Fractal Characterization of Regenerator of Micro Stirling Coolers
-
摘要: 为研究回热器中填充结构的微观结构特征,基于多孔介质分形理论,使用压汞法对回热器孔隙分布情况及分形维数进行研究。回热器是微型斯特林制冷机的关键部件,使用不锈钢网片或不锈钢毡填充制备的回热器是一种典型的多孔介质。采用压汞法对回热器进行微观结构测试,得出回热器内部孔隙分布范围。结合多孔介质分形分析的基础理论,计算得出回热器分形维数,说明了回热器具有分形特征,得出回热器的分形维数区间。Abstract: To investigate the microstructural characteristics of the filling structure in a regenerator, based on the fractal theory of porous media, the mercury intrusion method was used to study the pore distribution and fractal dimension of the regenerator. The regenerator is a key component of a miniature Stirling cooler. The regenerator prepared by filling stainless steel mesh or stainless steel felt is a typical porous medium. The microstructure of the regenerator was tested using the mercury intrusion method, and the pore distribution range inside the regenerator was obtained. Combined with the basic theory of fractal analysis of porous media, the fractal dimension of the regenerator is calculated, which shows that the regenerator has fractal characteristics, and the fractal dimension interval of the regenerator can be obtained.
-
Key words:
- Stirling cooler /
- regenerator /
- porous media /
- fractal
-
表 1 实验样品参数
Table 1. Sample parameters
Number 1# 4# 7# 10# 13# mesh number 500 420 220 420 500 mass/g 3.53 2.64 2.15 2.27 3.53 Filling method Manual Manual Manual Manual Mechanical 表 2 样品孔隙率及分形维数
Table 2. Porosity & Df
Number 1# 4# 7# 10# 13# Porosity 63.94% 69.41% 75.15% 72.44% 68.72% Df 2.592 2.639 2.763 2.681 2.351 -
[1] Barron R F. Cryogenic Systems[M]. Clarendon Press, 1985. [2] 陈曦, 郭永飞, 张华, 等. 回热式低温制冷机用回热器结构研究综述[J]. 制冷学报, 2011(3): 6-14, 28. https://www.cnki.com.cn/Article/CJFDTOTAL-ZLXB201103003.htmCHEN Xi, GUO Yongfei, ZHANG Hua, et al. Review of investigation on regenerator for regenerative cryocoolers[J]. Journal of Refrigeration, 2011(3): 6-14, 28. https://www.cnki.com.cn/Article/CJFDTOTAL-ZLXB201103003.htm [3] Katz A, Thompson A. Fractal sandstone pores: implications for conductivity and pore formation[J]. Physical Review Letters, 1985, 54(12): 1325. doi: 10.1103/PhysRevLett.54.1325 [4] Krohn C, Thompson A. Fractal sandstone pores: automated measurements using scanning-electron-microscope images[J]. Physical Review B, 1986, 33(9): 6366. doi: 10.1103/PhysRevB.33.6366 [5] Bartoli F, Philippy R, Doirisse M, et al. Structure and self-similarity in silty and sandy soils: the fractal approach[J]. Journal of Soil Science, 1991, 42(2): 167-185. doi: 10.1111/j.1365-2389.1991.tb00399.x [6] YU B, CHENG P. A fractal permeability model for Bi-dispersed porous media[J]. International Journal of Heat and Mass Transfer, 2002, 45(14): 2983-2993. doi: 10.1016/S0017-9310(02)00014-5 [7] Bo-ming Y, Kai-lun Y. Critical percolation probabilities for site problems on Sierpinski carpets[J]. Zeitschrift Für Physik B Condensed Matter. , 1988, 70(2): 209-212. doi: 10.1007/BF01318301 [8] Mandelbrot B B. The Fractal Geometry of Nature[M]. New York: Wh Freeman, 1982. [9] YU B, LI J. Some fractal characters of porous media[J]. Fractals, 2001, 9(3): 365-372. doi: 10.1142/S0218348X01000804 [10] 刘培生, 陈国锋. 多孔固体材料[M]. 北京: 化学工业出版社, 2014.LIU Peisheng, CHEN Guofeng. Porous Solid Materials[M]. Beijing: Chemical Industry Press, 2014. [11] YU B, Lee L J, CAO H. A fractal in‐plane permeability model for fabrics[J]. Polymer Composites, 2002, 23(2): 201-221. doi: 10.1002/pc.10426 [12] XU P, YU B. Developing a new form of permeability and Kozeny–carman constant for homogeneous porous media by means of fractal geometry[J]. Advances in Water Resources, 2008, 31(1): 74-81. doi: 10.1016/j.advwatres.2007.06.003 [13] 王欣, 齐梅, 胡永乐, 等. 高压压汞法结合分形理论分析页岩孔隙结构[J]. 大庆石油地质与开发, 2015, 34(2): 165-169. https://www.cnki.com.cn/Article/CJFDTOTAL-DQSK201502033.htmWANG Xin, QI Mei, Hu Yongle, et al. Analysis of the shale pore structures by the combination of high-pressure mercury injection and fractal theory[J]. Petroleum Geology and Oilfield Development in Daging, 2015, 34(2): 165-169. https://www.cnki.com.cn/Article/CJFDTOTAL-DQSK201502033.htm [14] Sing K S. Characterization of Porous Solids: an Introductory Survey[Z]. Elsevier, 1991: 1-9.