Stirling Engine Thermodynamics

Discussion on Stirling or "hot air" engines (all types)
Tom Booth
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Re: Stirling Engine Thermodynamics

Post by Tom Booth »

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

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)....

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.
What about a Stirling engine running on ice ?

Now you have heat going in at ambient.

The air expands, some of the heat is transformed into mechanical work, the remaining heat delivered to the heat sink (ice) is now below ambient - colder than the surrounding air, which surrounding air would be melting the ice faster than whatever heat is being expelled by the engine after converting some of that heat into work.

It would do well, I think, in this scenario, to insulate the ice and the cold end of the engine from heat infiltration from the warmer surrounding ambient. How much longer might the ice last ? Perhaps quite a while longer if it were insulated from all that surrounding heat.

I was also thinking, as I mentioned earlier, that if the throw of the piston were increased and the length of the cylinder increased the cooling effect of the expanding gas doing work to move the piston, along with the additional expansion carried out as a result of momentum... If some of these sources are correct that I've been referencing, that the gas is cooling to such a degree due to doing work while expanding, that its temperature is dropping even below what it was when it started, then I still think it might be possible to design an engine that would benefit by having the cold end insulated, even though powered by some heat source.

Or it might even be possible, due to this heat -> expansion -> work -> cooling effect to construct an engine that required no outside cooling (i.e. no displacer to shuttle the gas to the cold end, no displacer chamber). Just a longer than normal cylinder and a piston with the heated expanding gas doing work and in the process cooling itself and contracting again.
Tom Booth
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Re: Stirling Engine Thermodynamics

Post by Tom Booth »

This looks interesting,

I can't really be sure, from the description and photos, not enough information is provided, but I came across this Stirling engine while browsing around on the net last night:

http://www.stirlingengine.com/product/94

The description states,
"Until recently all Stirling engines had a piston and a displacer (which moved the air back and forth) or two pistons to move the air back and forth.

This engine only has one piston and no displacer. We aren't quite sure why it works...
Just from the look of this engine: "This is quite a large engine. It's about 18 inches long" (extra long throw on the piston ?) and its general description, it seems to have the characteristics of the theoretical engine I described at the end of my previous post.

As yet, I would not say that this proves anything, but given that the seller/maker states: "We aren't quite sure why it works" the thermodynamic principles discussed here might be one explanation.

By chance, does anyone know anything more about the operation of this engine ?
Longboy
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Re: Stirling Engine Thermodynamics

Post by Longboy »

Tom Booth
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Re: Stirling Engine Thermodynamics

Post by Tom Booth »

Hmmm..... well, thanks for that longboy.

Though, according to the statement at the link provided earlier:

http://www.stirlingengine.com/product/94

"We aren't quite sure why it works, but we are sure that some of the explanations you will read on the web are wrong."

I have a feeling that PDF may fall into the above described "wrong" category.

Here is what I believe is a simpler and more straightforward explanation based on known, relatively simple thermodynamic principles and not involving some mysterious sound waves magically generated from a wad of steel wool.

A couple basic rules:

1. Heat flows from hot to cold.

2. An expanding gas made to do work grows cold (i.e. heat is transformed into work)

Without getting into how the cycle is started - lets just say someone gives the flywheel a spin - -

Now taking things from the point of the outward power stroke:

The gas is expanding and doing work. As a result of doing work the gas gets cold and begins to contract.

The end of the regenerator (wad of steel wool) has been absorbing heat from the flame below it.

Now, after doing work, the gas begins to contract THROUGH the hot end of the regenerator (steel wool) picking up heat from the steel wool (heat traveling from hot steel wool to cool air) The air now beginning to expand back through the hot mesh of steel wool picks up some additional heat.

In the mean time the piston, now still on its inward stroke and carried mostly by the momentum of the flywheel, meets this hot expanding air and is pushed back outward again.

The "choke" allows for some slight delay. The expanding gas must pass through this bottleneck and so this gives the piston some time to finish its inward stroke before the hot expanding gas passing through the choke meets up with it.

So now the gas, having contracted into the regenerator and expanded back through the regenerator expands through the choke into the outer cylinder and pushes the piston in another power stroke. The gas again does work pushing the piston. As a result of doing work, the gas gets cold and again, contracts through the regenerator picking up heat. The process is repeated. Again the piston is pushed outward.

The "choke" causes a certain delay in this action (expansion and contraction) between the inner (regenerator) and outer (piston) cylinders (either side of the "choke") much as a displacer does working 90 degrees or so ahead of the piston.

The following to me sounds like fanciful nonsense:
---------------
The... engine works by converting sound waves into motion. The sound waves are generated by heating one end of a 'stack' of coiled material and allowing the other end to remain cool...
-----------------

As far as I can see, viewing a number of these KTA18 engines in operation:

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

the so-called "stack" is nothing more than your typical dollar store stainless steel scrubbing pad stuffed into a test tube, (these steel wool pads are very commonly used as make shift regenerators for small Stirling engines and have nothing to do with sound waves.)

How it is imagined by this author, that heating one end of a pot scrubber can generate some kind of "sound waves" that are then converted into motion I'm quite sure I don't know but I'm rather certain the "explanation" provided in that PDF is utter nonsense.

This is a simple Laminar Flow Engine. Referring to it as if it were a thermoacoustic engine is some kind of confusion or misunderstanding IMO.

As I look more closely at the so-called "Traveling Wave Stirling Engine" it also appears to be nothing more than an overblown Laminar Flow Engine using an electric heating element instead of a flame.
Longboy
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Re: Stirling Engine Thermodynamics

Post by Longboy »

............They're giving some ad hype in the description like an infomercial. At $2G a copy there gonna sit on the shelf for ages. Simple to build with the fewest parts of the hot air engines they run nice. You can take a look at the "Rijke tube" for an explaination on how sound energy can move heat to how these lamina/ thermoaccoustic engines work. :mrgreen:
Tom Booth
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Re: Stirling Engine Thermodynamics

Post by Tom Booth »

Longboy wrote:............They're giving some ad hype in the description like an infomercial. At $2G a copy there gonna sit on the shelf for ages. Simple to build with the fewest parts of the hot air engines they run nice. You can take a look at the "Rijke tube" for an explaination on how sound energy can move heat to how these lamina/ thermoaccoustic engines work. :mrgreen:
Interesting stuff.

So heating a wire mesh inside a tube can, under certain circumstances produce resonant sound waves.

I'm not at all convinced, however that this has any real relation to how a laminar (lamina or laminar ?) flow Stirling engine works. There is heating and expansion of air in both cases, but I don't think sound waves have anything to do with how a Stirling Engine works. The resemblance seems very superficial to me.
speedless
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Re: Stirling Engine Thermodynamics

Post by speedless »

Hi
To whom it may concern,a little comment.
As i understand termodynamic;
Heat alone does NOT do any work!
(heat really dont have any meaning without anything to warm up/cool down.)
It needs a medium to convert the POTENTIAL energi (from the heat/cold) to motion.
The medium transfer the POTENTIAL energi to the power end,not the heat.
In order to do work the medium has to expand (p.ex .pushing the power piston)
when expanding,the medium looses heat,not because of the work but through expanding.
as it will gain heat when compressed.
As the stirling works on both the expanding and the contraction of the medium
it will be a bit self-energizing.(No perpetual though .)
Hope i didnt offend anyone?
Jan
PS:sorry for my english.
goat
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Re: Stirling Engine Thermodynamics

Post by goat »

I was thinking it would be cool to use a light-collector Stirling engine to power a camera in an unmanned high-altitude balloon (like this: http://news.bbc.co.uk/1/hi/england/west ... 587749.stm), but reading this thread I'm worried that it wouldn't work. I've not built any Stirling engines before, so I'd appreciate it if you guys could lend your experience.

Longboy, you said:
The power piston is being acted upon by the EXTERNAL air pressure in its inward stroke. Without a free flow of atmosphere on the external side of the power piston the engine WILL NOT RUN.
Does that mean that as the balloon gets up into the high part of the atmosphere the Stirling Engine will stop working?

Another problem with Stirling engines is the weight of the fly wheel. Do you know if the fly wheel does anything important, or could I ditch it?

Sorry if these are stupid questions. Thanks for your help.
Longboy
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Re: Stirling Engine Thermodynamics

Post by Longboy »

goat wrote:I was thinking it would be cool to use a light-collector Stirling engine to power a camera in an unmanned high-altitude balloon (like this: http://news.bbc.co.uk/1/hi/england/west ... 587749.stm), but reading this thread I'm worried that it wouldn't work. I've not built any Stirling engines before, so I'd appreciate it if you guys could lend your experience.

Longboy, you said:
The power piston is being acted upon by the EXTERNAL air pressure in its inward stroke. Without a free flow of atmosphere on the external side of the power piston the engine WILL NOT RUN.
Does that mean that as the balloon gets up into the high part of the atmosphere the Stirling Engine will stop working?

Another problem with Stirling engines is the weight of the fly wheel. Do you know if the fly wheel does anything important, or could I ditch it?

Sorry if these are stupid questions. Thanks for your help.
..........Yes a Stirling literally runs outta gas in space. Its sealed air would be sucked out thru the displacer push rod gland where its leakage is acceptable on earth. Since Stirlings function on a temperature/ pressure differential of an atmosphere, its all over up there in the vaccuum! For a recipricating engine like Stirling you must have a flywheel. Its an "energy storage device" that keeps the moving parts moving in Stirling. They do use energy produced by the engine and receive it back to continue the cycle of motion. Read more about flywheels on WIKIPEDIA though its somewhat technical reading! Longboy.
selina50
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Re: Stirling Engine Thermodynamics

Post by selina50 »

Thank you.
Last edited by selina50 on Thu May 13, 2010 10:40 am, edited 1 time in total.
Longboy
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Re: Stirling Engine Thermodynamics

Post by Longboy »

.........if you have read the totality of this post subject you can see that Tom & I went several rounds in defining terms including "work". My position revolves back to you in what would be work defined to you for an engine that is running. An engine that does drive a load by means of a connection to an implement or just a running, free wheeling engine. We have heat energy converted to mechanical energy. I'm sure there are math formulas that can give a percentage of efficient use of that heat just to make an engines flywheel turn all the way to a percentage of this same engine driving a water pump or generator. I don't play with the math here but I find it interesting in the I/C world that if gas and air burned in the car engine is using 30% of the heat energy in gasoline, why does one engine make 200HP and another of the same size make 250HP? An increase in mechanical abilitys for sure but they tell you its still 30% of the heat energy making more HP. If I had 10 credits in a physics class it would be more clear to me I'm sure. Have to ask your "someone" for the details of no load efficiencys!
goat
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Re: Stirling Engine Thermodynamics

Post by goat »

Longpig,

Good point, it'd be difficult to stop the working gas from escaping unless you could make a properly sealed cylinder.



Tom,

I've had another read through of your first post & the wikipedia entry on Stirling engines and in the cold light of day here's what I'm thinking. Let me know if I'm tripping up along the way.

First of all, I believe that it is theoretically possible for a gas to compress or expand without a change in temperature. In order to achieve this, you have to feed in or take out an amount of heat energy at the same time. In an idealised Stirling engine the expansion and compression phases are, in fact, exactly this: Isothermal compression and isothermal expansion. The expansion takes place inside the hot cylinder, which transfers heat energy into the gas. The compression takes place in the cold cylinder, which absorbs some heat energy from the gas.

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.

Leaving that behind, I believe that you were right in thinking that the Stirling engine (or any other kind of heat engine) functions by means of a heat differential between the source and sink. In a heat engine heat-energy flows from the hot source to the cold sink and we divert a portion of that heat out as useful work. The thermodynamic efficiency of a heat engine is the proportion of the heat flowing in from the source that we have diverted out as useful work. It is, sadly, impossible to divert all of the heat-energy flowing through the engine out as work (a 100% efficient engine). In fact the best we can do is a Carnot or Stirling cycle.

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 think the best way to explain my reasoning is to refer to pressure-volume and temperature-entropy graphs for the cycle. I've put a scan of p-V and T-s sketches highlighting each of the phases here: http://i1009.photobucket.com/albums/af2 ... gcycle.jpg.

Say we start looking at the cycle where the gas is a minimum volume and maximum temperature (which looks like this: http://en.wikipedia.org/wiki/File:Alpha ... ame_8.png), which I've labelled as 'A' on my graphs. At this point the gas is mainly in the hot cyclinder and is at low volume, high temperature and high pressure.

Phase 1 of the cycle, going from 'A' to 'B', is an isothermal expansion: The gas stays at the same temperature, but increases in volume and entropy and decreases in pressure. As you point out in your post, if the gas is expanding at pressure within our cylinder then it is doing work. This is where the p-V graph is useful: The work done by the gas is the shaded area under the line on the p-V graph, which I've labelled W1. The work done by the gas is transferred to the fly wheel (or some similar energy store). The work going to the fly wheel is important, as we'll need it back later.

This is only half the story for phase 1. As I mentioned above, in order to have an isothermal expansion we need to put heat energy into the gas. The energy being put into the gas is the shaded area under the line on the T-s graph, which I've labelled Q1.

After phase 1 the engine looks a bit like this: http://en.wikipedia.org/wiki/File:Alpha ... ame_12.png, and is at the point I've labelled B. The gas is now at high volume, high temperature and high entropy, but lowish pressure.

In Phase 2, between points labelled 'B' and 'C' of the cycle, the gas is transferred through the regenerator. In doing so it undergoes constant volume (isochoric) cooling. The volume stays constant, but the temperature and the pressure drop. The entropy also drops slightly. Because the volume of the gas stays constant the line on the p-V graph is vertical and there is no area under it; no work is done in this phase (we're assuming no friction in the mechanism and no viscosity in the gas).

The T-s graph is a different matter. The area under the line, labelled Q2, is the heat energy that is transferred from the gas into the regenerator.

After phase 2 the engine looks a bit like this: http://en.wikipedia.org/wiki/File:Alpha ... ame_16.png, and is at the point I've labelled C. The gas is now at the cold temperature and low pressure, but the volume is still high and the entropy is still highish.

In Phase 3, between points 'C' and 'D' of the cycle, is an isothermal compression: The gas stays at the same temperature, but decreases in volume and entropy. The pressure of the gas rises. In order to make this happen two things must occur:

1) The fly-wheel (or similar) must do work on the gas. The amount of work needed is equal to the area under the p-V line, labelled W3. The fly-wheel should have this energy stored up, as we put W1 energy into it in phase 1, and W1 is greater than W3. However, imagine if we were using our Stirling engine to power a electricity generator. Imagine if, between phases 1 and 3 we had sucked more energy out than the difference between W1 and W3 as electricity. There would now be less than W3 energy left in the fly-wheel. We would not have enough energy left to compress the gas and the engine would stall.

2) Heat energy is lost to the cold sink. The quantity lost is equal to the shaded area under the line on the T-s graph. You can see that you can reduce the amount of energy lost by reducing the temperature at the cold sink. In order to eliminate the energy lost you'd have to have your cold sink at absolute zero. Good luck finding a gas that will work there.

As you probably noticed, phase 3 is a real bummer. We have to put work back into the gas and we lose energy to the cold sink. I guess you're trying to think of a way to eliminate phase 3. The trouble is that for this to be a cycle you have to get the gas back to the starting point - point A.

So why do we bother having a cycle? Well, if you can find an large supply of hot, compressed gas (like we have at point A) then you're onto a winner: You can do just phase 1 and let it all out through a turbine and get lots of work. You can sell that and be really rich. Sadly, there aren't many large supplies of hot, compressed gases just sitting around for the taking. Before you ask, Congress doesn't count - neither does parliament, as they're not sitting at the moment. If you want to be rich you'd probably be better off looking for the chemical or nuclear equivalent of a supply of hot, compressed gas. I guess the petrochemical and uranium industries got there first, though. The sun, perhaps? They can't monopolise the sun, can they? The trouble with energy from petrochemicals, uranium and the sun is that we have to turn it into useful work somehow....

Anyhow, I digress. The gas is now at point D. It is back at the starting volume, but it is still at the cold temperature and low pressure. The engine will look a bit like this: http://en.wikipedia.org/wiki/File:Alpha ... rame_4.png.

Phase 4 is the reverse of phase 2: The gas passes back through the regenerator, undergoing isochoric heating. The gas goes from point D to point A. The volume stays the same, so there's no work done, but the heat energy the gas lost to the regenerator in phase 2 is reabsorbed (so area Q4=Q2, assuming the regenerator is perfectly conservative and doesn't lose any energy down the back of the couch). This raises the temperature and pressure back up to the values the gas started with, at point A.

Sorry if you already know all that and I'm wasting your time, but hopefully it'll help to explain the path of my thinking. 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."

As I've noted above, I think that in a Stirling engine the compression and expansion strokes happen at constant temperature. I think what you're describing would be a different kind of engine; lets call it the Booth Engine. The p-V and T-s diagrams for the Booth cycle are here: http://i1009.photobucket.com/albums/af2 ... hcycle.jpg.

Starting at the same point, with the same gas as we did with the Sterling cycle: The gas has a high temperature and pressure, but low volume and entropy.

Phase 1 is an expansion where the gas increases in volume (by definition) and entropy, but decreases in temperature and pressure. The temperature of the working gas dips below that of the cold sink. As with the Stirling engine, heat energy is absorbed from the hot source and work is done by the gas.

Regenerators improve the efficiency of engines. However, a regenerator will be difficult to incorporate into the Booth engine, for the same reason that phase 3 will be tricky. We will miss out on phase 2.

In phase 3, we would like to reduce the entropy so that we can return the gas to its original state in phase 4. In order to do that we need the gas to lose some heat energy, as it does in phase 3 of the Stirling cycle. However, 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. The entropy of the gas will increase and get even further away from the starting point.

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. If it does, it will be impossible to complete that cycle.

In any case. you'll notice that we absorbed less energy and got less work in phase 1 of the Booth cycle than we did from the Stirling cycle. If we did think of a phase 3 that made the Booth cycle work then I still think it would be less efficient than the Stirling cycle.

So, what would happen if we kept with the Stirling cycle (ie isothermal expansion in phase 1), but lagged the heat sink? In our theoretical engine the sink has infinite thermal mass: it can absorb any amount of heat energy and not get hotter. Real heat sinks aren't like this. The cold piston absorbs heat energy from the gas and then passes it out to its surroundings. If more heat comes into the piston than it it can pass to the surroundings then it will begin to warm up. If it warms up then the temperature that the gas is reduced to (Tcold) will increase.

If Tcold increases then the line for process 3 on our p-V and T-s graphs will rise. The work needed to compress the gas and the heat rejected to the cold sink will increase. We will get less useful work out and the efficiency of the engine will drop. The efficiency of the engine depends on the difference in temperature between the hot source and the cold sink.

So, that's what I reckon about lagging the cold cylinder. How about the question of differing loads? Imagine you've set up your Stirling engine to lift a light weight or low gearing and you apply a source of heat to the hot cylinder. The engine starts off turning slowly. The engine goes through a cycle and a certain amount of work is left in the fly-wheel (remember that the amount of work got from a cycle was W1 - W3).

In turning over the engine also lifts the weight a distance. The work needed to do this is the product of the weight of the load and the distance it gets raised in one turn of the engine. However, what happens if this is less work than was left in fly-wheel? The energy stored in a fly wheel is related to the speed at which it is spinning, so if there is left over work, then the fly-wheel spins faster. If the fly-wheel is spinning faster then the engine is also turning over faster, so the engine also begins to speed up.

As the engine speeds up any mechanical inefficiencies will grow - greater energy will be lost due to friction in the working fluid and in the mechanism. More importantly the working gas will be in contact with the hot source, cold sink and regenerator for shorter periods each cycle. As the engine spins faster the working gas will cease to reach the temperature of the hot source when heated, or the cold sink when cooled. The efficiency of an engine is related to the temperature difference between the hottest temperature the gas reaches at one end of the cycle and the coolest temperature the gas reaches at the other end of the cycle, so as the engine spins faster it will become less efficient.

At some point the engine will have sped up to the point where the work put out in a cycle matches the work needed to lift the weight the distance it is set to go in one cycle. At that point it will settle at that speed.

If you put a heavier weight on the string then the same sort of process will occur, but the engine will settle at a lower speed (assuming the extra load doesn't stall it). Because it is running slower the gas will have more time to reach the higher and lower temperatures and it will run more efficiently.

That's all theory, though. Being from a country that has tended to favour empiricism over that nasty continental synthesis, I encourage people to test it. We can measure the work being output by lifting a weight. However, can anyone think of a way to measure the amount of heat going through? Perhaps we could measure the rate of ice melting at the cold end?

Bear in mind that this is more efficiently thermodynamically speaking. ie. You are getting more of the energy that passes through the cycled gas out as work. However, most of the engines we're looking at here are fueled by candles or suchlike. The heat put out by your fuel candle is unrelated to how fast your engine is running. Any heat that isn't taken up by the engine is just lost around outside into the atmosphere. You may get more useful work done in this situation by putting a lighter weight on. The engine will run fast an thermodynamically less efficiently, but the work will be done quicker and you can then snuff out the candle. Whilst the engine has been thermodynamically less efficient, you may have made a more efficient use of your fuel. That's why most engines have a device like Watt's governor (http://en.wikipedia.org/wiki/Centrifugal_governor) or a hit-and-miss mechanism (http://en.wikipedia.org/wiki/Hit-and-miss_engine) to match the fuel being used to the load applied and to stop the engine spinning too fast.

As I say, that's my tuppence-worth. Feel free to pick holes.
goat
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Re: Stirling Engine Thermodynamics

Post by goat »

Longpig,

By the way, there are a couple of main ways that engineers can make an engine put out more power with the same ccs:

1) They increase the incoming pressure by adding rams, a supercharger or a turbocharger (or two). The efficiency of the engine is related to the incoming pressure, so you get more work out (and therefore more power for a given rpm) for the same fuel/air mix input.

2) They make them spin faster. That's how they racing motorcycles and race replicas putting out lots of power for small engines; they just run at screamingly high revs. It's not higher efficiency and you don't get any more work out each rev, you just put more revs in per second.
goat
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Re: Stirling Engine Thermodynamics

Post by goat »

Longboy,

Many apologies, I've just noticed I called you 'Longpig' in my last two posts. :shock: Please forgive me, I didn't mean to be rude.
Longboy
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Re: Stirling Engine Thermodynamics

Post by Longboy »

Thanks Goat. Ya I'm familiar with increasing power levels with the same displacement in I/C. Getting to have the best of both worlds with tubo dirrect injected 4 cylinders over 200 HP and getting 30 plus MPG. Its all about pumping air in and out where as in Stirling......its about keeping it in!
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