Carnot was being too generous

[Stroller]

Far from being too restrictive with his estimate of maximum efficiency for heat engines:

η = 1 – (Tc / Th)

Chambadal and Novikov say Carnot was being too generous. Their formulation is:

η = 1 – √(Tc / Th)

If you thought Carnot was saying you were going to get naff-all power out of your engine, these guys are telling you that you're going to get the square root of naff-all.

Annoyingly, they seem to be right too. Have a look in the table below at their predictions for various types of energy production and the observed efficiencies.



The major difference between their analysis and Carnot's seems to be that they assume Newtonian heat conductance, i.e. the linear dependence of heat flux on the temperature difference between sink (source) and the working fluid. Newton's 'Law of cooling' comes with caveats however, so the Chambadal-Novikov efficiency 'rule' is an estimate, rather than a 'physical Law' rigourously derived from physics fundamentals.

The derivation of their rule is here:
http://large.stanford.edu/courses/2010/ph240/askarov2/

And the wikipedia discussion of Newton's law of cooling is here:
https://en.wikipedia.org/wiki/Newton%27s_law_of_cooling

Experiment and experience show more power can be coaxed from Stirling engines designed for power production by several methods; more heat in/out, denser working fluid, optimised regenerators etc.

At least one company (Cool Energy Inc) claims to have exceeded the Chambadal-Novikov efficiency,,, but only just. They use Nitrogen as their working fluid. How does removing diatomic Oxygen (plus trace gases Argon, Carbon Dioxide etc), leaving only diatomic Nitrogen help, I wonder?

It's obviously worth thinking about the physical constraints to the heat transfer coefficient used in Newton's law of cooling, and how we might get more power by considering the heat transfer properties of materials used, their thickness, surface topology etc. Maximising surface areas figures large in the design and experimental improvement of Stirling engines.

[Stroller]

How does removing diatomic Oxygen (plus trace gases Argon, Carbon Dioxide etc), leaving only diatomic Nitrogen help, I wonder?

Perhaps the main advantage has more to do with practical materials science than thermodynamics. Andy Ross had problems with flakes of iron oxide fouling one of his engines, despite the heater being made of high grade stainless steel. Removing Oxygen from the working fluid would obviously help with oxidation issues.

[Stroller]

A very nice geometrically demonstrated explanation of why the square root ends up in the equation is shown in this short and easy to understand paper by Manfred Bucher:

This will especially interest Matt Brown I think.

https://www.researchgate.net/publicatio ... not_engine

[Stroller]

It should be noted that this 'irreversible' Carnot engine has real 'Work' output, whereas the old Carnot efficiency deals with an 'ideal' engine with no time dimension, and consequently, no 'Work done'. This is one of the effects of introducing the rate of heat flow into (and out of) the engine. It's a quantity with respect to time, and it has a direction.

[Stroller]

I should have said Power output, not work. There is 'work done' internally in the Carnot cycle, but no power output. So this 'irreversible' Carnot cycle analysis is a step forward in relating thermodynamic theory to real world machines with a power output.

[Tom Booth]

A little strange the three "real world" examples chosen are antiquated steam power stations

West Thurrock station built in 1957 was decommissioned in 1993

Candu Nuclear Station built between 1950-60

Larderello dubbed "Oldest geothermal power plant in the world" operational since 1904.

Efficiency of geothermal generally is very very low in comparison with other technologies.

Those also appear to be "overall plant efficiencies".

In the case of geothermal I'm not sure how "observed efficiency" would be calculated based upon fuel consumption?

All three steam plants rely on closed loop recondensing of the steam by some cooling system.

The Thurrock plant for example dumps (or dumped before decommissioning) this heat of condensation from steam into the Thames river. Candu systems into nearby rivers, lakes etc.

In other words, cherry picking data using the most low efficiency antiquated systems on the planet, at least one of which is no longer in operation.

None powered by Stirling engines.

[Stroller]

Chambadal and Novikov published their work on this in the late 1950s. Not so much 'cherry picked' as 'up-to-date state of the art', back then. But they published in the Russian literature, which is likely why it didn't filter through to western physics until 1994.

Better late than never.

None powered by Stirling engines.

Cool Energy Inc. test result from their 'ThermoHeart' stirling engine in 2016:

At highest efficiency test condition represented by the red line on the chart, the peak measured thermal-to-electrical efficiency is 31.0%, which is 60.2% of the Carnot limit, and just higher than the Curzhon-Ahlborn (Chambadal-Novikov) efficiency of 30.4%.

A stirling engine running at the same efficiency on almost identical hot/cold temperatures as a 1950s built nuclear power station. Have nuclear power stations got a lot more efficient since?

In the case of geothermal I'm not sure how "observed efficiency" would be calculated based upon fuel consumption?

The observed efficiency is calculated from the heat input, not fuel consumption.

[Tom Booth]

"thermal-to-electrical" efficiency includes, presumably, conversion loses, mechanical transmission loses, and depends at least in part on the generator efficiency?

Admittedly the "overall system efficiency" of even a 100% efficient engine would be very low for a coal fired plant where most of the heat goes up the smokestack.

Overall system efficiency is apples to oranges for research considering actual heat conversion within and actual "waste heat" passing through the working fluid of a Stirling engine, so of little interest to me personally.

[Stroller]

This more advanced analysis of heat engines takes into account the temperatures of the working fluid, because it accounts for the heat flux across the engine walls by considering 4 temperatures, rather than the two used by Carnot.

[Fool]

Thanks.

[Stroller]

For anyone interested in the history of this maximum power-efficiency relationship, it goes back to a book by Henri B. Reitlinger in 1929:

Even if not so ancient, the history of the heat engine efficiency at maximum power expression has been yet turbulent. More than a decade after the publication of the seminal article by Curzon and Ahlborn in 1975, two older works by Chambadal and Novikov were rediscovered, both dating from 1957. Then, some years ago, the name of Yvon arose from a textual reference to this famous relation in a conference article published in 1955. Thanks to a historical study of French-written books not published for a long time, and since never translated into other languages, we bring to light in this paper that this relation was actually first proposed by Henri B. Reitlinger in 1929.

https://www.researchgate.net/publicatio ... at_Engines

Chambadal referenced this work in a 1949 paper.

[VincentG]

Good stuff. The fact is that anyone, myself included, trying to beat Carnot is going to have to present rigorous testing and all inclusive data to back up the claim, and that's just to get taken seriously in the first place. Then comes the naysayers and all the rest.

[Tom Booth]

Good stuff. The fact is that anyone, myself included, trying to beat Carnot is going to have to present rigorous testing and all inclusive data to back up the claim, and that's just to get taken seriously in the first place. Then comes the naysayers and all the rest.

Not really. Nobody cares a lick about all that if it works.

The main problem is, if it works, how to get past the offer you can't refuse, or past the government seizure of your invention for "national security" reasons and getting slapped with a gag order.

Unless of course that's what you mean by "all the rest".

https://fas.org/publication/invention_secrecy_2010/

[VincentG]

Right.

[Fool]

It's funny how an "offer that can't be refused", leaves all those inventors, poor, discredited, often I'll, and followed by ever becoming more stubborn fools.

Only the well educated seems capable of seeing through their veil of lies, and self delusion.