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

Devin-M · Jul 22, 2021

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 · Jul 22, 2021

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?

Devin-M · Jul 22, 2021

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.

russ_watters · Jul 22, 2021

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.

Devin-M · Jul 22, 2021

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

russ_watters · Jul 22, 2021

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.