In this paper, an endoreversible Carnot heat engine with irreversible heat transfer processes is analyzed based on generalized heat transfer law. The applicability of the entropy generation minimization, exergy analys...In this paper, an endoreversible Carnot heat engine with irreversible heat transfer processes is analyzed based on generalized heat transfer law. The applicability of the entropy generation minimization, exergy analyses method, and entransy theory to the analyses is discussed. Three numerical cases are presented. It is shown that the results obtained from the entransy theory are different from those from the entropy generation minimization, which is equivalent to the exergy analyses method. For the first case in which the application preconditions of the entropy generation minimization and entransy loss maximization are satisfied, both smaller entropy generation rate and larger entransy loss rate lead to larger output power. For the second and third cases in which the preconditions are not satisfied, the entropy generation minimization does not lead to the maximum output power, while larger entransy loss rate still leads to larger output power in the third case. For the discussed cases, the concept of entransy dissipation is not applicable for the analyses of output power.The problems in the negative comments on the entransy theory are pointed out and discussed. The related researchers are advised to focus on some new specific application cases to show if the entransy theory is the same as some other theories.展开更多
Taking the output power, thermal efficiency, and thermo-economic performance as the optimization objectives, we optimize the operation parameters of a thermodynamic system with combined endoreversible Carnot heat engi...Taking the output power, thermal efficiency, and thermo-economic performance as the optimization objectives, we optimize the operation parameters of a thermodynamic system with combined endoreversible Carnot heat engines in this paper. The applicabilities of the entropy generation minimization and entransy theory to the optimizations are discussed. For the discussed cases, only the entransy loss coefficient is always agreeable to the optimization of thermal efficiency. The applicabilities of the other discussed concepts to the optimizations are conditional. Different concepts and principles are needed for different optimization objectives, and the optimization principles have their application preconditions. When the preconditions are not satisfied, the principles may be not applicable.展开更多
Optimal configuration of a class of endoreversible heat engines with fixed duration,input energy and radiative heat transfer law (q∝Δ(T4)) is determined. The optimal cycle that maximizes the efficiency of the heat e...Optimal configuration of a class of endoreversible heat engines with fixed duration,input energy and radiative heat transfer law (q∝Δ(T4)) is determined. The optimal cycle that maximizes the efficiency of the heat engine is obtained by using opti-mal-control theory,and the differential equations are solved by the Taylor series expansion. It is shown that the optimal cycle has eight branches including two isothermal branches,four maximum-efficiency branches,and two adiabatic branches. The interval of each branch is obtained,as well as the solutions of the temperatures of the heat reservoirs and the working fluid. A numerical example is given. The obtained results are compared with those obtained with the Newton’s heat transfer law for the maximum efficiency objective,those with linear phe-nomenological heat transfer law for the maximum efficiency objective,and those with radiative heat transfer law for the maximum power output objective.展开更多
In this paper, the endoreversible Otto cycle is analyzed with the entropy generation minimization and the entransy theory. The output power and the heat-work conversion efficiency are taken as the optimization objecti...In this paper, the endoreversible Otto cycle is analyzed with the entropy generation minimization and the entransy theory. The output power and the heat-work conversion efficiency are taken as the optimization objectives, and the relationships of the output power, the heat-work conversion efficiency, the entropy generation rate, the entropy generation numbers, the entransy loss rate, the entransy loss coefficient, the entransy dissipation rate and the entransy variation rate associated with work are discussed. The applicability of the entropy generation minimization and the entransy theory to the analyses is also analyzed. It is found that smaller entropy generation rate does not always lead to larger output power, while smaller entropy generation numbers do not always lead to larger heat-work conversion efficiency, either. In our calculations, both larger entransy loss rate and larger entransy variation rate associated with work correspond to larger output power, while larger entransy loss coefficient results in larger heat-work conversion efficiency. It is also found that the concept of entransy dissipation is not always suitable for the analyses because it was developed for heat transfer.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
Based on a simple nonideal chemical reaction model, the closed system with reversible nonideal reactions and illumination is shown to be able to exhibit sustained oscillation. The essential points in the occurrence of...Based on a simple nonideal chemical reaction model, the closed system with reversible nonideal reactions and illumination is shown to be able to exhibit sustained oscillation. The essential points in the occurrence of such oscillations are the nonideality of reacting media, which gives rise to multiple chemical equilibria, and the energy flow through illumination and heat conduction, which gives rise to spontaneous transitions repeatedly between the multiple equilibrium states. During the oscillation, reacting media undergo only reversible chemical transformation and all irreversibilities are restricted to the coupling of the system to external world. This oscillation provides an example of the so-called endoreversible machine and a possible way to convert radiation energy of the light directly into mechanical energy.展开更多
An endoreversible model is used to simulate the dynamic behavior of a solar driven absorption refrigerator, the cycle under different operating and design conditions. A global time minimization procedure is performed ...An endoreversible model is used to simulate the dynamic behavior of a solar driven absorption refrigerator, the cycle under different operating and design conditions. A global time minimization procedure is performed to reach maximum performances. To evaluate the influence of the cold temperature on the system’s performances, results are carried out for three values of this temperature. They are presented in normalized charts for general applications. The minimum time set point temperature, entropy and maximum refrigeration load are sharp and therefore, are important to be considered for system design.展开更多
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 t...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△μis 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∝△μc,where △μc 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.展开更多
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
基金Project supported by the Youth Programs of Chongqing Three Gorges University,China(Grant No.13QN18)
文摘In this paper, an endoreversible Carnot heat engine with irreversible heat transfer processes is analyzed based on generalized heat transfer law. The applicability of the entropy generation minimization, exergy analyses method, and entransy theory to the analyses is discussed. Three numerical cases are presented. It is shown that the results obtained from the entransy theory are different from those from the entropy generation minimization, which is equivalent to the exergy analyses method. For the first case in which the application preconditions of the entropy generation minimization and entransy loss maximization are satisfied, both smaller entropy generation rate and larger entransy loss rate lead to larger output power. For the second and third cases in which the preconditions are not satisfied, the entropy generation minimization does not lead to the maximum output power, while larger entransy loss rate still leads to larger output power in the third case. For the discussed cases, the concept of entransy dissipation is not applicable for the analyses of output power.The problems in the negative comments on the entransy theory are pointed out and discussed. The related researchers are advised to focus on some new specific application cases to show if the entransy theory is the same as some other theories.
基金Project supported by the National Natural Science Foundation of China(Grant No.51376101)the Science Fund for Creative Research Groups,China(Grant No.51321002)
文摘Taking the output power, thermal efficiency, and thermo-economic performance as the optimization objectives, we optimize the operation parameters of a thermodynamic system with combined endoreversible Carnot heat engines in this paper. The applicabilities of the entropy generation minimization and entransy theory to the optimizations are discussed. For the discussed cases, only the entransy loss coefficient is always agreeable to the optimization of thermal efficiency. The applicabilities of the other discussed concepts to the optimizations are conditional. Different concepts and principles are needed for different optimization objectives, and the optimization principles have their application preconditions. When the preconditions are not satisfied, the principles may be not applicable.
基金the Program for New Century Excellent Talents in University of China (Grant No 20041006)the Foundation for the Author of National Excellent Doctoral Dissertation of China (Grant No 200136)
文摘Optimal configuration of a class of endoreversible heat engines with fixed duration,input energy and radiative heat transfer law (q∝Δ(T4)) is determined. The optimal cycle that maximizes the efficiency of the heat engine is obtained by using opti-mal-control theory,and the differential equations are solved by the Taylor series expansion. It is shown that the optimal cycle has eight branches including two isothermal branches,four maximum-efficiency branches,and two adiabatic branches. The interval of each branch is obtained,as well as the solutions of the temperatures of the heat reservoirs and the working fluid. A numerical example is given. The obtained results are compared with those obtained with the Newton’s heat transfer law for the maximum efficiency objective,those with linear phe-nomenological heat transfer law for the maximum efficiency objective,and those with radiative heat transfer law for the maximum power output objective.
基金supported by the Scientific and Technological Research Program of Chongqing Municipal Education Commission(Grant No.KJ1710251)
文摘In this paper, the endoreversible Otto cycle is analyzed with the entropy generation minimization and the entransy theory. The output power and the heat-work conversion efficiency are taken as the optimization objectives, and the relationships of the output power, the heat-work conversion efficiency, the entropy generation rate, the entropy generation numbers, the entransy loss rate, the entransy loss coefficient, the entransy dissipation rate and the entransy variation rate associated with work are discussed. The applicability of the entropy generation minimization and the entransy theory to the analyses is also analyzed. It is found that smaller entropy generation rate does not always lead to larger output power, while smaller entropy generation numbers do not always lead to larger heat-work conversion efficiency, either. In our calculations, both larger entransy loss rate and larger entransy variation rate associated with work correspond to larger output power, while larger entransy loss coefficient results in larger heat-work conversion efficiency. It is also found that the concept of entransy dissipation is not always suitable for the analyses because it was developed for heat transfer.
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.
基金Project supported by the National Natural Science Foundation of China.
文摘Based on a simple nonideal chemical reaction model, the closed system with reversible nonideal reactions and illumination is shown to be able to exhibit sustained oscillation. The essential points in the occurrence of such oscillations are the nonideality of reacting media, which gives rise to multiple chemical equilibria, and the energy flow through illumination and heat conduction, which gives rise to spontaneous transitions repeatedly between the multiple equilibrium states. During the oscillation, reacting media undergo only reversible chemical transformation and all irreversibilities are restricted to the coupling of the system to external world. This oscillation provides an example of the so-called endoreversible machine and a possible way to convert radiation energy of the light directly into mechanical energy.
文摘An endoreversible model is used to simulate the dynamic behavior of a solar driven absorption refrigerator, the cycle under different operating and design conditions. A global time minimization procedure is performed to reach maximum performances. To evaluate the influence of the cold temperature on the system’s performances, results are carried out for three values of this temperature. They are presented in normalized charts for general applications. The minimum time set point temperature, entropy and maximum refrigeration load are sharp and therefore, are important to be considered for system design.
基金supported by the Program for New Century Excellent Talents of China (NCET-04-1006)the Foundation for the Author of National Excellent Doctoral Dissertation of China(200136)
文摘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△μis 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∝△μc,where △μc 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.
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.
