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Entransy dissiaption minimization for isothermal throttling process

Xia Shao-Jun Chen Lin-Gen Ge Yan-Lin Sun Feng-Rui

Entransy dissiaption minimization for isothermal throttling process

Xia Shao-Jun, Chen Lin-Gen, Ge Yan-Lin, Sun Feng-Rui
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  • A class of isothermal throttling process with generalized mass transfer law is investigated, and the optimality condition for the minimum mass entransy dissipation of the process is obtained by applying optimal control theory. The results for special cases with mass transfer laws [g∝(Δp)m] and [g∝Δ(μ)] are further obtained based on the general optimization result, and the obtained results are also compared with other mass transfer strategies of the minimum entropy generation, constant pressure ratio and constant pressure difference. Numerical examples for the cases with the mass transfer laws [g∝(Δp)1/2], [g∝Δ(p)] and [g∝Δ(μ)] are also provided. The results obtained herein can provide some theoretical guidelines for the optimal design and operation of real throttling processes and devices.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 51176203, 10905093) and the Innovation Foundation for the Doctor of Naval University of Engineering, China (Grant No. HGDBSJJ201102).
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  • [1]

    Andresen B, Salamon P, Berry R S 1977 J. Chem. Phys. 66 1571

    [2]

    Bejan A 1996 J. Appl. Phys. 79 1191

    [3]

    Bejan A 1996 Entropy Generation Minimization (Boca Raton FL: CRC Press)

    [4]

    Chen L, Wu C, Sun F 1999 J. Non-Equilib. Thermodyn. 22 327

    [5]

    Berry R S, Kazakov V A, Sieniutycz S, Szwast Z, Tsirlin A M 1999 Thermodynamic Optimization of Finite Time Processes (Chichester: Wiley)

    [6]

    Chen L G 2005 Finite-Time Thermodynamic Analysis of Irreversible Processes and Cycles (Beijing: Higher Education Press) (in Chinese) [陈林根 2005 不可逆过程和循环的有限时间热力学分析 (北京: 高等教育出版社)]

    [7]

    He J Z, Wang L, Li J B 2005 Acta Phys. Sin. 54 24 (in Chinese) [何济洲, 王磊, 李俊彬 2005 物理学报 54 24]

    [8]

    Wu F, Chen L G, Sun F R, Yu J Y 2008 Finite Time Thermodynamic Optimization for Stirling Machines (Beijing: Chemical Industry Press) (in Chinese) [吴锋, 陈林根, 孙丰瑞, 喻九阳 2008 斯特林机的有限时间热力学优化 (北京: 化学工业出版社)]

    [9]

    Andresen B 2011 Angew. Chem. Int. Ed. 50 2690

    [10]

    Lin G X, Chen J C 2011 J. Xiamen University (Natural Science) 50 227 (in Chinese) [林国星, 陈金灿 2011 厦门大学学报(自然科学版) 50 227]

    [11]

    He B X, He J Z, Miao G L 2011 Acta Phys. Sin. 60 040509 (in Chinese) [贺兵香, 何济洲, 缪贵玲 2011 物理学报 60 040509]

    [12]

    Tu Z C 2012 Chin. Phys. B 21 020513

    [13]

    Cheng H T, He J Z, Xiao Y L 2012 Acta Phys. Sin. 61 010502 (in Chinese) [程海涛, 何济洲, 肖宇玲 2012 物理学报 61 010502]

    [14]

    Li J, Chen L G, Ge Y L, Sun F R 2013 Acta Phys. Sin. 62 130501 (in Chinese) [李俊, 陈林根, 戈延林, 孙丰瑞 2013 物理学报 62 130501]

    [15]

    Bejan A 1977 Trans. ASME J. Heat Transf. 99 374

    [16]

    Badescu V 2004 J. Phys. D: Appl. Phys. 37 2298

    [17]

    Andresen B, Gordon J M 1992 J. Appl. Phys. 71 76

    [18]

    Tsirlin A M, Kazakov V, Kolinko N 2003 Eur. Phys. J. B 35 565

    [19]

    Badescu V 2004 J. Non-Equilib. Thermodyn. 29 53

    [20]

    Andresen B, Gordon J M 1992 Int. J. Heat Fluid Flow 13 294

    [21]

    Chen L G, Xia S J, Sun F R 2009 J. Appl. Phys. 105 044907

    [22]

    Xia S J, Chen L G, Sun F R 2009 Brazilian J. Phys. 39 98

    [23]

    Tsirlin A M, Kazakov V A, Berry R S 1994 J. Phys. Chem. 98 3330

    [24]

    Gordon J M, Rubinstein I, Zarmi Y 1990 J. Appl. Phys. 67 81

    [25]

    Santoro M, Schon J C, Jansen M 2007 Phys. Rev. E 76 061120

    [26]

    Mironova V A 1994 Chimicheskaia Promis Hlennost 4 51

    [27]

    Bi Y H, Chen L G, Sun F R 2012 Int. J. Energy Res. 36 269

    [28]

    Tsirlin A M 1997 Methods of Averaging Optimization and Their Application (Moscow: Physical and Mathematical Literature Publishing Company) (in Russian)

    [29]

    Tsirlin A M 2002 Optimization Methods in Thermodynamics and Microeconomics (Moscow: Nauka) (in Russian)

    [30]

    Tsirlin A M 2003 Irreversible Estimates of Limiting Possibilities of Thermodynamic and Microeconomic Systems (Moscow: Nauka) (in Russian)

    [31]

    Tsirlin A M 2011 Optimization for Thermodynamic and Economic Systems (Moscow: Nauka) (in Russian)

    [32]

    Tsirlin A M, Mironova V A, Amelkin S A, Kazakov V A 1998 Phys. Rev. E 58 215

    [33]

    Mironova V A, Amelkin S A, Tsirlin A M 2000 Mathematical Methods of Finite Time Thermodynamics (Moscow: Khimia) (in Russian)

    [34]

    Guo Z Y, Zhu H Y, Liang X G 2007 Int. J. Heat Mass Transf. 50 2545

    [35]

    Guo Z Y 2008 J. Eng. Thermophys. 29 112 (in Chinese) [过增元 2008 工程热物理学报 29 112]

    [36]

    Guo Z Y, Liang X G, Zhu H Y 2006 Prog. Nat. Sci. 16 1288 (in Chinese) [过增元, 梁新刚, 朱宏晔 2006 自然科学进展 16 1288]

    [37]

    Zhu H Y, Chen Z J, Guo Z Y 2007 Prog. Nat. Sci. 17 1692 (in Chinese) [朱宏晔, 陈泽敬, 过增元 2007 自然科学进展 17 1692]

    [38]

    Hu G J, Guo Z Y 2011 J. Eng. Thermophys. 32 1005 (in Chinese) [胡帼杰, 过增元 2011 工程热物理学报 32 1005]

    [39]

    Cheng X T, Liang X G, Xu X H 2011 Acta Phys. Sin. 60 060512 (in Chinese) [程雪涛, 梁新刚, 徐向华 2011 物理学报 60 060512]

    [40]

    Hu G J, Cao B Y, Guo Z Y 2011 Chin. Sci. Bull. 56 2974

    [41]

    Xu M T 2012 Energy 44 973

    [42]

    Guo Z Y, Cheng X G, Xia Z Z 2003 Chin. Sci. Bull. 48 406

    [43]

    Han G Z, Guo Z Y 2006 J. Eng. Thermophys. 27 811 (in Chinese) [韩光泽, 过增元 2006 工程热物理学报 27 811]

    [44]

    Chen L G, Wei S H, Sun F R 2008 J. Phys. D: Appl. Phys. 41 195506

    [45]

    Chen L G, Wei S H, Sun F R 2009 J. Appl. Phys. 105 94906

    [46]

    Xie Z H, Chen L G, Sun F R 2009 Chin. Sci. Bull. 54 4418

    [47]

    Ge L, Xu M T, Cheng L 2011 J. Eng. Thermophys. 32 993 (in Chinese) [葛亮, 许明田, 程林 2011 工程热物理学报 32 993]

    [48]

    Chen L G 2012 Sci. China: Tech. Sci. 55 802

    [49]

    Chen L G, Feng H J, Xie Z H, Sun F R 2013 Acta Phys. Sin. 62 134401 (in Chinese) [陈林根, 冯辉君, 谢志辉, 孙丰瑞 2013 物理学报 62 134401]

    [50]

    Feng H J, Chen L G, Xie Z H, Sun F R 2013 Acta Phys. Sin. 62 134703 (in Chinese) [冯辉君, 陈林根, 谢志辉, 孙丰瑞 2013 物理学报 62 134703]

    [51]

    Chen Q, Ren J X 2008 Chin. Sci. Bull. 53 3753

    [52]

    Wang S P, Chen Q L, Zhang B J 2009 Chin. Sci. Bull. 54 3572

    [53]

    Xu M T, Guo J F, Cheng L 2009 Front. Energy Power Eng. China 3 402

    [54]

    Liu W, Liu Z C, Jia H, Fan A W, Nakayama A 2011 Int. J. Heat Mass Transf. 53 3049

    [55]

    Cheng X T, Zhang Q Z, Xu X H, Liang X G 2013 Chin. Phys. B 22 02503

    [56]

    Li Z X, Guo Z Y 2011 Advances Transp. Phenom. 2 1

    [57]

    Li Z X, Guo Z Y 2010 Field Synergy Theory for Convective Heat Transfer Optimization (Beijing: Science Press) (in Chinese) [李志信, 过增元 2010 对流传热优化的场协同理论 (北京: 科学出版社)]

    [58]

    Wu J, Liang X G 2008 Sci. China E: Tech. Sci. 51 1306

    [59]

    Cheng X T, Xu X H, Liang X G 2010 J. Eng. Thermophys. 31 1031 (in Chinese) [程雪涛, 徐向华, 梁新刚 2010 工程热物理学报 31 1031]

    [60]

    Cheng X T, Liang X G 2012 J. Eng. Thermophys. 33 311 (in Chinese) [程雪涛, 梁新刚 2012 工程热物理学报 33 311]

    [61]

    Wu J, Cheng X T 2013 Int. J. Heat Mass Transf. 58 374

    [62]

    Xia S J, Chen L G, Sun F R 2010 Sci. China E: Tech. Sci. 53 960

    [63]

    Liu X B, Guo Z Y 2009 Acta Phys. Sin. 58 4766 (in Chinese) [柳雄斌, 过增元 2009 物理学报 58 4766]

    [64]

    Xia S J, Chen L G, Sun F R 2009 Chin. Sci. Bull. 54 3587

    [65]

    Guo J F, Xu M T, Cheng L 2010 Sci. China E: Tech. Sci. 53 1309

    [66]

    Guo Z Y, Liu X B, Tao W Q, Shah R K 2010 Int. J. Heat Mass Transf. 53 2877

    [67]

    Xia S J, Chen L G, Sun F R 2010 Appl. Math. Model. 34 2242

    [68]

    Guo J F, Xu M T 2012 Appl. Thermal Eng. 36 227

    [69]

    Guo J F, Huai X L 2012 Energy 41 335

    [70]

    Wang W H, Cheng X T, Liang X G 2013 Sci. China E: Tech. Sci. 56 529

    [71]

    Cheng X T, Liang X G 2012 Energy 44 964

    [72]

    Zhou B, Cheng X T, Liang X G 2013 Sci. China E: Tech. Sci. 56 228

    [73]

    Chen L G 2012 Chin. Sci. Bull. 57 4404

    [74]

    Chen Q, Liang X G, Guo Z Y 2013 Int. J. Heat Mass Transf. 63 65

    [75]

    Chen Q, Meng J A 2008 Int. J. Heat Mass Transf. 51 2863

    [76]

    Chen Q, Ren J X, Guo Z Y 2008 Int. J. Heat Mass Transf. 51 873

    [77]

    Chen Q, Ren J, Guo Z 2009 Chin. Sci. Bull. 54 2862

    [78]

    Jiang Y, Liu X H, Xie X Y 2011 Heating Ventilating & Air Conditioning 41 1 (in Chinese) [江亿, 刘晓华, 谢晓云 2011 暖通空调 41 1]

    [79]

    Jiang Y, Xie X Y, Liu X H 2011 Heating Ventilating & Air Conditioning 41 51 (in Chinese) [江亿, 谢晓云, 刘晓华 2011 暖通空调 41 51]

    [80]

    Liu X H, Jiang Y, Zhang T, Zhang L 2011 Heating Ventilating & Air Conditioning 41 29 (in Chinese) [刘晓华, 江亿, 张涛, 张伦 2011 暖通空调 41 29]

    [81]

    Zhang T, Liu X H, Zhang L, Jiang Y 2012 Energy Convers. Manage. 59 103

    [82]

    Chen L, Chen Q, Li Z, Guo Z Y 2010 Chin. Sci. Bull. 55 1445

    [83]

    Chen Q, Yang K, Wang M R, Pan N, Guo Z Y 2010 Energy 35 2448

    [84]

    Chen Q, Pan N, Guo Z Y 2011 Energy 36 2890

    [85]

    Yuan F, Chen Q 2012 Chin. Sci. Bull. 57 687

    [86]

    Yuan F, Chen Q 2012 Energy 42 181

    [87]

    Xia S J, Chen L G, Sun F R 2011 Sci. China E: Tech. Sci. 53 352

    [88]

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  • Received Date:  04 May 2013
  • Accepted Date:  18 June 2013
  • Published Online:  05 September 2013

Entransy dissiaption minimization for isothermal throttling process

  • 1. Institute of Thermal Science and Power Engineering, Naval University of Engineering, Wuhan 430033, China;
  • 2. Military Key Laboratory for Naval Ship Power Engineering, Naval University of Engineering, Wuhan 430033, China;
  • 3. College of Power Engineering, Naval University of Engineering, Wuhan 430033, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant Nos. 51176203, 10905093) and the Innovation Foundation for the Doctor of Naval University of Engineering, China (Grant No. HGDBSJJ201102).

Abstract: A class of isothermal throttling process with generalized mass transfer law is investigated, and the optimality condition for the minimum mass entransy dissipation of the process is obtained by applying optimal control theory. The results for special cases with mass transfer laws [g∝(Δp)m] and [g∝Δ(μ)] are further obtained based on the general optimization result, and the obtained results are also compared with other mass transfer strategies of the minimum entropy generation, constant pressure ratio and constant pressure difference. Numerical examples for the cases with the mass transfer laws [g∝(Δp)1/2], [g∝Δ(p)] and [g∝Δ(μ)] are also provided. The results obtained herein can provide some theoretical guidelines for the optimal design and operation of real throttling processes and devices.

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