Abstract
An isothermal endoreversible chemical engine operating between the finite potential capacity high-chemical-potential reservoir and the infinite potential capacity low-chemical-potential reservoir has been studied in this work. Optimal control theory was applied to determine the optimal cycle configurations corresponding to the maximum work output per cycle for the fixed total cycle time and a universal mass transfer law. Analyses of special examples showed that the optimal cycle configuration with the mass transfer law g ∝ Δµ, where Δµ is the chemical potential difference, is an isothermal endoreversible chemical engine cycle, in which the chemical potential (or the concentration) of the key component in the working substance of low-chemical-potential side is a constant, while the chemical potentials (or the concentrations) of the key component in the finite potential capacity high-chemical-potential reservoir and the corresponding side working substance change nonlinearly with time, and the difference of the chemical potentials (or the ratio of the concentrations) of the key component between the high-chemical-potential reservoir and the working substance is a constant. While the optimal cycle configuration with the mass transfer law g ∝ Δc, where Δc is the concentration difference, is different from that with the mass transfer law g ∝ Δµ significantly. When the high-chemical-potential reservoir is also an infinite potential capacity chemical potential reservoir, the optimal cycle configuration of the isothermal endoreversible chemical engine consists of two constant chemical potential branches and two instantaneous constant mass-flux branches, which is independent of the mass transfer law. The object studied in this paper is general, and the results can provide some guidelines for optimal design and operation of real chemical engines.
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References
Andresen B, Berry RS, Ondrechen MJ, Salamon P. Thermodynamics for processes in finite time. Acc Chem Res, 1984, 17: 266–271
Berry RS, Kazakov VA, Sieniutycz S, Szwast Z, Tsirlin AM. Thermodynamic Optimization of Finite Time Processes. Chichester: Wiley, 1999
Chen L, Wu C, Sun F. Finite time thermodynamic optimization or entropy generation minimization of energy systems. J Non-Equilib Thermodyn, 1999, 24: 327–359
Chen L, Sun F. Advances in Finite Time Thermodynamics: Analysis and optimization. New York: Nova Science Publishers, 2004
Chen L. Finite Time Thermodynamic Analysis of Irreversible Progresses and Cycles (in Chinese). Beijing: High Education Press, 2005
Wang J, He J, Mao Z. Performance of quantum heat engine cycle with harmonic system. Sci China Ser G-Phys Mech Astron, 2007, 50: 163–176
Song H, Chen L, Sun F. Optimal configuration of a class of endoreversible heat engines for maximum efficiency with radiative heat transfer law. Sci China Ser G-Phys Mech Astron, 2008, 51: 1272–1286
Xia S, Chen L, Sun F. The optimal path of piston motion for Otto cycle with linear phenomenological heat transfer law. Sci China Ser G-Phys Mech Astron, 2009, 52: 708–719
Shu L, Chen L, Sun F. The minimal average heat consumption for heat-driven binary separation process with linear phenomenological heat transfer law. Sci China Ser B-Chem, 2009, 52: 1154–1163
Ma K, Chen L, Sun F. Optimal paths for a light-driven engine with linear phenomenological heat transfer law. Sci China Chem, 2010, 53(4): 917–926
Curzon FL, Ahlborn B. Efficiency of a Carnot engine at maximum power output. Am J Phys, 1975, 43: 22–24
Cutowicz-Krusin D, Procaccia J, Ross J. On the efficiency of rate process: Power and efficiency of heat engines. J Chem Phys, 1978, 69: 3898–3906
Ondrechen MJ, Andresen B, Mozurkewich M, Berry RS. Maximum work from a finite reservoir by sequential Carnot cycles. Am J Phys, 1981, 49: 681–685
Ondrechen MJ, Rubin MH, Band YB. The generalized Carnot cycles: a working fluid operating in finite time between heat sources and sinks. J Chem Phys, 1983, 78: 4721–4727
Amelkin SA, Andresen B, Burzler JM, Hoffmann KH, Tsirlin AM. Maximum power process for multi-source endoreversible heat engines. J Phys D: Appl Phys, 2004, 37: 1400–1404
Amelkin SA, Andresen B, Burzler JM, Hoffmann KH, Tsirlin AM. Thermo-mechanical systems with several heat reservoirs: maximum power processes. J Non-Equlib Thermodyn, 2005, 30: 67–80
Sieniutycz S. Spakovsky M. Finite time generalization of thermal exergy. Energy Convers Mgmt, 1998, 39:1423–1447
Sieniutycz S. Nonlinear thermokinetics of maximum work in finite time. Int J Engng Sci, 1998, 36: 577–597
de Vos A. Endoreversible Thermodynamics of Solar Energy Conversion. Oxford: Oxford University, 1992
de Vos A. Is a solar cell an endoreversible engine? Solar Cells, 1991, 31: 181–196
de Vos A. Endoreversible thermodynamics and chemical reactions. J Phys Chem, 1991, 95: 4534–4540
de Vos A. Entropy flaxes, endoreversibility and solar energy conversion. J Appl Phys, 1993, 74: 3631–3637
Tsirlin AM, Kazakov V, Kan NM, Trushkov VV. Thermodynamic analysis and thermodynamic efficiency of chemical reactors. J Phys Chem B, 2006, 110: 2338–2342
Gordon JM. Maximum work from isothermal chemical engines. J Appl Phys, 1993, 73: 8–11
Gordon JM, Orlov VN. Performance characteristics of endoreversible chemical engines. J Appl Phys, 1993, 74: 5303–5308
Chen L, Sun F, Wu C. Performance characteristics of isothermal chemical engines. Energy Convers Mgmt, 1997, 38: 1841–1846
Chen L, Sun F, Wu C. Performance of chemical engines with a mass leak. J Phys D: Appl Phys, 1998, 31: 1595–1600
Chen L, Sun F, Wu C, Gong J. Maximum power of a combined cycle isothermal chemical engine. Appl Thermal Engng, 1997, 17: 629–637
Chen L, Duan H, Sun F, Wu C. Performance of a combined-cycle chemical engine with mass leak. J Non-Equibri Thermodyn, 1999, 24: 280–290
Lin G, Chen J, Bruck E. Irreversible chemical-engines and their optimal performance analysis. Appl Energy, 2004, 78: 123–136
Tsirlin AM, Leskov EE, Kazakov V. Finite time thermodynamics: limiting performance of diffusion engines and membrane systems. J. Phys Chem A, 2005, 109: 9997–10003
Chen L, Xia D, Sun F. Optimal performance of an endoreversible chemical engine with diffusive mass transfer law. Proc IMechE, Part C: J Mech. Engng Sci, 2008, 222: 1535–1539
Sieniutycz S. Analysis of power and entropy generation in a chemical engine. Int J Heat Mass Transfer, 2008, 51: 5859–5871
Sieniutycz S. Thermodynamics of chemical power generators. Chem Process Engng, 2008, 29: 321–335
Sieniutycz S. Complex chemical systems with power production driven by heat and mass transfer. Int J Heat Mass Transfer, 2009, 52: 2453–2465
Xia S, Chen L, Sun F. Maximum power configuration for multi-reservoir chemical engines. J Appl Phys, 2009, 105: 114905
Yan Z, Chen J. Optimal performance of a generalized Carnot cycle for another linear heat transfer law. J Chem Phys, 1990, 92: 1994–1998
Chen L, Sun F, Wu C. Optimal configuration of a two-heat-reservoir heat-engine with heat leak and finite thermal capacity. Appl Energy, 2006, 83: 71–81
Xiong G, Chen J, Yan Z. The effect of heat transfer law on the performance of a generalized Carnot cycle (in Chinese). J Xiamen University (Nature Science), 1989, 28: 489–494
Chen L, Zhu X, Sun F, Wu C. Optimal configurations and performance for a generalized Carnot cycle assuming the heat transfer law Q ∝ (ΔT)m. Appl Energy, 2004, 78: 305–313
Chen L, Zhu X, Sun F, Wu Chih. Effect of mixed heat resistance on the optimal configuration and performance of a heat-engine cycle. Appl Energy, 2006, 83: 537–544
Li J, Chen L, Sun F. Optimal configuration for a finite high-temperature source heat engine cycle with complex heat transfer law. Sci China Ser G-Phys Mech Astron, 2009, 52: 587–592
Lin G, Chen J. Optimal analysis on the cyclic performance of a class of chemical pumps. Appl Energy, 2001, 70: 35–47
Lin G, Chen J, Brück E, Hua B. Optimization of performance characteristics in a class of irreversible chemical pumps. Math Compu Modell, 2006, 43: 743–753
Xia D, Chen L, Sun F. Optimal performance of a chemical pump with diffusive mass transfer law. Int J Sustainable Energy, 2008, 27: 39–47
Lin G, Chen J, Hua B. General performance characteristics of an irreversible three source chemical pump. Energy Convers Mgmt, 2003, 44: 1719–1731
Lin G, Chen J, Wu C. The equivalent combined cycle of an irreversible chemical potential transformer and its optimal performance. Exergy, An Int J, 2002, 2: 119–124
Xia D, Chen L, Sun F, Wu C. Optimal performance of an endoreversible three-mass-reservoir chemical potential transformer with diffusive mass transfer law. Int J Ambient Energy, 2008, 29: 9–16
Xia D, Chen L, Sun F, Wu C. Endoreversible four-mass-reservoir chemical pump. Appl Energy, 2007, 84: 56–65
Chen L, Xia D, Sun F. Fundamental optimal relation of a generalized irreversible four-reservoir chemical pump. Proc IMechE, Part C: J Mech Engng Sci, 2008, 222: 1523–1534
Xia D, Chen L, Sun F. Performance of a four-reservoir chemical potential transformer with irreversible mass transfer and mass leakage. Appl Thermal Engng, 2007, 27: 1534–1542
Xia D, Chen L, Sun F. Optimal performance of a generalized irre-versible four-reservoir isothermal chemical potential transformer. Sci China Ser B-Chem, 2008, 51: 958–970
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Xia, S., Chen, L. & Sun, F. Maximum work configurations of finite potential capacity reservoir chemical engines. Sci. China Chem. 53, 1168–1176 (2010). https://doi.org/10.1007/s11426-010-0132-x
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DOI: https://doi.org/10.1007/s11426-010-0132-x