The research on the output rate performance limit of the multi-stage energy conversion system based on modern optimal control theory is one of the hot spots of finite time thermodynamics.The existing research mainly f...The research on the output rate performance limit of the multi-stage energy conversion system based on modern optimal control theory is one of the hot spots of finite time thermodynamics.The existing research mainly focuses on the multi-stage heat engine system with pure heat transfer and the multi-stage isothermal chemical engine(ICE)system with pure mass transfer,while the multi-stage non ICE system with heat and mass transfer coupling is less involved.A multistage endoreversible non-isothermal chemical engine(ENICE)system with a finite high-chemical-potential(HCP)source(driving fluid)and an infinite low-chemical-potential sink(environment)is researched.The multistage continuous system is treated as infinitesimal ENICEs located continuously.Each infinitesimal ENICE is assumed to be a single-stage ENICE with stationary reservoirs.Extending single-stage results,the maximum power output(MPO)of the multistage system is obtained.Heat and mass transfer processes between the reservoir and working fluid are assumed to obey Onsager equations.For the fixed initial time,fixed initial fluid temperature,and fixed initial concentration of key component(CKC)in the HCP source,continuous and discrete models of the multistage system are optimized.With given initial reservoir temperature,initial CKC,and total process time,the MPO of the multistage ENICE system is optimized with fixed and free final temperature and final concentration.If the final concentration and final temperature are free,there are optimal final temperature and optimal final concentration for the multistage ENICE system to achieve MPO;meanwhile,there are low limit values for final fluid temperature and final concentration.Special cases for multistage endoreversible Carnot heat engines and ICE systems are further obtained.For the model in this paper,the minimum entropy generation objective is not equivalent to MPO objective.展开更多
Compared with endoreversible heat engine with pure heat transfer and endoreversible isothermal chemical engine with pure mass transfer,endoreversible non-isothermal chemical engine(ENICE)is a more reasonable model of ...Compared with endoreversible heat engine with pure heat transfer and endoreversible isothermal chemical engine with pure mass transfer,endoreversible non-isothermal chemical engine(ENICE)is a more reasonable model of practical mass exchanger,solid device and chemo-electric systems.There exists heat and mass transfer(HMT)simultaneously between working fluid and chemical potential reservoir in ENICE.There is coupled HMT effect that in ENICE should be considered.There are two ways to consider this coupled effect.One is based on Onsager equations,and another is based on Lewis analogy.For the mathematical and physical description of the above HMT process,the model using Onsager equations are more appropriate in the linear HMT region not far from the equilibrium state,while that based on Lewis analogy is more appropriate in nonlinear HMT region far from the equilibrium state.Different from the previous research on the power optimization of ENICEs with Onsager equations,this paper optimizes power and efficiency of ENICE based on Lewis analogy.HMT processes are assumed to obey Newtonian heat transfer law(q∝ΔT,and T is temperature)and Fick's diffusive mass transfer law(g∝Δc,and c is concentration),respectively.Analytical results of power output and corresponding vector efficiency(η_(T)andη_(μ))of ENICE are obtained,which provide important parallel results with those based on Onsager equations.They include special cases for endoreversible Carnot heat engine with q∝ΔT and endoreversible isothermal chemical engine with g∝Δc.Adopting Lewis analogy in the modelling of ENICEs with simultaneous HMT is an important work.It provides important analytical and numerical results different from those with Onsager equations obtained previously and enriches the research contents of FTT.The research results in this paper have a certain guiding significance for the optimal designs of single irreversible NICEs,multistage NICE systems,practical mass exchangers,solid devices,chemo-electric systems,and so on.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.51976235 and 52171317)。
文摘The research on the output rate performance limit of the multi-stage energy conversion system based on modern optimal control theory is one of the hot spots of finite time thermodynamics.The existing research mainly focuses on the multi-stage heat engine system with pure heat transfer and the multi-stage isothermal chemical engine(ICE)system with pure mass transfer,while the multi-stage non ICE system with heat and mass transfer coupling is less involved.A multistage endoreversible non-isothermal chemical engine(ENICE)system with a finite high-chemical-potential(HCP)source(driving fluid)and an infinite low-chemical-potential sink(environment)is researched.The multistage continuous system is treated as infinitesimal ENICEs located continuously.Each infinitesimal ENICE is assumed to be a single-stage ENICE with stationary reservoirs.Extending single-stage results,the maximum power output(MPO)of the multistage system is obtained.Heat and mass transfer processes between the reservoir and working fluid are assumed to obey Onsager equations.For the fixed initial time,fixed initial fluid temperature,and fixed initial concentration of key component(CKC)in the HCP source,continuous and discrete models of the multistage system are optimized.With given initial reservoir temperature,initial CKC,and total process time,the MPO of the multistage ENICE system is optimized with fixed and free final temperature and final concentration.If the final concentration and final temperature are free,there are optimal final temperature and optimal final concentration for the multistage ENICE system to achieve MPO;meanwhile,there are low limit values for final fluid temperature and final concentration.Special cases for multistage endoreversible Carnot heat engines and ICE systems are further obtained.For the model in this paper,the minimum entropy generation objective is not equivalent to MPO objective.
基金supported by the National Natural Science Foundation of China(Grant Nos.51976235 and 52171317)。
文摘Compared with endoreversible heat engine with pure heat transfer and endoreversible isothermal chemical engine with pure mass transfer,endoreversible non-isothermal chemical engine(ENICE)is a more reasonable model of practical mass exchanger,solid device and chemo-electric systems.There exists heat and mass transfer(HMT)simultaneously between working fluid and chemical potential reservoir in ENICE.There is coupled HMT effect that in ENICE should be considered.There are two ways to consider this coupled effect.One is based on Onsager equations,and another is based on Lewis analogy.For the mathematical and physical description of the above HMT process,the model using Onsager equations are more appropriate in the linear HMT region not far from the equilibrium state,while that based on Lewis analogy is more appropriate in nonlinear HMT region far from the equilibrium state.Different from the previous research on the power optimization of ENICEs with Onsager equations,this paper optimizes power and efficiency of ENICE based on Lewis analogy.HMT processes are assumed to obey Newtonian heat transfer law(q∝ΔT,and T is temperature)and Fick's diffusive mass transfer law(g∝Δc,and c is concentration),respectively.Analytical results of power output and corresponding vector efficiency(η_(T)andη_(μ))of ENICE are obtained,which provide important parallel results with those based on Onsager equations.They include special cases for endoreversible Carnot heat engine with q∝ΔT and endoreversible isothermal chemical engine with g∝Δc.Adopting Lewis analogy in the modelling of ENICEs with simultaneous HMT is an important work.It provides important analytical and numerical results different from those with Onsager equations obtained previously and enriches the research contents of FTT.The research results in this paper have a certain guiding significance for the optimal designs of single irreversible NICEs,multistage NICE systems,practical mass exchangers,solid devices,chemo-electric systems,and so on.
