Optimal configuration of a finite mass reservoir isothermal chemical engine for maximum work output with linear mass transfer law
Shaojun Xia, Lingen Chen*, and Fengrui Sun
Postgraduate School, Naval University of Engineering, Wuhan 430033, P.R. China.
*. To whom all correspondence should be addressed:
e–mail address: lgchenna@yahoo.com , lingenchen@hotmail.com , ]]>
Fax: 0086–27–83638709
Tel: 0086–27–83615046.
Recibido el 27 de julio de 2009
Aceptado el 30 de septiembre de 2009
Abstract
An isothermal endoreversible chemical engine operating between a finite high–chemical– potential reservoir and an infinite low–chemical–potential reservoir in which the mass transfer between the working fluid and the mass reservoirs obeys the linear mass–transfer law [g α Δµ], is put forward in this paper. Optimal control theory is applied to determine the optimal cycle configuration corresponding to the maximum work output for the fixed total cycle time. The optimal cycle configuration is an isothermal endoreversible chemical engine cycle in which the chemical potential (concentration) of the key component in the finite high–chemical– potential mass reservoir and that in the working fluid change nonlinearly with time. The difference in chemical potentials (ratio of the concentrations) between the key component in the finite mass reservoir and the working fluid is a constant, and the chemical potential (concentration) of the key component in the working fluid at the low chemical potential side is also a constant. A numerical example is provided, and the effects of the concentration changes in the key component in the finite high–chemical–potential reservoir on the optimal configuration of the chemical engine are analyzed. The obtained results are compared with those obtained for an endoreversible heat engine operating between a finite heat source and an infinite heat sink with Newton's heat transfer law [q α ΔT ] in the heat transfer processes. The object studied in this paper is general, and the results could provide some guidelines for the optimal design and operation of real chemical engines.
Keywords: Finite high–chemical–potential reservoir; isothermal endoreversible chemical engine; maximum work output; optimal control; generalized thermodynamic optimization.
]]> Resumen
En el presente trabajo se presenta un motor químico endoreversible isotérmico trabajando entre un recipiente finito de alto potencial químico y un recipiente infinito de bajo potencial químico, en el cual, la transferencia de masa entre el fluido de trabajo y la masa contenida obedece a la ley lineal de transferencia de masa [g α Δµ]. Se aplica la teoría del control óptimo para determinar la configuración óptima del ciclo, correspondiente al máximo trabajo de salida para el tiempo total del ciclo. La configuración del ciclo óptimo es el de un motor químico endoreversible isotérmico en el cual, el potencial químico (concentración) de la componente clave en el recipiente finito masivo de alto potencial químico y el del fluido de trabajo cambian de forma no lineal con el tiempo. La diferencia en los potenciales químicos (cociente de las concentraciónes) entre el componente clave del recipiente finito masivo y el fluido de trabajo es una constante, y el potencial químico (concentración) del componente clave en el fluido de trabajo del lado del potencial químico bajo es también una constante. Se proporciona un ejemplo numérico donde se analizan los efectos del cambio en la concentración en la componente clave del recipiente finito con alto potencial químico respecto de la configuración óptima del motor químico. Los resultados obtenidos se comparan con los obtenidos para un motor térmico endoreversible que trabaja entre una fuente de calor finita y un disipador de calor infinito, que obedece a la ley de Newton de transferencia de calor (q α ΔT) en los procesos de tranferencia de calor. El objeto de estudió en el presente trabajo es general y los resultados podrían proporcionar algunas pautas para el diseño óptimo y funcionamiento de motores químicos reales.
Descriptores: Recipiente finito de alto potencial químico; motor químico isotérmico endoreversible; máximo trabajo de salida; control óptimo; optimización termodinámica generalizada.
PACS: 05.70.–a; 05.30–d
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Acknowledgements
This paper is supported by the Program for New Century Excellent Talents in University of P.R. China (Project No. 20041006) and The Foundation for the Author of National Excellent Doctoral Dissertation of P.R. China (Project No. 200136). The authors wish to thank the reviewer for his careful, unbiased and constructive suggestions, which led to this revised manuscript.
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