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

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In two-phase heat exchangers, the average temperature can indeed exceed the logarithmic mean temperature due to the effects of phase change, particularly when considering latent heat in addition to sensible heat. The discussion highlights calculations involving a heat pump using CO2, where varying pressures and temperatures impact the efficiency and energy release during phase transitions. It is noted that when phase changes occur, the effective average temperature difference may be less than the logarithmic mean temperature difference, contradicting initial assumptions about temperature behavior. The importance of accurately integrating enthalpy changes to determine the effective average temperature difference is emphasized. Understanding these dynamics is crucial for optimizing heat pump performance in applications involving phase changes.
  • #61
russ_watters said:
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?
 
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  • #62
Devin-M said:
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.
 
  • #63
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
 
  • #64
Devin-M said:
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.
 
  • #65
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).
 
  • #66
https://www.researchgate.net/figure/Comparison-of-Carnot-and-Lorenz-cycles-respective-to-their-adapted-application-cases_fig2_37413723

7B0435F5-675C-452B-A537-F53E4440F10B.png
 
  • #67
Devin-M said:
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

cop-table2.jpg


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)...

cop-table-3.jpg


... 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):
cop-table-4.jpg
 
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  • #68
Devin-M said:
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.
Devin-M said:
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.
 
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  • #69
russ_watters said:
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...
cop-table-4.jpg
 
  • #70
Devin-M said:
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.
 
  • #71
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).

cop-table-3.jpg


cop-table-4.jpg
 
  • #72
Devin-M said:
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?
 
  • #73
russ_watters said:
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.
 
  • #74
Devin-M said:
"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.
 
  • #75
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.

Devin-M said:
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
 
  • #76
Devin-M said:
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.
 
  • #78
The heat pump process which I have asked about features temperature glide...

heat_pump3-jpg.jpg


5mpa-vs-2_5mpa-2-jpg.jpg


5mpa2-jpg-jpg.jpg
 

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