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Frontiers in Energy

ISSN 2095-1701

ISSN 2095-1698(Online)

CN 11-6017/TK

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2018 Impact Factor: 1.701

Front. Energy    2019, Vol. 13 Issue (2) : 399-410    https://doi.org/10.1007/s11708-017-0445-y
RESEARCH ARTICLE
Exergetic sustainability evaluation and optimization of an irreversible Brayton cycle performance
Mohammad H. AHMADI1(), Mohammad-Ali AHMADI2, Esmaeil ABOUKAZEMPOUR3, Lavinia GROSU4, Fathollah POURFAYAZ1, Mokhtar BIDI5
1. Department of Renewable Energies, Faculty of New Sciences and Technologies, University of Tehran, Tehran 1417466191, Iran
2. Department of Petroleum Engineering, Ahwaz Faculty of Petroleum Engineering, Petroleum University of Technology (PUT), Ahwaz 61963165, Iran
3. Graduate School of the Environment and Energy, Science and Research Branch, Islamic Azad University, Tehran 1417466191, Iran
4. University of Paris Ouest Nanterre La Defense, 50 rue Sevres, 92 410 Ville dAvray, France
5. Faculty of Mechanical & Energy Engineering, Shahid Beheshti University, A.C., Tehran 1417466191, Iran
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Abstract

Owing to the energy demands and global warming issue, employing more effective power cycles has become a responsibility. This paper presents a thermodynamical study of an irreversible Brayton cycle with the aim of optimizing the performance of the Brayton cycle. Moreover, four different schemes in the process of multi-objective optimization were suggested, and the outcomes of each scheme are assessed separately. The power output, the concepts of entropy generation, the energy, the exergy output, and the exergy efficiencies for the irreversible Brayton cycle are considered in the analysis. In the first scheme, in order to maximize the exergy output, the ecological function and the ecological coefficient of performance, a multi-objective optimization algorithm (MOEA) is used. In the second scheme, three objective functions including the exergetic performance criteria, the ecological coefficient of performance, and the ecological function are maximized at the same time by employing MOEA. In the third scenario, in order to maximize the exergy output, the exergetic performance criteria and the ecological coefficient of performance, a MOEA is performed. In the last scheme, three objective functions containing the exergetic performance criteria, the ecological coefficient of performance, and the exergy-based ecological function are maximized at the same time by employing multi-objective optimization algorithms. All the strategies are implemented via multi-objective evolutionary algorithms based on the NSGAII method. Finally, to govern the final outcome in each scheme, three well-known decision makers were employed.

Keywords entropy generation      exergy      Brayton cycle      ecological function      irreversibility     
Corresponding Author(s): Mohammad H. AHMADI   
Online First Date: 24 February 2017    Issue Date: 04 July 2019
 Cite this article:   
Mohammad H. AHMADI,Mohammad-Ali AHMADI,Esmaeil ABOUKAZEMPOUR, et al. Exergetic sustainability evaluation and optimization of an irreversible Brayton cycle performance[J]. Front. Energy, 2019, 13(2): 399-410.
 URL:  
https://academic.hep.com.cn/fie/EN/10.1007/s11708-017-0445-y
https://academic.hep.com.cn/fie/EN/Y2019/V13/I2/399
Fig.1  Ts diagram of irreversible Brayton cycles
Fig.2  Fitting curve for the cv
Fig.3  Fitting curve for the cp
Fig.4  Functional diagram of an irreversible Brayton cycle
Fig.5  Scheme for the multi-objective evolutionary algorithm used in the present study
Fig.6  Effects of the pressure ratio (x) at various values of the temperature of state point 1 (T1)
Fig.7  Effects of the temperature of state point 3 (T3)at various values of the temperature of state point 1 (T1 )
Fig.8  Pareto optimal frontier in the objectives’ space for first scenario
Decision making method Decision variables Objectives
hC hE T1/K T3/K x Ex/kW ECF/kW ECOP
TOPSIS 1.000 1.000 301.838 1199.908 5.553 511.919 101.859 1.502
LINMAP 1.000 1.000 301.383 1199.816 6.002 498.685 117.972 1.626
Fuzzy 1.000 1.000 335.300 1199.880 11.990 296.803 175.803 4.434
Tab.1  Decision making of multi-objective optimal solutions for first scenario
Decision making
Method
Objectives Max error/% Average error/%
TOPSIS Ex 1.695 1.100
ECF 9.169 4.956
ECOP 4.914 2.618
LINMAP Ex 6.333 3.311
ECF 25.489 10.991
ECOP 19.565 8.358
Fuzzy Ex 14.627 7.771
ECF 8.307 4.319
ECOP 16.782 10.030
Tab.2  Error analysis based on the mean absolute percent error (MAPE) method for first scenario
Fig.9  Pareto optimal frontier in the objectives’ space for second scenario
Decision making method Decision variables Objectives
hC hE T1/K T3/K x ECOP ECF/kW EPC
TOPSIS 1.000 1.000 349.880 1022.021 12.000 8.307 78.032 10.210
LINMAP 1.000 1.000 349.900 1032.834 12.000 7.962 83.805 9.828
Fuzzy 1.000 1.000 349.910 1124.969 12.000 5.933 130.245 7.581
Tab.3  Decision making of multi-objective optimal solutions for second scenario
Decision making
method
Objectives Max error/% Average error/%
TOPSIS Ex 1.695 1.100
ECF 9.169 4.956
ECOP 4.914 2.618
LINMAP Ex 6.333 3.311
ECF 25.489 10.991
ECOP 19.565 8.358
Fuzzy Ex 14.627 7.771
ECF 8.307 4.319
ECOP 16.782 10.030
Tab.4  Error analysis based on the mean absolute percent error (MAPE) method for second scenario
Fig.10  Pareto optimal frontier in the objectives’ space for third scenario
Decision making method Decision variables Objectives
hC hE T1/K T3/K x ECOP Ex/kW EPC
TOPSIS 1.000 1.000 349.467 1016.419 11.977 8.422 105.418 10.333
LINMAP 1.000 1.000 349.460 1018.815 11.978 8.336 107.448 10.237
Fuzzy 1.000 1.000 341.115 1195.147 11.450 4.415 293.156 5.839
Tab.5  Decision making of multi-objective optimal solutions for third scenario
Decision making
method
Objectives Max error/% Average error/%
TOPSIS ECOP 16.994 10.425
Ex 34.630 21.031
EPC 16.005 9.556
LINMAP ECOP 17.213 10.495
Ex 35.713 21.353
EPC 16.205 9.620
Fuzzy ECOP 9.433 5.424
Ex 6.826 4.183
EPC 7.711 4.501
Tab.6  Error analysis based on the mean absolute percent error (MAPE) method for third scenario
Fig.11  Pareto optimal frontier in the objectives’ space for fourth scenario
Decision making method Decision variables Objectives
hC hE T1/K T3/K x ECOP EECF/kW EPC
TOPSIS 1.000 1.000 339.033 1020.757 12.000 7.326 112.380 8.970
LINMAP 1.000 1.000 339.119 1026.538 12.000 7.186 116.445 8.819
Fuzzy 1.000 1.000 339.177 1171.013 11.996 4.846 220.405 6.278
Tab.7  Decision making of multi-objective optimal solutions for last scenario
Decision making
Method
Objectives Max error/% Average error/%
TOPSIS ECOP 28.972 14.073
EECF 36.983 16.038
EPC 26.630 13.726
LINMAP ECOP 29.063 13.941
EECF 36.409 15.741
EPC 26.671 13.570
Fuzzy ECOP 14.066 7.638
EECF 16.331 7.000
EPC 12.494 7.493
Tab.8  Error analysis based on the mean absolute percent error (MAPE) method for last scenario
cp Specific heats at constant pressure
cv Specific heats at constant volum
ECOP Ecological coefficient of performance
E ˙x Exergy flow
ECF Ecological function
EPC Exergetic performance criteria
EECF Exergy-based ecological function
nex The exergy efficiency
MAW Maximum available work
Q Heat
S ˙ge n Entropy generation rate
T1 Temperature of state point 1
T3 Temperature of state point 3
W ˙ Power
x The pressure ratio
m ˙ Mass flow rate
Subscript
ηC compression efficiency
ηE Expansion efficiency
η Energy efficiency
  
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