............That would be because Stirling is not.....a compressor.

It's not a mystery that dispelling energy does result in a cool down anyway.

So... are you saying I'm wrong by saying I'm right ?.............No. The book you referenced, that author is right.

If you have a basic grip of thermodynamic principles........that heat travels to cold, increasing Stirling efficiencys by having a colder ambient power cyl. do more work will not grant you a "seems to me" pass.

I said nothing in regard to a "colder ambient power cylinder". The temperature of the power cylinder is largely irrelevant.
unbelievable! Then I agree, you said nothing. (and doesn't read his own words). That would be where this piston that you said in your openning post the expanded air works against and should cool down when doing "ANY" work ........resides
..........

Its a givin that in modeling Stirlings that the hot side is insulated from the cold side, but heat will migrate to the cold side by working fluid and build materials conduction. Take the Senft fan engine, it is a verticle design and the heat rises into the model. Its power cylinder is very hot and it pulls a pretty good load driving the fan blades (work). There is enough heat differential to run and enough radiator to disperse exessive heat while being cooked by its burner. Chilling out the power side and having it pull more than its own flywheel will not give any efficiencys we wish to improve. You will run into a lack of torque here to even try a measured response to your premiss.

Ummm... Your reference to the Senft fan engine that "pulls a pretty good load driving the fan blades (work)" would seem to prove my point. Unlike many model Stirling Engines I've seen, the Senft fan engine does have a load - THE FAN!...........unbelievable, still doen't read his own words! But you would have a Stirling do some work ( no, "ANY work") instead of just turn over a flywheel...........and this proves your point how? (Please shoot me now!)

It is also pulling "more than its own flywheel". It appears that this engine uses the fan as a "flywheel".......Yes it does.
You could certainly measure the difference by replacing the fan blade with a smooth flywheel of the same weight as the fan to reduce the work load (it will no longer be pushing air) on the engine while using an external electric fan to maintain the same air flow around the engine........you could meassure RPM change if any.

If the theory is correct, then the Senft engine should run hotter with the reduced load, though everything else would remain the same.
Or alternatively, you could add any kind of load to an engine that would otherwise be running without a load - such as a small permanent magnet motor used as a generator to power a light bulb. In that case the engine should run cooler with the additional load.
.........now you run into the torque issues of Stirling.

My bets are with those thermodynamic principles. If two guys walked up to a model Stirling, one with a torch to the hot cylinder and the other with a bucket of ice for the power cylinder, guess where the smart money lies? I will be puttin' on the heat instead of standing in a puddle...........thats why they call them "heat" engines!

I'm not sure why you keep saying "Chilling out the power side" or "bucket of ice for the power cylinder" etc.
........see your openning post on this.
.........The majority of the gas expansion and contraction is taking place within the displacer chamber. The gas in the displacer chamber is doing work against the piston reducing the temperature of the gas in the displacer chamber to one degree or another. Only a fraction of that gas, hot, cold or otherwise ever enters the power cylinder.

..........You are not there yet with this understanding. A Stirling is a sealed air system. There is no "majority" air. The air does not work against a power piston. There is no "fractional" air. Now think in terms of expansion and contraction of air and why that happens in Stirling. What "outside" of this system contributes to Stirling opperation.[]

[Tom Booth]

Hi Tom,
1. Insulating the cold end will not help (or we would all have been doing so).

Seems reasonable.

Expanding the working fluid enough to cool the cold end would require mechanical power for “heat pumping” (see 3. below). That would reduce the power of the engine – for example, by reducing the pressure on the piston.

One thing I was thinking is that if the throw were increased there might be some additional expansion/cooling.

2. The reason the cold end is warming is that we are putting heat into the engine. Engines are not yet 100% efficient, therefore the power out is less than the heat input, and most of the excess heat is rejected at the cold end – which must be cooled.

Right. As I said, the insulation idea was a rather iffy proposition. It is unlikely that any engine would ever be built with an efficiency great enough for this to apply.

Setting that aside. I think it is a given that a Stirling Engines function is to convert heat into work, therefore, I would think that if a model engine isn't set up to have any external work output, (is not doing any work other than overcoming its own friction) there would tend to be a greater heat build up within the engine than there would be if it were given some actual work to do.

When the gas is heated and expands and does work against whatever load there is on the engine, a certain percentage of that heat is converted into work and therefore never reaches the heat sink. I would think then, that if the engine isn't given any work to perform, less heat would be converted into work and that excess heat would then have to be transfered to the heat sink reducing the temperature differential.

If heat is going into the engine but not leaving the engine by being converted into work, then that heat would tend to build up internally.

[Tom Booth]

That would be where this piston that you said in your openning post the expanded air works against and should cool down when doing "ANY" work ........resides

I'm sorry, but I think you misunderstood. I did not say, or mean to suggest that the piston should cool up, down or sideways. Rather the air in the displacer chamber, being heated and expanded to do work against the piston would cool down as a result of expending energy to perform work against the piston.

But you would have a Stirling do some work ( no, "ANY work") instead of just turn over a flywheel...........and this proves your point how?...

It is also pulling "more than its own flywheel". It appears that this engine uses the fan as a "flywheel".......Yes it does.

I'm not really sure how this isn't clear.

A flywheel isn't doing any appreciable work. A fan is doing work moving the air and transferring heat to the air.

you could measure RPM change if any.

That is a supposition. Certainly there would be a change in RPM but I don't think you can rule out a temperature change as well, without actually doing the experiment.

now you run into the torque issues of Stirling.

If the engine is not doing work, then the heat will gradually build up and result in a gradual reduction in the temperature differential and consequently a reduction in torque.

On the other hand, if the engine is given some work to do at the start, then there should be more heat being converted into work, less heat build up, a gradual increase in temperature differential and a consequent gradual increase in torque.

A Stirling is a sealed air system. There is no "majority" air.

So it is a sealed air system. The bulk of the air mass remains in the displacer chamber. A small portion of that air goes in and out of the power cylinder. The bulk of the heat transfers are taking place in the displacer chamber. I'm aware that there is no actual separation between the air in the displacer chamber and the air in the power cylinder.

The air does not work against a power piston.

If the air does not work against the power piston then what pray tell do you suppose is moving the piston?

[Tom Booth]

I found these statements in a patent application:

"When powering a Stirling engine with solar energy from a mirror array, the solar energy supplied to the engine is substantially constant, and so the load must be maintained at a sufficient level to use all the solar energy supplied by the mirror array. If the load drops, the engine very quickly overheats and is damaged.

"To provide a level of control, the flat mirror segments on the mirror array can be mounted such that they can be moved by an actuator. Controllers activate the actuators and pivot the mirrors to produce the focused cone-shaped solar beam. The amount of energy received by the receptor can thus be varied. Thus when overheating is detected the mirror segments are moved out of focus to reduce the amount of energy received, such as when the load on a Stirling engine drops.

http://www.wipo.int/pctdb/en/wo.jsp?IA= ... SPLAY=DESC

I personally would not consider a statement such as this made in a patent application to be authoritative, but it does seem to indicate that others have made this observation i.e. if the load is removed from a Stirling Engine it overheats.

Conversely I would suppose also that applying a load to a model Stirling engine that was otherwise being run without a load (and having a problem with overheating) would benefit if it were provided with some actual work to do.

[Longboy]

I'm sorry, but I think you misunderstood. I did not say, or mean to suggest that the piston should cool up, down or sideways. Rather the air in the displacer chamber, being heated and expanded to do work against the piston would cool down as a result of expending energy to perform work against the piston.

.........I get it Tom, but don't agree that the expanded air works "against" the power piston. That does not happen. How is the displacer gonna cool down if its function is to move hot air and it resides over a flame?

I'm not really sure how this isn't clear.

A flywheel isn't doing any appreciable work. A fan is doing work moving the air and transferring heat to the air.

..........I think you discount that way too easily. So if you take the fan off the Senft engine and replace it with a flywheel....... it no longer is doing work? It has nothing to do with the engine driving assessorys such as a fan, water pump or generator.

That is a supposition. Certainly there would be a change in RPM but I don't think you can rule out a temperature change as well, without actually doing the experiment.

.........definitely a limitation for us setting up those experiments.

If the engine is not doing work, then the heat will gradually build up and result in a gradual reduction in the temperature differential and consequently a reduction in torque.

.............That does not happen! Not for the reason of not doing work. You are not considering all the factors that go into the build of a Stirling engine that prevents this senario.

On the other hand, if the engine is given some work to do at the start, then there should be more heat being converted into work, less heat build up, a gradual increase in temperature differential and a consequent gradual increase in torque.

...........You can't back that conclussion up! Here's the analogy: You approach a hill in your car (work). You back off the throttle (less heat build up) Your engine has more work to do but to overcome the hill you need a greater temp differential and more torque (which you say should happen when given the hill/work with less heat buildup). It doen't fit! And I do understand heat converted to work dissapates heat. Why don't you? There goes your increase in differential and increase in torque, still at the bottom of the hill! This theory doesn't happen in the car, doen't happen in Stirling.

So it is a sealed air system. The bulk of the air mass remains in the displacer chamber. A small portion of that air goes in and out of the power cylinder. The bulk of the heat transfers are taking place in the displacer chamber. I'm aware that there is no actual separation between the air in the displacer chamber and the air in the power cylinder.

..............Its definitly an air system that Stirling functions on. How all the containment flows with in the engine I don't know. Temps and pressures change and the engine works.

If the air does not work against the power piston then what pray tell do you suppose is moving the piston?

...........You do alot of research I see. When you answer the question I asked about what outside of this sealed system influences its opperation (and must happen), you will have that answer. Here a clue! its not whats inside the system that moves it!:idea:

[jesterthought]

Tom,
There is a question of how we look at it. You say “If heat is going into the engine but not leaving the engine by being converted into work, then that heat would tend to build up internally.”

Instead of “going into the engine”, does it help to think of the engine TAKING heat in?

Running light, it takes little in because not much heat has been converted into power so the air is returned to the hot end without having been cooled much. Load it down to about half the free-running speed (ie, to about its maximum-power speed) and more heat is removed from the air. Then, more heat is taken in by the air to get fully hot again. (Additionally, the slower speed gives more time for the air to do that.)

If the same proportion of the heat input is converted into mechanical power in both cases (a wild assumption, but illustrative), then MORE heat is rejected to the cold end at the HIGHER power.

Instead of “heat would tend to build up internally”, think that it must be removed by cooling (to maintain the dT). Now, is it evident that increasing the load INCREASES the cooling requirement?

If the cooling is by ambient convection on a model engine, then the cold end will warm up MORE at high power, not less as you were hoping.

Jester.

[Tom Booth]

I get it Tom, but don't agree that the expanded air works "against" the power piston.

Is there a problem with the word "against" ?

From the dictionary: "a : in the direction of and into contact with (knocked against the ropes) b : in contact with (leaning against the wall).

Not in the sense of - "in opposition to".

That does not happen. How is the displacer gonna cool down if its function is to move hot air and it resides over a flame?

I didn't say anything about the displacer cooling down either. The air or gas cools down as a result of expending its own kinetic energy.

I'm not really sure how this isn't clear. A flywheel isn't doing any appreciable work. A fan is doing work moving the air and transferring heat to the air.
..........I think you discount that way too easily.

Discount what way too easily ?

So if you take the fan off the Senft engine and replace it with a flywheel....... it no longer is doing work?

Not as much work. It's no longer blowing air around the room. I think that should be fairly obvious.

It has nothing to do with the engine driving assessorys such as a fan, water pump or generator.

Just because in a Senft engine the fan is incorporated into the engine it doesn't mean the extra work needed for the fan to push the air can be discounted any more than if a generator were permanently coupled to the crankshaft.

Certainly there would be a change in RPM but I don't think you can rule out a temperature change as well, without actually doing the experiment.

.........definitely a limitation for us setting up those experiments.

I don't see why. You could just put a break on the flywheel. Run the engine and then gradually apply the brake.

If the engine is not doing work, then the heat will gradually build up and result in a gradual reduction in the temperature differential and consequently a reduction in torque.

.............That does not happen! Not for the reason of not doing work. You are not considering all the factors that go into the build of a Stirling engine that prevents this senario.

Like what ? But you are right, I said the heat would "gradually" build up. According to the previous reference, without a load, the heat builds up very quickly.

On the other hand, if the engine is given some work to do at the start, then there should be more heat being converted into work, less heat build up, a gradual increase in temperature differential and a consequent gradual increase in torque.

...........You can't back that conclusion up! Here's the analogy: You approach a hill in your car (work)...

A Stirling Engine is not an internal combustion engine. Your analogy is not applicable.

..............Its definitly an air system that Stirling functions on. How all the containment flows with in the engine I don't know. Temps and pressures change and the engine works.

Well, maybe that's the problem.

If the air does not work against the power piston then what pray tell do you suppose is moving the piston?

...........You do alot of research I see. When you answer the question I asked about what outside of this sealed system influences its operation (and must happen), you will have that answer. Here a clue! its not whats inside the system that moves it!:idea:

Your the one who made the assertion: "The air does not work against a power piston". I can only guess at what might be going through your mind there. Perhaps you believe that the piston is climbing up the cylinder of its own volition to escape the heat ?

[Tom Booth]

Tom,
There is a question of how we look at it. You say “If heat is going into the engine but not leaving the engine by being converted into work, then that heat would tend to build up internally.”

Instead of “going into the engine”, does it help to think of the engine TAKING heat in?

Same thing either way. Heat -> Engine.

Running light, it takes little in because not much heat has been converted into power so the air is returned to the hot end without having been cooled much.

This is irrational. If you are heating the engine with a candle, there is a steady invariable heat input. If the hot air is returned to the hot end then there is the additional heat being delivered by the candle that will be added to it - and so on with each cycle.

Load it down to about half the free-running speed (ie, to about its maximum-power speed) and more heat is removed from the air. Then, more heat is taken in by the air to get fully hot again. (Additionally, the slower speed gives more time for the air to do that.)

If the same proportion of the heat input is converted into mechanical power in both cases (a wild assumption, but illustrative), then MORE heat is rejected to the cold end at the HIGHER power.

Instead of “heat would tend to build up internally”, think that it must be removed by cooling (to maintain the dT). Now, is it evident that increasing the load INCREASES the cooling requirement?

If the cooling is by ambient convection on a model engine, then the cold end will warm up MORE at high power, not less as you were hoping.

Jester.

I think I follow your reasoning. What you are neglecting to factor in is the heat reduction in the gas that results as a consequence of the gas being made to do work.

For example you say:

"If the same proportion of the heat input is converted into mechanical power in both cases (a wild assumption, but illustrative), then MORE heat is rejected to the cold end at the HIGHER power."

On the contrary, with a heavier load, more heat is converted into work. Less heat is rejected to the cold end.

"Instead of “heat would tend to build up internally”, think that it must be removed by cooling (to maintain the dT). Now, is it evident that increasing the load INCREASES the cooling requirement?"

No. Increasing the load converts more of the kinetic energy (heat) in the gas into external work output. More heat is being converted into work, therefore the cooling requirement at the cold end of the displacer chamber is reduced as the heat is converted into work before it ever gets there.

"If the cooling is by ambient convection on a model engine, then the cold end will warm up MORE at high power, not less as you were hoping."

There are two ways the gas is being cooled.

1. The gas cools as a result of being made to do work. It's internal Kinetic (heat) energy is transfered to the piston, to the crankshaft and on to whatever external load is present. (If there is no load, then the energy has nowhere to go leaving #2 below to do all the cooling)

2. The heat sink at the cold end of the displacer chamber.

If #1 does less cooling (no load, no work output) then the excess heat must be taken up by #2 (the heat sink).

The principle involved in #1 is a bit difficult to understand.

In a gas "heat" and kinetic energy (motion) are identical.

When a gas is heated, its kinetic energy (motion) increases.

When you feel hot air against your skin, this is a subjective perception. The reality is that the "hot" energetic air molecules are bumping up against your skin and transferring some of their kinetic energy to the molecules in your skin which makes those molecules more energetic and this is perceived as "heat".

When a gas does work against a piston in a Stirling engine the kinetic energy is transfered to the piston. The gas molecules become less active or energetic as a consequence. Since, in a gas, "heat" and kinetic energy are the same thing, when the gas transfers energy to the piston it gets "cold" as a result of loosing kinetic energy to the piston.

If the piston moves easily (no load) less kinetic energy is transfered. If the piston is difficult to move (there is a load on the engine) then more kinetic energy must be transfered to the piston for it to move.

When a gas is full of kinetic energy it is hot. If it uses up its kinetic energy to move a piston it gets cold.

The greater the load on the engine the more cooling by transfer of kinetic energy from the gas.

Of course, this has to be balanced. You can't apply such a heavy load that the gas can not move the piston. In that case there would be no work output.

[Longboy]

Is there a problem with the word "against" ?

.....Ya, survey says "opposing", lets get on the same page and use "with" then.

I didn't say anything about the displacer cooling down either. The air or gas cools down as a result of expending its own kinetic energy.

.......but you did! "Rather the air in the displacer chamber, being heated and expanded to do work against the piston would cool down...." your words and you were clear this happens at this point. It doesn't. And don't come back with just the air there heats up, it just compounds your lack of understanding how these engines work.

Discount what way too easily ?

.........A flywheel isn't doing any appreciable work.

Not as much work. It's no longer blowing air around the room. I think that should be fairly obvious.

..........Unbelievable! No Tom, it is not obvious. You have to get some Stirling models and make the observation yourself someday.

It has nothing to do with the engine driving assessorys such as a fan, water pump or generator.

..............Its definitly an air system that Stirling functions on. How all the containment flows with in the engine I don't know. Temps and pressures change and the engine works.

Well, maybe that's the problem.

Just because in a Senft engine the fan is incorporated into the engine it doesn't mean the extra work needed for the fan to push the air can be discounted any more than if a generator were permanently coupled to the crankshaft.

..............now you got lost as this relates to your theory. So this extra work will cool the engine how?

I don't see why. You could just put a break on the flywheel. Run the engine and then gradually apply the brake.

.........."just coulds", I heard of it. Let us know when you complete the test and share the results!

Like what ? But you are right, I said the heat would "gradually" build up. According to the previous reference, without a load, the heat builds up very quickly.

.........I'm sorry you haven't made any engines, but any build up of heat is not detrimental to a running model.

A Stirling Engine is not an internal combustion engine. Your analogy is not applicable

......Thats right it isn't a Stirling. Thats why they call them analogys. But since you are holding hands with Thermodynamics, and it doen't care, why should you? That would be because you're still............("let em have it Longboy").............at the bottom of the hill!

..............Its definitly an air system that Stirling functions on. How all the containment flows with in the engine I don't know. Temps and pressures change and the engine works.

Well, maybe that's the problem.

.........just a motivation, any luck on the "outside influence" question in Stirling that gets them running yet?

Your the one who made the assertion: "The air does not work against a power piston". I can only guess at what might be going through your mind there. Perhaps you believe that the piston is climbing up the cylinder of its own volition to escape the heat ?

...............Hey I have a big mallot if that piston gets too high in the bore! I know the how and why the power piston moves in its bore. Guessing don't get you there, fact overrule theory, hands on helps alot if you have done models and experiance with understanding how these Stirling work is 8/10's in the forum! .............That question, hurry before my soup gets cold and I grow a beard!