B Is Mean Temp in 2 phase Heat Exchangers Higher Than Logarithmic Mean?

[Devin-M]

Energy stored in a flywheel powers the compressor. The compressor heats the 275K gas via the compression to 400K. Heat exits the C02 via the hot side of the stirling engine towards the cold side of the C02 loop. After the expansion valve, the temperature of the CO2 drops from 275K to 225K. The stirling engine heats this side from the heat from the hot side. The water ensures the C02 reaches 275K before it is recompressed.

If we assume the C02 is gas only on both sides, only sensible heat is involved. I used the logarithmic mean temp of the hot side and the logarithmic mean temp of the cold
side to calculate the stirling efficiency. The lorenz COP multiplied by the stirling efficiency gives the same mechanical power out from the stirling as goes into the compressor from the flywheel.

But the part I don’t understand is if we have phase changing in the heat exchangers, on the cold side where the C02 heats from a liquid to gas (absorbs heat from ocean water to 275k), the water is adding latent heat in addition to sensible heat. On the hot side, where the C02 changes phase from gas to liquid, it is discarding latent heat in addition to sensible heat.

What I’m trying to understand is how the latent heat in addition to the sensible heat affects the calculated efficiencies of ideal stirling engines, compared to the case where only sensible heat is involved.

 

[russ_watters]

The basic exercise here should start with the most basic system: A heat pump driving a heat engine, with nothing else in the system -- no external reservoirs. Using Carnot efficiencies you don't even need to define the cycles, you just note that your "reservoir" temperatures are your working fluid temperatures (since you don't have separate reservoirs), plug and chug the math and that shows the efficiencies are inverses (multiply to 1).

Anything you do to add complexity to the system or calculations will decrease the efficiency (they'll multiply to something less than 1) unless there's an error or another source of input not accounted for.

Here you seem to have added an external reservoir for an additional input of heat. That's a 2nd Law violation and worse it's the opposite of what your problem is. The problem with a non-ideal system is that it needs to reject more heat, not that it can provide excess cooling.

 

[russ_watters]

Energy stored in a flywheel powers the compressor.

No, get rid of the flywheel. It is an unnecessary complication and is probably a separate, additional wrong perpetual motion belief you hold. Flywheels are not continuous sources of power, so this hides an additional energy leak in your system.

After the expansion valve, the temperature of the CO2 drops from 275K to 225K. The stirling engine heats this side from the heat from the hot side.

To what temperature does the Stirling engine heat the CO2 and what temperature are you using in your efficiency calc for the Stirling engine cold side?

The water ensures the C02 reaches 275K before it is recompressed.

How do you know you even need a heat addition there? (hint: you don't)

What I’m trying to understand is how the latent heat in addition to the sensible heat affects the calculated efficiencies of ideal stirling engines, compared to the case where only sensible heat is involved.

To be honest, while the exercise @Chestermiller took you through is a nice learning experience, the intricacies of heat transfer should be learned after one has mastered the thermodynamics. I don't think you're ready yet for that level of complexity and it may not even be needed to begin with.

 

[Devin-M]

No, get rid of the flywheel. It is an unnecessary complication and is probably a separate, additional wrong perpetual motion belief you hold. Flywheels are not continuous sources of power, so this hides an additional energy leak in your system.

Constant 1kW mechanical (or 1MW for that matter) in from external power.

To what temperature does the Stirling engine heat the CO2 and what temperature are you using in your efficiency calc for the Stirling engine cold side?

The stirling engine cools the C02 on the hot side of the heat pump. As the hot heat exchanger passes the hot side of the stirling engine, the C02 cools from 400k to 275K. The hot stirling temperature is calculated from the logarithmic mean between 400k and 275k.

On the cold side, the stirling cold temperature is the logarithmic mean between 225K and 275K. 225k is the temperature as the C02 exits the expansion valve. It heats to 275K from the stirling and certainly, the water.

 

[russ_watters]

On the cold side, the stirling cold temperature is the logarithmic mean between 225K and 275K.

Great, then we can get rid of the water bath. And did you calculate and then use that temperature in the efficiency calc?

I don't think you've found the main energy leak yet. It's in the first point I made in the first post. The difference between the logarithmic means at the heat exchangers and the compressor temperatures is where the loss is.

 

[Devin-M]

And did you calculate and then use that temperature in the efficiency calc?

I did.

When you multiply the 3.95… lorenz cop by the .253… stirling efficiency it’s 1 exactly (at the very bottom).

 

[russ_watters]

I did.View attachment 286370

Yeah, so you're using the wrong temperatures to calculate the efficiency for the heat pump. They should be 400 and 225K.

Additional potential problem: these are the temperatures of the heat pump working fluid, not the temperatures of the Sterling engine working fluid (though perhaps we can ignore that and assume it can be made equal with a 100% effective heat exchanger).

 

[Devin-M]

Yeah, so you're using the wrong temperatures to calculate the efficiency for the heat pump. They should be 400 and 225K.

https://backend.orbit.dtu.dk/ws/portalfiles/portal/149827036/Contribution_1380_final.pdf

I used equations 2, 3 and 4 on this paper.

 

[russ_watters]

https://backend.orbit.dtu.dk/ws/portalfiles/portal/149827036/Contribution_1380_final.pdf

I used equations 2, 3 and 4 on this paper.

Those equations don't apply to what you are doing. The source and sink for your heat pump are the temperatures of the Stirling engine working fluid (which you aren't even looking at). You're applying the equation to calculate the mean temperature of the heat pump working fluid from its own inlet and outlet temps. That's just not what those equations are for.

That paper is still using ideal heat exchangers.

Note: I'm not sure I buy what the paper is trying to say; it says you can do better than Carnot efficiency by putting heat pumps in series. That doesn't seem right, but I don't have time to dig in right now. This problem may reduce to a question of whether you can apply the Lorenz efficiency to a heat pump while simultaneously applying a Carnot efficiency to the heat engine in order to violate conservation of energy.

Either way, in order to dig into this further I'd want to dispense with all the unnecessary complications and just use ideal cycles, constant temperatures.

 

[russ_watters]

Note: I'm not sure I buy what the paper is trying to say; it says you can do better than Carnot efficiency by putting heat pumps in series. That doesn't seem right, but I don't have time to dig in right now. This problem may reduce to a question of whether you can apply the Lorenz efficiency to a heat pump while simultaneously applying a Carnot efficiency to the heat engine in order to violate conservation of energy.

Either way, in order to dig into this further I'd want to dispense with all the unnecessary complications and just use ideal cycles, constant temperatures.

Ahh, ok, I've got it: the paper is talking about progressive cooling/heating of a source/sink. For example, if you want to heat your house from 10C to 20C if you first supply it 11C air, then 12C air, then 13C air, etc. you get higher efficiency than if you'd provided 20C air from the start. That's true, but that isn't what we are doing with your system. Your system is operating at steady state.

 

[Devin-M]

Ahh, ok, I've got it: the paper is talking about progressive cooling/heating of a source/sink. For example, if you want to heat your house from 10C to 20C if you first supply it 11C air, then 12C air, then 13C air, etc. you get higher efficiency than if you'd provided 20C air from the start. That's true, but that isn't what we are doing with your system. Your system is operating at steady state.

If that’s true, and you remove the part of the pipe that goes through the water (so the heat pump is a closed loop entirely enclosed in vacuum with no contact with the water), and the stirling outputs less than than the compressor mechanical input (when the system reaches steady operation), where is the energy going that’s not coming out of the stirling engine?

 

[russ_watters]

If that’s true, and you remove the part of the pipe that goes through the water (so the heat pump is a closed loop entirely enclosed in vacuum with no contact with the water), and the stirling outputs less than than the compressor mechanical input (when the system reaches steady operation), where is the energy going that’s not coming out of the stirling engine?

The Stirling engine has two outputs:
1. Heat (rejecting too much)
2. Mechanical power (not enough)

The loss can be in either or both.

Or if it isn't absorbing enough heat in the input, the heat pump loop just gets hotter and hotter.

 

[Devin-M]

Does this snippet have any applicability:

“ Transcritical CO2 refrigeration cycle integrated with mechanical subcooling (MS) cycle operating with zeotropic mixture is proposed in this study, based on the concept of Lorenz cycle. An energetic model is developed and analyses are conducted in detail. A maximum overall coefficient of performance (COP) is achieved at the optimum discharge pressure and optimum subcooling degree. The maximum overall COP, optimum subcooling degree and discharge pressure are closely related to the temperature glide of the mixtures. The energy efficiency of the transcritical CO2 refrigeration cycle can be efficiently improved, and the high pressure can be reduced when mixtures with proper temperature glide are used as MS cycle refrigerant. ”
https://www.researchgate.net/publication/323326860_Energetic_performance_of_transcritical_CO2_refrigeration_cycles_with_mechanical_subcooling_using_zeotropic_mixture_as_refrigerant

 

[russ_watters]

Does this snippet have any applicability:

Kind of. It's an article about picking the optimal temperatures/pressures for your refrigerant to maximize efficiency.

It's an interesting article. The broader issue they are investigating is alternative refrigerants to replace ozone depleting and global warming causing refrigerants. It's a problem in the industry right now because the refrigerants we have work really well and the "environmentally friendly" ones don't. It's saying CO2 is a leading candidate but its operating temperatures/pressures aren't good for normal HVACR needs.

 

[Devin-M]

It says “based on the concept of Lorenz cycle”

“The maximum overall COP, optimum subcooling degree and discharge pressure are closely related to the temperature glide of the mixtures.”

From my readings I had gathered that “temperature glide” means when the temperature in the C02 changes in the condenser. If the C02 was losing heat entirely during the gas to liquid transition (vapor % is changing), it’s temperature would remain constant, so temperature glide is when the temperature doesn’t remain constant across the condenser (ie releasing heat while CO2 is entirely liquid or gas).

From my reading I had gathered that the “lorenz COP” is the COP you get when the C02 does have temperature glide, and the “carnot cop” is the COP you get when the CO2 doesn’t have temperature glide.

For example with 400k to 275k on the hot side and 225k to 275k on the cold side, it’s more efficient to lift the temperature from 275k to 400k (lorenz cop) than it is to lift the temperature from 225k to 400k when there is no “temperature glide” (carnot cop).

 

[Devin-M]

https://www.researchgate.net/figure/Comparison-of-Carnot-and-Lorenz-cycles-respective-to-their-adapted-application-cases_fig2_37413723

 

[Devin-M]

For example with 400k to 275k on the hot side and 225k to 275k on the cold side, it’s more efficient to lift the temperature from 275k to 400k (lorenz cop) than it is to lift the temperature from 225k to 400k when there is no “temperature glide” (carnot cop).

From this paper:
https://backend.orbit.dtu.dk/ws/portalfiles/portal/149827036/Contribution_1380_final.pdf

If I use the same temperatures as circled in the table from the paper, I calculate the same lorenz cop and carnot cop as shown in the paper's table (see above and below)...

... but if the Cold in and Cold Out are both essentially the same temperature (15C - no temperature glide in the evaporator) and the hot in and hot out are the same temperature (90C - no temperature glide in the condenser), then the lorenz cop is the same as the carnot cop, and the carnot cop is the same carnot cop as shown in the paper's table (see below):

 

[russ_watters]

It says “based on the concept of Lorenz cycle”

“The maximum overall COP, optimum subcooling degree and discharge pressure are closely related to the temperature glide of the mixtures.”

From my readings I had gathered that “temperature glide” means when the temperature in the C02 changes in the condenser. If the C02 was losing heat entirely during the gas to liquid transition (vapor % is changing), it’s temperature would remain constant, so temperature glide is when the temperature doesn’t remain constant across the condenser (ie releasing heat while CO2 is entirely liquid or gas).

Almost. For the Lorenz cycle, there isn't just a temperature change in the condenser, there is more than one heat pump/condenser. To put the issue another way: ordinarily you want a constant temperature with a phase transition in each heat exchanger. Due to the poor characteristics of CO2 as a refrigerant, they are mixing in with it a more traditional refrigerant, which results in a varying temperature instead of a constant temperature. This is a bad thing, not a good thing. One way to mitigate this problem is to add additional heat pumps, moving energy at different delta-Ts. You don't have this.

From my reading I had gathered that the “lorenz COP” is the COP you get when the C02 does have temperature glide, and the “carnot cop” is the COP you get when the CO2 doesn’t have temperature glide.

No. The Lorenz COP comes from combining/using multiple refrigerant cycles. It helps reduce the downside of the temperature glide by having separate cycles for the different temperatures. The paper describes a system with two heat pumps working together.

None of this has anything to do with your cycle, though. Your system only has one heat pump. You're taking bits and pieces of papers about cycles that aren't the same as yours and mis-applying them. You really need to go back to the basic principles and analyze your cycle for what it is, according to those principles:

• What is the temperature at the outlet of your compressor? If that temperature needs to be higher, does that help or hurt your efficiency? In other words, does it increase or decrease the compressor input power?
• What is the temperature of the Stirling engine working fluid? If this temperature is lowered, does that help or hurt your efficiency? In other words, does it increase or decrease the power output of the Stirling engine?

The answers to these questions and implications for your idea should be obvious. The problem you are having - not knowing what temperatures to use in the equations - is part of the reason I prefer using energy to calculate efficiency. It's obvious what the input and output states are at the compressor. There's no way to accidentally use the wrong state.

But still; you're attempting to use an equation meant to be applied to an infinite series of heat pumps. Clearly, you don't have that.

P.S. I still have my college thermodynamics book. It doesn't mention Lorenz cycles. I hade to google that. To me, what Lorenz did is more of a mathematical curiosity than a useful/real-world concept. It seems that it is being resurrected - sort of - as a way to help mitigate performance/efficiency problems with new refrigerants.

 

[Devin-M]

The Lorenz COP comes from combining/using multiple refrigerant cycles.

The lorenz cop is the same as the carnot cop when there is no temperature glide...

See below COP Lor and COP Car...

 

[russ_watters]

The lorenz cop is the same as the carnot cop when there is no temperature glide...

Yes...
[note, there were some late edits to my post]

I really think you need to take a step back and define and evaluate the problem you are trying to solve for what it is. I think you are getting lost in the weeds.

 

[Devin-M]

So if the CO2 stays a gas (never a liquid -- no phase change), and as it comes out of the expansion valve it's 15C, it heats (from the some water) to 43C, after compression, it's 90C, and as it transfers heat to another fluid, the CO2 gas cools to 50C (as shown in the table below), the COP of the heat pump is 8.39 (the lorenz cop). If it was a vapor/liquid mixture at constant 90C after the compressor and constant 15C after the expansion valve, the COP would be 4.84 (the carnot cop), and the lorenz cop would be the same as the carnot cop (see second table).

 

[russ_watters]

So if the CO2 stays a gas (never a liquid -- no phase change), and as it comes out of the expansion valve it's 15C, it heats (from the some water) to 43C, after compression, it's 90C, and as it transfers heat to another fluid, the CO2 gas cools to 50C (as shown in the table below), the COP of the heat pump is 8.39 (the lorenz cop). If it was a vapor/liquid mixture at constant 90C after the compressor and constant 15C after the expansion valve, the COP would be 4.84 (the carnot cop), and the lorenz cop would be the same as the carnot cop (see second table).

No, that's not how this works. Lorenz COP does not apply here because you only have one cycle. Your compressor does not care about the poor performance of your working fluid, it only cares about its own inlet and outlet conditions. Please think about what your cycle is actually doing. If the temperature out of the compressor is 90C instead of some value between 50 and 90C does that mean you needed more or less input power at the compressor?

 

[Devin-M]

No, that's not how this works. Lorenz COP does not apply here because you only have one cycle.

"The use of the Lorenz cycle together with the inverse Carnot cycle increases the conversion efficiency of a heat pump by 25–30%. The Lorenz cycle may be implemented either through the use of nonazeatropic substances or by multistage circuits."

https://link.springer.com/article/10.1007/s10556-018-0410-6

^Multistage circuits OR nonazeatropic substances.

 

[russ_watters]

"The use of the Lorenz cycle together with the inverse Carnot cycle increases the conversion efficiency of a heat pump by 25–30%. The Lorenz cycle may be implemented either through the use of nonazeatropic substances or by multistage circuits."

https://link.springer.com/article/10.1007/s10556-018-0410-6

^Multistage circuits OR nonazeatropic substances.

That article is behind a paywall and there is no context provided. Maybe to harness the nonazeatropic substance they have a variable temperature heat sink? And you're ignoring my questions, ignoring your own cycle, choosing instead to pick and choose out of context one-liners about cycles that may or may not be related to yours (usually not). This is not an approach I'm going to be willing to humor much longer.

 

[Devin-M]

This other article (not behind a pay wall) also mentions using zeotropic (which is the same as nonazeatropic) substances and the Lorenz cycle. The point is you don’t need a multistage heat pump to use the Lorenz cycle. In this case I’m looking at C02 very near (but slightly below) the critical pressure on the hot side. It mentions mixing other substances with the C02 to lower the necessary pressures but I’m looking at the simpler case with just C02 for now.

“ Transcritical CO2 refrigeration cycle integrated with mechanical subcooling (MS) cycle operating with zeotropic mixture is proposed in this study, based on the concept of Lorenz cycle. An energetic model is developed and analyses are conducted in detail. A maximum overall coefficient of performance (COP) is achieved at the optimum discharge pressure and optimum subcooling degree. The maximum overall COP, optimum subcooling degree and discharge pressure are closely related to the temperature glide of the mixtures. The energy efficiency of the transcritical CO2 refrigeration cycle can be efficiently improved, and the high pressure can be reduced when mixtures with proper temperature glide are used as MS cycle refrigerant. ”
https://www.researchgate.net/publication/323326860_Energetic_performance_of_transcritical_CO2_refrigeration_cycles_with_mechanical_subcooling_using_zeotropic_mixture_as_refrigerant

 

[russ_watters]

This other article (not behind a pay wall) also mentions using zeotropic (which is the same as nonazeatropic) substances and the Lorenz cycle. The point is you don’t need a multistage heat pump to use the Lorenz cycle.

That other article *is* discussing a multistage heat pump (air conditioner). That's what "mechanical subcooling" means.

Anyway, this has to stop right now. The approach you are taking here is wrong. You need to start looking at your cycle for what it is and answering my questions, or this thread will be locked.

 

[Devin-M]

not behind paywall...

http://hpc2017.org/wp-content/uploa...sign-of-high-temperature-hybrid-heat-pump.pdf

 

[Devin-M]

The heat pump process which I have asked about features temperature glide...

 

[russ_watters]

OP is unresponsive, thread is locked.