Stirling Engine Thermodynamics

[goat]

Sorry again, my bad. I should have read your posts a bit more carefully and I'd have seen you knew about that.

You said that people say:

but they tell you its still 30% of the heat energy making more HP

In the case of super or turbocharging that won't be the case. I believe the higher pressure difference improves the efficiency, so surely you'll be getting more than 30% of the energy making for more HP?

Personally, I can dream of the day I have something that puts out 200HP, with or without forced induction.

As you say, in a theoretical Stirling Engine playing around with pressure by itself won't help: For a given load you'd have to increase the difference in temperature between the hot source and the cold sink to improve efficiency.

In a real world Stirling engine no doubt you could improve efficiency by making it work more like a theoretical Stirling engine.

[Tom Booth]

In one of your posts you quote someone saying 'Any gas when compressed rises in temperature. Conversely, if it is made to do work whilst expanding, the temperature will drop'. I think the guy is talking about a situation where the compression or expansion happens without much heat energy transfer from the surroundings. For example, when you let off a fire extinguisher the contents expand quickly and there is little heat transfer into the gas, which therefore gets cold.

Not quite,

Think of your fire extinguisher discharging through a turbo-generator that is lighting some light bulbs. What the sources are saying is that the additional work load of running the generator and lighting the light bulbs (which are giving off heat and light) results in more rapid and efficient cooling of the gas.

The energy to light the light bulbs has to come from somewhere and with a gas, the only additional energy the gas has to give up is its own latent heat energy. Though it is already cold due to expansion it gets much colder due to the additional work performed while expanding.

In other words, if the fire extinguisher is discharged through such a turbo-generator the gas will be much colder than if it were simply discharged into the air without doing additional work.

I can see the rationale behind what you propose in your posts: If we apply a greater load to the engine and lag the heat sink then two things should happen:
1) More of the heat energy will come out as useful work
2) We block more of the heat energy from being lost into the cold sink
which will cause the engine to run cooler and more efficiently.

I think that you're right about the load application, but not about lagging the cold sink.

I'm not at all sure what you mean here by "lagging the cold sink".

Sadly, there aren't many large supplies of hot, compressed gases just sitting around for the taking...

What about the earths atmosphere ?

You said:

"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."

...heat energy flows from hot to cold. If our working gas is colder than the sink then heat will flow from the sink into the gas.

My rationale for insulating the "heat sink" so as to prevent this backward flow.

What we need in order to complete the Booth cycle is something that will absorb the heat energy from the gas. Unfortunately that has to be a sink that is colder than the gas. I believe it is impossible to have a heat engine in which the working gas falls to a temperature below that of the coldest sink in the engine.

I'm not so sure,

Take the "free piston" type Stirling engine. For an example:

http://www.youtube.com/watch?v=cAyw_dOioMU

Here there is no flywheel to store energy to later compress the gas. It seems that the gas cools and contracts instantaneously on its own drawing the piston back to its starting position. How is this possible ?

Glass is a very poor heat conductor and yet this engine is running very rapidly.

I don't believe that this can be explained by the idea that heat is being conducted away to the "heat sink" through the glass so rapidly or efficiently as would be required to keep this engine running at such a rapid pace.

In my reading about free piston type Stirling engines I've seen it mentioned several times that a free piston engine REQUIRES a load and will not run without one. For example:

http://www.cnccookbook.com/CCStirlingGenerator.htm

My idea is that the reason a free piston Stirling requires a load is that it does not have a flywheel or any other apparent means of "compressing" the gas and bringing the piston back to its starting position. Instead it relies primarily on the heat loss due to the gas being made to do work against the load. Doing the "extra" work, the gas gets extra cold and contracts on its own without the need for any "compression".

This heat loss must be extremely rapid and complete, more so IMO than can be accounted for by relatively slow conduction to a heat sink alone.

In effect, the light and heat being dissipated by the LEDs constitutes a kind of "heat sink" causing the gas to cool and contract the instant it expands and does work powering the linear generator and the LEDs.

[goat]

I'm not at all sure what you mean here by "lagging the cold sink".

Over here we sometimes call insulation lagging - sorry I didn't realise you guys didn't use the word that way, too. I should have looked that up, apologies. Anyhow, what I meant was insulating the cold sink. Oh, and 'cold sink' and 'heat sink' are interchangable in my book; a sink has to be comparatively cold in order for heat to be given up there.

In other words, if the fire extinguisher is discharged through such a turbo-generator the gas will be much colder than if it were simply discharged into the air without doing additional work.

Sorry if I gave the impression that I was arguing that an unheated expanding gas wouldn't cool, I've no doubt that you're right on that point. What I was trying to focus on was that it's possible to expand a gas at constant temperature, as long as you add heat energy to it at the same time. I was trying to argue that this was what happens in the idealised Stirling Cycle.

Sadly, there aren't many large supplies of hot, compressed gases just sitting around for the taking...

What about the earths atmosphere ?"

I was thinking of hotter, more compressed gases than that when I wrote my post. However, you've got a good point; there's nothing to stop you making an engine powered by differences in pressure or temperature in the Earth's atmosphere.

What we need in order to complete the Booth cycle is something that will absorb the heat energy from the gas. Unfortunately that has to be a sink that is colder than the gas. I believe it is impossible to have a heat engine in which the working gas falls to a temperature below that of the coldest sink in the engine.

I'm not so sure,

If we're talking about a thermodynamic cycle - where a working fluid is taken through a sequence of thermodynamic states, returning to it's original state, then I'm pretty sure that it will be necessary to reject some heat at some point. The reason I think this is because:

dS = dQ / T (from http://en.wikipedia.org/wiki/Entropy)

ie the increase in entropy of a working fluid is equal to the heat transferred to the working fluid divided by the temperature at which that transfer occurs. Also, the decrease in entropy of a working fluid is equal to the heat transferred out of the working fluid divided by the temperature at which that transfer occurs.

So, if we add heat the working fluid at any point on the cycle then the entropy increases.

In order to get the working fluid back to to the state that it started from and complete the cycle, the entropy of the working fluid must be reduced back down to the value that it started at.

The only way for the entropy of the working fluid to reduce is for it to give up energy as heat. Losing energy by doing work alone does not reduce the entropy of the working fluid.

The only way for the working fluid to give up heat is for it to come into contact with something at a lower temperature than itself.

Note that if you want to reduce the entropy back to its starting value, then the amount of heat that you need to give up to do it will be lower the lower the temperature of the working fluid is when you give up the heat. That's why it's important for the cold sink to be cold.

Take the "free piston" type Stirling engine. For an example:

http://www.youtube.com/watch?v=cAyw_dOioMU

Here there is no flywheel to store energy to later compress the gas. It seems that the gas cools and contracts instantaneously on its own drawing the piston back to its starting position. How is this possible ?

Reading the discussion below the video you'll see that the builder and a commenter discuss a spring. The spring stores work and passes some back in compressing the working fluid in the same way that a flywheel does; the spring is a replacement for the flywheel.

A major thing to note is that at 2:08 he says that in his next iteration he's going to add fins to the sink: "The next stage is to... get some large cooling fins on the cold end to try and sink a lot more of the heat".

In effect, the light and heat being dissipated by the LEDs constitutes a kind of 'heat sink'

The LEDs are powered by the magnet moving in the coil. Any energy transferred to them from the working fluid will be in the form of work, rather than as heat. As I've noted above, I don't think that losing energy as work is the same as losing it as heat, as it doesn't reduce the entropy of the working fluid. Essentially, I don't think that the LEDs are equivalent to a heat sink.

Glass is a very poor heat conductor and yet this engine is running very rapidly. I don't believe that this can be explained by the idea that heat is being conducted away to the "heat sink" through the glass so rapidly or efficiently as would be required to keep this engine running at such a rapid pace.

I guess that may be one reason why he's planning to make the next one out of metal. I reckon it'll be running fast because it's not very heavily loaded. I certainly don't think anything is happening efficiently in this engine, great though it is. As I said in my previous post, I reckon you're right that a higher load will lead to better efficiency because it makes the engine run slower, giving more time for heat transfer.

I understand that you might not want to take my word for it; ask the guy who made it about the spring and whether he thinks insulating the sink would make it more efficient.

I hope my comments don't seem negative or critical, I certainly don't mean them to be. I find your posts very interesting and I'm enjoying spending time thinking them over. If you think I'm wrong on any point I'm arguing then that's fair enough - it won't be the first time I've been wrong, that's for sure. =]

[Tom Booth]

I'm not at all sure what you mean here by "lagging the cold sink".

What we need in order to complete the Booth cycle is something that will absorb the heat energy from the gas. Unfortunately that has to be a sink that is colder than the gas. I believe it is impossible to have a heat engine in which the working gas falls to a temperature below that of the coldest sink in the engine.

I'm not so sure,

If we're talking about a thermodynamic cycle - where a working fluid is taken through a sequence of thermodynamic states, returning to it's original state, then I'm pretty sure that it will be necessary to reject some heat at some point. The reason I think this is because:

dS = dQ / T (from http://en.wikipedia.org/wiki/Entropy)

ie the increase in entropy of a working fluid is equal to the heat transferred to the working fluid divided by the temperature at which that transfer occurs. Also, the decrease in entropy of a working fluid is equal to the heat transferred out of the working fluid divided by the temperature at which that transfer occurs.

So, if we add heat the working fluid at any point on the cycle then the entropy increases.

In order to get the working fluid back to to the state that it started from and complete the cycle, the entropy of the working fluid must be reduced back down to the value that it started at.

The only way for the entropy of the working fluid to reduce is for it to give up energy as heat. Losing energy by doing work alone does not reduce the entropy of the working fluid.

The only way for the working fluid to give up heat is for it to come into contact with something at a lower temperature than itself.

True enough I suppose, yet the "working fluid" in an air-cycle or other refrigeration, air-conditioner, heat pump or similar system is manipulated, compressed and expanded to change its temperature so as to direct heat flow to or from the working fluid as desired.

It can also give up heat by performing work.

In an air-cycle system for example, air is compressed in a tube or duct raising the temperature of the "working fluid", which in this case is the air itself. This allows the air to be cooled as it is now higher in temperature than the surrounding ambient air, It is however still under pressure. It is then depressurized by allowing it to escape through a turbo-generator at which point it cools not only due to expansion but also due to giving up additional energy to do work in turning the turbine coupled to a generator. In the process of cooling it comes into contact with nothing whatsoever colder than it's own initial ambient starting temperature.

"Air cycle refrigeration works on the reverse Brayton or Joule cycle. Air is compressed and
then heat removed, this air is then expanded to a lower temperature than before it was
compressed. Work must be taken out of the air during the expansion, otherwise the entropy
would increase. Work is taken out of the air by an expansion turbine, which removes energy
as the blades are driven round by the expanding air. This work can be usefully employed to
run other devices, such as generators or fans"

http://www.grimsby.ac.uk/documents/frpe ... search.pdf

Take the "free piston" type Stirling engine. For an example:

http://www.youtube.com/watch?v=cAyw_dOioMU

Here there is no flywheel to store energy to later compress the gas. It seems that the gas cools and contracts instantaneously on its own drawing the piston back to its starting position. How is this possible ?

Reading the discussion below the video you'll see that the builder and a commenter discuss a spring. The spring stores work and passes some back in compressing the working fluid in the same way that a flywheel does; the spring is a replacement for the flywheel.

A major thing to note is that at 2:08 he says that in his next iteration he's going to add fins to the sink: "The next stage is to... get some large cooling fins on the cold end to try and sink a lot more of the heat".

The spring was added to prevent the piston from banging into the orifice on the return stroke. The engine ran quite well without it. It had no role in storing energy as a replacement flywheel.

In effect, the light and heat being dissipated by the LEDs constitutes a kind of 'heat sink'

The LEDs are powered by the magnet moving in the coil. Any energy transferred to them from the working fluid will be in the form of work, rather than as heat.

I'm afraid that you are overlooking some physics fundamentals here. "energy can not be created or destroyed it can only change form"

What changes in the form of energy take place? The "heat" is converted into work or kinetic energy (motion of the piston driving the magnet past the coil), the kinetic energy is converted into electricity, the electricity into light and heat and the light is eventually also converted back into heat when the light from the LED's strike some distant object. Through all that the actual "heat" has been transferred out of the engine, out of the working fluid, just as effectively as if it had been transferred directly to a sink. The heat which has gone out of the engine as electricity and/or light does not have to be removed by any heat sink, Its conversion into another form of energy has effected its removal.

[Ian S C]

Just a note on free piston engines: These engines do in effect have a flywheel effect, the power piston is relatively heavy, and is bounced of a spring, this can be a mechanical spring, or compressed gas, or as in my motor, two magnets with the like poles facing each other.
Ian S C

[Rog Tallbloke]

I'm a newbie here, and so very late to this debate. I'd just like to add a couple of points which I hope will help.
If I understand correctly, Tom's hypothesis is that when the engine is under load, more energy is dissipated in converting thermal energy to kinetic energy, and so less energy is needed to be lost via the cold sink, resulting in cooler running under load.

What I think may have been overlooked (although I haven't read the whole thread, so forgive me if this has been covered already), is that for the same energy input at the hot end, the engine slows down under load. This reduces the rate at which the cooling system transports energy away by the same amount of energy as is converted to the work done electrically or mechanically (disregarding increased losses due to friction).This means that the engine won't run any cooler under load, because the rate of dissipation is reduced due to the lower frequency of contact between the heated working gas and the cold end of the system.

In fact the engine will tend to run slightly hotter under load, for three reasons:

1) As the engine slows, the working gas spends longer in contact with the hot end of the system and reaches a higher temperature. Of course it also spends longer at the cold end, but since more of the energy is converted to electrical or mechanical energy under load, the differential in the temperature of the working gas at the cold end and the cold sink is reduced, making energy transfer slower.

2) Working against a load, the pressure of the working gas increases, within the same average volume over the cycle. This will increase its temperature.

3) Friction increases, and friction generates heat, generally at the piston seal (due to increased pressure pressing the seal more tightly against the bore), wrist pin and con-rod bearing. In a non-pressurized engine, the latter two can be disregarded, as they dissipate heat to atmosphere.

[Ian S C]

Rog, I think you have summed it up pretty much as I would.
Ian S C

[Aviator168]

Rog, It is only true to a certain extend. That is, the working gas has not reached the temperature of the inner surface of the heater to begin with. In other words, if the engine was running fast and the working gas is at or near the temperature of the inner surface of the heater, slowing down WON'T increase power a bit.

[Rog Tallbloke]

Aviator, I didn't say slowing the engine down would increase the power, I said "As the engine slows, the working gas spends longer in contact with the hot end of the system and reaches a higher temperature", though as you correctly say, there will always be a gradient through the system.

There may be a very marginal power gain due to increased pressure, but I expect it wouldn't be any bigger than the loss caused by increased friction and a lower differential between hot and cold ends. That's only a guesstimate though, so I may well be wrong. Either way, the difference wouldn't be much.

[Ian S C]

If you run the engine without load so that the hot cap is red, then put on a load without changing the heating the temperature will drop, may go from red to black heat as the heat is transferred to the cooling system. This is where a IR thermometer comes in handy. You will find that increasing heat will increase power up to the stage where the cooling system can not cope, The cooling is probably the most important part of the motor, but the bit that gets the least attention.
Ian S C

[Rog Tallbloke]

That's interesting Ian. It indicates that the longer dwell of the working gas at the cold end when the engine slows under load has a bigger effect than the longer dwell of the working gas at the hot end. I wonder if it would be a different story in a pressurised engine, where there is greater molecular density to absorb the heat.

[Tom Booth]

If you run the engine without load so that the hot cap is red, then put on a load without changing the heating the temperature will drop, may go from red to black heat as the heat is transferred to the cooling system...

I hope you don't mind my abbreviating your statement but the part above is a very interesting and I think, vitally important observation. The conclusion though, that putting on a load results in more heat being transferred to the cooling system cannot possibly be right. IMO. But it is the crux of the whole issue under discussion here.

The same thing happens with a turbine... which I think is a more straightforward situation and easier to follow as far as what happens thermodynamically.

If a compressed gas (Air) is used to turn a turbine without a load, so the turbine is "freewheeling" without producing any output by turning a generator or some such, the air exits the turbine at a certain temperature. If a load is then put on the turbine, the temperature of the air leaving the turbine drops.

I believe the same principle is at work in the Stirling Engine as in the Turbine in such a case. The heat, or more of it, when the device is under a load, is converted to some other form of energy - electricity.

If MORE energy is converted to another form then LESS energy, not more would reach the sink when the engine is under load.

To illuistrate:

A no-load condition would look something like this:

100% Heat in
|
|
v
[ENGINE] ---> 0% of heat input converted to electricity (No Load)
|
|
V
100% Heat out to heat sink.


Running without any load, nearly all the heat is transferred to the sink. Little to none is converted to any other form of energy.

Under a load the situation looks more like this:

100% Heat in
|
|
V
[ENGINE] --> 25% of heat input converted to electricity
|
|
V
75% Heat out to heat sink.

Under a load, you do not get MORE heat transferred to the sink but less. For MORE heat to be transferred to the sink when the engine is under a load would be a violation of thermodynamic principles, a violation of physics. It would look like this:

100% Heat in
|
|
V
[ENGINE] --> 25% of heat input converted to electricity
|
|
V
125% Heat out to heat sink.

This is, of course ignoring losses due to conduction and friction and so forth.

You can't have the engine transferring 100% of the heat through the engine to the sink in a no-load condition and then have MORE heat transferred to the sink when some of the energy is being converted to power a load on the engine, such as running an electric generator. If that were the case you would have more energy out than in.

In other words, you can't have the same energy being converted to electricity and also reaching the sink as waste heat. If more heat is converted to electricity then it follows that less of that heat is reaching the sink.

The heat cannot be destroyed. Therefore, under a no load condition, the heat has nowhere to go but to be transferred to the heat sink.

But the heat can be converted into another form of energy. It is not destroyed when the engine is under a load, but it does in effect disappear. It no longer exists in the form of heat. The heat has become electricity, it has changed form. It is no longer there to be transferred to the sink at all. The result is an overall drop in temperature when the engine is put under a load so that some of the heat is converted to another form of energy rather than all of the heat having to be dissipated to the sink because none is being converted in the no-load condition.

[Tom Booth]

That's interesting Ian. It indicates that the longer dwell of the working gas at the cold end when the engine slows under load has a bigger effect than the longer dwell of the working gas at the hot end. I wonder if it would be a different story in a pressurised engine, where there is greater molecular density to absorb the heat.

The question of "where does the heat go when the engine is under a load?" or why does it turn from red-hot to black? is not answered by the increased dwell time because the engine is running slower under a load. IMO, but because the heat is in a sense literally disappearing. That is, the heat is being converted to electricity by the load on the engine. Assuming the load is an electric generator.

[Aviator168]

heat is in a sense literally disappearing. That is, the heat is being converted to electricity by the load on the engine. Assuming the load is an electric generator.

Right on. One of the laws of thermal dynamics.
Even without a load. Work is being done except the load is on the friction of the sliding piston, the rotating bearings and energy spent on moving the gas back and forth.

[Tom Booth]

heat is in a sense literally disappearing. That is, the heat is being converted to electricity by the load on the engine. Assuming the load is an electric generator.

Right on. One of the laws of thermal dynamics.
Even without a load. Work is being done except the load is on the friction of the sliding piston, the rotating bearings and energy spent on moving the gas back and forth.

True... though these "loses" from friction can be minimized or reduced to near zero, at least in theory, with magnetic bearings and such.