本研究之目的為進行三維史特靈熱泵之全模組數值模擬分析。由於史特靈熱泵的原理在於利用輸入功且在冷端吸收冷端水套能量後，在熱端進行放熱，將熱源傳遞給熱端水套以作為熱水進行應用，以至於除了內部工作流體之熱流場分析之外，水套分析也極為重要。全模組由內部工作流體、冷端水套與冷端固體以及熱端水套與熱端固體所組成。藉由CFD模擬將全模組進行數值計算並探討內部熱流場變化。除此之外，將全模組進行參數分析且探討對象可分為填充壓力、轉速、孔隙率以及流量等各項參數對史特靈熱泵之性能影響。其中，本模擬之參數分析中，最大放熱率在填充壓力為15bar的時候，其值為2975W；最大性能係數在轉速為500rpm的時候，其值為2.34。最後將模擬結果與實驗進行比較驗證。除此之外，全模組也透過基準組之模擬結果所知的不良因素影響而進行模組改良以利於改善史特靈熱泵之性能，並針對其模擬結果進行分析與討論。

The purpose of this study is to conduct a full module numerical simulation analysis of a three-dimensional Stirling heat pump. Stirling heat pumps are used as water heaters. In addition to analyzing the internal working fluid, water jacket analysis is also extremely important. The full module is composed of the heat pump’s internal working fluid, the cold end water jacket and solid part, as well as the hot end water jacket and solid part. Numerical calculations are carried out by the means of CFD simulations and the internal heat flow field changes are discussed. In the parametric analysis of this simulation, the maximum heat rejection rate is 2975W at the charged pressure of 15 bar, and the maximum COP is 2.34 at the rotational speed of 500 rpm. The simulation results are then compared to the experimental results. Finally, through the influence of the adverse factors known by the simulation results of the benchmark group, the module is improved to enhance the performance of the Stirling heat pump, and the simulation results are analyzed and discussed.

[1] A. Hepbasli and Y. Kalinci, "A Review of Heat Pump Water Heating Systems," Renewable and Sustainable Energy Reviews, vol. 13, no. 6-7, pp. 1211-1229, 2009.
[2] K. J. Chua, S. K. Chou, and W. Yang, "Advances in Heat Pump Systems: A Review," Applied Energy, vol. 87, no. 12, pp. 3611-3624, 2010.
[3] B. Kongtragool and S. Wongwises, "A Review of Solar-Powered Stirling Engines and Low Temperature Differential Stirling Engines," Renewable and Sustainable Energy Reviews, vol. 7, no. 2, pp. 131-154, 2003.
[4] H. Solmaz, S. M. S. Ardebili, F. Aksoy, A. Calam, E. Yılmaz, and M. Arslan, "Optimization of the Operating Conditions of a Beta-Type Rhombic Drive Stirling Engine by Using Response Surface Method," Energy, vol. 198, p. 117377, 2020.
[5] I. Urieli and D. M. Berchowitz, Stirling Cycle Engine Analysis, Taylor & Francis, 1984.
[6] D. Erol, H. Yaman, and B. Doğan, "A Review Development of Rhombic Drive Mechanism Used in the Stirling Engines," Renewable and Sustainable Energy Reviews, vol. 78, pp. 1044-1067, 2017.
[7] H. Hachem, M. Creyx, R. Gheith, E. Delacourt, C. Morin, F. Aloui, & S. B. Nasrallah, "Comparison Based on Exergetic Analyses of Two Hot Air Engines: A Gamma Type Stirling Engine and an Open Joule Cycle Ericsson Engine," Entropy, vol. 17, no. 11, pp. 7331-7348, 2015.
[8] J. L. Hess and A. M. O. Smith, "Calculation of Potential Flow about Arbitrary Bodies," Progress in Aerospace Sciences, vol. 8, pp. 1-138, 1967.
[9] G. Walker, R. Fauvel, R. Gustafson, and J. Van Bentham, "Stirling Engine Heat Pumps," International Journal of Refrigeration, vol. 5, no. 2, pp. 91-97, 1982.
[10] W. R. Martini, Stirling Engine Design Manual, Martini Engineering Richland, 1983.
[11] S. Petrescu, M. Costea, C. Harman, and T. Florea, "Application of the Direct Method to Irreversible Stirling Cycles with Finite Speed," International Journal of Energy Research, vol. 26, no. 7, pp. 589-609, 2002.
[12] K. Mahkamov, "An Axisymmetric Computational Fluid Dynamics Approach to the Analysis of the Working Process of a Solar Stirling Engine," Journal of Solar Energy Engineering, vol. 128, pp. 45-53, 2006.
[13] Y. Timoumi, I. Tlili, and S. B. Nasrallah, "Design and Performance Optimization of GPU-3 Stirling Engines," Energy, vol. 33, no. 7, pp. 1100-1114, 2008.
[14] E. Rogdakis, P. Bitsikas, G. Dogkas, and G. Antonakos, "Three-Dimensional CFD Study of a β-Type Stirling Engine," Thermal Science and Engineering Progress, vol. 11, pp. 302-316, 2019.
[15] J. Sauer and H.-D. Kuehl, "Numerical Model for Stirling Cycle Machines Including a Differential Simulation of the Appendix Gap," Applied Thermal Engineering, vol. 111, pp. 819-833, 2017.
[16] S. Abdullah, B. F. Yousif, and K. Sopian, "Design Consideration of Low Temperature Differential Double-Acting Stirling Engine for Solar Application," Renewable Energy, vol. 30, no. 12, pp. 1923-1941, 2005.
[17] M. H. Ahmadi, M.-A. Ahmadi, A. H. Mohammadi, M. Mehrpooya, and M. Feidt, "Thermodynamic Optimization of Stirling Heat Pump Based on Multiple Criteria," Energy Conversion and Management, vol. 80, pp. 319-328, 2014.
[18] M. H. Ahmadi, M. A. Ahmadi, R. Bayat, M. Ashouri, and M. Feidt, "Thermo-Economic Optimization of Stirling Heat Pump by Using Non-Dominated Sorting Genetic Algorithm," Energy Conversion and Management, vol. 91, pp. 315-322, 2015.
[19] C. H. Cheng, H. S. Yang, and H. X. Chen, "Development of a Beta‐type Stirling Heat Pump with Rhombic Drive Mechanism by a Modified Non‐Ideal Adiabatic Model," International Journal of Energy Research, vol. 44, no. 7, pp. 5197-5208, 2020.
[20] 謝宗晏，史特靈熱泵之設計與理論分析，國立成功大學航空及太空工程學系碩士學位論文，2017。
[21] 陳宏信，瓩級史特靈熱泵之實驗與理論分析，國立成功大學航空及太空工程學系碩士學位論文，2019。
[22] E. Marušić-Paloka and I. Pažanin, "Effects of Boundary Roughness and Inertia on the Fluid Flow Through a Corrugated Pipe and the Formula for the Darcy–Weisbach Friction Coefficient," International Journal of Engineering Science, vol. 152, p. 103293, 2020.
[23] L. F. Moody, "Friction Factors for Pipe Flow," Trans. Asme, vol. 66, pp. 671-684, 1944.
[24] E. Marušić-Paloka, "Effective Fluid Behavior in Domain with Rough Boundary and the Darcy–Weisbach Law," SIAM Journal on Applied Mathematics, vol. 79, pp. 1244-1270, 2019.
[25] G. Dogkas, E. Rogdakis, and P. Bitsikas, "3D CFD Simulation of a Vuilleumier Heat Pump," Applied Thermal Engineering, vol. 153, pp. 604-619, 2019.
[26] J. L. Salazar and W.-L. Chen, "A Computational Fluid Dynamics Study on the Heat Transfer Characteristics of the Working Cycle of a β-Type Stirling Engine," Energy Conversion and Management, vol. 88, pp. 177-188, 2014.
[27] A. K. Almajri, S. Mahmoud, and R. Al-Dadah, "Modelling and Parametric Study of an Efficient Alpha Type Stirling Engine Performance Based on 3D CFD Analysis," Energy Conversion and Management, vol. 145, pp. 93-106, 2017.
[28] H. Kuehl, "Numerically Efficient Modelling of Non-Ideal Gases and Their Transport Properties in Stirling Cycle Simulation," In Proceedings of the 17th International Stirling Engine Conference and Exhibition (ISEC), Newcastle Upon Tyne, UK, pp. 24-26, 2016.
[29] A. Fluent, Ansys Fluent 12.0 Theory Guide, ANSYS Inc., 2009.
[30] A. A. Boroujerdi and M. Esmaeili, "Characterization of the Frictional Losses and Heat Transfer of Oscillatory Viscous Flow Through Wire-Mesh Regenerators," Alexandria Engineering Journal, vol. 54, no. 4, pp. 787-794, 2015.
[31] M. Ghaneifar, H. Arasteh, R. Mashayekhi, A. Rahbari, R. Babaei Mahani, and P. Talebizadehsardari, "Thermohydraulic Analysis of Hybrid Nanofluid in a Multilayered Copper Foam Heat Sink Employing Local Thermal Non-Equilibrium Condition: Optimization of Layers Thickness," Applied Thermal Engineering, vol. 181, 2020.
[32] Y. Mahmoudi and N. Karimi, "Numerical Investigation of Heat Transfer Enhancement in a Pipe Partially Filled with a Porous Material under Local Thermal Non-Equilibrium Condition," International Journal of Heat and Mass Transfer, vol. 68, pp. 161-173, 2014.
[33] W. P. Jones and B. E. Launder, "The Prediction of Laminarization with a Two-Equation Model of Turbulence," International Journal of Heat and Mass Transfer, vol. 15, no. 2, pp. 301-314, 1972.
[34] Z. U. Warsi, Fluid Dynamics: Theoretical and Computational Approaches, CRC press, 2005.
[35] P. A. Durbin and B. P. Reif, Statistical Theory and Modeling for Turbulent Flows, John Wiley & Sons, 2011.
[36] R. I. Issa, "Solution of the Implicitly Discretised Fluid Flow Equations by Operator-splitting," Journal of Computational Physics, vol. 62, no. 1, pp. 40-65, 1986.
[37] W. K. Anderson and D. L. Bonhaus, "An Implicit Upwind Algorithm for Computing Turbulent Flows on Unstructured Grids," Computers & Fluids, vol. 23, no. 1, pp. 1-21, 1994.
[38] H. Hachem, R. Gheith, F. Aloui, S. B. Nasrallah, and M. Wang, "A CFD Analysis of the Air Flow Through the Stirling Engine’s Singularities," In Exergy for A Better Environment and Improved Sustainability 1, Green Energy and Technology, ch. Chapter 19, pp. 271-287, 2018.
[39] 游硯評，熱交換器設計對史特靈熱泵性能的影響，國立成功大學航空及太空工程學系碩士學位論文，2021。