The refrigerating effect

In the basic vapour compression cycle of refrigeration shown in Figure 9.2 a mixture of relatively cold, saturated liquid and saturated vapour enters the evaporator. The liquid part of the mixture is boiled to a saturated vapour and leaves the evaporator at state 1 (in Figure 9.2). The refrigerating effect (q{) is the enthalpy change across the evaporator. Using the notation of Figure 9.2, this is expressed by

Qx = (hx — h4) (9.4)

EXAMPLE 9.2

(a) Calculate the refrigerating effect for the plant used in example 9.1.

(,b) If the duty is 352 kW of refrigeration, determine the mass flow rate of refrigerant,

Table 9.4 Superheated properties of R717, ammonia (NH3)

T-t,	II 1 O O			U O <N 1 II			Ts = -1°C
K	P = 383.4 kPa		P = 398.3 kPa		P = 413.6 kPa
	V	H	S	V	H	S	V	H	S
0	0.3224	1439.8	5.3753	0.3109	1440.9	5.3620	0.3000	1442.0	5.3487
5	0.3302	1453.0	5.4237	0.3185	1454.2	5.4105	0.3073	1455.4	5.3973
10	0.3379	1465.9	5.4700	0.3259	1467.1	5.4567	0.3145	1468.3	5.4436
T-t,	U = o°c			T, = i°c			U = 2°C
K	P = 429.4 kPa		P = 445.7 kPa		P = 462.5 kPa
	V	H	S	V	H	S	V	H	S
0	0.2895	1443.1	5.3356	0.2795	1444.2	5.3225	0.2698	1445.2	5.3096
5	0.2966	1456.5	5.3842	0.2863	1457.6	5.3712	0.2765	1458.8	5.3584
10	0.3035	1469.5	5.4306	0.2930	1470.7	5.4177	0.2830	1471.9	5.4049
T-u	L = 3°C			Ts = 4°C			K = 5°c
K	P = 479.7 kPa		P = 497.5 kPa		P = 515.7 kPa
	V	H	S	V	H	S	V	H	S
0	0.2606	1446.3	5.2967	0.2517	1447.3	5.2839	0.2433	1448.3	5.2712
5	0.2670	1459.9	5.3456	0.2580	1461.0	5.3329	0.2493	1462.0	5.3203
10	0.2733	1473.1	5.3922	0.2641	1474.2	5.3796	0.2552	1475.4	5.3671
T — /s	Ts = 6°C			Ts = 7°C			/, = 8°C
K	P = 534.5 kPa		P = 553.8 kPa		P = 573.6 kPa
	V	H	S	V	H	S	V	H	S
0	0.2351	1449.2	5.2587	0.2273	1450.2	5.2461	0.2198	1451.1	5.2337
5	0.2410	1463.1	5.3078	0.2330	1464.1	5.2954	0.2253	1465.1	5.2831
10	0.2467	1475.5	5.3546	0.2385	1477.6	5.3423	0.2307	1478.7	5.3301
T-h	H = 9°C			U O O II			F, = ll°C
K	P = 594.0 kPa		P = 614.9 kPa		P = 636.4 kPa
	V	H	S	V	H	S	V	H	S
0	0.2126	1452.1	5.2214	0.2056	1453.0	5.2091	0.1990	1453.9	5.1969
5	0.2179	1466.2	5.2708	0.2108	1467.1	5.2587	0.2040	1468.1	5.2466
10	0.2231	1479.8	5.3179	0.2159	1480.8	5.3509	0.2089	1481.9	5.2939
T-h	T, = 26°C			H = 27 °C			U 0 00 CN II
K	P = 1034.0 kPa		P = 1066.0 kPa		P = 1098.7 kPa
	V	H	S	V	H	S	V	H	S
0	0.1245	1465.2	5.0232	0.1208	1465.9	5.0121	0.1173	1466.4	5.0011
5	0.1279	1480.8	5.0749	0.1241	1481.5	5.0640	0.1205	1482.2	5.0531
10	0.1311	1495.8	5.1238	0.1273	1496.6	5.1130	0.1236	1497.4	5.1023
15	0.1343	1510.3	5.1703	0.1304	1511.2	5.1597	0.1266	1512.1	5.1491
20	0.1374	1524.4	5.2149	0.1334	1525.4	5.2044	0.1296	1526.3	5.1939
25	0.1404	1538.2	5.2578	0.1364	1539.2	5.2473	0.1325	1540.3	5.2369
30	0.1434	1551.7	5.2992	0.1393	1552.8	5.2887	0.1353	1553.9	5.2784
35	0.1463	1565.0	5.3392	0.1421	1566.2	5.3288	0.1380	1567.3	5.3185

T-ts	Fs = 29 °C			II O O N			Ts = 31°C
K	P= 1132.2 kPa		P= 1166.5 kPa		P= 1201.6 kPa
	V	H	S	V	H	S	V	H	S
0	0.1139	1467.0	4.9902	0.1106	1467.6	4.9793	0.1075	1468.1	4.9685
5	0.1170	1482.9	5.0423	0.1137	1483.6	5.0316	0.1104	1484.2	5.0210
10	0.1201	1498.2	5.0916	0.1166	1498.9	5.0811	0.1133	1499.6	5.0706
15	0.1230	1512.9	5.1386	0.1195	1513.8	5.1281	0.1161	1514.6	5.1177
20	0.1259	1527.3	5.1834	0.1223	1528.2	5.1731	0.1189	1529.1	5.1628
25	0.1287	1541.2	5.2265	0.1250	1542.2	5.2163	0.1215	1543.2	5.2060
30	0.1314	1554.9	5.2681	0.1277	1556.0	5.2579	0.1241	1557.0	5.2477
35	0.1341	1568.4	5.3083	0.1303	1569.5	5.2982	0.1267	1570.6	5.2881
T~h	Ts = 32°C			Fs = 33°C			II O N
K	P = 1237.4 kPa		P = 1274.1 kPa		P= 1311.6 kPa
	V	H	S	V	H	S	V	H	S
0	0.1044	1468.6	4.9577	0.1014	1469.1	4.9469	0.0986	1469.6	4.9362
5	0.1073	1484.8	5.0103	0.1043	1485.4	4.9998	0.1014	1486.0	4.9893
10	0.1101	1500.4	5.0601	0.1070	1501.1	5.0497	0.1041	1501.7	5.0393
15	0.1129	1515.4	5.1074	0.1097	1516.2	5.0971	0.1067	1516.9	5.0869
20	0.1155	1529.9	5.1525	0.1123	1530.8	5.1424	0.1092	1531.7	5.1323
25	0.1181	1544.1	5.1959	0.1148	1545.1	5.1858	0.1117	1546.0	5.1758
30	0.1207	1558.0	5.2377	0.1173	1559.0	5.2277	0.1141	1560.0	5.2177
35	0.1232	1571.7	5.2781	0.1198	1572.7	5.2681	0.1165	1573.8	5.2582
T-ts	Fs = 35 °C			Ts = 36°C			Fs = 37°C
K	P = 1349.9 kPa		P = 1389.0 kPa		P = 1429.0 kPa
	V	H	S	V	H	S	V	H	S
0	0.0958	1470.0	4.9256	0.0931	1470.4	4.9149	0.0905	1470.8	4.9044
5	0.0985	1486.5	4.9788	0.0958	1487.1	0.9684	0.0931	1487.6	4.9580
10	0.1012	1502.4	5.0290	0.0984	1503.0	5.0188	0.0957	1503.7	5.0086
15	0.1037	1517.7	5.0767	0.1009	1518.4	5.0666	0.0981	1519.1	5.0565
20	0.1062	1532.5	5.1222	0.1033	1533.3	5.1122	0.1005	1534.1	5.0923
25	0.1086	1546.9	5.1658	0.1056	1547.8	5.1559	0.1028	1548.7	5.1461
30	0.1110	1561.0	5.2078	0.1079	1562.0	5.1980	0.1050	1562.9	5.1883
35	0.1133	1574.8	5.2484	0.1102	1575.9	5.2387	0.1072	1576.9	5.2290
40	0.1155	1588.4	5.2878	0.1124	1589.5	5.2781	0.1094	1590.6	5.2685
45	0.1178	1601.8	5.3260	0.1146	1603.0	5.3163	0.1115	1604.1	5.3068
50	0.1200	1615.1	5.3632	0.1167	1616.3	5.3536	0.1136	1617.4	5.3441
55	0.1222	1628.2	5.3995	0.1189	1629.4	5.3900	0.1157	1630.6	5.3805
60	0.1243	1641.1	5.4350	0.1210	1642.4	5.4255	0.1177	1643.7	5.4160
T-h	Fs = 38°C			Fs = 39°C			Rs = 40°C
K	P = 1469.9 kPa		P= 1511.7 kPa		P = 1554.3 kPa
	V	H	S	V	H	S	V	H	S
0	0.0880	1471.2	4.8938	0.0856	1471.5	4.8833	0.0833	1471.9	4.8728
5	0.0906	1488.1	4.9477	0.0881	1488.6	4.9374	0.0857	1489.0	4.9371
10	0.0931	1504.3	4.9984	0.0905	1504.8	4.9883	0.0881	1505.4	4.9783
15	0.0954	1519.8	5.0465	0.0929	1520.5	5.0366	0.0904	1521.2	5.0267
20	0.0977	1534.9	5.0924	0.0951	1535.7	5.0826	0.0926	1536.4	5.0728

Table 9.4 (Contd)

T-k	Ts = 38°C			Ts = 39°C			WT* II O O N
K	P = 1469.9 kPa		P= 1511.7 kPa		P = 1554.3 kPa
	V	H	S	V	H	S	V	H	S
25	0.1000	1549.6	5.1363	0.0973	1550.4	5.1266	0.0947	1551.2	5.1169
30	0.1022	1563.9	5.1786	0.0995	1564.8	5.1690	0.0968	1565.7	5.1594
35	0.1043	1577.9	5.2194	0.1016	1578.9	5.2098	0.0989	1579.8	5.2003
40	0.1065	1591.6	5.2589	0.1036	1592.7	5.2494	0.1009	1593.7	5.2400
45	0.1085	1605.2	5.2973	0.1057	1606.3	5.2878	0.1029	1607.4	5.2784
50	0.1106	1618.6	5.3346	0.1076	1619.8	5.3252	0.1048	1620.9	5.3159
60	0.1126	1631.8	5.3710	0.1096	1633.1	5.3617	0.1067	1634.3	5.3524
T-ts	/s = 41 °C			U O CM II			Rs = 43°C
K	P = 1597.9 kPa		P = 1642.4 kPa		P = 1687.8 kPa
	V	H	S	V	H	S	V	H	S
0	0.0810	1472.2	4.8623	0.0788	1472.4	4.8519	0.0767	1472.7	4.8414
5	0.0834	1489.4	4.9169	0.0812	1489.8	0.9067	0.0790	1490.2	4.8965
10	0.0857	1505.9	4.9682	0.0834	1506.5	4.9583	0.0812	1507.0	4.9483
15	0.0879	1521.8	5.0168	0.0856	1522.4	5.0070	0.0833	1523.0	4.9972
20	0.0901	1537.1	5.0631	0.0877	1537.9	5.0534	0.0854	1538.6	5.0438
25	0.0922	1552.0	5.1073	0.0898	1552.8	5.0978	0.0874	1553.6	5.0883
30	0.0943	1566.6	5.1499	0.0918	1567.4	5.1404	0.0894	1568.3	5.1310
35	0.0963	1580.8	5.1909	0.0937	1581.7	5.1815	0.0913	1582.7	5.1722
40	0.0982	1594.7	5.2306	0.0957	1595.8	5.2213	0.0932	1596.8	5.2120
45	0.1002	1608.5	5.2691	0.0976	1609.6	5.2599	0.0950	1610.6	5.2507
50	0.1021	1622.0	5.3066	0.0994	1623.2	5.2974	0.0968	1624.3	5.2882
60	0.1058	1648.7	5.3788	0.1031	1649.9	5.3697	0.1004	1651.1	5.3606

Reproduced from Thermodynamic Properties of Ammonia by W. B. Gosney and O. Fabris, with the kind permission of the authors.

Answer

(a) From Table 9.1, hx, leaving the evaporator, is 398.68 kJ kg-1. Since the value of h4, entering the evaporator, is the same as that of hj, leaving the condenser as a saturated liquid at a temperature of 35°C, the value of h4 is found from Table 9.1 to be 248.94 kJ kg-1. Hence by equation (9.4) the refrigerating effect is

Qt = (398.68 — 248.94) = 149.74 kJ kg’1

(b) The mass flow rate of refrigerant, m, is given by

M = QMt (9-5)

Where QT is the refrigeration duty in kW.

Hence the mass flow rate of refrigerant handled is

M = 352/149.74 = 2.351kg s“1

(c) Assuming that there is no pressure drop in the suction line and that there are no heat exchanges between the suction line and its surroundings, the state entering the compressor is the same as that leaving the evaporator, namely, 0°C saturated. From Table 9.1 the

Specific volume at this state is 0.06935 m3 kg Hence the volumetric flow rate at the suction state is

Vj = 2.351 X 0.06935 = 0.16304 m3 s’1

Posted in Engineering Fifth Edition

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