VASIMR

[93143]

The fact that we can estimate the efficiency of a good part of this apparatus with a "Carnot Cycle Efficiency" calculation does not mean that it is the way it should be calculated or that it is the limit efficiency of the apparatus.

You really need to start considering the possibility that you aren't correct.

This is very simple:

In an automotive engine, all useful power is derived from chemical energy that is converted into heat and goes through a thermal cycle. The system operates serially: combustion -> heat engine -> drivetrain. The entire power throughput follows this pathway, and energy either makes it through, or is lost to inefficiencies and does not end up as useful work.

In order to calculate the efficiency of a system that operates serially like this, you simply multiply together the efficiencies of the components. Since no step can have an efficiency above 1, this means that the efficiency of any component can be taken as a limiting efficiency; that is, the total efficiency can never exceed that of any one component even if the other components are 100% efficient.

Regeneration (recycling of "lost" heat energy, so that the path isn't just a straight line with no loopback) can improve the heat engine efficiency, but not past the Carnot limit. This can be shown by analysis of the power cycle. Recycling of losses from the other two components, if practicable, will happen at well below 100% and thus can never even bring the system efficiency back up to the point it would have been at if no combustion or drivetrain losses occurred.

So the thermal cycle efficiency is an upper bound on the efficiency of an IC engine.

This is also the reason why chemical process in fuel cells (and human beings) are not limited by "Carnot Cycle Efficiency".
These chemical process are still subject to thermodynamic laws (Gibbs and Helmholtz functions) but in these cases "Carnot Cycle Efficency" simply does not apply, because there is no thermal cycle.

Exactly. Stick in a thermal cycle, and you are instantly limited by Carnot, unless you have a significant parallel energy conversion pathway that doesn't pass through a thermal cycle at any point. IC engines don't have that.

No one ever said a heat engine had to involve heat transfer across a boundary as an essential operating principle.

MIT does.

No, they don't.

I assume you're referring to this link?

There is nothing in there that supports your contention. An Otto or Brayton cycle is clearly a heat engine, and heat transfer across a boundary is not a requirement (think about it). This comes of both cycles being open-loop...

Also, in case you missed it the first time, while it is true that the Otto cycle efficiency is the relevant limit for a spark-ignition car engine, the Otto cycle efficiency cannot exceed the Carnot efficiency under any circumstances whatsoever, so Carnot is also a relevant limit.

[ladajo]

No, try section 1.

http://web.mit.edu/16.unified/www/FALL/ ... node5.html

The otto cycle is the upper limit for IC, you can not exceed it, so Carnot becomes irrelevant, you can never get to it.

Otto also makes assumptions to allow analyzing the system.

[93143]

You mean Section 1.3.1 specifically?

That definition of heat is not relevant to the question.

Just so you know what level to aim your comments at, I've got two degrees in mechanical engineering and am halfway through a Ph.D. in aerospace engineering, focusing on compressible computational fluid dynamics of non-ideal fluids, specifically combusting sprays thereof as found in jet and rocket engines. During my undergraduate degree I showed a tendency to get perfect scores on thermodynamics exams while under unusual stress and preoccupied with other things.

Ideal (non-regenerative) internal-combustion cycles like Otto and Diesel do not require heat transfer across a boundary to occur at any point (theoretically. In a practical system, obviously, there will be a lot of heat transfer, but it doesn't show up in the ideal cycle). Yet we call them "heat engines" nonetheless.

The otto cycle is the upper limit for IC, you can not exceed it, so Carnot becomes irrelevant, you can never get to it.

We've been arguing about whether or not a system that includes a heat engine serially as an energy conversion step can do better than Carnot efficiency. I argue that it cannot. Do you disagree?

A heat engine can be driven past its basic cycle efficiency by using regeneration/reheat, but it can never exceed Carnot.

Otto also makes assumptions to allow analyzing the system.

The assumptions in an ideal Otto cycle all improve the calculated performance relative to the real system; you won't find an engine that does better than an ideal Otto cycle if it's run as a real Otto cycle. What's your point?

[MSimon]

During my undergraduate degree I showed a tendency to get perfect scores on thermodynamics exams while under unusual stress and preoccupied with other things.

A man after my own heart. My preoccupation was motorcycles.

[Giorgio]

The fact that we can estimate the efficiency of a good part of this apparatus with a "Carnot Cycle Efficiency" calculation does not mean that it is the way it should be calculated or that it is the limit efficiency of the apparatus.

You really need to start considering the possibility that you aren't correct.

This is very simple:

In an automotive engine, all useful power is derived from chemical energy that is converted into heat and goes through a thermal cycle. The system operates serially: combustion -> heat engine -> drivetrain. The entire power throughput follows this pathway, and energy either makes it through, or is lost to inefficiencies and does not end up as useful work.

Like I said before it all depends on using correct definitions.

As a mechanical engineer I have been teached to consider IC engines simply as a mean to transform potential energy (or Exergy) into work. The Carnot cycle is just one of the tools we have in our toolbox to make this happens.

The mistake you are making is that you apply Carnot cycle efficiency to a system that has already undergone a transformation (combustion) to give you a source of heat, while, in reality, you should consider the Exergy of the starting system at rest (bare fuel in this case).

Is this Exergy that gives you the work potential of your system.
Carnot cycle efficiency (and limit) has no meaning in this starting condition, as the engine is not working. You do not have an heat source, you have Exergy to transform in different ways, one of them being a heat source.

This is the first point that everyone should have clear when talking about engines and engines efficiency.

Having cleared this, we can now decide to transform the Exergy of the system in different ways, and by choosing a correct process or a series of processes much higher efficiencies can be obtained than a simple Carnot cycle.
The fact that until now most of the engines have been designed in a way where only the Carnot cycle was present or predominant has been due to our choice (economical and technical) of doing so.

I mentioned in my older posts Prof. Chris Edwards, well, he just made a new paper that expresses what I wrote in much better terms:
http://feerc.ornl.gov/pdfs/Chris_Edwards.pdf

[MSimon]

Well yes. Except the discussion was: can the engine AS DESIGNED reach 75% efficiency in conversion of fuel to work? Once the energy goes from chemical to thermal Carnot applies.

[Giorgio]

Well yes. Except the discussion was: can the engine AS DESIGNED reach 75% efficiency in conversion of fuel to work? Once the energy goes from chemical to thermal Carnot applies.

Well, that was your way to see the discussion.
Mine was more broad as I defined above.

As no one ever stated an exact definition of what we was discussing each one was discussing of something different.

This is why I stated that the main problem of this thread was (and is) to exactly define the terms of the discussion.

Edited to add:

I repeat again, Carnot applies ONLY to the thermal part. You can still get the waste heat and trasform it in something else, becouse the waste heat is part of your exergy available.
Of course you cannot use "another" Carnot cycle to recover work from that waste heat, you need another process, but this hopefully is osmething that s clear enough.

[93143]

No. Once the energy is converted into heat you are limited by Carnot no matter what you do.

If you use (say) an electrochemical fuel cell to convert chemical energy straight to electrical energy, you aren't limited by Carnot. But once the energy is in the form of heat there is nothing you can do to dodge the Second Law of Thermodynamics.

[WizWom]

Let's take a hypothetical system for nuclear power of an ion drive.

Fuel supplied runs past a nuclear core, which heats it. The hot gas is used to turn a turbine, which provides electricity. The electricity is used to accelerate the somewhat cooler fuel, and generates additional thrust.

If higher SI is desired, the hot fuel is mostly shunted into radiator panels, and recycled. The same amount of energy accelerating a lower amount of fuel leads to higher exhaust velocity and Specific Impulse, at the cost of lower total thrust.

VASIMR is suited to this application due to it being able to handle differing mass flow.

[Giorgio]

No. Once the energy is converted into heat you are limited by Carnot no matter what you do.

If you use (say) an electrochemical fuel cell to convert chemical energy straight to electrical energy, you aren't limited by Carnot. But once the energy is in the form of heat there is nothing you can do to dodge the Second Law of Thermodynamics.

Argh..... I am going to bump my head against the wall if we continue this discussion.

1) There is no Energy, there is Exergy, which gives you a completely different starting point.

2) Carnot limits hold true as long as you stay inside a Carnot cycle. Outside that type of cycle the Carnot limit looses meaning.

3) Rejected heat (which is residual Exergy of the starting system) is OUTSIDE the Carnot cycle, but that Exergy is still usable and nothing theoretical prevents me from recovering part of that unused Exergy and convert it to work by other process, thus increasing the "Exergy to work" conversion efficiency. I repeat, nothing.
The limitations we have now are just technical.

4) Because of this we can have a final Exergy to work conversion efficiency that is higher than if the simple Carnot cycle is applied to the starting Exergy. And we can do this without breaking the 2nd law of thermodynamics.

5) If still is not clear than do read the PDF I posted. It is explained in a very clear way, hopefully more clear than what I have been able to do until now....

[zapkitty]

So we point the exhaust of a VASIMR at a teakettle....

[MSimon]

No. Once the energy is converted into heat you are limited by Carnot no matter what you do.

If you use (say) an electrochemical fuel cell to convert chemical energy straight to electrical energy, you aren't limited by Carnot. But once the energy is in the form of heat there is nothing you can do to dodge the Second Law of Thermodynamics.

Argh..... I am going to bump my head against the wall if we continue this discussion.

1) There is no Energy, there is Exergy, which gives you a completely different starting point.

2) Carnot limits hold true as long as you stay inside a Carnot cycle. Outside that type of cycle the Carnot limit looses meaning.

3) Rejected heat (which is residual Exergy of the starting system) is OUTSIDE the Carnot cycle, but that Exergy is still usable and nothing theoretical prevents me from recovering part of that unused Exergy and convert it to work by other process, thus increasing the "Exergy to work" conversion efficiency. I repeat, nothing.
The limitations we have now are just technical.

4) Because of this we can have a final Exergy to work conversion efficiency that is higher than if the simple Carnot cycle is applied to the starting Exergy. And we can do this without breaking the 2nd law of thermodynamics.

5) If still is not clear than do read the PDF I posted. It is explained in a very clear way, hopefully more clear than what I have been able to do until now....

I do believe you gentlemen are in agreement.

[MSimon]

Actually: Once you are at the Carnot limit there is nothing you can do to get that energy out.

i.e. if you are rejecting heat at 300K to a 300K environment you got nothing left.

Or to put it in engineering terms: The heat sink has to get bigger the closer you get to Carnot.

[93143]

Giorgio, you've misunderstood that PDF.

He's not saying that you can do better than Carnot with an IC engine. He's saying that increasing the compression ratio of an internal-combustion cycle or combined cycle and adding regeneration can dramatically increase the thermal efficiency. Which is quite true - a simple Otto cycle with a 100:1 compression ratio (as mentioned in the PDF) has a very high theoretical efficiency. But so does a Carnot cycle with the same temperature ratio - the compression step raises the working fluid temperature massively, so the heat addition is at a very high temperature.

In both this PDF and your earlier links, the introductory wording sounds a lot like a claim that an IC engine can be driven past the Carnot limit by making it act more like a fuel cell. I can only assume that this was carelessly worded, because in the linked papers it is actually demonstrated that this analogy is a false one, that an IC engine operating on thermal energy is fundamentally different from a fuel cell, and that the efficiency increase in certain types of engines with lower peak temperatures is actually due to reduced heat transfer loss to the walls.

As far as I can tell, Edwards does not actually claim that thermal energy can be converted at higher than Carnot efficiency. His wording is strange in spots (for instance, he appears to classify internal combustion engines as separate from heat engines *cough*), but he does seem to understand what he's talking about. The stuff about the Carnot limitation being an exception seems to mean not that Carnot isn't a limit on a thermal engine, but rather that it is not what's holding us back; other things are in the way and need to be considered too.

3) Rejected heat (which is residual Exergy of the starting system) is OUTSIDE the Carnot cycle, but that Exergy is still usable and nothing theoretical prevents me from recovering part of that unused Exergy and convert it to work by other process, thus increasing the "Exergy to work" conversion efficiency. I repeat, nothing.
The limitations we have now are just technical.

4) Because of this we can have a final Exergy to work conversion efficiency that is higher than if the simple Carnot cycle is applied to the starting Exergy. And we can do this without breaking the 2nd law of thermodynamics.

This is wrong. Exceeding Carnot with thermal energy breaks the Second Law - period. And quit talking about "exergy" as if it's some brand-new concept that invalidates conventional thermodynamics. Rejected heat at the minimum available temperature (as in a Carnot cycle) is not exergy.

Rejected heat is only useful if you are able to access a state at a lower temperature than that of the rejected heat. Regenerative cooling is a good example of this - the fuel or intake air is at a lower temperature than the exhaust, so some of the thermal energy in the exhaust can still be made useful. A bottoming cycle in a combined-cycle power plant is another good example - using the exhausted heat as the heat source for another heat engine. But this does not break Carnot - it just gets you closer.

You can dodge Carnot if you use a "combined-cycle" power plant that involves non-thermal conversion, such as a solid-oxide fuel cell operated in combination with a gas turbine (this combination is actually a nice one for a couple of reasons). But from a conversion pathway perspective this is actually a parallel implementation in which some of the available chemical energy does not pass through a thermal state at all, and thus Carnot does not apply to the whole system.

Thermal energy cannot be utilized at better than Carnot efficiency - once you've converted it to thermal, it's game over for beating Carnot.

...

To touch on the original topic of the thread, it turns out that the optimal efficiency of a heat engine that has to dump its waste heat via radiators in a vacuum is around 25%. If you go any higher, the reduction in cold-side temperature causes the radiator efficiency to drop faster than the waste heat output, and you need bigger, heavier radiators. T^4 is something you want to work with, not against.

Adding a non-thermal converter won't help, because the waste heat is already thermal; you need a heat engine. And a string of heat engines is just as limited by Carnot efficiency as a single heat engine; the assembly can be treated as a black box and the result above still holds.

[zapkitty]

All you have to do to defeat the Carnot limit is to throw sufficient quantities of buzzwords such as "quantum" and "nano" at it...