Thermodynamics and refrigeration
The subject of thermodynamics was dealt with in part, in chapter 2, where it referred to the physics of air-water vapour mixtures. It is necessary to reconsider the topic here, as it refers to the behaviour of refrigerants in vapour compression cycles of refrigeration, in order to deal with such cycles quantitatively. As a preamble to this, some principles and definitions must be reviewed.
(a) Thermodynamics. This is simply the study of changes involving energy but it is also defined by ASHRAE (1997) as the study of energy, its transformations, and its relation to states of matter.
(b) Thermodynamic system. This is defined by ASHRAE (1997) as ‘… a region of space or quantity of matter, bounded by a closed surface’. There are two sorts of systems to be considered: closed systems, where there is no interchange of matter with the surroundings, and open systems where there is such an interchange. With a closed system the mass within the boundary of the system is constant as, for example, in a hermetic refrigeration plant. With an open system there is a mass flow through the system boundaries, for example with a pumping process that introduces a fluid to the system from the surroundings.
(c) The first law of thermodynamics. Otherwise interpreted as the conservation of energy, this law states that energy can neither be created nor destroyed.
For an open system, under steady-state conditions and with unit mass flow rate of a pure substance, the first law is expressed by the steady flow energy equation:
TOC o "1-5" h z ^ + (g — W) = 0 (9.1)
Where h = enthalpy J kg-1
V = velocity m s’1
G = local acceleration due to gravity m s-2
Z = elevation above a reference level m
Q — rate of heat transfer to the system W
W — rate of work done by the system W
Note that equation (2.19) offers an alternative expression of enthalpy.
(d) The second law of thermodynamics. In simple terms, this states that heat only flows from a higher temperature to a lower temperature. More formally, Spalding and Cole (1961) state: it is impossible for a system working in a cycle to have, as its sole effect, the transfer of heat from a system at a low temperature to a system at a high temperature.
(e) Heat. Energy has been described by ASHRAE (1997) as a capacity for producing an effect and it can be in a stored form or in a transient form. Stored energy is exemplified by such concepts as potential energy and kinetic energy, whereas heat is a form of transient energy. Heat can be defined as an interaction between two systems of differing temperatures and the flow is always from the higher to the lower temperature.
(/) Work. This is an aspect of energy. Work is the application of a force through a distance, transferring energy across the boundary between two systems.
(g) Entropy. This is a concept that is of value when analysing the behaviour of a thermodynamic system. It is expressed in terms of change in entropy, defined as the quantity of heat crossing the boundary of a reversible system, divided by the absolute temperature of the system, and is given by
|
|
(9.2)
Where s = specific entropy in kJ kg-1 K-1 q = heat energy in kJ kg-1 T = absolute temperature in K
Entropy is a property of the system and it depends on the state of the substance. For a pure substance, its value can be established since it depends on two other independent properties, heat and absolute temperature. Since it is defined as a difference, in equation (9.2), an arbitrary zero must be adopted if it is to be tabulated. This is usually at a temperature of zero degrees absolute.
Entropy can also be considered in terms of the disorder of the molecules in a system: if they are disordered the entropy is greater than if they are in some sort of order. Alternatively, it can be regarded as the availability of a given amount of heat: in equation (9.2) it is seen that if the entropy change is small, the absolute temperature must be large, for the given change of heat. Hence, it is possible to construct an absolute temperature-entropy diagram (see Figures 9.4 and 9.5), in which areas represent heat.
A process which occurs at constant entropy is termed isentropic.
(h) Reversibility. A reversible process is one which, after completion, has returned both the system and its surroundings to their original states. This is not true for an irreversible process, an example of which is any process involving friction.
If there were no heat exchange with the surroundings and no internal frictional losses, a reciprocating machine could either act as a compressor or as an expansion engine. When acting as a compressor the supply of power to the machine would be used to compress the gas handled. When acting as an expansion machine the pressure difference across the inlet and outlet ports would allow the gas handled to expand, driving the machine. The machine would liberate to the surroundings the same power that was taken from them when the machine acted as a compressor. The processes of compression and expansion would then be reversible.
It is possible to prove that the efficiency of a reversible engine is always greater than that of an irreversible engine, operating between the same two heat reservoirs. Hence it is desirable that refrigeration compressors should execute reversible compression, as far as possible.
(0 Adiabatic processes. If a system is isolated from its surroundings as regards heat transfer, the processes performed are termed adiabatic. Thus, an adiabatic process is one in which no heat is supplied or rejected.
All reversible, adiabatic processes are isentropic. The converse may not be true: all isentropic processes are not necessarily reversible and adiabatic.
The line joining the points 1 and 2 in Figure 9.2 depicts a reversible, adiabatic, isentropic process of compression from an evaporating pressure, pe, to a condensing pressure, pc.
(j) Saturated liquid. This is a substance existing at its saturated temperature and pressure. If the pressure falls, the substance can no longer exist as a saturated liquid and some of it flashes to vapour, with a corresponding fall in the temperature of the parent liquid, until it is again a saturated liquid, existing at a lower saturated temperature and pressure.
(k) Throttling expansion. This is an irreversible, adiabatic process of expansion that occurs at constant enthalpy, no heat being supplied or rejected and no work being done. It is the process occurring when liquid refrigerant flows through an expansion valve: the loss of pressure resulting from the frictional resistance to fluid flow causes some of the saturated liquid to flash to vapour, with a corresponding fall in temperature. The broken line joining the points 3 and 4 in Figure 9.2 represents a process of throttling expansion from the condensing pressure, pc, to the evaporating pressure, pc. It is customary to show the process by a broken line because it is irreversible.
(/) Sub-cooled liquid. This is liquid existing at a temperature less than the saturation temperature for the prevailing pressure. Figure 9.2 shows the region of sub-cooled liquid.
(m) Wet vapour. This is a mixture of saturated liquid and saturated vapour. The quality of the mixture is expressed in terms of its dryness fraction, defined as the mass of saturated vapour divided by the total mass of saturated vapour and saturated liquid. The point 4 in Figure 9.2 represents wet vapour: it is a mixture of saturated liquid at state 4′ and dry saturated vapour at state 1. The state of the wet vapour entering the evaporator can be defined in terms of the relevant enthalpies and its dryness fraction,/, at state 4, is given by
H4 — hr _ h3 — h4.
T hx- hr hx — hA. K ’
(n) Dry saturated vapour. This is the fluid existing as a vapour, without the presence of any saturated liquid, at its saturation vapour pressure. The points 1 and 2′ in Figure 9.2 represent states of dry saturated vapour, at saturated vapour pressures of pe and pc, respectively.
(o) Superheated vapour. This is the fluid existing as a vapour at a temperature greater than the saturated temperature for the pressure prevailing. The point 2 in Figure 9.2 is a state of superheated vapour.
In the following examples (9.1-9.6) R134a is used as the refrigerant but any other, single substance refrigerant would be dealt with using similar principles. Example 9.9 repeats these examples using ammonia as a refrigerant which, because of the format of Table 9.1, is an easier calculation. The treatment is likely to be different when mixtures of refrigerants are used.
EXAMPLE 9.1
An air conditioning plant using Refrigerant 134a has evaporating and condensing temperatures of 0°C and 35°C, respectively. Determine the dryness fraction of the vapour entering the evaporator.
Answer
Using the notation of Figure 9.2, refer to Table 9.1 and interpolate as necessary to determine the saturated liquid leaving the condenser at state 3:
Tc = 35°C pc = 887.11 kPa h3 = 248.94 kJ kg-1
|
Table 9.1 Saturated properties of R134a
|
Data reproduced with permission of the American Society of Heating, Refrigerating and Air-Conditioning Engineers from the (1997) ASHRAE Handbook.
For the mixture of saturated liquid and saturated vapour leaving the expansion valve at state 4:
Te = 0°C
Pe = 292.69 kPa
H4 = h3 = 248.94 kJ kg“1
|
Temperature °C |
Absolute Pressure KPa |
Vapour volume m3 kg“’ |
Liquid enthalpy kJ kg’1 |
Vapour enthalpy kJ kg’1 |
Vapour entropy kJ kg“1 K“1 |
|
Saturated — 10.07 |
200 |
0.099 90 |
186.69 |
392.71 |
1.7337 |
|
Superheated — 10 |
200 |
0.099 90 |
392.77 |
1.7339 |
|
|
-5 |
200 |
0.102 36 |
396.99 |
1.7496 |
|
|
0 |
200 |
0.104 82 |
401.21 |
1.7654 |
|
|
5 |
200 |
0.107 12 |
405.47 |
1.7808 |
|
|
10 |
200 |
0.109 53 |
409.73 |
1.7961 |
|
|
Saturated 8.94 |
400 |
0.051 23 |
212.08 |
403.80 |
1.7229 |
|
Superheated 10 |
400 |
0.051 52 |
404.78 |
1.7263 |
|
|
15 |
400 |
0.052 86 |
409.39 |
1.7423 |
|
|
20 |
400 |
0.054 20 |
414.00 |
1.7583 |
|
|
25 |
400 |
0.055 50 |
418.60 |
1.7738 |
|
|
30 |
400 |
0.056 79 |
423.21 |
1.7892 |
|
|
Saturated 21.58 |
600 |
0.034 33 |
229.62 |
410.67 |
1.7178 |
|
Superheated 25 |
600 |
0.035 00 |
414.04 |
1.7290 |
|
|
30 |
600 |
0.035 98 |
418.97 |
1.7455 |
|
|
35 |
600 |
0.036 92 |
423.84 |
1.7614 |
|
|
40 |
600 |
0.037 86 |
428.72 |
1.7772 |
|
|
45 |
600 |
0.038 74 |
433.58 |
1.7924 |
|
|
50 |
600 |
0.039 67 |
438.44 |
1.8077 |
|
|
Saturated 31.33 |
800 |
0.025 65 |
243.58 |
415.58 |
1.7144 |
|
Superheated 35 |
800 |
0.026 24 |
419.40 |
1.7268 |
|
|
40 |
800 |
0.027 04 |
424.61 |
1.7437 |
|
|
45 |
800 |
0.027 80 |
429.73 |
1.7598 |
|
|
50 |
800 |
0.028 55 |
434.85 |
1.7758 |
|
|
Saturated 39.39 |
1000 |
0.020 34 |
255.44 |
419.31 |
1.7117 |
|
Superheated 40 |
1000 |
0.020 43 |
419.99 |
1.7139 |
|
|
45 |
1000 |
0.022 12 |
415.45 |
1.7310 |
|
|
50 |
1000 |
0.021 81 |
430.91 |
1.7482 |
|
|
Saturated 46.32 |
1200 |
0.016 74 |
265.91 |
422.22 |
1.7092 |
|
Superheated 50 |
1200 |
0.017 21 |
426.51 |
1.7226 |
|
|
55 |
1200 |
0.017 81 |
432.17 |
1.7398 |
|
|
60 |
1200 |
0.018 41 |
437.83 |
1.7571 |
Data reproduced with permission of the American Society of Heating, Refrigerating and Air-Conditioning Engineers from the ASHRAE Handbook (1997).
|
Temperature °C |
Absolute Pressure KPa |
Liquid volume m3 kg“1 |
Vapour volume m3 kg’1 |
Liquid Enthalpy KJkg-‘ |
Vapour enthalpy kJ kg“1 |
Liquid entropy kJ kg“1 K“1 |
Vapour entropy kJ kg’1 K |
|
-5 |
3.549 |
0.001550 |
0.3468 |
158.0 |
1437.6 |
0.6297 |
5.4023 |
|
-4 |
3.689 |
0.001553 |
0.3343 |
162.6 |
1438.7 |
0.6467 |
5.3888 |
|
-3 |
3.834 |
0.001556 |
0.3224 |
167.2 |
1439.8 |
0.6637 |
5.3753 |
|
-2 |
3.983 |
0.001559 |
0.3109 |
171.8 |
1440.9 |
0.6806 |
5.3620 |
|
— 1 |
4.136 |
0.001563 |
0.3000 |
176.4 |
1442.0 |
0.6975 |
5.3487 |
|
0 |
4.294 |
0.001566 |
0.2895 |
181.1 |
1443.1 |
0.7143 |
5.3356 |
|
1 |
4.457 |
0.001569 |
0.2795 |
185.7 |
1444.2 |
0.7312 |
5.3225 |
|
2 |
4.625 |
0.001573 |
0.2698 |
190.3 |
1445.2 |
0.7479 |
5.3096 |
|
3 |
4.797 |
0.001576 |
0.2606 |
194.9 |
1446.3 |
0.7646 |
5.2967 |
|
4 |
4.975 |
0.001580 |
0.2517 |
199.6 |
1447.3 |
0.7813 |
5.2839 |
|
5 |
5.157 |
0.001583 |
0.2433 |
204.2 |
1448.3 |
0.7980 |
5.2712 |
|
6 |
5.345 |
0.001587 |
0.2351 |
208.9 |
1449.2 |
0.8146 |
5.2587 |
|
7 |
5.538 |
0.001590 |
0.2273 |
213.6 |
1450.2 |
0.8311 |
5.2461 |
|
8 |
5.736 |
0.001594 |
0.2198 |
218.2 |
1451.1 |
0.8477 |
5.2337 |
|
9 |
5.940 |
0.001597 |
0.2126 |
222.9 |
1452.1 |
0.8641 |
5.2214 |
|
10 |
6.149 |
0.001601 |
0.2056 |
227.6 |
1453.0 |
0.8806 |
5.2091 |
|
11 |
6.364 |
0.001604 |
0.1990 |
232.3 |
1453.9 |
0.8970 |
5.1949 |
|
12 |
6.585 |
0.001608 |
0.1926 |
237.0 |
1454.8 |
0.9134 |
5.1849 |
|
13 |
6.812 |
0.001612 |
0.1864 |
241.7 |
1455.6 |
0.9297 |
5.1728 |
|
14 |
7.044 |
0.001616 |
0.1805 |
246.4 |
1456.5 |
0.9460 |
5.1609 |
|
15 |
7.283 |
0.001619 |
0.1748 |
251.1 |
1457.3 |
0.9623 |
5.1490 |
|
16 |
7.528 |
0.001623 |
0.1693 |
255.8 |
1458.1 |
0.9785 |
5.1373 |
|
17 |
7.779 |
0.001627 |
0.1641 |
260.6 |
1458.9 |
0.9947 |
5.1255 |
|
18 |
8.037 |
0.001631 |
0.1590 |
265.3 |
1459.7 |
1.0109 |
5.1139 |
|
19 |
8.301 |
0.001635 |
0.1541 |
270.0 |
1460.4 |
1.0270 |
5.1023 |
|
20 |
8.571 |
0.001639 |
0.1494 |
274.8 |
1461.2 |
1.0432 |
5.0908 |
|
21 |
8.849 |
0.001643 |
0.1448 |
279.6 |
1461.9 |
1.0592 |
5.0794 |
|
22 |
9.133 |
0.001647 |
0.1405 |
284.3 |
1462.6 |
1.0753 |
5.0680 |
|
23 |
9.424 |
0.001651 |
0.1363 |
289.1 |
1463.3 |
1.0913 |
5.0567 |
|
24 |
9.722 |
0.001655 |
0.1322 |
293.9 |
1464.0 |
1.1073 |
5.0455 |
|
25 |
10.03 |
0.001659 |
0.1283 |
298.7 |
1464.6 |
1.1232 |
5.0343 |
|
26 |
10.34 |
0.001663 |
0.1245 |
303.5 |
1465.2 |
1.1391 |
5.0232 |
|
27 |
10.66 |
0.001667 |
0.1208 |
308.3 |
1465.9 |
1.1550 |
5.0121 |
|
28 |
10.99 |
0.001671 |
0.1173 |
313.1 |
1466.4 |
1.1708 |
5.0011 |
|
29 |
11.32 |
0.001676 |
0.1139 |
318.0 |
1467.0 |
1.1867 |
4.9902 |
|
30 |
11.66 |
0.001680 |
0.1106 |
322.8 |
1467.6 |
1.2025 |
4.9793 |
|
31 |
12.02 |
0.001684 |
0.1075 |
327.7 |
1468.1 |
1.2182 |
4.9685 |
|
32 |
12.37 |
0.001689 |
0.1044 |
332.5 |
1468.6 |
1.2340 |
4.9577 |
|
33 |
12.74 |
0.001693 |
0.1014 |
337.4 |
1469.1 |
1.2497 |
4.9469 |
|
34 |
13.12 |
0.001698 |
0.0986 |
342.2 |
1469.6 |
1.2653 |
4.9362 |
|
35 |
13.50 |
0.001702 |
0.0958 |
347.1 |
1470.0 |
1.2810 |
4.9256 |
|
36 |
13.89 |
0.001707 |
0.0931 |
352.0 |
1470.4 |
1.2966 |
4.9149 |
|
37 |
14.29 |
0.001711 |
0.0905 |
356.9 |
1470.8 |
1.3122 |
4.9044 |
|
38 |
14.70 |
0.001716 |
0.0880 |
361.8 |
1471.2 |
1.3277 |
4.8938 |
|
39 |
15.12 |
0.001721 |
0.0856 |
366.7 |
1471.5 |
1.3433 |
4.8833 |
|
40 |
15.54 |
0.001726 |
0.0833 |
371.6 |
1471.9 |
1.3588 |
4.8728 |
|
41 |
15.98 |
0.001731 |
0.0810 |
376.6 |
1472.2 |
1.3742 |
4.8623 |
|
Temperature °C |
Absolute Pressure KPa |
Liquid volume m3 kg"1 |
Vapour Volume 3 -1 M mg |
Liquid enthalpy kJ kg“1 |
Vapour enthalpy kJ kg’1 |
Liquid entropy kJ kg“1 K_1 |
Vapour entropy kJ kg“1 K’1 |
|
42 |
16.42 |
0.001735 |
0.0788 |
381.5 |
1472.4 |
1.3897 |
4.8519 |
|
43 |
16.88 |
0.001740 |
0.0767 |
386.5 |
1472.7 |
1.4052 |
4.8414 |
|
44 |
17.34 |
0.001745 |
0.0746 |
391.4 |
1472.9 |
1.4206 |
4.8310 |
|
45 |
17.81 |
0.001750 |
0.0726 |
396.4 |
1473.0 |
1.4360 |
4.8206 |
|
46 |
18.30 |
0.001756 |
0.0707 |
401.4 |
1473.2 |
1.4514 |
4.8102 |
|
47 |
18.79 |
0.001761 |
0.0688 |
406.4 |
1473.3 |
1.4668 |
4.7998 |
|
48 |
19.29 |
0.001766 |
0.0669 |
411.4 |
1473.3 |
1.4822 |
4.7893 |
|
49 |
19.80 |
0.001771 |
0.0652 |
416.5 |
1473.4 |
1.4977 |
4.7789 |
|
50 |
20.33 |
0.001777 |
0.0635 |
421.6 |
1473.4 |
1.5131 |
4.7684 |
|
Reproduced from Thermodynamic Properties of Ammonia by W. B. Gosney and O. Fabris, with the kind permission of the authors. |
For saturated liquid at a temperature of 0°C and a pressure of 292.69 kPa, h4> =
200.0 kJ kg"1.
For dry saturated vapour at 0°C and 292.69 kPa, h = 398.68 kJ kg-1.
Hence, by equation (9.3)
/= (248.94 — 200.00)/(398.68 — 200.00) = 0.25
Thus 25 per cent, by weight, of the liquid refrigerant entering the expansion valve flashes to vapour as the pressure drop through the valve occurs. Since the volume of the vapour is much greater than that of the liquid, the space occupied by the vapour is significantly large. Consequently, the mixture of liquid and vapour leaving the expansion valve must be distributed uniformly into the evaporator before the vapour and liquid get a chance to separate. This is because it is the liquid in the mixture that has the ability to provide refrigeration, by absorbing heat through the surfaces of the evaporator and boiling to a saturated vapour at the evaporating pressure.
Posted in Air Conditioning Engineering