Thermodynamic optimization for a quantum thermoacoustic refrigeration micro-cycle

Abstract

A model of quantum thermoacoustic refrigeration micro-cycle (QTARMC) is established in which heat leakage is considered. A single particle contained in a one-dimensional harmonic potential well is studied, and the system consists of countless replicas. Each particle is confined in its own potential well, whose occupation probabilities can be expressed by the thermal equilibrium Gibbs distributions. Based on the Schrodinger equation, the expressions of coefficient of performance (COP) and cooling rate for the refrigerator are obtained. Effects of heat leakage on the optimal performance are discussed. The optimal performance region of the refrigeration cycle is obtained by the using of Q objective function. The results obtained can enrich the thermoacoustic theory and expand the application of quantum thermodynamics.

Keywords

thermoacoustic refrigeration / quantum mechanics / thermal phonon / performance optimization / finite time thermodynamics

References

[1] SwiftG W. Thermoacoustic engine [J]. J Acoust Soc Am, 1988, 84(4): 1145-1180

[2] WuF, LiQ, GuoF Z, ShuA Q. Advance in thermoacoustic theory [J]. J Wuhan Inst Tech, 2012, 34(1): 1-6(in Chinese)

[3] HariharanN M, SivashanmugamP, KasthurirenganS. Studies on performance of thermoacoustic prime mover [J]. Experimental Heat Transfer, 2015, 28: 267-281

[4] WuF, ShuA Q, GuoF Z, WanT. Thermoacoustic oscillation basing on parameter exciting [J]. Energy, 2014, 68: 370-376

[5] GuoF Z, LiQHeat dynamics [M], 2007, Wuhan, Huazhong University of Science & Technology Press(in Chinese)

[6] TijaniM E H, ZeegersJ C H, De WaeleA T A M. Design of thermoacoustic refrigerators [J]. Cryogenics, 2002, 42(1): 49-57

[7] SwiftG W. Thermoacoustics: A unifying perspective for some engines and refrigerators [J]. J Acoust Soc Am, 2003, 113(5): 2379-2381

[8] GarrettS L, AdeffJ A, HoflerT J. A thermoacoustic refrigerator for space applications [J]. Trans AIAA J Thermophys & Heat Transfer, 2012, 85(7): 595-599

[9] DaiW, LuoE C, HuJ Y, LingH. A heat-driven thermoacoustic cooler capable of reaching liquid nitrogen temperature [J]. Appl Phys Lett, 2005, 86(22): 779-785

[10] KosloffR. Quantum thermodynamics: A dynamical viewpoit [J]. Entropy, 2013, 15(6): 2100-2128

[11] GevaE, KosloffR. A quantum-mechanical heat engine operating in finite time: A model consisting of spin-1/2 systems as working fluid [J]. J Chem Phys, 1992, 96(4): 3054-3067

[12] GevaE, KosloffR. On the classical limit of quantum thermodynamics in finite time [J]. J Chem Phys, 1992, 97(6): 4398-4412

[13] WuF, ChenL G, SunF R, WuC. Finite-time exergoeconomic performance bound for a quantum Stirling engine [J]. Int J Eng Sci, 2000, 38(2): 239-247

[14] WuF, ChenL G, SunF R, ZhuY H. Performance and optimization criteria for forward and reverse quantum Stirling cycles [J]. Energy Convers Mgmt, 1998, 39(8): 733-739

[15] WangJ H, HeJ Z, MaoZ Y. Performance of a quantum heat engine cycle working with harmonic oscillator systems [J]. Sci in China, Series G, Phys, Mech & Astron, 2007, 50(2): 163-176

[16] WuF, YangZ Z, ChenL G, LiuX W. Work output and efficiency of a reversible quantum Otto cycle [J]. Thermal Sci, 2010, 14(4): 879-886

[17] ChenL G, LiuX W, GeY L, WuF, SunF R. Ecological optimization of irreversible harmonic oscillator Carnot refrigerator [J]. J Energy Instit, 2016, 86(2): 85-96

[18] LiuS N, OuC J. Maximum power output of quantum heat engine with energy bath [J]. Entropy, 2016, 18(6): 205

[19] WuF, ChenL G, LiQ, WuC. Thermodynamic performance on a thermoacoustic micro-cycle under the condition of weak gas degeneracy [J]. Appl Energy, 2009, 86781119-1123

[20] FeldmannT, KosloffR. Performance of discrete heat engines and heat pumps in finite time [J]. Phys Rev E, 2000, 61(5): 4774-4790

[21] LiuX W, ChenL G, WuF, SunF R. Ecological optimization of an irreversible quantum Carnot heat engine with spin-1/2 systems [J]. Phys Scr, 2010, 81(2): 025003

[22] HoflerT J. Development of a miniature thermoacoustic refrigerator [J]. J Acous Soc Am, 2000, 10852554-2560

[23] SymkoO G, Abdel-RahmanE, KwonY S, EmmiM, BehuninR. Design and development of high-frequency thermoacoustic engines for thermal management in microelectronics [J]. Microelectron J, 2004, 35(2): 185-191

[24] LuoD L, WuF, GuoF Z, ZhangC P. Optimization design of the hot end heat exchanger in subminiature heat-driven thermoacoustic acoustic engine [J]. Cryo & Supercon, 2006, 34(4): 258-262(in Chinese)

[25] DENYS P. Performance measurement of a mini thermoacoustic refrigerator and associated drivers [D]. Naval Postgraduate School, 2002.

[26] MessiahAQuantum mechanics [M], 1999, New York, Dover Publications

[27] KieuT D. The second law, Maxwell’s demon, and work derivable from quantum heat engines [J]. Phys Rev Lett, 2004, 93(14): 140403

[28] HeX, HeJ Z. Thermal entangled four-level quantum Otto heat engine [J]. Sci in China, Series G: Phy, Mech & Astron, 2012, 55101751-1756

[29] YinY, ChenL G, WuF. Optimal power and efficiency of quantum Stirling heat engines [J]. Eur Phys J Plus, 2017, 132(1): 45

[30] VonS M R, GemmerJ. Some trends in quantum thermodynamics [J]. Entropy, 2014, 1663434-3470

[31] QingE, WuF, YinY, LiuX. Optimal power and efficiency of quantum thermoacoustic micro-cycle working in 1D harmonic trap [J]. Journal of Low Temperature Physics, 2017, 189(12): 84-97

[32] QingE, WuF. Performance analysis for quantum thermoacoustic refrigeration micro-cycle working in generalized 1D potential [J]. Journal of Central South University (Science and Technology), 2019, 50(3): 726-733(in Chinese)

[33] Calvo-HernandezA, MedinaA, RocoJ M M. Time, entropy generation, and optimization in low-dissipation heat devices [J]. New Journal of Physics, 2015, 17075011