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Licensed Unlicensed Requires Authentication Published by De Gruyter July 21, 2021

The Role of Internal Irreversibilities in the Performance and Stability of Power Plant Models Working at Maximum ϵ-Ecological Function

  • Gabriel Valencia-Ortega EMAIL logo , Sergio Levario-Medina and Marco Antonio Barranco-Jiménez

Abstract

The proposal of models that account for the irreversibilities within the core engine has been the topic of interest to quantify the useful energy available during its conversion. In this work, we analyze the energetic optimization and stability (local and global) of three power plants, nuclear, combined-cycle, and simple-cycle ones, by means of the Curzon–Ahlborn heat engine model which considers a linear heat transfer law. The internal irreversibilities of the working fluid measured through the r-parameter are associated with the so-called “uncompensated Clausius heat.” In addition, the generalization of the ecological function is used to find operating conditions in three different zones, which allows to carry out a numerical analysis focused on the stability of power plants in each operation zone. We noted that not all power plants reveal stability in all the operation zones when irreversibilities are considered through the r-parameter on real-world power plants. However, an improved stability is shown in the zone limited by the maximum power output and maximum efficiency regimes.

Award Identifier / Grant number: 288669

Award Identifier / Grant number: 308401

Funding statement: The authors gratefully acknowledge to CONACyT Grants: 288669 and 308401.

References

[1] F. L. Curzon and B. Ahlborn, Efficiency of a Carnot engine at maximum power output, Am. J. Phys. 43 (1975), 22–24.10.1119/1.10023Search in Google Scholar

[2] M. Rubin, Optimal configuration of a class of irreversible heat engines I, Phys. Rev. A 19 (1979), 272–276.10.1103/PhysRevA.19.1277Search in Google Scholar

[3] A. De Vos, Efficiency of some heat engines at maximum-power conditions, Am. J. Phys. 53 (1985), 570–573.10.1119/1.14240Search in Google Scholar

[4] A. Bejan, Theory of heat transfer-irreversible power plants, Int. Heat Mass Transf. 31 (1988), 1211–1219.10.1016/0017-9310(88)90064-6Search in Google Scholar

[5] J. M. Gordon and M. Huleihil, General performance characteristics of real heat engines, J. Appl. Phys. 72 (1992), 829–837.10.1063/1.351755Search in Google Scholar

[6] C. Wu and R. L. Kiang, Finite-time thermodynamics analysis of a Carnot engine with internal irreversibility, Energy 17 (1992), 1173–1178.10.1016/0360-5442(92)90006-LSearch in Google Scholar

[7] S. Özcaynak, S. Göktun and H. Yavuz, Finite-time thermodynamics analysis of a radiative heat engine with internal irreversibility, J. Phys. D Appl. Phys. 27 (1994), 1139–1143.10.1088/0022-3727/27/6/010Search in Google Scholar

[8] J. Chen, The maximum power output and maximum efficiency of an irreversible Carnot heat engine, J. Phys. D Appl. Phys. 27 (1994), 1144–1149.10.1088/0022-3727/27/6/011Search in Google Scholar

[9] A. Fischer and K. H. Hoffmann, Can a quantitative simulation of an Otto engine be accurately rendered by a simple Novikov model with heat leak? J. Non-Equilib.Thermodyn. 29 (2005), 9–28.10.1515/JNETDY.2004.002Search in Google Scholar

[10] R. C. Tolman and P. C. Fine, On the irreversible production of entropy, Rev. Mod. Phys. 20 (1948), 51–77.10.1103/RevModPhys.20.51Search in Google Scholar

[11] J. J. Silva-Martinez and L. A. Arias-Hernandez, Energetic performance of a series arrangement of irreversible power cycles, Rev. Mex. Fis. 59 (2013), no. 1, 192–198.Search in Google Scholar

[12] S. Sieniutycz and P. Salamon, Finite Time Thermodynamics and Thermoeconomics, 1st ed., Taylor and Francis, New York, 1990.Search in Google Scholar

[13] K. H. Hoffmann, J. M. Burzler and S. Schubert, Endoreversible Thermodynamics, J. Non-Equilib. Thermodyn. 22 (1997), 311–355.Search in Google Scholar

[14] C. Wu, L. Chen and J. Chen, Recent Advances in Finite Time Thermodynamics, 1st ed., Nova Science, New York, 1999.Search in Google Scholar

[15] A. Durmayaz, O. S. Sogut, B. Sahin and H. Yavuz, Optimization of thermal systems based on finite-time thermodynamics and thermoeconomics, Prog. Energy Combust. Sci. 30 (2004), 175–217.10.1016/j.pecs.2003.10.003Search in Google Scholar

[16] L. Chen, X. Zhu, F. Sun and C. Wu, Exergy-based ecological optimization of linear phenomenological heat-transfer law irreversible Carnot-engines, Appl. Energy 83 (2006), 573–582.10.1016/j.apenergy.2005.05.004Search in Google Scholar

[17] C. Sullivan, Newton’s law of cooling–A critical assessment, Am. J. Phys. 58 (1990), 956–960.10.1119/1.16309Search in Google Scholar

[18] S. Levario-Medina, Estudio del desempeño energético de un motor térmico operando a potencia eficiente generalizada, Master Thesis, ESFM-IPN, Mexico, 2016 (in Spanish).Search in Google Scholar

[19] S. Levario-Medina, G. Valencia-Ortega and M. A. Barranco-Jiménez, Energetic Optimization Considering a Generalization of the Ecological Criterion in Traditional Simple-Cycle and Combined-Cycle Power Plants, J. Non-Equilib. Thermodyn. 45 (2020), 269–290.10.1515/jnet-2019-0088Search in Google Scholar

[20] P. L. Curto-Riso, A. Medina, A. Calvo Hernández, L. Guzmán-Vargas and F. Angulo-Brown, On cycle-to-cycle heat release variations in a simulated spark ignition heat engine, Appl. Energy 88 (2011), 1557–1567.10.1016/j.apenergy.2010.11.030Search in Google Scholar

[21] T. Yilmaz, A new performance criterion for heat engines: efficient power, J. Energy Inst. 79 (2006), 38–41.10.1179/174602206X90931Search in Google Scholar

[22] S. Velasco, J. M. M. Roco, A. Medina, J. A. White and A. Calvo-Hernández, Optimization of heat engines including the saving of natural resources and the reduction of thermal pollution, J. of Phys. D: App. Phys. 33 (2000), 355–359.10.1088/0022-3727/33/4/307Search in Google Scholar

[23] A. Calvo Hernández, A. Medina, J. M. M. Roco J.A. White and S. Velasco, Unified optimization criterion for energy converters, Phys. Rev. E 63 (2001), 037102.10.1103/PhysRevE.63.037102Search in Google Scholar PubMed

[24] F. Angulo-Brown, An ecological optimization criterion for finite-time heat engines, J. Appl. Phys. 69 (1991), 7465–7469.10.1063/1.347562Search in Google Scholar

[25] L. A. Arias-Hernandez and F. Angulo-Brown, A general property of endoreversible thermal engines, J. Appl. Phys. 81 (1997), 2973–2979.10.1063/1.364090Search in Google Scholar

[26] F. Angulo-Brown and L. A. Arias-Hernandez, Reply to “Comment on ‘A general property of endoreversible thermal engines’” [J. Appl. Phys. 89, 1518 (2001)], J. Appl. Phys. 89 (2001), 1520–1521.10.1063/1.1335619Search in Google Scholar

[27] L. Partido-Tornez, Aplicación de los criterios omega y ecológico generalizado a diferentes covertidores de energía, Master thesis, ESFM-IPN, Mexico, 2006 (in Spanish).Search in Google Scholar

[28] S. Levario-Medina, G. Valencia-Ortega and L. A. Arias-Hernandez, Thermal optimization of Curzon-Ahlborn heat engines operating under some generalized efficient power regimes, Eur. Phys. J. Plus 134 (2019), no. 348. 1–13.10.1140/epjp/i2019-12711-2Search in Google Scholar

[29] S. Levario-Medina, Estudio de algunas funciones compromiso y sus efectos en la optimización termodinámica en los modelos de convertidores de energía, Ph.D. thesis, ESFM-IPN, Mexico, 2021 (in Spanish).Search in Google Scholar

[30] M. Santillán, G. Maya and F. Angulo-Brown, Local stability analysis of an endoreversible Curzon-Ahlborn-Novikov engine working in a maximum-power-like regime, J. Phys. D: Appl. Phys. 34 (2001), 2068–2072.10.1088/0022-3727/34/13/318Search in Google Scholar

[31] L. Guzmán-Vargas, I. Reyes-Ramírez and N. Sánchez, The effect of heat transfer laws and thermal conductances on the local stability of an endoreversible heat engines, J. Phys. D: Appl. Phys. 38 (2005), 1282–1291.10.1088/0022-3727/38/8/028Search in Google Scholar

[32] R. T. Paéz-Hernández, F. Angulo-Brown and M. Santillán, Dynamics Robustness and Thermodynamics Optimization in a Non-Endoreversible Curzon-Ahlborn Engine, J. Non-Equilib. Thermodyn. 31 (2006), 173–188.10.1515/JNETDY.2006.008Search in Google Scholar

[33] I. Reyes-Ramírez, M. A. Barranco-Jiménez, A. Rojas-Pacheco and L. Guzmán-Vargas, Global stability analysis of a Curzon-Ahlborn heat engine using the Lyapunov method, Phys. A Stat. Mech. Appl. 399 (2014), 98–105.10.1016/j.physa.2013.12.044Search in Google Scholar

[34] L. G. Chen, X. H. Wu and X. W. Liu, Local Stability of a generalized irreversible heat engine with linear phenomenological heat transfer law working in an ecological regime, Therm. Sci. Eng. Prog. 8 (2018), 537–541.10.1016/j.tsep.2018.10.010Search in Google Scholar

[35] J. González-Ayala, J. Guo, A. Medina, J. M. M. Roco and A. Calvo-Hernández, Optimization induced by stability and the role of limited control near a steady state, Phys. Rev. E 100 (2019), 062128.10.1103/PhysRevE.100.062128Search in Google Scholar PubMed

[36] G. Valencia-Ortega, S. Levario-Medina and M. A. Barranco-Jiménez, Local and global stability analysis of a Curzon-Ahlborn model applied to power plants working at maximum k-efficient power, Phys. A Stat. Mech. Appl. 571 (2021), 125863.10.1016/j.physa.2021.125863Search in Google Scholar

[37] Y. Huang and D. Sun, Local Stability Analysis of a Non-Endoreversible Heat Pump, J. Non-Equilib. Thermodyn. 33 (2008), 61–74.10.1515/JNETDY.2008.004Search in Google Scholar

[38] X. H. Wu, L. G. Chen, Y. L. Ge and F. R. Sun, Local of an endoreversible Carnot heat pump with linear phenomenological heat transfer law working in an ecological regime, Scientia Iranica, Trans. B: Mech. Eng. 19 (2012), 1519–1525.10.1016/j.scient.2012.10.012Search in Google Scholar

[39] Y. Huang and D. Sun, The effect of cooling load and thermal conductance on the local stability of an endoreversible refrigerator, Int. J. Refrig. 31 (2008), 483–489.10.1016/j.ijrefrig.2007.07.004Search in Google Scholar

[40] X. Wu, L. Chen, Y. Ge and F. Sun, Local stability of a non-endoreversible Carnot refrigerator working at the maximum ecological function, Appl. Math. Model. 39 (2015), 1689–1700.10.1016/j.apm.2014.09.031Search in Google Scholar

[41] P. A. N. Wouagfack and G. Keune, Local stability analysis of an irreversible refrigerator working at the maximum thermoecological functions: a comparison, Int. J. Refrig. 65 (2017), 38–51.10.1016/j.ijrefrig.2017.01.006Search in Google Scholar

[42] G. Keune, P. A. N. Wouagfack and R. Tchinda, Local stability analysis of an irreversible absortion refrigerator powered by a wood boile, Int. J. Refrig. 115 (2020), 83–95.10.1016/j.ijrefrig.2020.02.027Search in Google Scholar

[43] G. Valencia-Ortega, S. Levario-Medina and M. A. Barranco-Jiménez, Thermal stability analysis of nuclear and fossil fuel power plants including the Dulong-Petit heat transfer law and economic features, Therm. Sci. Eng. Prog. 23 (2021), 1–12.10.1016/j.tsep.2021.100879Search in Google Scholar

[44] J. González-Ayala, A. Medina, J. M. M. Roco and A. Calvo Hernández, Thermodynamic optimization subsumed in stability phenomena, Sci. Rep. 10 (2020), 1–16.10.1038/s41598-020-71130-7Search in Google Scholar PubMed PubMed Central

[45] J. González-Ayala, J. M. M. Roco, A. Medina and A. Calvo Hernández, Optimization, Stability and Entropy in Endoreversible Heat Engines, Entropy 22 (2020), 1323.10.3390/e22111323Search in Google Scholar PubMed PubMed Central

[46] H. T. Odum and R. C. Pinkerton, Time’s speed regulator: the optimum efficiency for maximum power output in physical and biological systems, Am. Sci. 43 (1955), 331–343.Search in Google Scholar

[47] A. Bejan, G. Tsatsaronis and M. Moran, Thermal Design and Optimization, 1st ed., John Wiley & Sons, New York, 1996.Search in Google Scholar

[48] S. Petrescu, M. Costea, C. Harman and T. Florea, Application of the Direct Method to irreversible Stirling cycles with finite speed, Int. J. Energy Res. 26 (2002), 589–609.10.1002/er.806Search in Google Scholar

[49] M. Feidt, Finite Physical Dimension Optimal Thermodynamics 1-Fundamentals, 1st ed., ISTE Press Elsevier, London, 2017.10.1016/B978-1-78548-232-8.50001-7Search in Google Scholar

[50] R. Clausius, The Mechanical Theory of Heat, 1st ed., Mac Millan and Co., London, 1879.Search in Google Scholar

[51] L. García-Colín Scherer and P. Goldstein Menache, Procesos Irreversibles-Teoría y Aplicaciones 1, 1st ed., El Colegio Nacional, Mexico City, 2013 (in Spanish).Search in Google Scholar

[52] L. A. Arias-Hernandez, M. A. Barranco-Jiménez and F. Angulo-Brown, Comparative analysis of two ecological type modes of performance for a simple energy converter, J. Energy Inst. 82 (2009), 223–227.10.1179/014426009X12448189963432Search in Google Scholar

[53] L. Chen, D. Xia and F. Sun, Ecological optimization of generalized irreversible chemical engines, Int. J. Chem. React. Eng. 8 (2010), 2361.10.2202/1542-6580.2361Search in Google Scholar

[54] M. A. Barranco-Jiménez, A. Ocampo-García and F. Angulo-Brown, Thermodynamic analysis of an array of isothermal endoreversible electric engines, Eur. Phys. J. Plus 135 (2020), no. 153. 1–14.10.1140/epjp/s13360-019-00038-7Search in Google Scholar

[55] I. I. Novikov, The efficiency of atomic power stations (a review), J. Nucl. Energy 7 (1958), 125–128.10.1016/0891-3919(58)90244-4Search in Google Scholar

[56] F. Angulo-Brown and R. Páez-Hernández, Endoreversible thermal cycle with a nonlinear heat transfer law, J. Appl. Phys. 74 (1993), 2216–2219.10.1063/1.354728Search in Google Scholar

[57] L. Chen, F. Sun and C. Wu, Thermo-economics for endoreversible heat-engines, Appl. Energy 81 (2005), 388–396.10.1016/j.apenergy.2004.09.008Search in Google Scholar

[58] M. A. Ramírez-Moreno, S. González-Hernández and F. Angulo-Brown, The role of the Stefan-Boltzmann law in the thermodynamics optimization of an n-Müser engine, Phys. A Stat. Mech. Appl. 444 (2016), 914–921.10.1016/j.physa.2015.10.094Search in Google Scholar

[59] M. A. Barranco-Jiménez, R. T. Páez-Hernández, I. Reyes-Ramírez and L. Guzmán-Vargas, Local Stability Analysis of a Thermo-Economic Model of a Chambadal-Novikov-Curzon-Ahlborn Heat Engine, Entropy 16 (2011), 1584–1594.10.3390/e13091584Search in Google Scholar

[60] I. Reyes-Ramírez, M. A. Barranco-Jiménez, A. Rojas-Pacheco and L. Guzmán-Vargas, Global Stability Analysis of a Curzon-Ahlborn Heat Engine under Different Regimes of Performance, Entropy 16 (2014), 5796–5809.10.3390/e16115796Search in Google Scholar

[61] M. A. Barranco-Jiménez, N. Sánchez-Salas and I. Reyes-Ramírez, Local Stability Analysis for a Thermo-Economic Irreversible Heat Engine Model under Different Performance Regimes, Entropy 17 (2015), 8019–8030.10.3390/e17127860Search in Google Scholar

[62] H. Jeffreys, Asymptotic approximations, 1st ed., Claredon Press, Oxford, 1962.Search in Google Scholar

[63] S. H. Strogatz, Nonlinear Dynamics and Chaos with Applications to Physics, Biology, Chemistry and Engineering, 1st ed., Addison-Wesley Publishing Company, New York, 1994.10.1063/1.4823332Search in Google Scholar

[64] S. G. Tzafestas, Introduction to Mobile Robot Control, 1st ed., Elsevier, London, 2014.10.1016/B978-0-12-417049-0.00001-8Search in Google Scholar

[65] H. K. Khalil, Nonlinear Control, 1st ed., Pearson, London, 2015.Search in Google Scholar

Received: 2021-04-14
Revised: 2021-06-08
Accepted: 2021-07-01
Published Online: 2021-07-21
Published in Print: 2021-10-31

© 2021 Walter de Gruyter GmbH, Berlin/Boston

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