本文介紹了史特靈引擎再生器中壓降與熱傳特性之初步實驗和數值分析研究。
設計史特靈再生器測試平台用於分析評估與比較不同再生器在穩態條件下的壓降特性，同時進行三維 (3-D) 數值模擬以數值表徵在不同孔隙率和流動邊界條件下通過絲網再生器的壓降現象。
在實驗中，以#300目、#400目、#500目三種不銹鋼網目，以及#300/400/500和 #500/400/300的混合網目，製成直徑5 mm與長45 mm之再生器。穩流測試平台由氦氣罐、浮子流量計、兩個壓力傳感器、與一個特別設計的組件組成，其組件主要放置多孔性結構樣品。目的是在單向流實驗中測量再生器流力特性，如摩擦係數（Cf）、雷諾數（Re）、壓降等。
在數值研究中，使用CFD(計算流體力學)中的FVM(有限體積法)對不同配置的金屬網目進行研究。由標準的二參數 Ergun equation分析計算出之壓降和雷諾數關係式，可應用於等效多孔介質再生器之流力設計。

In this study, the pressure drops and friction factor characteristics of the Stirling engine regenerator were experimentally and numerically studied. The Stirling regenerator test bench is designed to analyze and evaluate different wire mesh regenerators' pressure drop characteristics under steady-state flow conditions. At the same time, 3-D numerical simulations are performed to numerically characterize the pressure loss inside the wire mesh regenerator under different porosity and flow boundary conditions.
 In the experiment, three stainless steel Meshes of #300 Mesh, #400 Mesh, #500 Mesh and a hybrid mesh of #300/400/500 and #500/400/300 mesh of 5 mm diameter and a length of 45 mm were fabricated. The steady flow test bench comprises a helium gas tank, rotameter, two pressure transducers, and a specially designed module that houses the porous structure sample. The goal is to measure the hydrodynamic properties of the regenerator during the single flow experiment. In addition, pressure drop and friction factor correlation were calculated for the set of regenerator wire mesh.
 For different configurations of wire mesh regenerators, the numerical research uses a finite volume method on CFD (computational fluid dynamics) models. The conventional two-parameter Ergun is obtained from the pressure drop and Reynolds number equations, and it may be confidently applied in an identical porous media for future regenerator flow.

Acknowledgement	iv
List of Figures	vii
List of tables	ix
Nomenclature	x
CHAPTER 1. INTRODUCTION	1
1.1 Working principle of Stirling Regenerator	2
1.2 Literature Study	4
1.3 Aim and Scope of Research	8
CHAPTER 2. THEORY OF STIRLING REGENERATOR	9
2.1 Flow characteristics of the Stirling regenerator	9
CHAPTER 3. EXPERIMENTAL METHODOLOGY	13
3.1 Experimental components	13
3.1.1 regenerator	13
3.1.2 Flowmeter	16
3.1.3 Pressure sensor	17
3.2 Experimental measurement	18
CHAPTER 4. DESIGN AND CFD ANALYSIS	22
4.1 Design of regenerator mesh screens	22
4.2 Computational fluid dynamics	24
4.1.1 Computational domain	25
4.1.2 Meshing	27
4.1.3 Boundary conditions	28
4.1.4 Numerical approach	28
4.1.5 Mesh Independence Study	30
4.3 CFD Results	33
CHAPTER 5. CONCLUSION	41
References	43
Appendix Ⅰ	47
Appendix Ⅱ	52
List of Figures
Figure 1. Stirling engine design by R. Stirling in the 19th century [1].	2
Figure 2. (a) Pressure–Volume diagram of the Stirling cycle and (b) Temperature vs. Specific entropy diagram of Stirling cycle.	3
Figure 3. Piston motion of Stirling cycle	3
Figure 4. Actual Stirling cycle	4
Figure 5. Shows regenerator mesh screen parameters.	10
Figure 6. Types of Stirling regenerator matrix. (a) Wire mesh regenerator with a uniform porosity (b) Wire mesh regenerator with multiple porosities.	14
Figure 7. SEM analysis of various wire mesh numbers (a) #300, (b) #400 and (c) #500 wire mesh screens.	15
Figure 8. Regenerator mesh screen filler	15
Figure 9. Experimental setup regenerator housing	16
Figure 10. Flowmeter	17
Figure 11. Pressure sensor	17
Figure 12. (a) The experimental setup and (b) Illustration of the experimental setup.	19
Figure 13. Steady flow pressure drops vs velocity	21
Figure 14. Friction coefficient vs Reynolds Number.	21
Figure 15. Comparison of steel wire mesh with mesh design.	23
Figure 16. Design layouts of stacked wire mesh screens (a) Stacked aligned and (b) Stacked misaligned configurations.	23
Figure 17. Typical CFD modelling workflow.	25
Figure 18. 3-D view of computational fluid domain.	26
Figure 19. Meshing of the fluid domain.	27
 Figure 20. Comparasion of pressure drop for different designs.	31
Figure 21. Comparison of a velocity profile for different mesh designs.	32
Figure 22. Pressure drops vs velocity for aligned mesh configuration of regenerator.	34
Figure 23. Pressure drops vs Velocity for misaligned mesh configuration of regenerator.	35
 Figure 24. Friction coefficient and Reynolds number for aligned mesh configuration.	36
Figure 25. Friction coefficient and Reynolds number for misaligned mesh configuration.	37
Figure 26. Comparison of friction factor vs reynold’s number for aligned and misaligned mesh configuration	40
Figure 27. Comparison of CFD friction factor with the other researchers.	40
List of tables
Table 1. Wire mesh Regenerator parameters.	15
Table 2. Number of mesh screen for different regenerators	26
Table 3. Comparison of Skewness and Orthogonal quality for different design.	31
Table 4. Inlet and Outlet (a) Pressure drop data and (b) Velocity data.	32
Table 5. Correlation equation for aligned wire mesh.	36
Table 6. Correlation equation for misaligned wire mesh.	38
Table 7. Comparison of friction Factor correlation obtained from cited researchers and the present study.	39
Table 8. Summary of steady flow tests for 300 mesh	47
Table 9.  Summary of steady flow tests for 400 mesh.	48
Table 10. Summary of steady flow tests for 500 mesh	49
Table 11. Summary of steady flow tests for 300/400/500 mesh	50
Table 12.  Summary of steady flow tests for 500/400/300 mesh	51
Table 13. CFD pressure drop contour for aligned mesh and misaligned mesh configuration.	52

1. Ackermann, Robert A. Cryogenic regenerative heat exchangers. Springer Science & Business Media, (2013).
2. Kehlhofer, Rolf, Bert Rukes, Frank Hannemann, and Franz Stirnimann. Combined-cycle gas & steam turbine power plants. Pennwell Books, LLC, (2009).
3. Biwa, Tetsushi, Yusuke Tashiro, and Taichi Yazaki. "How does Stirling engine work?." Journal of Power and Energy Systems 2, no. 5 (2008): 1254-1260.
4. He, Mike Miao. Stirling engine for solar thermal electric generation. University of California, Berkeley, (2016).
5. Kays, William Morrow, and Alexander Louis London. "Compact heat exchangers." (1984).
6. Urieli I, Berchowitz DM. Stirling cycle engine analysis. Institute of Physics Publishing; (1984).
7. Simon, Terrence W., and Jorge R. Seume. "A survey of oscillating flow in Stirling engine heat exchangers." NASA STI/Recon Technical Report N 88 (1988): 22322.
8. Sodre, J. R., and J. A. R. Parise. "Friction factor determination for flow through finite wire-mesh woven-screen matrices." (1997): 847-851.
9. Ergun, Sabri. "Fluid flow through packed columns." Chem. Eng. Prog. 48 (1952): 89-94.
10. Miyabe H, Takahashi S, Hamaguchi K. An approach to the design of Stirling ENGINE Regenerator matrix using packs of wire gauzes. Proc IECEC 1982;17:1839–44.
11. Tanaka, Makoto, Iwao Yamashita, and Fumitake Chisaka. "Flow and heat transfer characteristics of the Stirling engine regenerator in an oscillating flow." JSME international journal. Ser. 2, Fluids engineering, heat transfer, power, combustion, thermophysical properties 33, no. 2 (1990): 283-289.
12. Xiao, Gang, Hao Peng, Haoting Fan, Umair Sultan, and Mingjiang Ni. "Characteristics of steady and oscillating flows through regenerator." International Journal of Heat and Mass Transfer 108 (2017): 309-321.
13. Hsu, Chin-Tsau, Huili Fu, and Ping Cheng. "On pressure-velocity correlation of steady and oscillating flows in regenerators made of wire screens." (1999): 52-56.
14. Gedeon D, Wood JG. Oscillating-flow regenerator test rig: hardware and theory with derived correlations for screens and felts. NASA CR-198442; (1996).
15. Garg, Shital Kumar, B. Premachandran, Manmohan Singh, Sunil Sachdev, and Mukesh Sadana. "Effect of Porosity of the regenerator on the performance of a miniature Stirling cryocooler." Thermal Science and Engineering Progress 15 (2020): 100442.
16. J.C. Armour, J.N. Cannon, Fluid flow through woven screens, AIChE J. 14 (3) (1968) 415–420.
17. Thomas, Bernd, and Deborah Pittman. "Update on the evaluation of different correlations for the flow friction factor and heat transfer of Stirling engine regenerators." In Collection of Technical Papers. 35th Intersociety Energy Conversion Engineering Conference and Exhibit (IECEC) (Cat. No. 00CH37022), vol. 1, pp. 76-84. IEEE, (2000).
18. Choi S, Nam K, Jeong S. Investigation on the pressure drop characteristics of cryocooler regenerators under oscillating flow and pulsating pressure conditions. Cryogenics 2004;44(3):203–10.
19. Costa, S. C., Harritz Barrutia, Jon Ander Esnaola, and Mustafa Tutar. "Numerical study of the pressure drop phenomena in wound woven wire matrix of a Stirling regenerator." Energy Conversion and Management 67 (2013): 57-65.
20. Costa, S. C., Igor Barreno, Mustafa Tutar, Jon-Ander Esnaola, and Harritz Barrutia. "The thermal non-equilibrium porous media modelling for CFD study of woven wire matrix of a Stirling regenerator." Energy conversion and management 89 (2015): 473-483.
21. Pathak, M. G., V. C. Patel, S. M. Ghiaasiaan, T. I. Mulcahey, B. P. Helvensteijn, A. Kashani, and J. R. Feller. "Hydrodynamic parameters for erpr cryocooler regenerator fillers under steady and periodic flow conditions." Cryogenics 58 (2013): 68-77.
22. Tao, Y. B., Y. W. Liu, F. Gao, X. Y. Chen, and Y. L. He. "Numerical analysis on pressure drop and heat transfer performance of mesh regenerators used in cryocoolers." Cryogenics 49, no. 9 (2009): 497-503.
23. J. Cha, S. Ghiaasiaan and C. Kirkconnell, Oscillatory flow in microporous media applied in pulse–tube and Stirling–cycle cryocooler regenerators, Experimental thermal and fluid science 32 (2008), no. 6, 1264-1278.
24. Thombare, D. G., and N. Umale. "Theoretical Analysis of Effect of Regenerator Geometry and Material on Stirling Engine Performance." In Proceedings of the 1st National, PG Conference RIT ncon PG–2015, Sangli, Maharashtra, India, vol. 1. (2015).
25. Duygu, İ. P. C. İ. "Investigation on hydrodynamic characteristics of a Stirling regenerator matrix using porous media approach: a CFD study." International Journal of Automotive Engineering and Technologies 9, no. 4: 171-177.
26. Yadav, C. O., U. V. Joshi, and L. N. Patel. " CFD assisted prediction oh hudrodynamic parameters for regenerator of cryocooler." Procedia Technology 14 (2014): 328-335.
27. Clearman, W. M., J. S. Cha, S. M. Ghiaasiaan, and C. S. Kirkconnell. "Anisotropic steady-flow hydrodynamic parameters of microporous media applied to pulse tube and Stirling cryocooler regenerators." Cryogenics 48, no. 3-4 (2008): 112-121.