Comparison of COP of the Standard Refrigerator
(Indoor condensing temperature) and the Window Refrigerator (Outdoor
condensing temperature)
Assumptions:
1. The calculations are based on R-134a refrigerant
thermodynamics properties as R134a is the refrigerant used in the refrigerators
nowadays.
2. The simple vapor compression cycle is used: no
pressure drops in condensing and cooling coils isentropic compression, and no
superheat and sub-cooling.
3. The largest deviation from the simple compression
cycle is the non-isentropic process.
Since the deviation is compressor dependent, it is not included in the
current calculation.
4. The actual heat transfer effectiveness is not
considered. Thus, the temperature
differences between the indoor/outdoor temperature and condensing temperature
and between the cold storage temperature and the evaporating temperature are
ignored.
Case 1: Indoor Refrigerator
Refer to the attached P-h
diagram for the state points (1-4) designation in the vapor compression cycle.
T1 = T0
= 70 F
T0= T3
= TR = 40 F
(T0 = condensing
temperature and TR = evaporating temperature)
Based on the vapor
compression cycle, the COP can be computed as:
COP = 2Q3 / 3W4 = m (h3
- h2) / m (h4 - h3)
where 2Q3 = heat
removal rate
3W4 = power input to the
compressor
m = mass flow rate of the refrigerant
Note that the actual
property values are obtained by the ALLPROPS computer program which uses a different reference enthalpy value than the
one used in the P-h diagram. The P-h
diagram is based on hf = 0 at – 40oF saturated
liquid. The computer generated
properties are given in the Appendix.
Using the property values from either the table or P-h diagram is fine
in the COP calculation as they all produce the same value, except the computer
table is easier to look up the property.
From the property table
given in the Appendix,
h1 = h2
= 98.4672, P1 = P4
= 85.8039
h3 =
172.472, S3 = 0.411944 = S4
Use (P1 & S4),
We can locate state point 4 properties: h4 = 177.312, T4
= 73.76oF
Therefore,
COP = (172.472 - 98.4672) / (177.312 - 172.472) = 15.29
In comparison, the COP based
on the reverse Carnot cycle is
COP = (TR∆S) / (T0 - TR)∆S
= (40+460)R / 30R = 16.67
Case 2: Window Refrigerator
T1 = T0 = 63oF
T2= T3 = TR = 40oF
h1 = h2
= 96.1209, P1 = P4 = 76.0259
h3 = 172.472, S3
= 0.4119444 = S4
Use (P1 & S4),
we can locate state point 4 properties: h4 = 176.228, T4
= 65.89oF
Therefore,
COP = (h3-h2)
/ (h4-h3) = (172.472 - 96.1209) / (176.228 - 172.472) =
20.33
The COP based on the reverse
Carnot cycle is
COPCarnot = TR / (T0 - TR) = (40+460)/23 = 21.74
Energy savings based on
the vapor compression cycle COP's
3W4 = 2Q3 / COP or
3W4 = 3Q4 / COP
2Q3 is the thermal energy removed by the
evaporating coil and is also equal to the stored heat capacity reduction of the
air inside the refrigerator,
2Q3 = Mair Cp (Text - Tint)
where
Text = exterior
temperature of the refrigerator
Tint = interior
temperature of the refrigerator at the end of testing
Use the temperature data
obtained from http://g2cu.com/wref/3h-cmt.html:
For case 1, Text = 70oF and Tint
= 40oF
For case 2, Text = (5A.70 + 1A.63) / 6A = 68.83oF (where A is the side area of the refrigerator) and Tint = 40oF
Note that in the case 2,
assuming only one side (the back side) of the refrigerator is exposed to the
outdoor temperature of 63oF and the other 5 sides are still exposed
to indoor temperature of 70oF.
Therefore, an average exterior temperature is used.
Ww = compressor
work input for window refrigerator
Wi = compressor
work input for indoor refrigerator
Ww / Wi
= [Mair Cp (Text - Tint) / COPw]
/ [Mair Cp (Text - Tint) / COPi]
=
[(68.83 - 40) / 20.33 ] / [(70 - 40) / 15.29]
=
0.7227
Energy Savings = 1 - Ww
/ Wi = 1 - 0.7227 = 27.73%
In comparison, the energy
saving based on the reverse Carnot cycle COPs and the incorrect temperature
used in the web page,
Ww / Wi = [(63 - 40) / 21.74 ] / [(70 - 40) / 16.67]
= 0.5879
Energy Savings = 1 - Ww/Wi
= 1- 0.5879 = 41.21 %
There is an over estimate of
13.5% in the energy saving.
Suggestions
1. Follow the
given procedure and recalculate the energy saving rates.
2. Integrate
the power consumption data over time to obtain the Ww and Wi
and then compare the measured energy savings vs. the calculated energy savings.
3. To further
improve the COP calculation, the condensing and evaporating pressures can be
measured and the correction to the compressor isentropic process has to be
made.
4. Due to the
superheat and non-isentropic compression, the actual (h4 –h5)
will be larger than that shown in the calculation. This leads to lower actual COP value.
Appendix
Thermodynamic
Properties of R-134a
=============================================================================
P T
D H S Cv W
psia F lbm/ft3 Btu/lbm Btu/lbm-R
Btu/lbm-R ft/s
=============================================================================
Liquid 7.42716
-40.000 88.5043 63.6798
.190004 .199163 2647.79
Vapor 7.42716
-40.000 .172907 160.775
.421365 .156375 471.152
(Note many property table use H of saturated liquid at -40 F as
reference point and set it at 0 Btu/lbm)
Liquid 40.7841
30.0000 81.0591 85.3430
.237546 .209706 2056.16
Vapor 40.7841
30.0000 .866307 171.086
.412651 .181137 482.138
Liquid 41.6192
31.0000 80.9449 85.6634
.238196 .209868 2047.79
Vapor 41.6192
31.0000 .883387 171.226
.412576 .181517 482.103
Liquid 42.4674
32.0000 80.8305 85.9842
.238845 .210031 2039.42
Vapor 42.4674
32.0000 .900734 171.366
.412502 .181899 482.063
Liquid 43.3288
33.0000 80.7158 86.3053
.239493 .210194 2031.05
Vapor 43.3288
33.0000 .918352 171.505
.412429 .182281 482.016
Liquid 44.2037
34.0000 80.6008 86.6268
.240141 .210357 2022.68
Vapor 44.2037
34.0000 .936244 171.645
.412357 .182663 481.964
Liquid 45.0920
35.0000 80.4855 86.9487
.240788 .210521 2014.31
Vapor 45.0920
35.0000 .954413 171.783
.412286 .183047 481.905
Liquid 45.9940
36.0000 80.3699 87.2709
.241435 .210685 2005.94
Vapor 45.9940
36.0000 .972863 171.922
.412216 .183431 481.839
Liquid 46.9097
37.0000 80.2540 87.5935
.242081 .210850 1997.57
Vapor 46.9097
37.0000 .991598 172.060
.412146 .183816 481.768
Liquid 47.8394
38.0000 80.1378 87.9164
.242726 .211015 1989.20
Vapor 47.8394
38.0000 1.01062 172.198
.412078 .184201 481.690
Liquid 48.7832
39.0000 80.0213 88.2398
.243371 .211180 1980.83
Vapor 48.7832
39.0000 1.02993 172.335
.412010 .184588 481.605
Liquid 49.7412
40.0000 79.9046 88.5635
.244015 .211346 1972.46
Vapor 49.7412
40.0000 1.04954 172.472
.411944 .184975 481.515
Liquid 50.7135
41.0000 79.7875 88.8876
.244658 .211512 1964.09
Vapor 50.7135
41.0000 1.06945 172.609
.411878 .185363 481.417
Liquid 51.7003
42.0000 79.6701 89.2121
.245301 .211678 1955.72
Vapor 51.7003
42.0000 1.08966 172.746
.411812 .185751 481.313
Liquid 52.7017
43.0000 79.5523 89.5370
.245944 .211845 1947.34
Vapor 52.7017
43.0000 1.11017 172.882
.411748 .186141 481.203
Liquid 53.7179
44.0000 79.4343 89.8623
.246585 .212012 1938.97
Vapor 53.7179
44.0000 1.13099 173.018
.411685 .186531 481.086
Liquid 54.7490
45.0000 79.3159 90.1879
.247227 .212180 1930.60
Vapor 54.7490
45.0000 1.15213 173.153
.411622 .186922 480.963
Liquid 55.7952
46.0000 79.1972 90.5140
.247867 .212348 1922.22
Vapor 55.7952
46.0000 1.17358 173.288
.411560 .187313 480.833
Liquid 56.8566
47.0000 79.0782 90.8404
.248507 .212516 1913.85
Vapor 56.8566
47.0000 1.19536 173.423
.411498 .187705 480.696
Liquid 57.9333
48.0000 78.9589 91.1673
.249147 .212685 1905.47
Vapor 57.9333
48.0000 1.21746 173.557
.411438 .188099 480.552
Liquid 59.0255
49.0000 78.8392 91.4946
.249786 .212854 1897.09
Vapor 59.0255
49.0000 1.23988 173.692
.411378 .188492 480.402
Liquid 60.1334
50.0000 78.7191 91.8223
.250424 .213024 1888.71
Vapor 60.1334
50.0000 1.26265 173.825
.411318 .188887 480.245
Liquid 61.2570
51.0000 78.5988 92.1504
.251062 .213194 1880.33
Vapor 61.2570
51.0000 1.28574 173.958
.411260 .189282 480.081
Liquid 62.3966
52.0000 78.4780 92.4789
.251700 .213365 1871.95
Vapor 62.3966
52.0000 1.30918 174.091
.411202 .189678 479.910
Liquid 63.5522
53.0000 78.3569 92.8078
.252336 .213536 1863.56
Vapor 63.5522
53.0000 1.33297 174.224
.411144 .190075 479.732
Liquid 64.7241
54.0000 78.2355 93.1371
.252973 .213707 1855.18
Vapor 64.7241
54.0000 1.35710 174.356
.411088 .190473 479.548
Liquid 65.9124
55.0000 78.1137 93.4669
.253609 .213879 1846.79
Vapor 65.9124
55.0000 1.38159 174.488
.411031 .190871 479.356
Liquid 67.1172
56.0000 77.9915 93.7971
.254244 .214051 1838.40
Vapor 67.1172
56.0000 1.40644 174.619
.410976 .191270 479.157
Liquid 68.3386
57.0000 77.8690 94.1278
.254879 .214224 1830.01
Vapor 68.3386
57.0000 1.43164 174.750
.410921 .191670 478.952
Liquid 69.5769
58.0000 77.7460 94.4588
.255514 .214397 1821.62
Vapor 69.5769
58.0000 1.45722 174.880
.410867 .192071 478.739
Liquid 70.8321
59.0000 77.6227 94.7904
.256148 .214570 1813.22
Vapor 70.8321
59.0000 1.48317 175.010
.410813 .192472 478.519
Liquid 72.1045
60.0000 77.4990 95.1223
.256781 .214744 1804.83
Vapor 72.1045
60.0000 1.50949 175.140
.410759 .192875 478.291
Liquid 73.3942
61.0000 77.3750 95.4547
.257414 .214919 1796.43
Vapor 73.3942
61.0000 1.53620 175.269
.410706 .193278 478.057
Liquid 74.7013
62.0000 77.2505 95.7876
.258047 .215094 1788.03
Vapor 74.7013
62.0000 1.56329 175.398
.410654 .193681 477.815
Liquid 76.0259
63.0000 77.1256 96.1209
.258679 .215269 1779.62
Vapor 76.0259
63.0000 1.59077 175.526
.410602 .194086 477.566
Liquid 77.3683
64.0000 77.0003 96.4547
.259311 .215445 1771.22
Vapor 77.3683
64.0000 1.61865 175.654
.410551 .194492 477.310
Liquid 78.7286
65.0000 76.8746 96.7889
.259942 .215621 1762.81
Vapor 78.7286
65.0000 1.64693 175.782
.410500 .194898 477.046
Liquid 80.1070
66.0000 76.7485 97.1236
.260573 .215798 1754.40
Vapor 80.1070
66.0000 1.67562 175.909
.410449 .195305 476.774
Liquid 81.5035
67.0000 76.6220 97.4588
.261204 .215976 1745.98
Vapor 81.5035
67.0000 1.70471 176.035
.410399 .195713 476.495
Liquid 82.9184
68.0000 76.4951 97.7945
.261834 .216153 1737.57
Vapor 82.9184
68.0000 1.73423 176.161
.410349 .196121 476.209
Liquid 84.3518
69.0000 76.3677 98.1306
.262464 .216332 1729.15
Vapor 84.3518
69.0000 1.76416 176.287
.410300 .196531 475.915
Liquid 85.8039
70.0000 76.2399 98.4672
.263094 .216511 1720.72
Vapor 85.8039
70.0000 1.79452 176.412
.410251 .196941 475.613
Liquid 87.2748
71.0000 76.1116 98.8043
.263723 .216690 1712.30
Vapor 87.2748
71.0000 1.82532 176.537
.410202 .197352 475.304
Liquid
88.7647 72.0000 75.9829
99.1419 .264351 .216870
1703.87
Vapor
88.7647 72.0000 1.85655
176.661 .410154 .197764
474.987
Case 1: state point 4
properties based on given (P, s)
=============================================================================
P T D H S Cv W
psia F lbm/ft3 Btu/lbm Btu/lbm-R
Btu/lbm-R ft/s
=============================================================================
85.8039 73.7569 1.77250 177.312 .411944
.196423 479.058
Case 2: state point 4
properties based on given (P, s)
=============================================================================
P T D H S Cv W
psia F lbm/ft3 Btu/lbm Btu/lbm-R
Btu/lbm-R ft/s
=============================================================================
76.0259 65.9911 1.57564 176.228 .411940
.193725 480.199