有限势库化学机最大输出功时循环最优构型

Maximum work configurations of finite potential capacity reservoir chemical engines

基于有限势容高化学势库和无限势容低化学势库间工作的等温内可逆化学机,在循环总时间一定的条件下,应用最优控制理论导出了一类普适传质规律下对应于最大输出功时化学机循环最优构型.特例分析表明传质定律为g∝△μ(△μ为化学势差)时循环最优构型为低化学势侧工质中关键组分的化学势(或浓度)为常数,而工质与有限势容高化学势库间关键组分的化学势(或浓度)均随时间呈非线性变化且化学势之差(浓度之比)为常数的等温内可逆化学机循环;传质定律为g∝△c(△c为浓度差)时循环最优构型与传质定律g∝△μ下循环最优构型存在显著不同;当高化学势库也为无限势容化学势库时,循环最优构型由两个等化学势传质分支和两个等质量流率分支组成,且与具体的传质定律无关.本文的研究对象具有一定的普适性,研究结果对于实际化学机的优化设计与最优运行具有一定参考价值.

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 ∝△μ,where △μ 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 ∝ △c,where △c is the concentration difference,is different from that with the mass transfer law g ∝ △μ 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.