Calculate the coefficient of performance of a refrigerant

[Kakolio]

First of all, I'm not a native english speaker. So I could do some english mistakes in my post, I'm sorry about that.

Currently, I'm trying to compare the efficiency of several natural refrigerants. I would like to calculate their coefficient of performance to know which one is the most efficient.

I calculated the COP for cooling with this formula:

COPc.png

I used the Rankin cycle and I set up the high temperature at 50°C, the low temperature at 10°C and the high pressure for the carbon dioxyde at 10 MPa. I did that to be able to compare those refrigerants. I don't really know if it's a good method or no.

I found those results:
COPc R134a = 5,540709812
COPc R410A = 4,975144092
COPc Propane = 5,398954704
COPc Propylène = 5,370772176
COPc CO2 = 1,326384142

I would like you know what do you think about my approach.

I just found this paper. Inside the author compares the butane with other refrigerants and I would like to know how did he find the value of the Rankine COP, because it's not really explained in his paper. You can see his results at "Figure 1: Comparison of theoretical capacity and COP for a reverse Rankine cycle without any losses." If someone has an idea of how did he do that? And if you know what is the x-axis, because I have no idea.

Also, I noticed he used the LBF CECOMAF. I know now what is that. But I still don't really understand, because I didn't find any official paper of this norm. And when I check on this website for example. The LBP CECOMAF could be: CECOMAF LBP, -25/55 °C, CECOMAF LBP, -25/45 °C, CECOMAF HBP, +5/45 °C, CECOMAF LBP, -25/45 °C. So, I'm a little lost. If you know a website where I could find this documentation, it could really help me.

Thank you for reading me and your help!

[The Viking]

Coefficient Of Performance...

Welcome to the forum Kakolio,

Unfortunately I believe I'm right in saying that most of us on this forum are hands on engineers which are good at the systems themselves, the hardware if you like.
I for one openly admit that your question above is outside my field of expertise.

However,
When we (in Europe ?) refer to COP, we are looking at the Coefficient Of Performance for systems as a whole. Therefore the mechanical components of the system will have greater impact on COP then what refrigerant it is operating on.

If we accept your figures as correct for the refrigerants themselves you might still find that a system operating on Propane ends up with a COP of 2 and a CO2 system also manages to get a COP of 2, it all depends on what system they are dropped in to..

But then again, I might be wrong...
The only thing I use COP for in my daily work is as a selling point, I read it from a specification sheet and tell my customer how good (or bad) the system as a whole is.



.

[frank]

To determine the COP of any 'working' system, you need to log the operating measurements and plot them on a Mollier chart, then do the calculations.

If you are trying to determne the COP of a theoretical system, this can be subject to any number of external influences wthin your calculations, which may lead to false results.

The Rankine cycle is a theoretical system so your results will always be subject to interpretation.

You might be better off downloading Coolpack and play with the variables in there

[Rob White]

First of all, I'm not a native english speaker. So I could do some english mistakes in my post, I'm sorry about that.

Currently, I'm trying to compare the efficiency of several natural refrigerants. I would like to calculate their coefficient of performance to know which one is the most efficient.

I calculated the COP for cooling with this formula:

COPc.png

I used the Rankin cycle and I set up the high temperature at 50°C, the low temperature at 10°C and the high pressure for the carbon dioxyde at 10 MPa. I did that to be able to compare those refrigerants. I don't really know if it's a good method or no.

I found those results:
COPc R134a = 5,540709812
COPc R410A = 4,975144092
COPc Propane = 5,398954704
COPc Propylène = 5,370772176
COPc CO2 = 1,326384142

I would like you know what do you think about my approach.

I just found this paper. Inside the author compares the butane with other refrigerants and I would like to know how did he find the value of the Rankine COP, because it's not really explained in his paper. You can see his results at "Figure 1: Comparison of theoretical capacity and COP for a reverse Rankine cycle without any losses." If someone has an idea of how did he do that? And if you know what is the x-axis, because I have no idea.

Also, I noticed he used the LBF CECOMAF. I know now what is that. But I still don't really understand, because I didn't find any official paper of this norm. And when I check on this website for example. The LBP CECOMAF could be: CECOMAF LBP, -25/55 °C, CECOMAF LBP, -25/45 °C, CECOMAF HBP, +5/45 °C, CECOMAF LBP, -25/45 °C. So, I'm a little lost. If you know a website where I could find this documentation, it could really help me.

Thank you for reading me and your help!

Your numbers are correct by my calculations but you are working a perfect
cycle with no superheat, subcooling or pressure drops, plus you are calculating
your compressor with an Isentropic efficiency of 1.00 which again is almost perfect.

The COP's you calculate are theroreticaly perfect but will not reflect real applications.

I do not know how the auther of the paper you state came to his conclusions
but I do know that compressors are Low Back Pressure (LBP) High Back Pressure (HBP).
I'm not aware of LBF except for this

http://www.bau.fraunhofer.de/en/details/LBF.html

And

http://www.inmar.info/press/PI_Fraun...R_arial_EN.pdf

Which describ LBF as a messure of noise and vibration?

Regards

Rob

.

[desA]

A key indicator in your cycle comparison will be compressor discharge temperature. This will practically determine if the refrigerants investigated can even operate in a real, practical system, at the saturation temperatures you have selected.

Once you have this concept absorbed, we could tackle a few more real-world impacts on the theoretical models you are investigating.

[sterl]

The standard for the test setup and conditions to be maintained is described in the EN 12900. CECOMAF=Comite Europeen des Constructeurs de Materiel Frigorifique
They publish standards for the testing of refrigeration components much like ASHRAE or ARI. In the case of Danfoss and these small compressors: Its a black box type of calorimeter tests run at a standardized set of temperatures. The calculation basis also gives a means for predicting the overall performance of a motor-compressor set from the measurements made on an alternate fluid; which is essentially what the Danfoss engineers are doing.

[sterl]

And comparing carbon dioxide on a reverse Rankin at ordinary discharge conditions (comparable to 55-deg C) is very misleading because that cycle is transcritical: There is no condensing happening at those temperatures. So no latent heat. So COP comparison based on the ideal of a Rankin cycle won't mean much.

[Kakolio]

Thank you already for all your answer!

I found a new paper recently, you can find it here. This paper compares the efficiency of several refrigerants. Right now, I'm trying to follow this diagram:

Flow diagram for working fluids except R744.png

I'm using the refrigerant R22 with a temperature of evaporation at 5°C and the temperature at the end of the condensor is at 45°C.
But in this paper they indicate others parameters at the page 5.
-Degree of superheated = 10°C
-Degree of sub-cooled = 5°C

Thanks to Refpro7, I get the differents datas of the cycle:

chart for heat pump system.png

T1' = 5 °C
P1' = 0,58411 MPa
H1' = 406,85 kJ/kg
S1' = 1,7436 kJ/kg.K

T1 = 15 °C
P1 = 0,58411 MPa
H1 = 414,38 kJ/kg
S1 = 1,7702 kJ/kg.K

T2 = 72,29 °C
P2 = 1,7292 MPa
H2 = 442,88 kJ/kg
S2 = 1,7702 kJ/kg.K

T3' = 45 °C
P3' = 1,7292 MPa
H3' = 256,36 kJ/kg
S3' = 1,1872 kJ/kg.K

T3 = 40 °C
P3 = 1,7292 MPa
H3 = 249,59 kJ/kg
S3 = 1,1657 kJ/kg.K

I have several problems of understanding with this system.


- First of all, I find the Qmax,cd lower than the Qcd. You can read here my calculations:

Cc = mc * Cp,c = 0.05kg/s * 4179 J/kg.K = 208.95 W/K
Ch = mh * Cp,h = 0.028kg/s * 1495 J/kg.K = 41.86 W/K
(mc is given in the paper page 5: flow rate of water=3liters/min and I chose a mh of 0.028kg/s, because if you check the figure 4 page 6 the flowrate of the R22 should be around this value)

So Cmin = 41.86 W/K

I use the equation 5, page 3 in the paper:
Qcd = mr * (h2-h3) = 0.028 ( 442.88 - 249.59 ) = 5.41212 kW
This result looks good if you check with the figure 6 page 6.

But after when I use the equation 11 page 6 to get the Qmax,cd, I get something totally wrong:
Qmax,cd = Cmin ( Thi - Tci ) = (41.86/1000) * ( 72.29 - 20 ) + 2.1888 kW

Because if I'm right this valu should be really close to Qcd or maybe a little bit upper.

Do you know where did I do a mistake?


- My second problem of understanding is with this paragraph page 3:
"For the effectiveness calculation, equation (9) is used for sub-cooled and superheated parts. Equation (10) is used for the condensation part."
Does it mean I have to calculate three times the efficiency for three differents parts in the condensor? And after do an average to get the general efficiency?

Thank you again for your help.