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Second law based thermodynamic analysis of ammonia–water absorption systems
Energy Conversion and Management 45 (2004) 2355–2369 www.elsevier.com/locate/enconman
Second law based thermodynamic analysis of ammonia–water absorption systems S.A. Adewusi, Syed M. Zubair
*
Department of Mechanical Engineering, King Fahd University of Petroleum and Minerals, KFUPM Box # 1474, Dhahran 31261, Saudi Arabia Received 6 May 2003; received in revised form 14 October 2003; accepted 23 November 2003 Available online 24 January 2004
Abstract The second law of thermodynamics is used to study the performance of single-stage and two-stage ammonia–water absorption refrigeration systems (ARSs) when some input design parameters are varied. The entropy generation of each component and the total entropy generation ðS_ tot Þ of all the system components as well as the coefficient of performance (COP) of the ARSs are calculated from the thermodynamic properties of the working fluids at various operating conditions. The results show that the twostage system has a higher S_ tot and COP, while the single-stage system has a lower S_ tot and COP. This is a paradox since one would expect that an efficient thermal system should have a higher COP and lower S_ tot . This anomaly is explained with respect to the performance results for both single and two-stage systems. The trend in COP and S_ tot with the change in heat exchangers effectiveness, absorbers temperatures and condenser and evaporator temperatures for both systems investigated conform with expectation, i.e. an increase in COP corresponds to a decrease in S_ tot . Ó 2003 Elsevier Ltd. All rights reserved. Keywords: Absorption; Refrigeration; Ammonia–water; Second-law analysis
1. Introduction The continuous increase in the cost and demand for energy has led to more research and development to utilize available energy resources efficiently by minimizing waste energy. It is important to note that system performance can be enhanced by reducing the irreversible losses in the system by using the principles of the second law of thermodynamics. A better understanding *
Corresponding author. Tel.: +966-3-860-2540; fax: +966-3-860-2949. E-mail addresses: [email protected] (S.A. Adewusi), [email protected] (S.M. Zubair).
0196-8904/$ - see front matter Ó 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.enconman.2003.11.020
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Nomenclature COP coefficient of performance CEHX condenser–evaporator heat exchanger h enthalpy (kJ/kg) m_ mass flow rate (kg/s) P pressure (kPa) Q quality of working fluid Q ¼ 0 means saturated liquid, Q ¼ 1 means saturated vapor, Q < 0 means subcooled state and Q > 1 means superheated state Q_ thermal energy rate (kW) s entropy (kJ/kg Æ K) SHX solution heat exchanger S_ entropy generation rate (kW/K) S_ tot total entropy generation rate (kW/K) S_ tots total entropy generation rate for single-stage absorption system (kW/K) S_ totd total entropy generation rate for double-stage absorption system (kW/K) T temperature (°C) v specific volume (m3 /kg) W_ pump power (kW) x ammonia mass fraction (kg/kg sol.) e heat exchanger effectiveness Subscripts a absorber c condenser cehx condenser–evaporator heat exchanger e evaporator g generator i state point or index i ¼ 1, 2, 3 . . . o ambient condition p pump r rectifier shx solution heat exchanger tot total v throttling valve of the second law of thermodynamics [1] has revealed that entropy generation minimization is an important technique in achieving optimal system configurations and/or better operating conditions. Some researchers [2,3] have used the principles of entropy generation minimization to analyze different systems to improve the systems performance. The absorption refrigeration system (ARS) is becoming more important because it can produce higher cooling capacity than vapor compression systems, and it can be powered by other sources of energy (like waste heat from gas and steam turbines, sun, geothermal, biomass) than electricity.
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Furthermore, an ARS does not deplete the ozone layer and hence, it poses no danger to the environment. Theoretical and experimental works on the performance characteristics and thermodynamic analysis of ARSs are available in the literature. Chen and Schouten [4] studied the optimal performance of an irreversible ARS. They considered irreversibility via an irreversibility factor and optimized the expression for COP with respect to a number of system parameters. Chua et al. [5] modeled an irreversible ammonia–water absorption chiller by considering the internal entropy production and thermal conductance of the heat exchangers. The model was applied to a single-stage chiller, and the results showed that the highest heat dissipation occurred in the rectifier. Sun [6] compared the performance of NH3 –H2 O, NH3 –LiO2; and NH3 –NaSCN ARSs. Kececiler et al. [7] performed an experimental study on the thermodynamic analysis of a reversible lithium bromide–water ARS. It has been observed that single state ARSs cannot efficiently utilize a high temperature heat source. This fact motivated the development of multi-stage ARSs. Kaita [8] compared the coefficient of performance (COP) of different configurations of triple stage lithium bromide ARSs, namely parallel flow, series flow, and reverse flow. The results showed that the parallel flow configuration has the highest COP. Detailed first law based thermodynamic performance analysis of single and multi-stage ARSs was discussed by Herold et al. [9]. It is important to emphasize that in the past, the performance analysis of ARSs was based only on the first law of thermodynamics, which involves energy and mass balances. However, recent analyses of ARSs have included the second law of thermodynamics to provide better understanding of the thermal performance characteristics of each of the system components. This facilitated the detection of a component with high energy dissipation or irreversible losses. Attention can then be focused on such component to minimize its irreversibile losses. Lee and Sherif [10] applied both the first and second law of thermodynamics to analyze multi-stage lithium bromide–water ARSs. The second law efficiency of the chillers was calculated from the thermal properties, as well as the entropy generation and exergy of the working fluids. Furthermore, Lee and Sherif [10] used the second law efficiency to quantify the irreversible losses compared to the total entropy generation, which represents the energy dissipation of the system. The present study applies the second law of thermodynamics to study the performance of single-stage and double stage ammonia–water ARSs when some design parameters are varied. The entropy generation of each component, the total entropy generation of all the components and the COP of the ARSs are calculated from the thermodynamic properties of the working fluids at various working conditions using the Engineering Equation Solver (EES) software [11]. The variations of total entropy generation of all the components and the COP are then studied. It is important to note that this study is an extension of the single-stage and two-stage ammonia–water ARSs discussed in Ref. [9], which considered only the COP of the systems based only on energy analysis without considering entropy generation in various components of the systems.
2. The ammonia–water absorption refrigeration cycle The single-stage ammonia–water ARS cycle consists of four main components, namely the condenser, evaporator, absorber and generator, as shown in Fig. 1. Other auxiliary components include the expansion valves, pump, rectifier and heat exchangers. Low pressure, but strong,
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S.A. Adewusi, S.M. Zubair / Energy Conversion and Management 45 (2004) 2355–2369 Qc @ To Qr @ T0
9 Condenser
Rectifier 8
7
10 Generator Qg @ Tg
4
3
14 CEHX
SHX
5
11 13
V2 12
V1
2
6
Evaporator Q e @ Te
Absorber
1
Q a @ To
Wp
Fig. 1. Schematic of a single-stage ammonia–water absorption refrigeration system.
ammonia solution from the absorber is pumped through the solution heat exchanger (SHX) to the generator operating at a high pressure. The generator separates the binary solution of water and ammonia by causing the ammonia to vaporize, and the rectifier purifies the ammonia vapor. High pressure ammonia gas (if the separation is perfect) or high pressure ammonia gas with some amount of water vapor from the rectifier is condensed in the condenser, and the condensate is then passed through the condenser–evaporator heat exchanger (CEHX) and the throttling value ðV 2Þ to the evaporator as low pressure liquid ammonia, which is classified as a very strong ammonia solution. The high pressure transport fluid, water, from the generator is returned to the absorber through the solution heat exchanger (SHX) and the throttling value ðV 1Þ. The low pressure liquid ammonia in the evaporator is used to cool the space to be refrigerated. During the cooling process, the liquid ammonia vaporizes and the transport fluid, water, absorbs the vapor to form a strong ammonia solution in the absorber. The following are the performance equations for each of the components considering continuity (mass balance), the first law of thermodynamics (energy balance) and the second law of thermodynamics (entropy generation). The absorber m_ 1 ¼ m_ 14 þ m_ 6
ðfor mixtureÞ
m_ 1 x1 ¼ m_ 14 x14 þ m_ 6 x6
ðfor ammoniaÞ
m_ 6 h6 Q_ a þ m_ 14 h14 ¼ m_ 1 h1
ð1Þ ð2Þ ð3Þ
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Q_ a S_ a ¼ m_ 1 s1 m_ 6 s6 m_ 14 s14 þ To
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ð4Þ
The pump m_ 1 m1 ðP2 P1 Þ W_ p ¼ gp
ð5Þ
m_ 1 h1 ¼ m_ 2 h2 W_ p
ð6Þ
S_ p ¼ m_ 2 s2 m_ 1 s1
ð7Þ
Solution heat exchanger (SHX) eshx ¼
T4 T5 T4 T2
m_ 4 h4 þ m_ 2 h2 ¼ m_ 5 h5 þ m_ 3 h3 S_ shx ¼ m_ 5 s5 þ m_ 3 s3 m_ 4 s4 m_ 2 s2
ð8Þ ð9Þ ð10Þ
Generator m_ 8 þ m_ 3 ¼ m_ 7 þ m_ 4
ð11Þ
m_ 3 x3 þ m_ 8 x8 ¼ m_ 7 x7 þ m_ 4 x4
ð12Þ
Q_ g S_ g ¼ m_ 7 s7 þ m_ 4 s4 m_ 3 s3 m_ 8 s8 Tg
ð13Þ
Absorber throttle valve ðV 1Þ m_ 6 ¼ m_ 5 ;
x6 ¼ x5
ð14Þ
h6 ¼ h5
ð15Þ
S_ V 1 ¼ m_ 6 s6 m_ 5 s5
ð16Þ
Condenser m_ 9 ¼ m_ 10 ;
x9 ¼ x10
ð17Þ
m_ 9 h9 ¼ m_ 10 h10 þ Q_ c
ð18Þ
Q_ c S_ c ¼ m_ 10 s10 m_ 9 s9 þ To
ð19Þ
Condenser–evaporator heat exchanger (CEHX) T10 T11 ecehx ¼ T10 T13
ð20Þ
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m_ 10 h10 þ m_ 13 h13 ¼ m_ 11 h11 þ m_ 14 h14
ð21Þ
S_ cehx ¼ m_ 11 s11 þ m_ 14 s14 m_ 10 s10 m_ 13 s13
ð22Þ
Evaporator throttle valve ðV 2Þ m_ 11 ¼ m_ 12 ;
x11 ¼ x12
ð23Þ
h11 ¼ h12
ð24Þ
S_ V 2 ¼ m_ 12 s12 m_ 11 s11
ð25Þ
Evaporator m_ 12 ¼ m_ 13 ;
x12 ¼ x13
ð26Þ
m_ 13 h13 ¼ m_ 12 h12 þ Q_ e
ð27Þ
Q_ e S_ e ¼ m_ 13 s13 m_ 13 s13 To
ð28Þ
Rectifier m_ 7 ¼ m_ 9 þ m_ 8
ð29Þ
m_ 7 x7 ¼ m_ 9 x9 þ m_ 8 x8
ð30Þ
m_ 7 h7 ¼ m_ 9 h9 þ m_ 8 h8 þ Q_ r
ð31Þ
Q_ r S_ r ¼ m_ 8 s8 þ m_ 9 s9 m_ 7 s7 þ To
ð32Þ
COP ¼
Q_ e Q_ g þ W_ p
S_ tot ¼ S_ e þ S_ g þ S_ c þ S_ a þ S_ r þ S_ cehx þ S_ shx þ S_ p þ S_ v1 þ S_ v2
ð33Þ ð34Þ
Fig. 2 represents a two-stage ARS. We note that the left hand side of the system is similar to Fig. 1. The heat rejected by absorber 2 serves as the heat input for generator 1. Ammonia vapor at low pressure from the evaporator is divided between the two absorbers while ammonia vapor at high pressure from the rectifiers of the two-stages are combined before entering the condenser. Just like the single-stage ARS, the two-stage has one evaporator and one condenser, but it has two generators and two absorbers. Following a procedure similar to that of the single-stage discussed earlier, energy and mass balances, as well as entropy generation equations, for each component and the mixing streams of the two-stage system were obtained.
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Qr3 @ T0 Q r1@ T0
Qc @ To 25
27 Qr 2 @ T0
24
Rectifier3
Rectifier2 Q g @ Tg
9
23
Rectifier1
Condenser
22
28 8
Generator2
7
18
19
10 Generator1
Q a 2 @ T7
SHX2
3
4
14 CEHX
20
SHX1
17
V2 11
21
5
V3
2361
V1
13
2
Absorber2
16
6
12 26
1
29
Absorber1
Evaporator
15
Qa1 @ T o
W p2
Wp1
Q e @ Te
Fig. 2. Schematic of a two-stage ammonia–water absorption refrigeration system.
3. Numerical example A typical example, discussed by Herold et al. [9], is considered in this study to examine the variation in COP and total entropy generation of the ammonia–water ARSs at various operating conditions. For the single-stage system, the evaporator outlet saturation temperature is taken as )10 °C, the mass flow rate of solution through the pump is 1 kg/s, the saturated liquid leaving the absorber and condenser is at 40 °C and the difference in mass fraction of the two solution streams is 0.10. The evaporator produces saturated vapor with a mass fraction of 99.96% ammonia. The efficiency of the pump is 50%, while the effectivenesses of the SHX and CEHX are 100% and 95%, respectively. For the two-stage system, the vapor leaving rectifiers 1 and 3 has a mass ratio of 0.995, the efficiency of the pumps and the effectivenesses of the heat exchangers, the condenser and evaporator temperatures and the mass flow through pump 1 are the same as those for the single-stage system. The temperature of the refrigerant entering the second stage absorber is the same as that of the refrigerant leaving the first stage absorber. The temperature of the refrigerant leaving the second stage absorber is 0.10 °C higher than T4 . The mass fraction difference in the first stage solution cycle is 0.04, while that in the second stage is 0.06. Liquid leaving the absorbers and generators, and vapor leaving the generators and rectifiers are saturated. The vapor quality leaving the evaporator is 0.9. The properties for all states points, COP and total entropy generation for the ammonia–water ARSs are obtained using the Engineering Equation Solver (EES)
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Table 1 State points for the single-stage ammonia–water absorption refrigeration system and the calculated results Point
hi (kJ/kg)
mi (kg/s)
Pi (kPa)
Qi
si (kJ/kg/ K)
Ti (°C)
vi (m3 /kg)
xi (kg/ kg sol)
1 2 3 4 5 6 7 8 9 10 11 12 13 14
)43.25 )40.20 303.11 397.21 )0.71 )0.71 1544.09 260.56 1294.18 190.79 78.86 78.86 1259.13 1371.05
1.000 1.000 1.000 0.863 0.863 0.863 0.150 0.013 0.137 0.137 0.137 0.137 0.137 0.137
244.85 1555.76 1555.76 1555.76 1555.76 244.85 1555.76 1555.76 1555.76 1555.76 1555.76 244.85 244.85 244.85
0.000 )0.001 0.022 0.000 )0.001 )0.001 1.000 0.000 1.000 0.000 )0.001 0.109 0.998 1.001
0.47 0.48 1.46 1.64 0.53 0.54 4.88 1.35 4.17 0.66 0.29 0.32 4.87 5.25
40.00 40.45 110.06 130.31 40.45 40.71 107.33 107.36 44.07 40.00 16.88 )14.14 )10.00 37.39
0.001 0.001 0.004 0.001 0.001 0.001 0.110 0.001 0.083 0.002 0.002 0.055 0.512 0.605
0.3709 0.3709 0.3709 0.2709 0.2709 0.2709 0.9460 0.3709 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996
Calculated results COP ¼ 0:598 Q_ a ¼ 231 kW Q_ g ¼ 267:9 kW S_ cehx ¼ 0:001427 kW/K S_ p ¼ 0:004897 kW/K S_ v2 ¼ 0:004918 kW/K
S_ tot ¼ 0:1973 kW/K Q_ cehx ¼ 15:4 kW Q_ r ¼ 50:7 kW S_ c ¼ 0:03414 kW/K S_ r ¼ 0:03047 kW/K
W_ p ¼ 3:0 kW Q_ c ¼ 151 kW Q_ shx ¼ 343:3 kW S_ e ¼ 0:008259 kW/K S_ shx ¼ 0:01886
Q_ e ¼ 162:0 kW S_ a ¼ 0:07741 kW/K S_ g ¼ 0:01285 kW/K S_ v1 ¼ 0:00403 kW/K
software [11]. The design point results are presented in Tables 1 and 2, while the variation in COP and total entropy generation of the systems due to changes in heat exchangers effectivenesses, absorber and condenser temperatures and solution mass fraction differences in the circuits are also studied. These results are presented in Figs. 3–7.
4. Results and discussion Table 1 shows the thermodynamic properties of the single-stage ARS at all state points, while Table 2 shows the thermodynamic properties of the two-stage ARS at all state points. The predicted performance results of the single-stage and two-stage ARSs at the same evaporator temperature are shown in Table 3. The heat transfer and entropy generation for the absorbers, generators, rectifiers, solution heat exchangers and pumps for the two-stage ARS are also shown. At an evaporator temperature of )10 °C with the heat exchangers and pumps having the same effectivenesses and efficiencies, the results show that the two-stage system is more efficient, with a COP of 0.734 as against 0.598 for the single-stage system. On the other hand, the second law analysis via total entropy generation shows that the single state system is more efficient, since it has less energy dissipation of 0.1973 kW/K compared to 0.4627 kW/K, for the two-stage system. This seems to be contradictory, since a more efficient system should have the higher COP and the
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Table 2 State points for the two-stage ammonia–water absorption refrigeration system and the calculated results Point
hi (kJ/kg)
mi (kg/s)
Pi (kPa)
Qi
si (kJ/kg/ K)
Ti (°C)
vi (m3 /kg)
xi (kg/ kg sol)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
)48.62 )45.65 252.71 283.96 )34.16 )34.16 1521.46 235.40 1365.33 187.36 )36.71 )36.71 1123.94 1348.01 1348.01 423.43 426.20 777.80 840.46 466.13 466.13 2389.62 736.23 1568.12 1365.33 1348.01 1365.33 79.15 1381.88
1.000 1.000 1.000 0.938 0.938 0.938 0.066 0.004 0.062 0.079 0.079 0.079 0.079 0.079 0.016 0.270 0.270 0.270 0.253 0.253 0.253 0.062 0.043 0.019 0.079 0.062 0.016 0.003 0.016
277.97 1548.03 1548.03 1548.03 1548.03 277.97 1548.03 1548.03 1548.03 1548.03 1548.03 277.97 277.97 277.97 277.97 277.97 1548.03 1548.03 1548.03 1548.03 277.97 1548.03 1548.03 1548.03 1548.03 277.97 1548.03 1548.03 277.97
0.000 )0.001 0.009 0.000 )0.001 )0.001 1.000 0.000 1.000 0.000 )0.001 0.013 0.900 0.998 0.998 0.000 )0.001 0.021 0.000 )0.001 )0.001 1.000 0.001 1.000 0.996 0.998 1.000 0.000 1.001
0.464 0.469 1.331 1.399 0.486 0.491 4.827 1.285 4.392 0.662 )0.113 )0.105 4.299 5.115 5.115 1.479 1.483 2.313 2.329 1.455 1.458 6.259 2.222 4.943 4.393 5.115 4.392 0.830 5.225
40.0 40.4 103.8 111.4 40.4 40.7 102.7 102.8 67.1 40.0 )7.4 )11.0 )10.0 27.3 27.3 111.5 112.0 183.4 198.0 112.0 112.2 182.1 182.1 112.0 63.3 27.3 67.1 67.1 40.7
0.001 0.001 0.002 0.001 0.001 0.001 0.109 0.001 0.094 0.002 0.002 0.007 0.395 0.511 0.511 0.001 0.001 0.004 0.001 0.001 0.001 0.127 0.001 0.112 0.094 0.511 0.094 0.001 0.537
0.3913 0.3913 0.3913 0.3513 0.3513 0.3513 0.9562 0.3913 0.9950 0.9950 0.9950 0.9950 0.9950 0.9950 0.9950 0.0671 0.0671 0.0671 0.0071 0.0071 0.0071 0.3360 0.0671 0.9329 0.9950 0.9950 0.9950 0.5949 0.9950
Calculated results COP ¼ 0:734 Q_ a1 ¼ 100 kW Q_ cehx ¼ 18 kW Q_ r3 ¼ 8 kW S_ a1 ¼ 0:02597 kW/K S_ cehx ¼ 0:003231 kW/K S_ p2 ¼ 0:00361 kW/K S_ shx2 ¼ 0:002145 kW/K
S_ tot ¼ 0:4627 kW/K Q_ a2 ¼ 27 kW Q_ e ¼ 91 kW Q_ shx1 ¼ 298 kW S_ a2 ¼ 0:0363 kW/K S_ c ¼ 0:02262 kW/K S_ r1 ¼ 0:009632 kW/K S_ ¼ 0:004373 kW/K
W_ p1 ¼ 3:0 kW Q_ g ¼ 120 kW Q_ r1 ¼ 15 kW Q_ shx2 ¼ 95 kW S_ g1 ¼ 0:2275 kW/K S_ e ¼ 0:005954 kW/K S_ r2 ¼ 0:103 kW/K S_ v2 ¼ 0:000882 kW/K
W_ p2 ¼ 0:7 kW Q_ c ¼ 93 kW Q_ r2 ¼ 87 kW S_ g2 ¼ 0:00599 kW/K S_ p1 ¼ 0:00477 kW/K S_ shx1 ¼ 0:006064 kW/K S_ v3 ¼ 0:00059 kW/K
lower total energy dissipation. This can be explained from the fact that the increase in S_ tot of the two-stage ARS was primarily due to the introduction of more thermal components, as was also noted by Lee and Sherif [10]. A careful study of Table 3 reveals the effect of the two-stage system. While it reduced the energy input to the system from 267.9 kW for the single-stage to 120 kW; it also reduced the useful
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Table 3 Performance comparison of the single and two-stage Ammonia–Water absorption systems at an evaporator temperature of )10 °C Parameter
Single-stage
Double-stage
COP S_ tot (kW/K) Q_ e (kW) S_ e (kW/K) Q_ g (kW) S_ g (kW/K) Q_ a (kW) S_ a (kW/K) Q_ r (kW) S_ r (kW/K) W_ p (kW) S_ p (kW/K) Q_ cehx (kW) S_ cehx (kW/K) Q_ shx (kW) S_ shx (kW/K) Plow (kPa) Phigh (kPa)
0.5980 0.1973 162.0 0.008259 267.9 0.01285 231 0.07741 50.7 0.03047 3.0 0.004897 15.4 0.001427 343.3 0.01886 244.85 1555.76
0.734 0.4627 91.0 0.005954 120.0 0.23349 127 0.06227 110 0.112632 3.7 0.00838 18.0 0.003231 393 0.00821 277.97 1548.03
0.8 0.75
COP and Sgen (kW/K)
0.7 0.65
COPs
0.6
Stots
0.55
COPd
0.5
Stotd
0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1
1.1 1.2 1.3
Condender HX Effectiveness
Fig. 3. Effect of condenser–evaporator heat exchanger effectiveness on COP and S_ tot .
cooling load from 162 kW for the single-stage system to 91 kW. It is interesting to note that this reduction in the thermal energy is accompanied with high energy dissipation of 0.2335 kW/K in the generator of the two-stage system, 50.5% of the total entropy generation, compared to 0.01285
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1.4
COP and Sgen (kW/K)
1.3 1.2
COPs
1.1
Stots
1
COPd Stotd
0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Solution HX Effectiveness
Fig. 4. Effect of solution heat exchanger effectiveness on COP and S_ tot .
1.2 1.1 COPs
COP and Sgen (kW/K)
1
Stots
0.9
COPd
0.8
Stotd
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 10
15
20 25 30 35 40 45 50 55 60 Absorber Temperature (Deg. Celsius)
65
70
Fig. 5. Effect of absorber temperature on COP and S_ tot .
kW/K in the generator of the single-stage system. As discussed above, Lee and Sherif [10] attributed the better thermodynamic efficiency of the single-stage lithium bromide–water ARS over the two-stage and triple stage systems to the irreversibility in the additional heat exchange components present in multi-stage systems. They calculated the total entropy generation without studying the entropy contribution of each of the system components. The present study, however, has shown that the lesser thermal efficiency (higher-energy dissipation) of two-stage ARSs is due
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COPs
COP and Sgen (kW/K)
0.9
Stots COPd
0.8
Stotd
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
10
15
20 25 30 35 40 45 50 55 60 Condenser Outlet Temperature (Deg. Celsius)
65
70
Fig. 6. Effect of condenser outlet temperature on COP and S_ tot .
1.3 1.2 COPs
COP and Sgen (kW/K)
1.1
Stots
1
COPd Stotd
0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -10
-8
-6
-4
-2
0
2
4
6
8
10
Evaporator Temperature (Deg. Celsius)
Fig. 7. Effect of evaporator temperature on COP and S_ tot .
to the irreversibility in the generator as a result of the reduction in the generator heat requirement due to the introduction of more stages. It is important to emphasize, that the COP is sensitive to the output and input energies alone, and since the input energy is reduced by 55.2% while the cooling load is reduced by 43.8%, the COP is increased. Since the evaporator of the single-stage system is at )10 °C, it produced a load of 162 kW, while the two-stage system produced less cooling capacity, i.e. 91 kW at the same
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evaporator temperature with high energy dissipation. It seems that the COP is less sensitive to the dynamics of the ARSs, while the total entropy generation is more sensitive to the dynamics of the systems. It, therefore seems that the entropy generation criterion is a better performance measurement criterion than the COP, particularly if one is interested to examine the distribution of irreversible losses. Fig. 3 presents the effect of the condenser–evaporator effectiveness on COP and S_ tot . As expected, the COP of both the single-stage and two-stage ARSs increased with an increase in the effectiveness. However, the increase in the COP of the two-stage system (COPd ) is greater than the increase in the COP of the single-stage system (COPs ), while the total entropy generation of the two-stage system ðStotd Þ is greater than that of the single-stage system ðStots Þ, but the effect of changes in the effectivenesses is negligible on the total entropy generation of the two ammonia– water ARSs. The reason for this observation can be found in Table 3. The entropy generation of the condenser–evaporator heat exchanger contributes only 0.724% for the single-stage and 0.698% for the two-stage to the total entropy generation of each system, respectively. As explained above, the COP is more sensitive to changes in the working conditions of the evaporator and the generator or any other component that affects them, while the total entropy generation considers the effect of all the components. Fig. 4 shows the effect of the solution heat exchanger (SHX) effectivenesses on COP and Stot . For the two-stage ARS, there are two SHXs. An increase in the effectivenesses of the SHXs results in an increase in the COP and a decrease in Stot . This observation conforms with our expectation, since a more efficient system is expected to have a higher COP and less entropy generation. At an effectiveness of less that 50%, the increase in COPs and COPd are almost the same while the increase in COPd is greater than the increase in COPs for an effectiveness greater than 50%. As has been observed in Table 3 and Fig. 3, the entropy generation for the two-stage is greater than that of the single-stage, which suggests that the two-stage is less efficient, whereas the COP of the two-stage is greater than that of the single-stage, which suggests that the twostage is more efficient. The reason for the paradox has already been discussed earlier. Fig. 4 also indicates that the two-stage ARS is grossly inefficient without the SHXs since it has the same COP as the single-stage ARS and a higher total entropy generation than the single-stage ARS at a lower SHX effectiveness. Fig. 4 clearly shows that the SHX is one of the critical components of the ammonia–water ARSs, as its performance affected the COP and total entropy generation of the ARSs in the expected manner, i.e. an increase in COP corresponds to a decrease in total entropy generation. Fig. 5 shows the effect of absorber outlet temperature on COP and total entropy generation of the ARSs. For the two-stage system, the absorber in the first stage, i.e. absorber 1 is considered. Fig. 6 presents the effect of condenser outlet temperature on COP and total entropy generation of the ARSs. Both figures show that an increase in temperature results in a decrease in COP of both the single-stage and two-stage systems and an increase in the total entropy generation of the systems. As has been observed in Table 3 and Figs. 3 and 4, the entropy generation for the twostage is greater than that of the single-stage, which suggests that the two-stage is less efficient, while the COP of the two-stage is greater than that of the single-stage, which suggests that the two-stage is more efficient. The reason for the paradox has been discussed above. Fig. 7 shows the effect of the evaporator temperature on COP and total entropy generation of the ARSs. This figure shows that an increase in the evaporator temperature results in an increase in COP of both
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the single-stage and two-stage systems and a decrease in the total entropy generation of the systems.
5. Conclusions The second law of thermodynamics is used to study the performance of single-stage and twostage ammonia–water absorption refrigeration systems (ARSs) when some parameters are varied. The entropy generation of each component, the total entropy generation ðS_ tot Þ of all components and the COPs of the ARSs are calculated from the thermodynamic properties of the working fluids at various working conditions using the Engineering Equation Solver (EES) software. The results show that the total entropy generation for the two-stage is greater than that of the singlestage, which suggests that the two-stage is less efficient, while the COP of the two-stage is greater than that of the single-stage, which suggests that the two-stage is more efficient. This is a paradox. Both COP and S_ tot are measures of thermal performance and from established knowledge, a more efficient thermal system should have a higher COP and a lower S_ tot . However, what has been reported in the literature and what the results of this study show is a paradox. This observation deserves further investigation. It is important to note that the increase in S_ tot of the two-stage ARS was due to the introduction of more thermal components, as also noted by Lee and Sherif [10]. The present study, however, has shown that the high S_ tot (high energy dissipation) of multi-stage ARSs is due to the irreversibility in the generator as a result of the reduction in generator heat requirement due to the presence of more stages, since the generator produced above 50% of the total entropy generation in the two-stage ARS. We emphasize that the second law analysis used in this study also facilitated a means of identifying the components with high exergy dissipation.
Acknowledgements The authors acknowledge the support provided by King Fahd University of Petroleum and Minerals for this research project.
References [1] Lieb EH, Yngvason J. A fresh look at entropy and the second law of thermodynamics. Phys Today 2000;53(4): 32–6. [2] Ogulata RT, Doba F. Experiments and entropy generation minimization of a cross-flow heat exchanger. Int J Mass Transfer 1998;41(2):373–81. [3] Vargas J, Bejan A, Siems D. Integrative thermodynamic optimization of cross-flow heat exchanger for an aircraft environmental control system. J Heat transfer 2001;128:760–9. [4] Chen J, Schouten JA. Optimum performance characteristics of an irreversible absorption refrigeration system. Energ Convers Manage 1998;39:999–1007. [5] Chua HT, Toh HK, Ng KC. Thermodynamic modeling of an ammonia/water absorption chiller. Int J Refrig 2002;25:896–906.
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[6] Sun D-W. Comparison of the performance of NH3 –H2 O, NH3 –LiNO3 and NH3 –NaSCN refrigeration systems. Energ Convers Manage 1998;39:357–68. [7] Kececiler A, Acar HI, Dogan A. Thermodynamic analysis of absorption refrigeration system with geothermal energy: an experimental study. Energ Convers Manage 2000;41:37–48. [8] Kaita Y. Simulation results of triple-effect absorption cycles. Int J Refrig 2002;25:999–1007. [9] Herold KE, Radermacher R, Klein SA. Absorption chillers and heat pumps. USA: CRC Press; 1996. [10] Lee SF, Sherif SA. Second-law analysis of multi-effect lithium bromide/water absorption chillers. ASHRAE Trans 1999;105(1):1256–66. [11] Klein SA, Alvardo FL. EES-Engineering Equation Solver. Users manual for Microsoft Windows Operating Systems. Version 6.826, F-Chart Software, Madison, WI; 2003.
Second law based thermodynamic analysis of ammonia–water absorption systems S.A. Adewusi, Syed M. Zubair
*
Department of Mechanical Engineering, King Fahd University of Petroleum and Minerals, KFUPM Box # 1474, Dhahran 31261, Saudi Arabia Received 6 May 2003; received in revised form 14 October 2003; accepted 23 November 2003 Available online 24 January 2004
Abstract The second law of thermodynamics is used to study the performance of single-stage and two-stage ammonia–water absorption refrigeration systems (ARSs) when some input design parameters are varied. The entropy generation of each component and the total entropy generation ðS_ tot Þ of all the system components as well as the coefficient of performance (COP) of the ARSs are calculated from the thermodynamic properties of the working fluids at various operating conditions. The results show that the twostage system has a higher S_ tot and COP, while the single-stage system has a lower S_ tot and COP. This is a paradox since one would expect that an efficient thermal system should have a higher COP and lower S_ tot . This anomaly is explained with respect to the performance results for both single and two-stage systems. The trend in COP and S_ tot with the change in heat exchangers effectiveness, absorbers temperatures and condenser and evaporator temperatures for both systems investigated conform with expectation, i.e. an increase in COP corresponds to a decrease in S_ tot . Ó 2003 Elsevier Ltd. All rights reserved. Keywords: Absorption; Refrigeration; Ammonia–water; Second-law analysis
1. Introduction The continuous increase in the cost and demand for energy has led to more research and development to utilize available energy resources efficiently by minimizing waste energy. It is important to note that system performance can be enhanced by reducing the irreversible losses in the system by using the principles of the second law of thermodynamics. A better understanding *
Corresponding author. Tel.: +966-3-860-2540; fax: +966-3-860-2949. E-mail addresses: [email protected] (S.A. Adewusi), [email protected] (S.M. Zubair).
0196-8904/$ - see front matter Ó 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.enconman.2003.11.020
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Nomenclature COP coefficient of performance CEHX condenser–evaporator heat exchanger h enthalpy (kJ/kg) m_ mass flow rate (kg/s) P pressure (kPa) Q quality of working fluid Q ¼ 0 means saturated liquid, Q ¼ 1 means saturated vapor, Q < 0 means subcooled state and Q > 1 means superheated state Q_ thermal energy rate (kW) s entropy (kJ/kg Æ K) SHX solution heat exchanger S_ entropy generation rate (kW/K) S_ tot total entropy generation rate (kW/K) S_ tots total entropy generation rate for single-stage absorption system (kW/K) S_ totd total entropy generation rate for double-stage absorption system (kW/K) T temperature (°C) v specific volume (m3 /kg) W_ pump power (kW) x ammonia mass fraction (kg/kg sol.) e heat exchanger effectiveness Subscripts a absorber c condenser cehx condenser–evaporator heat exchanger e evaporator g generator i state point or index i ¼ 1, 2, 3 . . . o ambient condition p pump r rectifier shx solution heat exchanger tot total v throttling valve of the second law of thermodynamics [1] has revealed that entropy generation minimization is an important technique in achieving optimal system configurations and/or better operating conditions. Some researchers [2,3] have used the principles of entropy generation minimization to analyze different systems to improve the systems performance. The absorption refrigeration system (ARS) is becoming more important because it can produce higher cooling capacity than vapor compression systems, and it can be powered by other sources of energy (like waste heat from gas and steam turbines, sun, geothermal, biomass) than electricity.
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Furthermore, an ARS does not deplete the ozone layer and hence, it poses no danger to the environment. Theoretical and experimental works on the performance characteristics and thermodynamic analysis of ARSs are available in the literature. Chen and Schouten [4] studied the optimal performance of an irreversible ARS. They considered irreversibility via an irreversibility factor and optimized the expression for COP with respect to a number of system parameters. Chua et al. [5] modeled an irreversible ammonia–water absorption chiller by considering the internal entropy production and thermal conductance of the heat exchangers. The model was applied to a single-stage chiller, and the results showed that the highest heat dissipation occurred in the rectifier. Sun [6] compared the performance of NH3 –H2 O, NH3 –LiO2; and NH3 –NaSCN ARSs. Kececiler et al. [7] performed an experimental study on the thermodynamic analysis of a reversible lithium bromide–water ARS. It has been observed that single state ARSs cannot efficiently utilize a high temperature heat source. This fact motivated the development of multi-stage ARSs. Kaita [8] compared the coefficient of performance (COP) of different configurations of triple stage lithium bromide ARSs, namely parallel flow, series flow, and reverse flow. The results showed that the parallel flow configuration has the highest COP. Detailed first law based thermodynamic performance analysis of single and multi-stage ARSs was discussed by Herold et al. [9]. It is important to emphasize that in the past, the performance analysis of ARSs was based only on the first law of thermodynamics, which involves energy and mass balances. However, recent analyses of ARSs have included the second law of thermodynamics to provide better understanding of the thermal performance characteristics of each of the system components. This facilitated the detection of a component with high energy dissipation or irreversible losses. Attention can then be focused on such component to minimize its irreversibile losses. Lee and Sherif [10] applied both the first and second law of thermodynamics to analyze multi-stage lithium bromide–water ARSs. The second law efficiency of the chillers was calculated from the thermal properties, as well as the entropy generation and exergy of the working fluids. Furthermore, Lee and Sherif [10] used the second law efficiency to quantify the irreversible losses compared to the total entropy generation, which represents the energy dissipation of the system. The present study applies the second law of thermodynamics to study the performance of single-stage and double stage ammonia–water ARSs when some design parameters are varied. The entropy generation of each component, the total entropy generation of all the components and the COP of the ARSs are calculated from the thermodynamic properties of the working fluids at various working conditions using the Engineering Equation Solver (EES) software [11]. The variations of total entropy generation of all the components and the COP are then studied. It is important to note that this study is an extension of the single-stage and two-stage ammonia–water ARSs discussed in Ref. [9], which considered only the COP of the systems based only on energy analysis without considering entropy generation in various components of the systems.
2. The ammonia–water absorption refrigeration cycle The single-stage ammonia–water ARS cycle consists of four main components, namely the condenser, evaporator, absorber and generator, as shown in Fig. 1. Other auxiliary components include the expansion valves, pump, rectifier and heat exchangers. Low pressure, but strong,
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S.A. Adewusi, S.M. Zubair / Energy Conversion and Management 45 (2004) 2355–2369 Qc @ To Qr @ T0
9 Condenser
Rectifier 8
7
10 Generator Qg @ Tg
4
3
14 CEHX
SHX
5
11 13
V2 12
V1
2
6
Evaporator Q e @ Te
Absorber
1
Q a @ To
Wp
Fig. 1. Schematic of a single-stage ammonia–water absorption refrigeration system.
ammonia solution from the absorber is pumped through the solution heat exchanger (SHX) to the generator operating at a high pressure. The generator separates the binary solution of water and ammonia by causing the ammonia to vaporize, and the rectifier purifies the ammonia vapor. High pressure ammonia gas (if the separation is perfect) or high pressure ammonia gas with some amount of water vapor from the rectifier is condensed in the condenser, and the condensate is then passed through the condenser–evaporator heat exchanger (CEHX) and the throttling value ðV 2Þ to the evaporator as low pressure liquid ammonia, which is classified as a very strong ammonia solution. The high pressure transport fluid, water, from the generator is returned to the absorber through the solution heat exchanger (SHX) and the throttling value ðV 1Þ. The low pressure liquid ammonia in the evaporator is used to cool the space to be refrigerated. During the cooling process, the liquid ammonia vaporizes and the transport fluid, water, absorbs the vapor to form a strong ammonia solution in the absorber. The following are the performance equations for each of the components considering continuity (mass balance), the first law of thermodynamics (energy balance) and the second law of thermodynamics (entropy generation). The absorber m_ 1 ¼ m_ 14 þ m_ 6
ðfor mixtureÞ
m_ 1 x1 ¼ m_ 14 x14 þ m_ 6 x6
ðfor ammoniaÞ
m_ 6 h6 Q_ a þ m_ 14 h14 ¼ m_ 1 h1
ð1Þ ð2Þ ð3Þ
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Q_ a S_ a ¼ m_ 1 s1 m_ 6 s6 m_ 14 s14 þ To
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ð4Þ
The pump m_ 1 m1 ðP2 P1 Þ W_ p ¼ gp
ð5Þ
m_ 1 h1 ¼ m_ 2 h2 W_ p
ð6Þ
S_ p ¼ m_ 2 s2 m_ 1 s1
ð7Þ
Solution heat exchanger (SHX) eshx ¼
T4 T5 T4 T2
m_ 4 h4 þ m_ 2 h2 ¼ m_ 5 h5 þ m_ 3 h3 S_ shx ¼ m_ 5 s5 þ m_ 3 s3 m_ 4 s4 m_ 2 s2
ð8Þ ð9Þ ð10Þ
Generator m_ 8 þ m_ 3 ¼ m_ 7 þ m_ 4
ð11Þ
m_ 3 x3 þ m_ 8 x8 ¼ m_ 7 x7 þ m_ 4 x4
ð12Þ
Q_ g S_ g ¼ m_ 7 s7 þ m_ 4 s4 m_ 3 s3 m_ 8 s8 Tg
ð13Þ
Absorber throttle valve ðV 1Þ m_ 6 ¼ m_ 5 ;
x6 ¼ x5
ð14Þ
h6 ¼ h5
ð15Þ
S_ V 1 ¼ m_ 6 s6 m_ 5 s5
ð16Þ
Condenser m_ 9 ¼ m_ 10 ;
x9 ¼ x10
ð17Þ
m_ 9 h9 ¼ m_ 10 h10 þ Q_ c
ð18Þ
Q_ c S_ c ¼ m_ 10 s10 m_ 9 s9 þ To
ð19Þ
Condenser–evaporator heat exchanger (CEHX) T10 T11 ecehx ¼ T10 T13
ð20Þ
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m_ 10 h10 þ m_ 13 h13 ¼ m_ 11 h11 þ m_ 14 h14
ð21Þ
S_ cehx ¼ m_ 11 s11 þ m_ 14 s14 m_ 10 s10 m_ 13 s13
ð22Þ
Evaporator throttle valve ðV 2Þ m_ 11 ¼ m_ 12 ;
x11 ¼ x12
ð23Þ
h11 ¼ h12
ð24Þ
S_ V 2 ¼ m_ 12 s12 m_ 11 s11
ð25Þ
Evaporator m_ 12 ¼ m_ 13 ;
x12 ¼ x13
ð26Þ
m_ 13 h13 ¼ m_ 12 h12 þ Q_ e
ð27Þ
Q_ e S_ e ¼ m_ 13 s13 m_ 13 s13 To
ð28Þ
Rectifier m_ 7 ¼ m_ 9 þ m_ 8
ð29Þ
m_ 7 x7 ¼ m_ 9 x9 þ m_ 8 x8
ð30Þ
m_ 7 h7 ¼ m_ 9 h9 þ m_ 8 h8 þ Q_ r
ð31Þ
Q_ r S_ r ¼ m_ 8 s8 þ m_ 9 s9 m_ 7 s7 þ To
ð32Þ
COP ¼
Q_ e Q_ g þ W_ p
S_ tot ¼ S_ e þ S_ g þ S_ c þ S_ a þ S_ r þ S_ cehx þ S_ shx þ S_ p þ S_ v1 þ S_ v2
ð33Þ ð34Þ
Fig. 2 represents a two-stage ARS. We note that the left hand side of the system is similar to Fig. 1. The heat rejected by absorber 2 serves as the heat input for generator 1. Ammonia vapor at low pressure from the evaporator is divided between the two absorbers while ammonia vapor at high pressure from the rectifiers of the two-stages are combined before entering the condenser. Just like the single-stage ARS, the two-stage has one evaporator and one condenser, but it has two generators and two absorbers. Following a procedure similar to that of the single-stage discussed earlier, energy and mass balances, as well as entropy generation equations, for each component and the mixing streams of the two-stage system were obtained.
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Qr3 @ T0 Q r1@ T0
Qc @ To 25
27 Qr 2 @ T0
24
Rectifier3
Rectifier2 Q g @ Tg
9
23
Rectifier1
Condenser
22
28 8
Generator2
7
18
19
10 Generator1
Q a 2 @ T7
SHX2
3
4
14 CEHX
20
SHX1
17
V2 11
21
5
V3
2361
V1
13
2
Absorber2
16
6
12 26
1
29
Absorber1
Evaporator
15
Qa1 @ T o
W p2
Wp1
Q e @ Te
Fig. 2. Schematic of a two-stage ammonia–water absorption refrigeration system.
3. Numerical example A typical example, discussed by Herold et al. [9], is considered in this study to examine the variation in COP and total entropy generation of the ammonia–water ARSs at various operating conditions. For the single-stage system, the evaporator outlet saturation temperature is taken as )10 °C, the mass flow rate of solution through the pump is 1 kg/s, the saturated liquid leaving the absorber and condenser is at 40 °C and the difference in mass fraction of the two solution streams is 0.10. The evaporator produces saturated vapor with a mass fraction of 99.96% ammonia. The efficiency of the pump is 50%, while the effectivenesses of the SHX and CEHX are 100% and 95%, respectively. For the two-stage system, the vapor leaving rectifiers 1 and 3 has a mass ratio of 0.995, the efficiency of the pumps and the effectivenesses of the heat exchangers, the condenser and evaporator temperatures and the mass flow through pump 1 are the same as those for the single-stage system. The temperature of the refrigerant entering the second stage absorber is the same as that of the refrigerant leaving the first stage absorber. The temperature of the refrigerant leaving the second stage absorber is 0.10 °C higher than T4 . The mass fraction difference in the first stage solution cycle is 0.04, while that in the second stage is 0.06. Liquid leaving the absorbers and generators, and vapor leaving the generators and rectifiers are saturated. The vapor quality leaving the evaporator is 0.9. The properties for all states points, COP and total entropy generation for the ammonia–water ARSs are obtained using the Engineering Equation Solver (EES)
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Table 1 State points for the single-stage ammonia–water absorption refrigeration system and the calculated results Point
hi (kJ/kg)
mi (kg/s)
Pi (kPa)
Qi
si (kJ/kg/ K)
Ti (°C)
vi (m3 /kg)
xi (kg/ kg sol)
1 2 3 4 5 6 7 8 9 10 11 12 13 14
)43.25 )40.20 303.11 397.21 )0.71 )0.71 1544.09 260.56 1294.18 190.79 78.86 78.86 1259.13 1371.05
1.000 1.000 1.000 0.863 0.863 0.863 0.150 0.013 0.137 0.137 0.137 0.137 0.137 0.137
244.85 1555.76 1555.76 1555.76 1555.76 244.85 1555.76 1555.76 1555.76 1555.76 1555.76 244.85 244.85 244.85
0.000 )0.001 0.022 0.000 )0.001 )0.001 1.000 0.000 1.000 0.000 )0.001 0.109 0.998 1.001
0.47 0.48 1.46 1.64 0.53 0.54 4.88 1.35 4.17 0.66 0.29 0.32 4.87 5.25
40.00 40.45 110.06 130.31 40.45 40.71 107.33 107.36 44.07 40.00 16.88 )14.14 )10.00 37.39
0.001 0.001 0.004 0.001 0.001 0.001 0.110 0.001 0.083 0.002 0.002 0.055 0.512 0.605
0.3709 0.3709 0.3709 0.2709 0.2709 0.2709 0.9460 0.3709 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996
Calculated results COP ¼ 0:598 Q_ a ¼ 231 kW Q_ g ¼ 267:9 kW S_ cehx ¼ 0:001427 kW/K S_ p ¼ 0:004897 kW/K S_ v2 ¼ 0:004918 kW/K
S_ tot ¼ 0:1973 kW/K Q_ cehx ¼ 15:4 kW Q_ r ¼ 50:7 kW S_ c ¼ 0:03414 kW/K S_ r ¼ 0:03047 kW/K
W_ p ¼ 3:0 kW Q_ c ¼ 151 kW Q_ shx ¼ 343:3 kW S_ e ¼ 0:008259 kW/K S_ shx ¼ 0:01886
Q_ e ¼ 162:0 kW S_ a ¼ 0:07741 kW/K S_ g ¼ 0:01285 kW/K S_ v1 ¼ 0:00403 kW/K
software [11]. The design point results are presented in Tables 1 and 2, while the variation in COP and total entropy generation of the systems due to changes in heat exchangers effectivenesses, absorber and condenser temperatures and solution mass fraction differences in the circuits are also studied. These results are presented in Figs. 3–7.
4. Results and discussion Table 1 shows the thermodynamic properties of the single-stage ARS at all state points, while Table 2 shows the thermodynamic properties of the two-stage ARS at all state points. The predicted performance results of the single-stage and two-stage ARSs at the same evaporator temperature are shown in Table 3. The heat transfer and entropy generation for the absorbers, generators, rectifiers, solution heat exchangers and pumps for the two-stage ARS are also shown. At an evaporator temperature of )10 °C with the heat exchangers and pumps having the same effectivenesses and efficiencies, the results show that the two-stage system is more efficient, with a COP of 0.734 as against 0.598 for the single-stage system. On the other hand, the second law analysis via total entropy generation shows that the single state system is more efficient, since it has less energy dissipation of 0.1973 kW/K compared to 0.4627 kW/K, for the two-stage system. This seems to be contradictory, since a more efficient system should have the higher COP and the
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Table 2 State points for the two-stage ammonia–water absorption refrigeration system and the calculated results Point
hi (kJ/kg)
mi (kg/s)
Pi (kPa)
Qi
si (kJ/kg/ K)
Ti (°C)
vi (m3 /kg)
xi (kg/ kg sol)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
)48.62 )45.65 252.71 283.96 )34.16 )34.16 1521.46 235.40 1365.33 187.36 )36.71 )36.71 1123.94 1348.01 1348.01 423.43 426.20 777.80 840.46 466.13 466.13 2389.62 736.23 1568.12 1365.33 1348.01 1365.33 79.15 1381.88
1.000 1.000 1.000 0.938 0.938 0.938 0.066 0.004 0.062 0.079 0.079 0.079 0.079 0.079 0.016 0.270 0.270 0.270 0.253 0.253 0.253 0.062 0.043 0.019 0.079 0.062 0.016 0.003 0.016
277.97 1548.03 1548.03 1548.03 1548.03 277.97 1548.03 1548.03 1548.03 1548.03 1548.03 277.97 277.97 277.97 277.97 277.97 1548.03 1548.03 1548.03 1548.03 277.97 1548.03 1548.03 1548.03 1548.03 277.97 1548.03 1548.03 277.97
0.000 )0.001 0.009 0.000 )0.001 )0.001 1.000 0.000 1.000 0.000 )0.001 0.013 0.900 0.998 0.998 0.000 )0.001 0.021 0.000 )0.001 )0.001 1.000 0.001 1.000 0.996 0.998 1.000 0.000 1.001
0.464 0.469 1.331 1.399 0.486 0.491 4.827 1.285 4.392 0.662 )0.113 )0.105 4.299 5.115 5.115 1.479 1.483 2.313 2.329 1.455 1.458 6.259 2.222 4.943 4.393 5.115 4.392 0.830 5.225
40.0 40.4 103.8 111.4 40.4 40.7 102.7 102.8 67.1 40.0 )7.4 )11.0 )10.0 27.3 27.3 111.5 112.0 183.4 198.0 112.0 112.2 182.1 182.1 112.0 63.3 27.3 67.1 67.1 40.7
0.001 0.001 0.002 0.001 0.001 0.001 0.109 0.001 0.094 0.002 0.002 0.007 0.395 0.511 0.511 0.001 0.001 0.004 0.001 0.001 0.001 0.127 0.001 0.112 0.094 0.511 0.094 0.001 0.537
0.3913 0.3913 0.3913 0.3513 0.3513 0.3513 0.9562 0.3913 0.9950 0.9950 0.9950 0.9950 0.9950 0.9950 0.9950 0.0671 0.0671 0.0671 0.0071 0.0071 0.0071 0.3360 0.0671 0.9329 0.9950 0.9950 0.9950 0.5949 0.9950
Calculated results COP ¼ 0:734 Q_ a1 ¼ 100 kW Q_ cehx ¼ 18 kW Q_ r3 ¼ 8 kW S_ a1 ¼ 0:02597 kW/K S_ cehx ¼ 0:003231 kW/K S_ p2 ¼ 0:00361 kW/K S_ shx2 ¼ 0:002145 kW/K
S_ tot ¼ 0:4627 kW/K Q_ a2 ¼ 27 kW Q_ e ¼ 91 kW Q_ shx1 ¼ 298 kW S_ a2 ¼ 0:0363 kW/K S_ c ¼ 0:02262 kW/K S_ r1 ¼ 0:009632 kW/K S_ ¼ 0:004373 kW/K
W_ p1 ¼ 3:0 kW Q_ g ¼ 120 kW Q_ r1 ¼ 15 kW Q_ shx2 ¼ 95 kW S_ g1 ¼ 0:2275 kW/K S_ e ¼ 0:005954 kW/K S_ r2 ¼ 0:103 kW/K S_ v2 ¼ 0:000882 kW/K
W_ p2 ¼ 0:7 kW Q_ c ¼ 93 kW Q_ r2 ¼ 87 kW S_ g2 ¼ 0:00599 kW/K S_ p1 ¼ 0:00477 kW/K S_ shx1 ¼ 0:006064 kW/K S_ v3 ¼ 0:00059 kW/K
lower total energy dissipation. This can be explained from the fact that the increase in S_ tot of the two-stage ARS was primarily due to the introduction of more thermal components, as was also noted by Lee and Sherif [10]. A careful study of Table 3 reveals the effect of the two-stage system. While it reduced the energy input to the system from 267.9 kW for the single-stage to 120 kW; it also reduced the useful
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Table 3 Performance comparison of the single and two-stage Ammonia–Water absorption systems at an evaporator temperature of )10 °C Parameter
Single-stage
Double-stage
COP S_ tot (kW/K) Q_ e (kW) S_ e (kW/K) Q_ g (kW) S_ g (kW/K) Q_ a (kW) S_ a (kW/K) Q_ r (kW) S_ r (kW/K) W_ p (kW) S_ p (kW/K) Q_ cehx (kW) S_ cehx (kW/K) Q_ shx (kW) S_ shx (kW/K) Plow (kPa) Phigh (kPa)
0.5980 0.1973 162.0 0.008259 267.9 0.01285 231 0.07741 50.7 0.03047 3.0 0.004897 15.4 0.001427 343.3 0.01886 244.85 1555.76
0.734 0.4627 91.0 0.005954 120.0 0.23349 127 0.06227 110 0.112632 3.7 0.00838 18.0 0.003231 393 0.00821 277.97 1548.03
0.8 0.75
COP and Sgen (kW/K)
0.7 0.65
COPs
0.6
Stots
0.55
COPd
0.5
Stotd
0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1
1.1 1.2 1.3
Condender HX Effectiveness
Fig. 3. Effect of condenser–evaporator heat exchanger effectiveness on COP and S_ tot .
cooling load from 162 kW for the single-stage system to 91 kW. It is interesting to note that this reduction in the thermal energy is accompanied with high energy dissipation of 0.2335 kW/K in the generator of the two-stage system, 50.5% of the total entropy generation, compared to 0.01285
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1.4
COP and Sgen (kW/K)
1.3 1.2
COPs
1.1
Stots
1
COPd Stotd
0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Solution HX Effectiveness
Fig. 4. Effect of solution heat exchanger effectiveness on COP and S_ tot .
1.2 1.1 COPs
COP and Sgen (kW/K)
1
Stots
0.9
COPd
0.8
Stotd
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 10
15
20 25 30 35 40 45 50 55 60 Absorber Temperature (Deg. Celsius)
65
70
Fig. 5. Effect of absorber temperature on COP and S_ tot .
kW/K in the generator of the single-stage system. As discussed above, Lee and Sherif [10] attributed the better thermodynamic efficiency of the single-stage lithium bromide–water ARS over the two-stage and triple stage systems to the irreversibility in the additional heat exchange components present in multi-stage systems. They calculated the total entropy generation without studying the entropy contribution of each of the system components. The present study, however, has shown that the lesser thermal efficiency (higher-energy dissipation) of two-stage ARSs is due
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COPs
COP and Sgen (kW/K)
0.9
Stots COPd
0.8
Stotd
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
10
15
20 25 30 35 40 45 50 55 60 Condenser Outlet Temperature (Deg. Celsius)
65
70
Fig. 6. Effect of condenser outlet temperature on COP and S_ tot .
1.3 1.2 COPs
COP and Sgen (kW/K)
1.1
Stots
1
COPd Stotd
0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -10
-8
-6
-4
-2
0
2
4
6
8
10
Evaporator Temperature (Deg. Celsius)
Fig. 7. Effect of evaporator temperature on COP and S_ tot .
to the irreversibility in the generator as a result of the reduction in the generator heat requirement due to the introduction of more stages. It is important to emphasize, that the COP is sensitive to the output and input energies alone, and since the input energy is reduced by 55.2% while the cooling load is reduced by 43.8%, the COP is increased. Since the evaporator of the single-stage system is at )10 °C, it produced a load of 162 kW, while the two-stage system produced less cooling capacity, i.e. 91 kW at the same
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evaporator temperature with high energy dissipation. It seems that the COP is less sensitive to the dynamics of the ARSs, while the total entropy generation is more sensitive to the dynamics of the systems. It, therefore seems that the entropy generation criterion is a better performance measurement criterion than the COP, particularly if one is interested to examine the distribution of irreversible losses. Fig. 3 presents the effect of the condenser–evaporator effectiveness on COP and S_ tot . As expected, the COP of both the single-stage and two-stage ARSs increased with an increase in the effectiveness. However, the increase in the COP of the two-stage system (COPd ) is greater than the increase in the COP of the single-stage system (COPs ), while the total entropy generation of the two-stage system ðStotd Þ is greater than that of the single-stage system ðStots Þ, but the effect of changes in the effectivenesses is negligible on the total entropy generation of the two ammonia– water ARSs. The reason for this observation can be found in Table 3. The entropy generation of the condenser–evaporator heat exchanger contributes only 0.724% for the single-stage and 0.698% for the two-stage to the total entropy generation of each system, respectively. As explained above, the COP is more sensitive to changes in the working conditions of the evaporator and the generator or any other component that affects them, while the total entropy generation considers the effect of all the components. Fig. 4 shows the effect of the solution heat exchanger (SHX) effectivenesses on COP and Stot . For the two-stage ARS, there are two SHXs. An increase in the effectivenesses of the SHXs results in an increase in the COP and a decrease in Stot . This observation conforms with our expectation, since a more efficient system is expected to have a higher COP and less entropy generation. At an effectiveness of less that 50%, the increase in COPs and COPd are almost the same while the increase in COPd is greater than the increase in COPs for an effectiveness greater than 50%. As has been observed in Table 3 and Fig. 3, the entropy generation for the two-stage is greater than that of the single-stage, which suggests that the two-stage is less efficient, whereas the COP of the two-stage is greater than that of the single-stage, which suggests that the twostage is more efficient. The reason for the paradox has already been discussed earlier. Fig. 4 also indicates that the two-stage ARS is grossly inefficient without the SHXs since it has the same COP as the single-stage ARS and a higher total entropy generation than the single-stage ARS at a lower SHX effectiveness. Fig. 4 clearly shows that the SHX is one of the critical components of the ammonia–water ARSs, as its performance affected the COP and total entropy generation of the ARSs in the expected manner, i.e. an increase in COP corresponds to a decrease in total entropy generation. Fig. 5 shows the effect of absorber outlet temperature on COP and total entropy generation of the ARSs. For the two-stage system, the absorber in the first stage, i.e. absorber 1 is considered. Fig. 6 presents the effect of condenser outlet temperature on COP and total entropy generation of the ARSs. Both figures show that an increase in temperature results in a decrease in COP of both the single-stage and two-stage systems and an increase in the total entropy generation of the systems. As has been observed in Table 3 and Figs. 3 and 4, the entropy generation for the twostage is greater than that of the single-stage, which suggests that the two-stage is less efficient, while the COP of the two-stage is greater than that of the single-stage, which suggests that the two-stage is more efficient. The reason for the paradox has been discussed above. Fig. 7 shows the effect of the evaporator temperature on COP and total entropy generation of the ARSs. This figure shows that an increase in the evaporator temperature results in an increase in COP of both
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the single-stage and two-stage systems and a decrease in the total entropy generation of the systems.
5. Conclusions The second law of thermodynamics is used to study the performance of single-stage and twostage ammonia–water absorption refrigeration systems (ARSs) when some parameters are varied. The entropy generation of each component, the total entropy generation ðS_ tot Þ of all components and the COPs of the ARSs are calculated from the thermodynamic properties of the working fluids at various working conditions using the Engineering Equation Solver (EES) software. The results show that the total entropy generation for the two-stage is greater than that of the singlestage, which suggests that the two-stage is less efficient, while the COP of the two-stage is greater than that of the single-stage, which suggests that the two-stage is more efficient. This is a paradox. Both COP and S_ tot are measures of thermal performance and from established knowledge, a more efficient thermal system should have a higher COP and a lower S_ tot . However, what has been reported in the literature and what the results of this study show is a paradox. This observation deserves further investigation. It is important to note that the increase in S_ tot of the two-stage ARS was due to the introduction of more thermal components, as also noted by Lee and Sherif [10]. The present study, however, has shown that the high S_ tot (high energy dissipation) of multi-stage ARSs is due to the irreversibility in the generator as a result of the reduction in generator heat requirement due to the presence of more stages, since the generator produced above 50% of the total entropy generation in the two-stage ARS. We emphasize that the second law analysis used in this study also facilitated a means of identifying the components with high exergy dissipation.
Acknowledgements The authors acknowledge the support provided by King Fahd University of Petroleum and Minerals for this research project.
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