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Optimization of cogeneration systems under alternative performance criteria
Energy Conversion and Management 45 (2004) 939–945 www.elsevier.com/locate/enconman
Optimization of cogeneration systems under alternative performance criteria Tamer Yilmaz
*
Department of Naval Architecture, Yıldız Technical University, Besiktas 80750, Istanbul, Turkey Received 10 October 2002; received in revised form 17 March 2003; accepted 16 July 2003
Abstract In this study, a performance analysis based on alternative performance criteria has been performed for a reversible Carnot cycle, modified for cogeneration, with external irreversibilities. The optimum values of the design parameters of the cogeneration cycle were determined for different criteria. In this context, the effects of design parameters on the exergetic performance are investigated, and the results are discussed. The obtained results may guide towards a more realistic criterion for actual cogeneration plants. Ó 2003 Elsevier Ltd. All rights reserved. Keywords: Performance criteria; Performance optimization; Cogeneration cycle; Reversible Carnot
1. Introduction Cogeneration is widely used in the chemistry, textile and paper industries, which need electric power and heat together, and it reduces the energy cost almost 50%. In the past, many studies on performance analysis have been conducted for cogeneration systems using classical and finite time thermodynamics [1–6]. Usually, in these studies, different performance criteria, such as exergy, thermoeconomics and ecological benefits, have been investigated. No performance analysis based on compared performance criteria was found in the literature about cogeneration plants using classical or finite time thermodynamics. In this study, an investigation of a cogeneration cycle has been conducted by using alternative performance criteria. In the analysis, a reversible Carnot cycle is modified for cogeneration with external irreversibilities of heat transfer. The effects of the ratio of power to heat demanded by the
*
Fax: +90-212-258-2157/958-2157. E-mail address: [email protected] (T. Yilmaz).
0196-8904/$ - see front matter Ó 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0196-8904(03)00191-2
940
T. Yilmaz / Energy Conversion and Management 45 (2004) 939–945
Nomenclature E_ Q_ R S T W_ a, c, d g / w
exergy rate rate of heat transfer power to process heat ratio entropy temperature power generated from cogeneration system thermal conductances in the heat source, heat sink and heat consumer sides, respectively efficiency ratio of heat source to heat sink temperature ratio of heat consumer to heat sink temperature
Subscripts CA Curzon–Ahlborn H heat source L heat sink K heat consumer max maximum X warm working fluid Y cold working fluid Z process working fluid T total Superscripts dimensionless * optimum
heat consumer process, extreme temperatures and heat consumer temperature on the global and optimal performances have been determined and discussed.
2. The theoretical model The model of a reversible Carnot cycle for a cogeneration system and its T –S diagram are shown in Fig. 1. In the model, the external irreversibilities of heat transfer are considered, and other irreversibilities are neglected. The shown cogeneration cycle model operates between three heat reservoirs of temperatures TH , TL and TK . The temperatures of the working fluids exchanging heat with the reservoirs at TH , TL and TK are TX , TY and TZ , respectively. In the cycle, Q_ H is the rate of heat transfer from the heat source at temperature TH to the warm working fluid at constant temperature TX in process 2–3, Q_ L is the rate of heat transfer from the cold working fluid at constant temperature TY to the heat sink at temperature TL in process 6–1 and Q_ K is the rate of
T. Yilmaz / Energy Conversion and Management 45 (2004) 939–945
941
T
.
QH
TH
TH
TX
TX
. QH 3
2
.
TZ
TK
. QK
W
5
TZ
. QL
TK TY
TY
TL
1
. QL
. 4 QK
6
TL S
Fig. 1. A reversible Carnot cycle for cogeneration system and its T –S diagram.
heat transfer from the working fluid at constant temperature TZ to the heat consuming device at temperature TK in process 4–5. The model given in Fig. 1 is an appropriate model for cogeneration plants in practice that have pass out condensing steam turbines. In these plants, some steam is extracted from the turbine at an intermediate pressure and transferred to a heat consumer for any heating process. Then, the condensate is returned to the plant. This operation is equivalent to process 4–5 in the given model for a closed system with the only exception that the heat transfer takes place without mass transfer. When the heat transfer obeys NewtonÕs law, we can write Q_ H ¼ aðTH TX Þ;
ð1Þ
Q_ L ¼ bðTY TL Þ;
ð2Þ
Q_ K ¼ cðTZ TK Þ;
ð3Þ
where a, b and c are the thermal conductances of the heat source, heat sink and heat consumer sides, respectively. The power output of the cogeneration cycle according to the first law is W_ ¼ Q_ H Q_ L Q_ K :
ð4Þ
Substituting Eqs. (1)–(3) into Eq. (4), the power output becomes W_ ¼ aðTH TX Þ bðTY TL Þ cðTZ TK Þ:
ð5Þ
The exergy rate of the power output is E_ W ¼ W_ ;
ð6Þ
and the exergy rate of the process heat is E_ Q ¼ Q_ K ð1 TL =TZ Þ;
ð7Þ
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T. Yilmaz / Energy Conversion and Management 45 (2004) 939–945
where TL in this equation is taken to be the environment temperature. Then, the total exergy rate delivered by the cogeneration system is E_ T ¼ E_ W þ E_ Q :
ð8Þ
By using Eqs. (3), (5)–(7) in Eq. (8), it becomes E_ T ¼ aðTH TX Þ bðTY TL Þ cðTZ TK ÞTL =TZ :
ð9Þ
The second law of thermodynamics applied to the cycle requires that aðTH TX Þ=TX bðTY TL Þ=TY cðTZ TK Þ=TZ ¼ 0:
ð10Þ
We also require that the ratio of power to the heat demanded by the heat consumer be known and constant, i.e ½aðTH TX Þ bðTY TL Þ cðTZ TK Þ=cðTZ TK Þ ¼ R:
ð11Þ
After adopting the above definitions, alternative performance criteria can be defined as follows: ii(i) Energy utilization factor [5] Energy utilization factor (EUF) can be defined by using Eqs. (1), (3) and (4) as EUF ¼
W_ þ Q_ K bðTY TL Þ : ¼1 aðTH TX Þ Q_ H
ð12Þ
EUF has the advantage of simplicity. However, EUF cannot discriminate the quality difference between work and heat. i(ii) Artificial thermal efficiency [5] An alternative performance criterion is the artificial thermal efficiency (gA ). The energy given to the cogeneration plant (QH ) is supposed to be reduced by the consuming heat rate (Q_ K ). The artificial thermal efficiency is then given by gA ¼
W_ bðTY TL Þ ¼1 aðTH TX Þ cðTZ TK Þ Q_ H Q_ K
ð13Þ
(iii) Exergy efficiency [5,6] The exergy efficiency describes the quality difference of energy with the parameter exergy, so this criterion is more reasonable. The exergy efficiency (gE ) can be defined as gE ¼
E_ T aðTH TX Þ bðTY TL Þ cðTZ TK ÞTL =TZ ¼ aðTH TX Þ Q_ H
ð14Þ
It is possible to optimize the total exergy output given in Eq. (9), the energy utilization factor given in Eq. (12), the artificial thermal efficiency given in Eq. (13) and the exergy efficiency given in Eq. (14) with respect to TX , TY and TZ using the constraints given in Eqs. (10) and (11). This optimization has been performed numerically, and the results have been discussed in the next section.
T. Yilmaz / Energy Conversion and Management 45 (2004) 939–945
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3. Performance analysis The variations of the dimensionless total exergy rate (E_ ¼ E_ T =aTL ) with respect to EUF, gA and gE for various R (ratio of power output to process heat) are shown in Fig. 2a–c, respectively. As can be seen from Fig. 2, the maximum values of the total exergy rate (E_ max ) decrease with increasing R. The EUF at maximum exergy rate (EUF ) and the exergy efficiency at maximum exergy rate (gE ) increases with decreasing R, however, the artificial thermal efficiency at maximum exergy rate (gA ) increases rapidly with decreasing R until R ¼ 1 and then gradually decreases after R ¼ 1. This result can be observed more clearly in Fig. 3, which shows the variations of EFU , gA and gE with respect to R. It is interesting to observe that for a cogeneration system, the performance criteria investigation can be divided into two different regions, 0 < R < 1 and 1 < R < 1. For the first region, the evolution of the artificial thermal efficiency at maximum exergy rate is more critical than the other criteria. The maximum value of the optimal artificial thermal efficiency will be obtained for R ¼ 1. It can also be observed from the figure that if R increases, the values of the performance criteria get closer together, and for the R ! 1 limit case, they reach the same value. This value is the thermal efficiency at maximum power output forp anffiffiffiffiffiffiffiffiffiffiffiffi endoreversible ffi heat engine, and it is known as the Curzon–Ahlborn efficiency [7] (gCA ¼ 1 TL =TH ). The effects of the process heat temperature ratio (w ¼ TK =TL ) on the optimal performance criteria can be seen in Fig. 4. While EUF and gA are gradually decreasing with increasing process
0.9
0.9
R=0.1
0.8 0.7
0.8
R=0.5
0.6
. E
R=0.5
0.6
R=1
0.5 0.4
0.5
. E
R=2
R=2
0.3
R=4
0.2
R=1
0.4
0.3
0.2
R=20
0.1
R=20
0.1
0
R=4
0
0
(a)
R=0.1
0.7
0.2
0.4
0.6
0.8
1
0
0.2
0.4
0.6
0.8
1
ηA
(b)
EUF 0.9
R=0.1 R=0.5 R=1 R=2 R=4 R=20
0.8 0.7 0.6
. E
0.5 0.4 0.3 0.2 0.1 0 0
(c)
0.1
0.2
0.3
0.4
ηE
0.5
0.6
0.7
0.8
Fig. 2. Variations of normalized total exergy rate with respect to EUF: (a) gA ; (b) gE and (c) for different R (w ¼ 1:67, / ¼ 4, a ¼ b ¼ c).
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T. Yilmaz / Energy Conversion and Management 45 (2004) 939–945 0.9 0.8
EUF* EUF*
0.7
η *A
0.6
η *E
0.5
η*A η*E
0.4 0.3 0
2
4
6
8
10
R
Fig. 3. Variations of the optimal performance criteria with respect to R (w ¼ 1:67, / ¼ 4, a ¼ b ¼ c).
0.9 0.8
EUF*
η*A
0.7
η*A
0.6 0.5
η*E
EUF*
η*E
0.4 0.3 0.2 1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2
Ψ
Fig. 4. Variations of the optimal performance criteria with respect to w (R ¼ 1, / ¼ 4, a ¼ b ¼ c).
heat temperature ratio, gE stays approximately constant. For small values of w, the optimal artificial thermal efficiency is greater than the optimal exergy efficiency, but after w ¼ 1:8, the optimal artificial thermal efficiency is smaller than the optimal exergy efficiency. Since the extreme temperature ratio (/ ¼ TH =TL ) is one of the most important parameters for any heat engine, the effect of this parameter on the alternative performance criteria for a cogeneration cycle is investigated, and the obtained results are presented in Fig. 5. As can be seen from the figure, the optimal performance criteria increase with increasing /, and the EUF is greater than the other performance criteria for all value of /. The optimal artificial thermal efficiency and exergy efficiency have the same value for / ¼ 3:5.
T. Yilmaz / Energy Conversion and Management 45 (2004) 939–945
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0.9 0.8
EUF* EUF* 0.7
η*A η*E
η*A
0.6
η*E
0.5 0.4 0.3 0.2 2
3
4
5
6
7
8
φ
Fig. 5. Variations of the optimal performance criteria with respect to / (R ¼ 1, w ¼ 1:67, a ¼ b ¼ c).
4. Conclusion In this study, alternative performance criteria have been investigated for a reversible Carnot cycle modified for a cogeneration system with external irreversibilities. The effects of different operating conditions on these performance criteria have been evaluated and the results discussed. At the end of the investigation, it is observed that R ¼ 1 is a critical value for the optimal artificial thermal efficiency. If the process heat is equal to the work output, then the optimal artificial thermal efficiency has a maximum value. On the other hand, R has a negative effect on the energy utilization factor and the exergy efficiency. Increasing the consuming side temperature (TK ) decreases all of the performance criteria, and increasing the extreme temperature ratio (TH =TL ) increases all of the performance criteria. Finally, it is shown that the EUF is greater than the optimal artificial thermal efficiency and exergy efficiency for all cases.
References [1] [2] [3] [4]
Lucas K. On the thermodynamics of cogeneration. Int J Therm Sci 2000;39:1039–46. Bilgen E. Exergetic and engineering analyses of gas turbine based cogeneration systems. Energy 2000;25:1215–29. Habib MA. Thermodynamic analysis of the performance of cogeneration plants. Energy, Int J 1992;17:485–91. Guarinello F, Cerqueira SAAG, Nebra SA. Thermoeconomic evaluation of a gas turbine cogeneration system. Energy Conver Manage 2000;41:1191–200. [5] Feng X, Cai Y, Qian L. A new performance criterion for cogeneration system. Energy Conver Manage 1998;39:1607–9. [6] S ß ahin B, Kodal A, Ekmekcßi I, Yilmaz T. Exergy optimization for an endoreversible cogeneration cycle. Energy 1997;22:551–7. [7] Curzon FL, Ahlborn B. Efficiency of a Carnot engine at maximum power conditions. Am J Phys 1975;43:22–4.
Optimization of cogeneration systems under alternative performance criteria Tamer Yilmaz
*
Department of Naval Architecture, Yıldız Technical University, Besiktas 80750, Istanbul, Turkey Received 10 October 2002; received in revised form 17 March 2003; accepted 16 July 2003
Abstract In this study, a performance analysis based on alternative performance criteria has been performed for a reversible Carnot cycle, modified for cogeneration, with external irreversibilities. The optimum values of the design parameters of the cogeneration cycle were determined for different criteria. In this context, the effects of design parameters on the exergetic performance are investigated, and the results are discussed. The obtained results may guide towards a more realistic criterion for actual cogeneration plants. Ó 2003 Elsevier Ltd. All rights reserved. Keywords: Performance criteria; Performance optimization; Cogeneration cycle; Reversible Carnot
1. Introduction Cogeneration is widely used in the chemistry, textile and paper industries, which need electric power and heat together, and it reduces the energy cost almost 50%. In the past, many studies on performance analysis have been conducted for cogeneration systems using classical and finite time thermodynamics [1–6]. Usually, in these studies, different performance criteria, such as exergy, thermoeconomics and ecological benefits, have been investigated. No performance analysis based on compared performance criteria was found in the literature about cogeneration plants using classical or finite time thermodynamics. In this study, an investigation of a cogeneration cycle has been conducted by using alternative performance criteria. In the analysis, a reversible Carnot cycle is modified for cogeneration with external irreversibilities of heat transfer. The effects of the ratio of power to heat demanded by the
*
Fax: +90-212-258-2157/958-2157. E-mail address: [email protected] (T. Yilmaz).
0196-8904/$ - see front matter Ó 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0196-8904(03)00191-2
940
T. Yilmaz / Energy Conversion and Management 45 (2004) 939–945
Nomenclature E_ Q_ R S T W_ a, c, d g / w
exergy rate rate of heat transfer power to process heat ratio entropy temperature power generated from cogeneration system thermal conductances in the heat source, heat sink and heat consumer sides, respectively efficiency ratio of heat source to heat sink temperature ratio of heat consumer to heat sink temperature
Subscripts CA Curzon–Ahlborn H heat source L heat sink K heat consumer max maximum X warm working fluid Y cold working fluid Z process working fluid T total Superscripts dimensionless * optimum
heat consumer process, extreme temperatures and heat consumer temperature on the global and optimal performances have been determined and discussed.
2. The theoretical model The model of a reversible Carnot cycle for a cogeneration system and its T –S diagram are shown in Fig. 1. In the model, the external irreversibilities of heat transfer are considered, and other irreversibilities are neglected. The shown cogeneration cycle model operates between three heat reservoirs of temperatures TH , TL and TK . The temperatures of the working fluids exchanging heat with the reservoirs at TH , TL and TK are TX , TY and TZ , respectively. In the cycle, Q_ H is the rate of heat transfer from the heat source at temperature TH to the warm working fluid at constant temperature TX in process 2–3, Q_ L is the rate of heat transfer from the cold working fluid at constant temperature TY to the heat sink at temperature TL in process 6–1 and Q_ K is the rate of
T. Yilmaz / Energy Conversion and Management 45 (2004) 939–945
941
T
.
QH
TH
TH
TX
TX
. QH 3
2
.
TZ
TK
. QK
W
5
TZ
. QL
TK TY
TY
TL
1
. QL
. 4 QK
6
TL S
Fig. 1. A reversible Carnot cycle for cogeneration system and its T –S diagram.
heat transfer from the working fluid at constant temperature TZ to the heat consuming device at temperature TK in process 4–5. The model given in Fig. 1 is an appropriate model for cogeneration plants in practice that have pass out condensing steam turbines. In these plants, some steam is extracted from the turbine at an intermediate pressure and transferred to a heat consumer for any heating process. Then, the condensate is returned to the plant. This operation is equivalent to process 4–5 in the given model for a closed system with the only exception that the heat transfer takes place without mass transfer. When the heat transfer obeys NewtonÕs law, we can write Q_ H ¼ aðTH TX Þ;
ð1Þ
Q_ L ¼ bðTY TL Þ;
ð2Þ
Q_ K ¼ cðTZ TK Þ;
ð3Þ
where a, b and c are the thermal conductances of the heat source, heat sink and heat consumer sides, respectively. The power output of the cogeneration cycle according to the first law is W_ ¼ Q_ H Q_ L Q_ K :
ð4Þ
Substituting Eqs. (1)–(3) into Eq. (4), the power output becomes W_ ¼ aðTH TX Þ bðTY TL Þ cðTZ TK Þ:
ð5Þ
The exergy rate of the power output is E_ W ¼ W_ ;
ð6Þ
and the exergy rate of the process heat is E_ Q ¼ Q_ K ð1 TL =TZ Þ;
ð7Þ
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T. Yilmaz / Energy Conversion and Management 45 (2004) 939–945
where TL in this equation is taken to be the environment temperature. Then, the total exergy rate delivered by the cogeneration system is E_ T ¼ E_ W þ E_ Q :
ð8Þ
By using Eqs. (3), (5)–(7) in Eq. (8), it becomes E_ T ¼ aðTH TX Þ bðTY TL Þ cðTZ TK ÞTL =TZ :
ð9Þ
The second law of thermodynamics applied to the cycle requires that aðTH TX Þ=TX bðTY TL Þ=TY cðTZ TK Þ=TZ ¼ 0:
ð10Þ
We also require that the ratio of power to the heat demanded by the heat consumer be known and constant, i.e ½aðTH TX Þ bðTY TL Þ cðTZ TK Þ=cðTZ TK Þ ¼ R:
ð11Þ
After adopting the above definitions, alternative performance criteria can be defined as follows: ii(i) Energy utilization factor [5] Energy utilization factor (EUF) can be defined by using Eqs. (1), (3) and (4) as EUF ¼
W_ þ Q_ K bðTY TL Þ : ¼1 aðTH TX Þ Q_ H
ð12Þ
EUF has the advantage of simplicity. However, EUF cannot discriminate the quality difference between work and heat. i(ii) Artificial thermal efficiency [5] An alternative performance criterion is the artificial thermal efficiency (gA ). The energy given to the cogeneration plant (QH ) is supposed to be reduced by the consuming heat rate (Q_ K ). The artificial thermal efficiency is then given by gA ¼
W_ bðTY TL Þ ¼1 aðTH TX Þ cðTZ TK Þ Q_ H Q_ K
ð13Þ
(iii) Exergy efficiency [5,6] The exergy efficiency describes the quality difference of energy with the parameter exergy, so this criterion is more reasonable. The exergy efficiency (gE ) can be defined as gE ¼
E_ T aðTH TX Þ bðTY TL Þ cðTZ TK ÞTL =TZ ¼ aðTH TX Þ Q_ H
ð14Þ
It is possible to optimize the total exergy output given in Eq. (9), the energy utilization factor given in Eq. (12), the artificial thermal efficiency given in Eq. (13) and the exergy efficiency given in Eq. (14) with respect to TX , TY and TZ using the constraints given in Eqs. (10) and (11). This optimization has been performed numerically, and the results have been discussed in the next section.
T. Yilmaz / Energy Conversion and Management 45 (2004) 939–945
943
3. Performance analysis The variations of the dimensionless total exergy rate (E_ ¼ E_ T =aTL ) with respect to EUF, gA and gE for various R (ratio of power output to process heat) are shown in Fig. 2a–c, respectively. As can be seen from Fig. 2, the maximum values of the total exergy rate (E_ max ) decrease with increasing R. The EUF at maximum exergy rate (EUF ) and the exergy efficiency at maximum exergy rate (gE ) increases with decreasing R, however, the artificial thermal efficiency at maximum exergy rate (gA ) increases rapidly with decreasing R until R ¼ 1 and then gradually decreases after R ¼ 1. This result can be observed more clearly in Fig. 3, which shows the variations of EFU , gA and gE with respect to R. It is interesting to observe that for a cogeneration system, the performance criteria investigation can be divided into two different regions, 0 < R < 1 and 1 < R < 1. For the first region, the evolution of the artificial thermal efficiency at maximum exergy rate is more critical than the other criteria. The maximum value of the optimal artificial thermal efficiency will be obtained for R ¼ 1. It can also be observed from the figure that if R increases, the values of the performance criteria get closer together, and for the R ! 1 limit case, they reach the same value. This value is the thermal efficiency at maximum power output forp anffiffiffiffiffiffiffiffiffiffiffiffi endoreversible ffi heat engine, and it is known as the Curzon–Ahlborn efficiency [7] (gCA ¼ 1 TL =TH ). The effects of the process heat temperature ratio (w ¼ TK =TL ) on the optimal performance criteria can be seen in Fig. 4. While EUF and gA are gradually decreasing with increasing process
0.9
0.9
R=0.1
0.8 0.7
0.8
R=0.5
0.6
. E
R=0.5
0.6
R=1
0.5 0.4
0.5
. E
R=2
R=2
0.3
R=4
0.2
R=1
0.4
0.3
0.2
R=20
0.1
R=20
0.1
0
R=4
0
0
(a)
R=0.1
0.7
0.2
0.4
0.6
0.8
1
0
0.2
0.4
0.6
0.8
1
ηA
(b)
EUF 0.9
R=0.1 R=0.5 R=1 R=2 R=4 R=20
0.8 0.7 0.6
. E
0.5 0.4 0.3 0.2 0.1 0 0
(c)
0.1
0.2
0.3
0.4
ηE
0.5
0.6
0.7
0.8
Fig. 2. Variations of normalized total exergy rate with respect to EUF: (a) gA ; (b) gE and (c) for different R (w ¼ 1:67, / ¼ 4, a ¼ b ¼ c).
944
T. Yilmaz / Energy Conversion and Management 45 (2004) 939–945 0.9 0.8
EUF* EUF*
0.7
η *A
0.6
η *E
0.5
η*A η*E
0.4 0.3 0
2
4
6
8
10
R
Fig. 3. Variations of the optimal performance criteria with respect to R (w ¼ 1:67, / ¼ 4, a ¼ b ¼ c).
0.9 0.8
EUF*
η*A
0.7
η*A
0.6 0.5
η*E
EUF*
η*E
0.4 0.3 0.2 1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2
Ψ
Fig. 4. Variations of the optimal performance criteria with respect to w (R ¼ 1, / ¼ 4, a ¼ b ¼ c).
heat temperature ratio, gE stays approximately constant. For small values of w, the optimal artificial thermal efficiency is greater than the optimal exergy efficiency, but after w ¼ 1:8, the optimal artificial thermal efficiency is smaller than the optimal exergy efficiency. Since the extreme temperature ratio (/ ¼ TH =TL ) is one of the most important parameters for any heat engine, the effect of this parameter on the alternative performance criteria for a cogeneration cycle is investigated, and the obtained results are presented in Fig. 5. As can be seen from the figure, the optimal performance criteria increase with increasing /, and the EUF is greater than the other performance criteria for all value of /. The optimal artificial thermal efficiency and exergy efficiency have the same value for / ¼ 3:5.
T. Yilmaz / Energy Conversion and Management 45 (2004) 939–945
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0.9 0.8
EUF* EUF* 0.7
η*A η*E
η*A
0.6
η*E
0.5 0.4 0.3 0.2 2
3
4
5
6
7
8
φ
Fig. 5. Variations of the optimal performance criteria with respect to / (R ¼ 1, w ¼ 1:67, a ¼ b ¼ c).
4. Conclusion In this study, alternative performance criteria have been investigated for a reversible Carnot cycle modified for a cogeneration system with external irreversibilities. The effects of different operating conditions on these performance criteria have been evaluated and the results discussed. At the end of the investigation, it is observed that R ¼ 1 is a critical value for the optimal artificial thermal efficiency. If the process heat is equal to the work output, then the optimal artificial thermal efficiency has a maximum value. On the other hand, R has a negative effect on the energy utilization factor and the exergy efficiency. Increasing the consuming side temperature (TK ) decreases all of the performance criteria, and increasing the extreme temperature ratio (TH =TL ) increases all of the performance criteria. Finally, it is shown that the EUF is greater than the optimal artificial thermal efficiency and exergy efficiency for all cases.
References [1] [2] [3] [4]
Lucas K. On the thermodynamics of cogeneration. Int J Therm Sci 2000;39:1039–46. Bilgen E. Exergetic and engineering analyses of gas turbine based cogeneration systems. Energy 2000;25:1215–29. Habib MA. Thermodynamic analysis of the performance of cogeneration plants. Energy, Int J 1992;17:485–91. Guarinello F, Cerqueira SAAG, Nebra SA. Thermoeconomic evaluation of a gas turbine cogeneration system. Energy Conver Manage 2000;41:1191–200. [5] Feng X, Cai Y, Qian L. A new performance criterion for cogeneration system. Energy Conver Manage 1998;39:1607–9. [6] S ß ahin B, Kodal A, Ekmekcßi I, Yilmaz T. Exergy optimization for an endoreversible cogeneration cycle. Energy 1997;22:551–7. [7] Curzon FL, Ahlborn B. Efficiency of a Carnot engine at maximum power conditions. Am J Phys 1975;43:22–4.