量子斯特林制冷循环性能研究
|
摘要
建立了以无数个无限深势阱中的粒子为工质的不可逆量子斯特林制冷循环模型。势阱中粒子在能级上的分布由吉布斯分布函数决定。该制冷循环由两个等能量过程与两个等势阱壁宽度过程组成,具有高低温热源间的热漏和不完全回热因素。导出了性能系数、致冷率、熵产率和生态学目标函数性能解析式,制冷率与生态学函数的关系曲线是回原点的扭叶型。分析了热漏系数与不完全回热因子对性能系数、制冷率和生态学函数的影响。
An irreversible quantum Stirling refrigeration model is established in which working substance is a single particle contained in a one-dimensional infinite potential well, and the system consists of countless replicas. The occupation probabilities in each eigenstates of the particle are expressed by the thermal equilibrium Gibbs distributions. The cycle is made of two iso-energy branches and two isochoric branches and with heat leakage between heat reservoirs and imperfect regeneration. Analytical expressions of COP, cooling rate, entropy generation rate and ecological function are derived. The curve between cooling rate and ecological function is a loop-shaped one.Effects of heat leakage and imperfect regeneration on COP, cooling rate and ecological function are analyzed.
An irreversible quantum Stirling refrigeration model is established in which working substance is a single particle contained in a one-dimensional infinite potential well, and the system consists of countless replicas. The occupation probabilities in each eigenstates of the particle are expressed by the thermal equilibrium Gibbs distributions. The cycle is made of two iso-energy branches and two isochoric branches and with heat leakage between heat reservoirs and imperfect regeneration. Analytical expressions of COP, cooling rate, entropy generation rate and ecological function are derived. The curve between cooling rate and ecological function is a loop-shaped one.Effects of heat leakage and imperfect regeneration on COP, cooling rate and ecological function are analyzed.
引文
[1]WU Feng,CHEN Lingen,SUN Fengrui,et al.Performance Characteristics of a Magnetic Stirling Cooler[J].International Journal of Energy Research,2002,26(3):217-228
[2]WU Feng,CHEN Lingen,Wu Chi,et al.Optimization of Irreversible Magnetic Stirling Cryocoolers[J].International Journal of Engineering Science,2001,39(4):361-368
[3]WU Feng,CHEN Lingen,SUN Fengrui.Finite-time Exergoeconomic Performance Bound for a Quantum Stirling Engine[J].International Journal of Engineering Science,2000,38(2):239-247
[4]Vroylandt H,Bonfils A,Verley G.Efficiency Fluctuations of Small Machines with Unknown Losses[J].Physical Review E,2016,93(5):052123
[5]Curzon F L,Ahlborn B.Efficiency of a Carnot Engine at Maximum Power Output[J].American Journal of Physics,1975,43(1):22-24
[6]Andresen B,Salamon P,Berry R S.Thermodynamics in Finite Time[J].Physics Today,1984(Sept.):62-70
[7]CHEN Lingen,WU Chi,SUN Fengrui.Finite Time Thermodynamic Optimization or Entropy Generation Minimization of Energy Systems[J].Journal of NonEquilibrium Thermodynamics,1999,24(4):327-359
[8]Hoffman K H,Burzler J,Fischer A,et al.Optimal Process Paths for Endoreversible Systems[J].Journal of NonEquilibrium Thermodynamics,2003,28(3):233-268
[9]CHEN Lingen,SUN Fengrui.Advances in Finite Time Thermodynamics:Analysis and Optimization[M].New York:Nova Science Publishers,2004
[10]陈林根.不可逆过程和循环的有限时间热力学分析[M].北京:高等教育出版社,2005CHEN Lingen.Finite Time Thermodynamics Analysis for Irreversible Processes and Cycles[M].Beijing:Higher Education Press,2005
[11]Andresen B.Current Trends in Finite-time Thermodynamics[J].Angewandte Chemie International Edition,2011,50(12):2690-2704
[12]CHEN Lingen,MENG Fankai,SUN Fengrui.Thermo-dynamic Analyses and Optimizations for Thermoelectric Devices:the State of the Arts[J].Science China:Technological Sciences,2016,2016,59(3):442-455
[13]陈林根,夏少军.不可逆过程的广义热力学动态优化[M].北京:科学出版社,2016CHEN Lingen,XIA Shaojun.Generalized Thermodynamic Dynamic-Optimization for Irreversible Processes.Beijing:Science Press,2016
[14]陈林根,夏少军.不可逆循环的广义热力学动态优化[M].北京:科学出版社,2016CHEN Lingen,XIA Shaojun.Generalized Thermodynamic Dynamic-Optimization for Irreversible Cycles.Beijing:Science Press,2016
[15]Kosloff R.Quantum Thermodynamics:A Dynamical Viewpoit J].Entropy,2013,15(6):2100-2128
[16]YIN Yong,CHEN Lingen,WU Feng.Optimal Power and Efficiency of Quantum Stirling Heat Engines[J].European Physical Journal Plus,2017,132:45
[17]吴锋.斯特林机的有限时间热力学研究[D].武汉:海军工程学院,1998.WU Feng.Finite Time Thermodynamics Research for Stirling Engine[D].Doctorial Dissertations,WuHan:Naval Engineering College,1998
[18]吴锋,陈林根,孙丰瑞,等.斯特林机的有限时间热力学优化[M].北京:化学工业出版社,2008.WU Feng,CHEN Lingen,SUN Fengrui,et al.Finite Time Thermodynamic Optimization for Stirling Engine[M].BeiJing:Chemical Industry Press,2008
[19]Kosloff R.A Quantum Mechanical Open System as a Model of a Heat Engine[J].Journal of Chemical Physics,1984,80(4):1625-1631
[20]Geva E,Kosloff R.On the Classical Limit of Quantum Thermodynamics in Finite Time[J].Journal of Chemical Physics,1992,97(5):4398-4412
[21]吴锋,孙丰瑞,陈林根.活塞式量子Stirling发动机最优性能[J].电站系统工程,1996,12(1):41-43WU Feng,SUN Fengrui,CHEN Lingen.Optimum Performance of a Piston Quantum Stirling Engine[J].Power System Engineering,1996,12(1):41-43
[22]WU Feng,YANG Zhichun,CHEN Lingen,et al.Work Output and Efficiency of a Reversible Quantum Otto Cycle[J].Thermal Science,2010,14(4):879-886
[23]吴锋,汪拓,陈林根,等.量子斯特林热机的输出功和热效率[J].机械工程学报,2014,50(4):150-154WU Feng,WANG Tuo,CHEN Lingen,et al.Work Output and Efficiency of Quantum Stirling Engine[J].Journal of Mechanical Engineering,2014,50(4):150-154
[24]王建辉,熊双泉,何济洲,等.以一维谐振子势阱中的单粒子为工质的量子热机性能分析[J].物理学报,2012,61(8):080509WANG Jinhui,XIONG Shuangquan,HE Jizhou,et al.Performance Analysis of a Quantum Heat Engine Working with a Particle in a One-dimensional Harmonic Trap[J].Acta Physica Sinica,2012,61(8):080509
[25]Correa L A,Palao J P,Alonso D.Internal Dissipation and Heat Leaks in Quantum Thermodynamic Cycles[J].Physical Review E,2015,92(3):032136
[26]金晓昌,吴锋,孙丰瑞,等.经典极限下量子卡诺热机拥经济最优性能[J].电站系统工程,1996,12(6):42-45JIN Xiaochang,WU Feng,SUN Fengrui,et al.OptimumExergoeconomic Performance of Quantum Carnot Heat Engine Under the Classical Limit[J].Power System Engineering,1996,12(6):42-45
[27]Feldmann T,Kosloff R.Performance of Discrete Heat Engines and Heat Pumps in Finite Time[J].Physical Review E,2000,61(5):4774-4790
[28]吴锋,孙丰瑞.不可逆量子斯特林制冷机的最大制冷率[J].应用科学学报,1997,15(2):223-228WU Feng,SUN Fengrui.Maximum Cooling Rate of a Irreversible Quantum Stirling Refrigerator[J].Journal of Applied Science,1997,15(2):223-228
[29]金晓昌.量子斯特林制冷机拥经济优化准则[J].武汉化工学院学报,1997,19(3):85-88JIN Xiaochang.Exergoeconomic Optimum Criterion of Quantum Stirling Refrigerator[J].Journal of Wuhan institute of Chemical Technology,1997,19(3):85-88
[30]Acikkalp E,Caner N.Application of Exergetic Sustainable Index to the Quantum Irreversible Diesel Refrigerator Cycles for 1D Box System[J].The European Physical Journal Plus,2015,130:73
[31]Angulo-Brown F.An Ecological Optimization Criterion for Finite-Time Heat Engines[J].Journal of Applied Physics,1991,69(11):7465-7469
[32]Yan Z.Comment on“Ecological Optimization Criterion for Finite-Time Heat Engines”[J].Journal of Applied Physics,1993,73(7):3583
[33]陈林根,孙丰瑞,陈文振.热力循环的生态学品质因素[J].热能动力工程,1994,9(6):374-376CHEN Lingen,SUN Fengrui,CHEN Wenzheng.The Ecological Quality Factor for Thermodynamic Cycles[J].Journal of Engineering for Thermal Energy and Power,1994,9(6):374-376
[2]WU Feng,CHEN Lingen,Wu Chi,et al.Optimization of Irreversible Magnetic Stirling Cryocoolers[J].International Journal of Engineering Science,2001,39(4):361-368
[3]WU Feng,CHEN Lingen,SUN Fengrui.Finite-time Exergoeconomic Performance Bound for a Quantum Stirling Engine[J].International Journal of Engineering Science,2000,38(2):239-247
[4]Vroylandt H,Bonfils A,Verley G.Efficiency Fluctuations of Small Machines with Unknown Losses[J].Physical Review E,2016,93(5):052123
[5]Curzon F L,Ahlborn B.Efficiency of a Carnot Engine at Maximum Power Output[J].American Journal of Physics,1975,43(1):22-24
[6]Andresen B,Salamon P,Berry R S.Thermodynamics in Finite Time[J].Physics Today,1984(Sept.):62-70
[7]CHEN Lingen,WU Chi,SUN Fengrui.Finite Time Thermodynamic Optimization or Entropy Generation Minimization of Energy Systems[J].Journal of NonEquilibrium Thermodynamics,1999,24(4):327-359
[8]Hoffman K H,Burzler J,Fischer A,et al.Optimal Process Paths for Endoreversible Systems[J].Journal of NonEquilibrium Thermodynamics,2003,28(3):233-268
[9]CHEN Lingen,SUN Fengrui.Advances in Finite Time Thermodynamics:Analysis and Optimization[M].New York:Nova Science Publishers,2004
[10]陈林根.不可逆过程和循环的有限时间热力学分析[M].北京:高等教育出版社,2005CHEN Lingen.Finite Time Thermodynamics Analysis for Irreversible Processes and Cycles[M].Beijing:Higher Education Press,2005
[11]Andresen B.Current Trends in Finite-time Thermodynamics[J].Angewandte Chemie International Edition,2011,50(12):2690-2704
[12]CHEN Lingen,MENG Fankai,SUN Fengrui.Thermo-dynamic Analyses and Optimizations for Thermoelectric Devices:the State of the Arts[J].Science China:Technological Sciences,2016,2016,59(3):442-455
[13]陈林根,夏少军.不可逆过程的广义热力学动态优化[M].北京:科学出版社,2016CHEN Lingen,XIA Shaojun.Generalized Thermodynamic Dynamic-Optimization for Irreversible Processes.Beijing:Science Press,2016
[14]陈林根,夏少军.不可逆循环的广义热力学动态优化[M].北京:科学出版社,2016CHEN Lingen,XIA Shaojun.Generalized Thermodynamic Dynamic-Optimization for Irreversible Cycles.Beijing:Science Press,2016
[15]Kosloff R.Quantum Thermodynamics:A Dynamical Viewpoit J].Entropy,2013,15(6):2100-2128
[16]YIN Yong,CHEN Lingen,WU Feng.Optimal Power and Efficiency of Quantum Stirling Heat Engines[J].European Physical Journal Plus,2017,132:45
[17]吴锋.斯特林机的有限时间热力学研究[D].武汉:海军工程学院,1998.WU Feng.Finite Time Thermodynamics Research for Stirling Engine[D].Doctorial Dissertations,WuHan:Naval Engineering College,1998
[18]吴锋,陈林根,孙丰瑞,等.斯特林机的有限时间热力学优化[M].北京:化学工业出版社,2008.WU Feng,CHEN Lingen,SUN Fengrui,et al.Finite Time Thermodynamic Optimization for Stirling Engine[M].BeiJing:Chemical Industry Press,2008
[19]Kosloff R.A Quantum Mechanical Open System as a Model of a Heat Engine[J].Journal of Chemical Physics,1984,80(4):1625-1631
[20]Geva E,Kosloff R.On the Classical Limit of Quantum Thermodynamics in Finite Time[J].Journal of Chemical Physics,1992,97(5):4398-4412
[21]吴锋,孙丰瑞,陈林根.活塞式量子Stirling发动机最优性能[J].电站系统工程,1996,12(1):41-43WU Feng,SUN Fengrui,CHEN Lingen.Optimum Performance of a Piston Quantum Stirling Engine[J].Power System Engineering,1996,12(1):41-43
[22]WU Feng,YANG Zhichun,CHEN Lingen,et al.Work Output and Efficiency of a Reversible Quantum Otto Cycle[J].Thermal Science,2010,14(4):879-886
[23]吴锋,汪拓,陈林根,等.量子斯特林热机的输出功和热效率[J].机械工程学报,2014,50(4):150-154WU Feng,WANG Tuo,CHEN Lingen,et al.Work Output and Efficiency of Quantum Stirling Engine[J].Journal of Mechanical Engineering,2014,50(4):150-154
[24]王建辉,熊双泉,何济洲,等.以一维谐振子势阱中的单粒子为工质的量子热机性能分析[J].物理学报,2012,61(8):080509WANG Jinhui,XIONG Shuangquan,HE Jizhou,et al.Performance Analysis of a Quantum Heat Engine Working with a Particle in a One-dimensional Harmonic Trap[J].Acta Physica Sinica,2012,61(8):080509
[25]Correa L A,Palao J P,Alonso D.Internal Dissipation and Heat Leaks in Quantum Thermodynamic Cycles[J].Physical Review E,2015,92(3):032136
[26]金晓昌,吴锋,孙丰瑞,等.经典极限下量子卡诺热机拥经济最优性能[J].电站系统工程,1996,12(6):42-45JIN Xiaochang,WU Feng,SUN Fengrui,et al.OptimumExergoeconomic Performance of Quantum Carnot Heat Engine Under the Classical Limit[J].Power System Engineering,1996,12(6):42-45
[27]Feldmann T,Kosloff R.Performance of Discrete Heat Engines and Heat Pumps in Finite Time[J].Physical Review E,2000,61(5):4774-4790
[28]吴锋,孙丰瑞.不可逆量子斯特林制冷机的最大制冷率[J].应用科学学报,1997,15(2):223-228WU Feng,SUN Fengrui.Maximum Cooling Rate of a Irreversible Quantum Stirling Refrigerator[J].Journal of Applied Science,1997,15(2):223-228
[29]金晓昌.量子斯特林制冷机拥经济优化准则[J].武汉化工学院学报,1997,19(3):85-88JIN Xiaochang.Exergoeconomic Optimum Criterion of Quantum Stirling Refrigerator[J].Journal of Wuhan institute of Chemical Technology,1997,19(3):85-88
[30]Acikkalp E,Caner N.Application of Exergetic Sustainable Index to the Quantum Irreversible Diesel Refrigerator Cycles for 1D Box System[J].The European Physical Journal Plus,2015,130:73
[31]Angulo-Brown F.An Ecological Optimization Criterion for Finite-Time Heat Engines[J].Journal of Applied Physics,1991,69(11):7465-7469
[32]Yan Z.Comment on“Ecological Optimization Criterion for Finite-Time Heat Engines”[J].Journal of Applied Physics,1993,73(7):3583
[33]陈林根,孙丰瑞,陈文振.热力循环的生态学品质因素[J].热能动力工程,1994,9(6):374-376CHEN Lingen,SUN Fengrui,CHEN Wenzheng.The Ecological Quality Factor for Thermodynamic Cycles[J].Journal of Engineering for Thermal Energy and Power,1994,9(6):374-376