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Ecological optimization of an irreversible Diesel cycle

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Abstract

Applying finite-time thermodynamics and air standard assumption, the irreversible Diesel cycle model is established with friction loss, heat transfer loss and internal irreversibility loss considered. Calculating the entropy generation rate by loss items, the cycle ecological function performance is optimized. The performance characteristics of ecological function and entropy generation rate are derived, and the impacts of three losses on ecological function performance are examined by the numerical method. The work in this paper can provide some guidelines for designers and manufacturers to assess the practical Diesel cycle performance.

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Abbreviations

A :

Heat rate released by fuel (kW)

B :

Constant related to heat transfer (\({\text{kJ}}\;{\text{kg}}^{ - 1} \;{\text{K}}^{ - 1}\))

C :

Specific heat (kJ·kg−1·K−1)

E :

Ecological function (kW)

L :

Stroke length (m)

m :

Mass flow rate (kg/s)

n :

Cycles running during one second

P :

Power output (kW)

Q :

Heat rate of added or rejected by the working fluid (kW)

T :

Temperature (K)

V :

Volume (m3)

\(\gamma\) :

Compression ratio

\(\eta\) :

Efficiency

\(\eta_{{\text{c}}}\) :

Compression efficiency

\(\eta_{{\text{e}}}\) :

Expansion efficiency

\(\sigma\) :

Entropy generation rate

\(E\) :

The max ecological function point

in:

Heat added

leak:

Heat leakage

di:

Diesel cycle

out:

Heat rejected

p:

The max power output point

pq:

Exhaust stroke

q:

The effect of heat transfer

\(\mu\) :

The effect of friction loss

\(\eta\) :

The max thermal efficiency point

0:

Environment

AS:

Air standard

DC:

Diesel cycle

ECF:

Ecological function

EGR:

Entropy generation rate

FL:

Friction loss

FTT:

Finite-time thermodynamics

HTL:

Heat transfer loss

IIL:

Internal irreversibility loss

LF:

Linear function

NLF:

Nonlinear function

SH:

Specific heat

References

  1. B. Andresen, R.S. Berry, M.J. Ondrechen et al., Thermodynamics for processes in finite time. Acc. Chem. Res. 17(8), 266–271 (1984)

    Article  Google Scholar 

  2. R.S. Berry, V.A. Kazakov, S. Sieniutycz et al., Thermodynamic Optimization of Finite Time Processes (Wiley, Chichester, 1999).

    Google Scholar 

  3. L.G. Chen, C. Wu, F.R. Sun, Finite time thermodynamic optimization or entropy generation minimization of energy systems. J. Non-Equilib. Thermodyn. 22(4), 327–359 (1999)

    ADS  MATH  Google Scholar 

  4. A. Al-Sarkhi, B. Akash, J.O. Jaber, M.S. Mohsen, E. Abu-Nada, Efficiency of Miller engine at maximum power density. Int. Comm. Heat Mass Transf. 29, 1159–1157 (2002)

    Article  Google Scholar 

  5. E. Abu-Nada, I. Al-Hinti, A. Al-Sarkhi, B. Akash, Thermodynamic modeling of spark-ignition engine: Effect of temperature dependent specific heats. Int. Comm. Heat Mass Transf. 33(10), 1264–1272 (2006)

    Article  Google Scholar 

  6. B. Andresen, Current trends in finite-time thermodynamics. Angew. Chem. Int. Ed. 50(12), 2690–2704 (2011)

    Article  Google Scholar 

  7. Y.L. Ge, L.G. Chen, F.R. Sun, Progress in finite time thermodynamic studies for internal combustion engine cycles. Entropy 18(4), 139 (2016)

    Article  ADS  Google Scholar 

  8. V. Badescu, Optimal Control in Thermal Engineering (Springer, New York, 2017).

    Book  MATH  Google Scholar 

  9. E. Açıkkalp, Analysis of a Brownian heat engine with ecological criteria. The Eur. Phys. J. Plus 131(12), 426 (2016)

    Article  Google Scholar 

  10. Y. Apertet, Causality in thermoelectric systems: Insights from block diagrams. The Eur. Phys. J. Plus 131(12), 434 (2016)

    Article  Google Scholar 

  11. L.G. Chen, Z.M. Ding, J.L. Zhou, W.H. Wang, F.R. Sun, Thermodynamic performance optimization for an irreversible vacuum thermionic generator. The Eur. Phys. J. Plus 132(7), 293 (2017)

    Article  Google Scholar 

  12. W.L. Peng, Y.C. Zhang, Z.M. Yang, J.C. Chen, Performance evaluation and comparison of three-terminal energy selective electron devices with different connective ways and filter configurations. The Eur. Phys. J. Plus 133(2), 38 (2018)

    Article  Google Scholar 

  13. J.F. Shen, L.G. Chen, Y.L. Ge, F.L. Zhu, Z.X. Wu, Optimum ecological performance ofirreversible reciprocating Maisotsenko-Brayton cycle. The Eur. Phys. J. Plus 134(6), 293 (2019)

    Article  Google Scholar 

  14. S.S. Qiu, Z.M. Ding, L.G. Chen, F.K. Meng, F.R. Sun, Optimal performance regions of energy selective electron cooling devices consisting of three reservoirs. The Eur. Phys. J. Plus 132(6), 273 (2019)

    Article  Google Scholar 

  15. L.G. Chen, F.K. Meng, Z.M. Ding, S.J. Xia, H.J. Feng, Thermodynamic modeling and analysis of an air-cooled small space thermoelectric cooler. The Eur. Phys. J. Plus 135(1), 80 (2020)

    Article  Google Scholar 

  16. M.A. Barranco-Jiménez, A. Ocampo-García, F. Angulo-Brown, Thermodynamic analysis of an array of isothermal endoreversible electric engines. The Eur. Phys. J. Plus 132(2), 153 (2020)

    Article  Google Scholar 

  17. S.S. Qiu, Z.M. Ding, L.G. Chen, Performance evaluation and parametric optimum design of irreversible thermionic generators based on van der Waals heterostructures. Energy Convers. Manage. 225, 113360 (2020)

    Article  Google Scholar 

  18. L.G. Chen, H.J. Feng, Y.L. Ge, Maximum energy output chemical pump configuration with an infinite-low- and a finite-high-chemical potential mass reservoirs. Energy Convers. Manage. 223, 113261 (2020)

    Article  Google Scholar 

  19. H.J. Feng, W.J. Chen, L.G. Chen, W. Tang, Power and efficiency optimizations of an irreversible regenerative organic Rankine cycle. Energy Convers. Manage. 220, 113079 (2020)

    Article  Google Scholar 

  20. L.G. Chen, J.F. Shen, Y.L. Ge, Z.X. Wu, W.H. Wang, F.L. Zhu, H.J. Feng, Power and efficiency optimization of open Maisotsenko-Brayton cycle and performance comparison with traditional open regenerated Brayton cycle. Energy Convers. Manage. 217, 113001 (2020)

    Article  Google Scholar 

  21. Z.X. Wu, H.J. Feng, L.G. Chen, W. Tang, J.Z. Shi, Y.L. Ge, Constructal thermodynamic optimization for ocean thermal energy conversion system with dual-pressure organic Rankine cycle. Energy Convers. Manage. 210, 112727 (2020)

    Article  Google Scholar 

  22. H.J. Feng, W.X. Qin, L.G. Chen, C.G. Cai, Y.L. Ge, S.J. Xia, Power output, thermal efficiency and exergy-based ecological performance optimizations of an irreversible KCS-34 coupled to variable temperature heat reservoirs. Energy Convers. Manage. 205, 112424 (2020)

    Article  Google Scholar 

  23. L.G. Chen, B. Yang, H.J. Feng, Y.L. Ge, S.J. Xia, Performance optimization of an open simple-cycle gas turbine combined cooling, heating and power plant driven by basic oxygen furnace gas in China’s steelmaking plants. Energy 203, 117791 (2020)

    Article  Google Scholar 

  24. L. Zhang, L.G. Chen, S.J. Xia, Y.L. Ge, C. Wang, H.J. Feng, Multi-objective optimization for helium-heated reverse water gas shift reactor by using NSGA-II. Int. J. Heat Mass Transf. 148, 119025 (2020)

    Article  Google Scholar 

  25. L.G. Chen, F.K. Meng, Y.L. Ge, H.J. Feng, S.J. Xia, Performance optimization of a class of combined thermoelectric heating devices. Sci. China Technol. Sci. 63(12), 2640–2648 (2020)

    Article  ADS  Google Scholar 

  26. L.G. Chen, C.Q. Tang, H.J. Feng, Y.L. Ge, Power, efficiency, power density and ecological function optimizations for an irreversible modified closed variable-temperature reservoir regenerative Brayton cycle with one isothermal heating process. Energies 13(19), 5133 (2020)

    Article  Google Scholar 

  27. L.G. Chen, K. Ma, H.J. Feng, Y.L. Ge, Optimal configuration of a gas expansion process in a piston-type cylinder with generalized convective heat transfer law. Energies 13(12), 3229 (2020)

    Article  Google Scholar 

  28. C.Q. Tang, L.G. Chen, H.J. Feng, W.H. Wang, Y.L. Ge, Power optimization of a closed binary Brayton cycle with isothermal heating processes and coupled to variable-temperature reservoirs. Energies 13(12), 3212 (2020)

    Article  Google Scholar 

  29. S.S. Shi, Y.L. Ge, L.G. Chen, F.J. Feng, Four objective optimization of irreversible Atkinson cycle based on NSGA-II. Entropy 22(10), 1150 (2020)

    Article  ADS  Google Scholar 

  30. L.G. Chen, K. Ma, Y.L. Ge, F. Huijun, Re-optimization of expansion work of a heated working fluid with generalized radiative heat transfer law. Entropy 22(7), 720 (2020)

    Article  ADS  Google Scholar 

  31. S.A. Klein, An explanation for observed compression ratios in internal combustion engines. Trans. ASME J. Eng. Gas Turbine Power 113(4), 511–513 (1991)

    Article  Google Scholar 

  32. D.A. Blank, C. Wu, The effects of combustion on a power-optimized endoreversible Diesel cycle. Energy Convers. Manage. 34(6), 493–498 (1993)

    Article  Google Scholar 

  33. L.G. Chen, F.M. Zen, F.R. Sun, C. Wu, Heat transfer effects on the network output and power as function of efficiency for air standard Diesel cycle. Energy 21(12), 1201–1205 (1996)

    Article  Google Scholar 

  34. A. Parlak, The effect of heat transfer on performance of the Diesel cycle and exergy of the exhaust gas stream in a LHR Diesel engine at the optimum injection timing. Energy Convers. Manage. 46(2), 167–179 (2005)

    Article  Google Scholar 

  35. A. Parlak, H. Yasar, O. Eldogan, The effect of thermal barrier coating on a turbo-charged Diesel engine performance and exergy potential of the exhaust gas. Energy Convers. Manage. 46(3), 489–499 (2005)

    Article  Google Scholar 

  36. O.A. Ozsoysal, Heat loss as a percentage of fuel’s energy in air standard Otto and Diesel cycles. Energy Convers. Manage. 47(7/8), 1051–1062 (2006)

    Article  Google Scholar 

  37. I. Al-Hinti, B. Akash, E. Abu-Nada et al., Performance analysis of air-standard Diesel cycle using an alternative irreversible heat transfer approach. Energy Convers. Manage. 49(11), 3301–3304 (2008)

    Article  Google Scholar 

  38. L.G. Chen, J.X. Lin, F.R. Sun, Friction effects on power vs efficiency characteristics for air-standard Diesel cycles. J. Eng. Thermophys. 18(5), 533–535 (1997). ((in Chineses))

    Google Scholar 

  39. W.Z. Chen, F.R. Sun, New solutions of power and efficiency for Diesel cycles with friction. J. Naval Univ. Eng. 13(3), 24–26 (2001). ((in Chineses))

    Google Scholar 

  40. X.Y. Qin, L.G. Chen, F.R. Sun, The universal power and efficiency characteristics for irreversible reciprocating heat engine cycles. Eur. J. Phys. 24(4), 359–366 (2003)

    Article  MATH  Google Scholar 

  41. Y.L. Ge, L.G. Chen, F.R. Sun, C. Wu, Reciprocating heat-engine cycles. Appl. Energy 81(3), 180–186 (2005)

    Google Scholar 

  42. A. Parlak, Comparative performance analysis of irreversible Dual and Diesel cycles under maximum power conditions. Energy Convers. Manage. 46(3), 351–359 (2005)

    Article  Google Scholar 

  43. Y.R. Zhao, B.H. Lin, Y. Zhang et al., Performance analysis and parametric optimum design of an irreversible Diesel heat engine. Energy Convers. Manage. 47(18–19), 3383–3392 (2006)

    Article  Google Scholar 

  44. S.Y. Zheng, Z. Xia, Y. Zhou et al., Optimization on the work output, efficiency and other performance parameters of an irreversible Diesel heat engine. J. Xiamen Univ. (Nat. Sci.) 45(2), 182–185 (2006). ((in Chinese))

    Google Scholar 

  45. S.Y. Zheng, The effect of ratio of high temperature to low temperature on the performance of Diesel engine cycle. Energy Environ. 1, 18–19 (2009). ((in Chinese))

    Google Scholar 

  46. S. Zheng, G.X. Lin, Optimization of power and efficiency for an irreversible Diesel heat engine. Front. Energy Power Eng. China 4(4), 560–565 (2010)

    Article  Google Scholar 

  47. R. Ebrahimi, Performance optimization of a Diesel cycle with specific heat ratio. J. American Sci. 5(8), 59–63 (2009)

    Google Scholar 

  48. O.A. Ozsoysal, Effects of varying air-fuel ratio on the performance of a theoretical Diesel cycle. Int. J. Exergy 7(6), 654–666 (2010)

    Article  Google Scholar 

  49. Y.L. Ge, L.G. Chen, F.R. Sun et al., Performance of an endoreversible Diesel cycle with variable specific heats of working fluid. Int. J. Ambient Energy 29(3), 127–136 (2008)

    Article  Google Scholar 

  50. Y.L. Ge, L.G. Chen, F.R. Sun et al., Performance of Diesel cycle with heat transfer, friction and variable specific heats of working fluid. J. Energy Inst. 80(4), 239–242 (2007)

    Article  Google Scholar 

  51. A. Al-Sarkhi, J.O. Jaber, M. Abu-Qudais et al., Effects of friction and temperature-dependent specific-heat of the working fluid on the performance of a Diesel-engine. Appl. Energy 83(2), 153–165 (2006)

    Article  Google Scholar 

  52. M. Fallahipanah, M.A. Ghazavi, M. Hashemi, et al., omparison of the performance of Biodiesel, Diesel, and their compound in Diesel ari standard irreversible cycles. Int. Conf. on Environ. Agric. Eng., IPCBEE 15 (2011)

  53. Y.R. Zhao, J.C. Chen, Optimum performance analysis of an irreversible Diesel heat engine affected by variable heat capacities of working fluid. Energy Convers. Manag. 48(9), 2595–2603 (2007)

    Article  Google Scholar 

  54. J.Z. He, J.X., Lin, Effect of multi-irreversibilities on the performance characteristics of an irreversible ari-standard Diesel heat engine. Pow. Energy Eng. Conf., 2010 Asia-Pacific, p. 1–4, (2010)

  55. Y.L. Ge, L.G. Chen, F.R. Sun, Finite time thermodynamic modeling and analysis for an irreversible Diesel cycle. Proc. IMechE, Part D: J. Automob. Eng. 222(D5), 887–894 (2008)

    Article  Google Scholar 

  56. S.M. Aithal, Impact of EGR fraction on diesel engine performance considering heat loss and temperature-dependent properties of the working fluid. Int. J. Energy Res. 33(4), 415–430 (2009)

    Article  Google Scholar 

  57. E. Açıkkalp, H. Yamık, Modeling and optimization of maximum available work for irreversible gas power cycles with temperature dependent specific heat. J. Non-Equilib. Thermodyn. 40(1), 25–39 (2015)

    Article  ADS  Google Scholar 

  58. R. Ebrahimi, Effects of variable specific heat ratio of working fluid on performance of an endoreversible Diesel cycle. J. Energy Inst. 83(1), 1–5 (2010)

    Article  MathSciNet  Google Scholar 

  59. R. Ebrahimi, L.G. Chen, Effects of variable specific heat ratio of working fluid on performance of an irreversible Diesel cycle. Int. J. Ambient Energy 31(2), 101–108 (2010)

    Article  Google Scholar 

  60. A. Sakhrieh, E. Abu-Nada, B. Akash, I. Al-Hinti, A. Al-Ghandoor, Performance of a Diesel engine using a gas mixture with variable specific heats model. J. Energy Inst. 83(4), 217–224 (2010)

    Article  Google Scholar 

  61. R. Ebrahimi, Performance of an irreversible Diesel cycle under variable stroke length and compression ratio. J. Am. Sci. 5(7), 58–64 (2009)

    Google Scholar 

  62. F. Angulo-Brown, Ecological optimization criterion for finite-time heat engines. J. Appl. Phys. 69(11), 7465–7469 (1991)

    Article  ADS  Google Scholar 

  63. Z.J. Yan, Comment on “ecological optimization criterion for finite-time heat engines.” J. Appl. Phys. 73(7), 3583 (1993)

    Article  ADS  Google Scholar 

  64. L.G. Chen, F.R. Sun, W.Z. Chen, On the ecological figures of merit for thermodynamic cycles. J. Eng. Therm. Energy Power 9(6), 374–376 (1994). ((in Chinese))

    Google Scholar 

  65. F. Angulo-Brown, J. Fernandez-Betanzos, C.A. Diaz-Pico, Compression ratio of an optimized Otto-cycle model. Eur. J. Phys. 15(1), 38–42 (1994)

    Article  Google Scholar 

  66. Y. Ust, Ecological performance analysis of irreversible Otto cycle. J. Eng. Nat. Sci. 3, 106–117 (2005)

    Google Scholar 

  67. H.B. Mehta, O.S. Bharti, Performance analysis of an irreversible Otto cycle using finite time thermodynamics, in Proceedings of the World Congress on Engineering, Vol. II, WCE 2009, July 1–3, London, UK (2009)

  68. J.C. Lin, Ecological optimization for an Atkinson engine. JP J. Heat Mass Transf. 4(1), 95–112 (2010)

    ADS  MATH  Google Scholar 

  69. Y. Ust, B. Sahin, O.S. Sogut, Performance analysis and optimization of an irreversible dual-cycle based on an ecological coefficient of performance criterion. Appl. Energy 82(1), 23–39 (2005)

    Article  Google Scholar 

  70. Y.L. Ge, L.G. Chen, F.R. Sun, Ecological optimization of an irreversible Otto cycle. Arab. J. Sci. Eng. 38(2), 373–381 (2013)

    Article  Google Scholar 

  71. Y.L. Ge, L.G. Chen, X.Y. Qin, Z.H. Xie, Exergy-based ecological performance of an irreversible Otto cycle with temperature-linear-relation variable specific heats of working fluid. The Eur. Phys. J. Plus 132(5), 209 (2017)

    Article  ADS  Google Scholar 

  72. Y.L. Ge, L.G. Chen, X.Y. Qin, Effect of specific heat variations on irreversible Otto cycle performance. Int. J. Heat Mass Transf. 122, 403–409 (2018)

    Article  Google Scholar 

  73. M. Mozurkewich, R.S. Berry, Finite-time thermodynamics: engine performance improved by optimized piston motion. Proc. Natl. Acad. Sci. USA 78(4), 1986–1988 (1981)

    Article  ADS  Google Scholar 

  74. M. Mozurkewich, R.S. Berry, Optimal paths for thermodynamic systems: the ideal Otto cycle. J. Appl. Phys. 53(1), 34–42 (1982)

    Article  ADS  Google Scholar 

  75. L.G. Chen, Y.L. Ge, F.R. Sun, C. Wu, Effects of heat transfer, friction and variable specific heats of working fluid on performance of an irreversible Dual cycle. Energy Convers. Manag. 47(18/19), 3224–3234 (2006)

    Article  Google Scholar 

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Acknowledgements

This paper was supported by the National Natural Science Foundation of China (Project No. 51779262). The authors wish to thank the reviewers and the editor for their careful, unbiased and constructive suggestions, which led to this revised manuscript.

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Ge, Y., Chen, L. & Feng, H. Ecological optimization of an irreversible Diesel cycle. Eur. Phys. J. Plus 136, 198 (2021). https://doi.org/10.1140/epjp/s13360-021-01162-z

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