"Thermoacoustic" Stirling - theory of operation

[Tom Booth]

While heat is not a substance, if we're working with fluid, we better equate it to one. All matter reacts in a predictable way to heat input. So whether Carnot meant pure energy or its effect on matter, they are the same thing.

The point is, from a "heat is a fluid" point of view, 25% Carnot efficiency is 25% of the VOLUME of fluid between 0°K and 400°K (using the above example)

From a heat as energy added to the system (raising the temperature from 300 to 400°K 25% Carnot efficiency is 100% utilization of the energy required to raise the temperature from the 300°K ambient to 400°K steam.(then back to 300°K at the exhaust, after passing through the engine)

After all, why should a "perfect" frictionless engine not be able to utilize 100% of the heat provided to it?

To claim, completely arbitrarily based only on the temperature difference that 75% of the thermal energy ADDED above the 300°K ambient starting point, MUST absolutely by some cosmic law of the universe be thrown away is IMO completely ridiculous

No other form of energy conversion is subject to any such arbitrary so-called "LAW".

[Jack]

Ah now I get what you mean. That's odd indeed.

[matt brown]

After all, why should a "perfect" frictionless engine not be able to utilize 100% of the heat provided to it?

To claim, completely arbitrarily based only on the temperature difference that 75% of the thermal energy ADDED above the 300°K ambient starting point, MUST absolutely by some cosmic law of the universe be thrown away is IMO completely ridiculous

Jack, what Tom continually fails to grasp is Carnot's "cycle" theory and easiest seen with a Stirling cycle. Consider a simple piston engine where a perfect Stirling cycle has 400k source, 300k sink, and vacuum buffer pressure. Regardless of charge pressure, when the volume ratio is the same for expansion and compression, 4x units of 400k 'heat' source input will produce 4x units of work output during isothermal expansion, but to complete the cycle, 3x units of this work output will be required as work input during isothermal compression and produce 3x units of 300k 'heat' sink output. Value of 'x' will depend upon charge pressure.

I used vacuum buffer pressure to make this more precise and indicate that a simple engine will require a flywheel. The "Carnot equation" is just a mathematical reduction, not a conspiracy.

OK, that's the nickel tour on isothermal compression cycles, but if you endeavor to mess with adiabatic compression cycles or non-compression cycles, you'll need formal study...

[matt brown]

Tom - several of the Khan Academy videos now relate gas temperature as the measure of gas speed. Thermodynamics is loaded with ratios and proportions, so here's another...gas speed varies by the sq rt of temperature ratio, ex: 400k gas is moving twice as fast as 100k gas (sq rt of 400/100=2). Thus, any 300-1200k cycle has a max speed variation of 2 (and this taps out that issue).

[Tom Booth]

..., and vacuum buffer pressure. Regardless of charge pressure, .

I used vacuum buffer pressure to make this more precise and indicate that a simple engine will require a flywheel. ...

LOL...

Vacuum buffer pressure?

It requires such a completely unrealistic and impossible scenario to make your analysis even begin to make sense.

I don't think the Carnot formula is a "conspiracy" so much as utter stupidity. The only thing it's a derivation of is the temperature difference in terms of the volume of a non-existent "caloric". An archaic fallacy Carnot himself abandoned after its publication.

Anyway, sure, I think I can agree that if you have a vacuum for buffer pressure you'll need more than a flywheel to bring the piston back to TDC.

So what actual engine has a vacuum buffer pressure?

If you push a car up a hill against gravity then let it roll back down,, is the work of pushing it up hill used to push it back down the hill?

I guess you could make that as a philosophic argument, but a vacuum buffer would be the equivalent of the car rolling down hill, so there would be no work involved in the first place. Your grasping at straws.

[Tom Booth]

Tom - several of the Khan Academy videos now relate gas temperature as the measure of gas speed. Thermodynamics is loaded with ratios and proportions, so here's another...gas speed varies by the sq rt of temperature ratio, ex: 400k gas is moving twice as fast as 100k gas (sq rt of 400/100=2). Thus, any 300-1200k cycle has a max speed variation of 2 (and this taps out that issue).

Maybe you could post some kind of reference, proof, experimental demonstration, link to one or more of these videos or a video title or anything?

Assuming you mean kinetic energy of some sort, that a 400 k gas is "moving" only twice the speed of the same gas at 100k looks wrong but might be interesting.

[Tom Booth]

One thing I came across is "speed" and "kinetic energy" are not proportional but depend on mass.

That is, a slow moving bowling ball has much more kinetic energy than a fast ping pong ball.

Anyway, without some reference it's not possible to put whatever you might be talking about in perspective. Some chemistry videos maybe?

[VincentG]

Kinetic energy goes up with velocity squared, so it's lost to chaotic motion in systems that just rely on the brute force of pressure alone. If harnessed it should allow more work to be done with less gas, and consequently less BTU's.

[Tom Booth]

Kinetic energy goes up with velocity squared, so it's lost to chaotic motion in systems that just rely on the brute force of pressure alone. If harnessed it should allow more work to be done with less gas, and consequently less BTU's.

In trying to find something on what Matt may be talking about I came across references to "the root mean square speed (velocity)".

But that applies, apparently to a given axis (direction of motion)

So yes, that makes sense, as I had mentioned, adding heat to gas without controlling and directing the expansion in some way just results in an expanded chaotic motion. On average, the molecules going in any one direction go only a little faster as Matt pointed out, but even that is cancelled out by an equal number of molecules going faster in the opposite direction.

In an engine, though, the expansion is made (more) uniformly directional by having a "movable wall" (piston) which allows effective expansion in only one direction. Gas bouncing off (fixed) walls is not particularly relevant.

The venturi becomes more important in light of this as it gives additional direction to the otherwise chaotic expansion.

So, I would say Matt is correct (sort of) but does that support the Carnot theory/limit? Maybe I'm wrong but I got the impression that was the intent behind bringing it up.

IMO the whole idea of a hot air engine is turning "heat", or the Chaotic motion of the gas into orderly motion that can be harnessed. As opposed to the Carnot theory that heat of its own accord has a tendency to "flow" from a hot "reservoir" down to a cold "reservoir".

Our job as mechanical engineers trying to get power out of "heat" or hot air is a lot more complicated and difficult than simply dropping a paddle wheel into a river of heat flowing between two "reservoirs'.

On the contrary we are trying to bring some actual order out of a complete and utter chaos. "Nature" is not really helping us much at all. There is no river of heat we can tap into.

[Tom Booth]

A "NASA" type "free piston" engine, like my 3kw INFINIA/Stirling Technology test engine (basically mock "thermoacoustic" as defined here) is, IMO crippled and inefficient due to having been largely based upon and modeled after this over simplification, Carnot heat flow between "reservoirs" mythology.

From a perspective of hot helium being a chaotic cloud of random motion, the engine is poorly designed and does practically nothing to improve on "nature", or the supposed (but practically non-existent) natural tendency for heat to flow between a heat source and a sink.

I've gone into some detail before regarding what I consider the shortcomings and how the engine might be improved, in spite of it being the culmination of hundreds of millions of dollars in corporate and government R&D dollars spanning decades.

Once heated, the heat from the hot gas is dumped almost immediately into a water jacket, cold regenerator, the passages for heat flow to the piston lined with a copper "sink", all, apparently to fulfill the requirements spelled out by the Carnot formula. Provisions having been made to carry off the 80% "waste heat" to the "cold reservoir" that the supposedly inescapable 2nd LAW insists upon as a universal heat "Tax".

It cannot be improved by, say, simply not supplying cooling water as the heat would damage the linear generator and other components that rely on the effectiveness of the cooling system.

[Tom Booth]

There is a kind of seeming contradiction in that a greater ∆T improves power and efficiency but cooling the engine robs it of power and efficiency.

The cold side of the engine only serves, or should only serve as a kind of insulation.

Heat only travels between hot and cold. (Not by a "flow" but by random dispersal of energy in all directions) so if an already cold gas collides with a cold surface the cold gas does not take in any heat and so is then easily compressed for the completion of the cycle.

But for this insulating effect to be beneficial the gas needs to cool by expansion and work output BEFORE it comes in contact with the cold side, otherwise the cold side acts as a "sink" which is of no benefit. It is just throwing away fuel (heat) which could have been utilized.

So really the cold side should be no colder than what the gas can become "on its own" through expansion and dissipation of "internal" thermal energy through work output.

But ACTUAL insulation, apparently, can work just as effectively as using a cold surface as "insulation" to prevent the heating of cooled gas which is about to be compressed to TDC.

As I think has been pretty thoroughly demonstrated, experimentally:


https://m.youtube.com/playlist?list=PLp ... Q9pQZzY7Eu

A colder temperature on the cold expansion side of the engine, in other words has limited benefit in that it can allow the working fluid to cool to the maximum extent possible by its own "self refrigeration" by expansion and work output.

Cooling further than that, however, only begins to waste valuable "fuel".

That's my theory anyway.

[Jack]

I get where you're coming from, but I think cold sinks are used for a different reason.

I don't think it's mechanically possible to get every last bit of heat turned into energy or work. It gets easier the smaller you go though. But you run into the law of diminishing returns.
Cold sinks do waste fuel, but they allow a heavier or bigger engine to operate. It allows for bigger differences in temperature because that big machine can't get anything out of the "waste" heat. So the fluid needs to be cooled down to reduce the work input needed.

In theory you're correct that all heat can be taken out by allowing the fluid to expand to wherever, but that inherently ruins any kind of power we can get from it.

[Jack]

I'll add that I'm also looking for a way to let the fluid do its work before it actually gets close to a sink. Similarly I want to have it do its work before it touches a regenerator. Because that just steals work output at the wrong moment.

[Tom Booth]

I get where you're coming from, but I think cold sinks are used for a different reason.

I don't think it's mechanically possible to get every last bit of heat turned into energy or work. It gets easier the smaller you go though. But you run into the law of diminishing returns.
Cold sinks do waste fuel, but they allow a heavier or bigger engine to operate. It allows for bigger differences in temperature because that big machine can't get anything out of the "waste" heat. So the fluid needs to be cooled down to reduce the work input needed.

In theory you're correct that all heat can be taken out by allowing the fluid to expand to wherever, but that inherently ruins any kind of power we can get from it.

Can you explain that last paragraph?

I understand your point of view, I think, and I would even agree that IF an engine, of whatever size cannot,for whatever reason, utilize all the heat supplied to it, the excess might need to be removed one way or another for the engine to continue running, maybe. (Though I think there are probably better solutions that have not been explored due to the prevailing theory that "waste heat" is inevitable and discarding it is somehow beneficial to the "flow" of heat through the engine, that is considered to be what actually powers the engine)

But to revisit that last paragraph:

"In theory you're correct that all heat can be taken out by allowing the fluid to expand to wherever, but that inherently ruins any kind of power we can get from it."

In my mind the process of expansion during the power stroke IS the process of "getting the power out of" the gas as it expands.

So I don't understand how you figure that "inherently ruins any kind of power we can get from it".

To my way of thinking it ("allowing the fluid to expand to wherever") is akin to driving your car until the tank runs out of gas, wherever it happens to run out, as opposed to driving your car a little way down the road and then dumping 80% of the "waste gasoline" on the road and then refueling.

I'm just curious about the thought process that leads to the conclusion that: "all heat can be taken out by allowing the fluid to expand to wherever, but that inherently ruins any kind of power we can get from it"

How, or in what way is the power "ruined"?

[matt brown]

Kinetic energy goes up with velocity squared...

Yep, kinetic energy (KE) varies by velocity squared, so my 'suggestion' that gas moves twice as fast at 400k than 100k can be easily surmised without a calculator, online search, or trip to the unicorn forest. Simply consider my premise where KE varies by v^2 and a constant volume heating process between 100k and 400k. If I'm correct, then KE at 400k is 4x KE at 100k, so fill in the blanks...

100k KE = 1x
200k KE = ?
300k KE = ?
400k KE = 4x

Looks good to me, and looks like KE parallels another common value here.

This 'velocity' is technically called the translational speed and this ain't rocket science.

Maybe Tom can explain why Einstein's famous E=mc^2 is not E=(mc^2)/2 similar KE=(mv^2)/2