7 replies to this topic

[greens]

Hi, 

 

I have an example question however I am struggling to solve it. I have a solution (may not be correct) and my answer is completely different. Could anyone help me please?

 

A refrigerator uses carbon dioxide as a refrigerant. The refrigeration temperature is -20°C and the condenser temperature is 10°C.

 

Assume that the condenser and refrigerator operate at constant pressure and that the expansion (throttling) and the compressor are isentropic.

The carbon dioxide is a saturated liquid when it leaves the condenser and has a dryness fraction of 0.9 when it leaves the refrigerator.

 

a)     Determine the circulation rate required to give 0.17 tons of refrigeration. Determine the COP.

 

1 ton of refrigeration = 3923W.                               

 

 

 

 

 

 

 

Solution

 

We first must evaluate T,P,S and H of the 4 streams of a refrigeration cycle.

The values can be obtained from refrigerant tables.

Remember in the 2-phase region, a temperature fixes a pressure.

 

Stream                                                                        T(°C)   P(atm) S(kJ/kgK)  H(kJ/kg)

Entering the refrigerator                                  -20       19.7     0.46          109.1***     

Entering compressor                                      -20       19.7     1.168*       295.3*

Leaving compressor                                         10      45.0     1.168        275**

Leaving condenser                                           10      45.0     0.407        109.1***      ([8] for correct enthalpies)

 

*Dryness fraction 0.9 means that S = 0.158 + 0.9(1.28-0.158) = 1.168kJ/kgK

and H = 39.7+ 0.9(323.7-39.7)  =  295.3kJ/kg.         

 

 

** We have to use a diagram for carbon dioxide – e.g. in Perry.

 

*** Isenthalpic process d-a

-20 and 19.7atm H is 109.1.

 

This is equivalent to a dryness fraction of

(109.7-39.7)/(323.7-39.7) = 0.27

 

This gives an entropy of 0.158+0.27(1.280-0.158)  =  0.46kJ/kgK

 

Q in the refrigerator = h_B - h_A = 295.3-109.1  = 186.2kJ/kg

 

0.17 tons of refrigeration = 0.17*3923 = 667W  =  0.667kW

 

Therefore mass flowrate required = 0.667/186.2  =  0.0036kg/s  =  12.9kg/hr     [2]

 

Q in the condenser  =  h_C – h_D  =  275-109.1 = 265.9kJ/kg

 

COP = Q_refrigerator/(Q_condenser-Q_refrigerator)  =  186.2/(265.9-186.2)  =  2.34                 [2]

                                                                                                                                   

 

 

 

My Solution

P₁ = 1.97 MPa            h₁ = 154.45+(0.9×282.44) = 408.65 KJ/Kg

 

T₁ = -20 °C                  S₁ = 0.8328 + 0.9(1.1157) = 1.837 KJ/Kg

 

Ref: https://www.ohio.edu...rty_tables/CO2/

 

 

P₂ = 45 MPa

T₂ = 10 °C

S₂ = s₁

h₂ = 422.8 KJ/Kg

 

P₃ = 45 MPa               h₃ = h_f =225.73 KJ/Kg

h₄ = h₃ = 225.73 KJ/Kg

 

0.17×3923 = 666.91 w

 

Q_L = m(h₁-h₄)

m = 0.0036 Kg/s

 

w_in = 0.0036 (422.8 – 408.65) = 0.051 kW

Q_H = 0.0036 (422.8 – 225.73) = 0.709 KW

 

COP = 0.6691/0.051 = 13.1

Attached Files

•  A refrigerator uses carbon dioxide as a refrigerant.docx   14.84KB   8 downloads

[Art Montemayor]

greens:

 

The best, fastest, and most accurate way to check your calculations is to first have some accurate and detailed explanation in your problem write-up.  What you present is very badly (or sloppily) written and difficult to decipher.  Why don't you furnish a simple flow diagram of what you (or your prof) call a "refrigerator" and a refrigeration cycle.

 

I have to presume you are dealing with a mechanical compression refrigeration cycle and the refrigerant fluid is CO₂.  If I am correct, then you have a closed cycle composed basically of 4 items:

1. a mechanical compressor;
2. a refrigerant condenser;
3. an expansion valve; and,
4. a refrigerant vaporizer.

Is this the cycle that you are trying to describe?  If not, then describe your cycle.

 

In order to understand your problem statement, supply a flow diagram of the cycle, showing the items involved and the given conditions at the correct locations within the flow diagram.  Use a spread sheet (Excel) to develop the flow diagram and the calculations.  That is the engineering way to generate legible calculations.  Use the available, accurate thermodynamic database at http://webbook.nist....hemistry/fluid/by copying and pasting them in a spreadsheet within your workbook and do your calculations by using the available database.  That is SO EASY. 

 

If you haven't been taught this conventional and simple way of doing process engineering calculations, then refer to all the various spread sheets I have contributed to our Forums regarding refrigeration calculations - especially CO₂ and NH₃.  I have been doing this for many years and the spreadsheets can be found if you use our SEARCH machine.

 

I don't know what you mean by such terms as: "refrigerator", "refrigeration temperature" (of what?), "condenser temperature" (of what?), "dryness factor", etc.

 

The important streams you need to identify, and their conditions, in any mechanical refrigeration cycle are:

1. The saturated vapor exiting the evaporator or vaporizer; (is this what you call the "refrigerator"?)
2. The vapor entering the compressor;
3. The vapor exiting the compressor;
4. The saturated liquid exiting the condenser and entering the expansion valve;
5. The 2-phase, saturated stream exiting the expansion valve and entering the evaporator.

Show these streams in a simplified flow diagram.

[greens]

Art Montemayor,

 

Thank you for the reply. I have looked at your excel files, and I have included the information on an excel sheet together with a simple PFD. I hope it is clear. All comments are welcome.

 

I think your assumptions are correct. The solution I have listed was provided by the course lecturer however I don't think it's correct. 

 

The dryness fraction refers to the 2 phase nature of the CO2 as it leaves the evaporator I think.

 

I hope I have provided sufficient information, as this is all of the information I have received. 

 

Also:

 

-- If the system is modified to allow isobaric subcooling to 5°C in the condenser, what will be the increase in refrigeration effect, Δq_L?

 

Any and all help would be greatly appreciated.

Attached Files

•  E&U T4.xlsx   24.21KB   7 downloads

Edited by greens, 09 December 2016 - 10:26 AM.

[breizh]

greens,

To support your work and confirm your calculation you can also used the Mollier diagram attached in the resource . It's always good to visualize the cycle .

 

 

Good luck

 

Breizh

 

[Art Montemayor]

Greens:

 

I haven't given up on reviewing and commenting on your submitted work.  Unfortunately, I changed my Internet service to Fiber Optic cable and the system was interrupted 4 days ago and I haven't been able to finish my planned submittal.  The new system is now operational.

 

Please bear with me and I shall submit my detailed comments on your workbook, complete with my analysis of how you should proceed to study, understand, and resolve a compression refrigeration problem like the one you are working on.

 

In the mean time, take the time and make the effort to diligently follow our Colleague Breizh's advice using the excellent material he has submitted.  You will never regret following his recommendation.  His idea of depicting the entire refrigeration cycle on the Mollier Diagram is a positive and constructive way to fully understand exactly what is happening in the depicted cycle - and why it behaves the way that it does.  My work will deal with this cycle in each step and also use the Mollier Diagram to illustrate the Unit Operations taking place.  I am taking this time and making the effort because I sense that you (and probably a lot of the students reading this) are lacking a full understanding of what thermodynamics processes are taking place in this system that has tremendous applications and plays an important role in many industrial processes.

 

In approximately a day or so I should be able to post my product.

[greens]

breizh,

Thank you for the information you have sent. I have been reviewing the material and ideas. It is helping me understand the process better.

 

Art,

Thank you for taking the time to review this work. I do apologise about its rudimentary nature and I do appreciate any help that would help me understand the thermodynamic cycle better. Although my knowledge of refrigeration is very limited it is an interest outside of the questions I need to do.

 

Thank you both again.

Edited by greens, 13 December 2016 - 05:37 AM.

[Art Montemayor]

greens:

 

The attached workbook is a copy of yours but with several more spreadsheets added that contain my input and comments to your submitted problem.

 

I don't try to calculate the specific answers to your problem - which I identify as routine, easy calculations when you apply the basic steps and logic I outline in my comments and supporting calculations.  However, I do have an issue with the manner in which you have presented the basic data.  The basic data furnished seems to be a direct copy of what your instructor may have issued to you.  If so, then you should clarify just exactly what is the background and FULL explanation for the basic data.  For example:

• Is entrained liquid refrigerant being specified as included in the vapor stream entering the refrigerant compressor?  This cannot be allowed without first vaporizing the entrained liquid.  You cannot vaporize the liquid inside the compressor without risk of rupturing the machine.
• Is a centrifugal compressor being applied?  If so, then the polytropic coefficient must be either supplied or calculated in order to apply it to the horsepower calculations and the discharge temperature.

 Greens CO2 Refrigeration Cycle.xlsx   626.87KB   18 downloads

 Thermodynamics of Refrigeration.pdf   1.39MB   18 downloads

[breizh]

Hi,

 

As usual Art submitted great material.  You also can consider Youtube to support your work.  Search for refrigeration cycle .

 

Good luck .

Breizh