Weight Analysis of Influencing Factors of Clearance Seal Leakage in Stirling Cryocoolers
-
摘要: 为分析斯特林制冷机间隙密封泄漏量影响因素权重,结合同心环形缝隙流动理论,确定影响因素包括间隙厚度、密封长度、间隙两端压差、转速、间隙内径以及活塞冲程。通过正交试验搭建32组数学模型,基于计算流体CFD数值模拟的方法,研究分析不同密封间隙的泄漏情况。利用方差分析对仿真结果进行处理,结果表明间隙厚度对斯特林制冷机的泄漏量影响最大;压差、密封长度、活塞冲程以及转速对泄漏量影响依次减小;间隙内径对泄漏量影响最小。这对斯特林制冷机间隙密封减小泄漏量的设计提供了参考。Abstract: In this study, the weight analysis of the influencing factors of clearance seal leakage of Stirling cryocoolers was conducted based on the concentric annular gap flow theory. Influencing factors, including sealing gap height, length, pressure difference, motor speed, clearance diameter, and piston stroke, were determined. Through an orthogonal test, 32 sets of mathematical models were established, and the leakages of different seal clearances were analyzed based on the numerical simulation method of computational fluid dynamics. The simulation results were processed using variance analysis, and indicated that the clearance thickness exhibited the most significant influence on the leakage of a Stirling refrigerator. Pressure difference, sealing gap length, piston stroke, and motor speed exhibited a lower influence, where as clearance diameter demonstrated a minimal impact on leakage. This study provides a reference for the design of a Stirling cryocooler clearance seal to reduce leakage.
-
Key words:
- clearance seal /
- orthogonal test /
- weight analysis /
- leakage
-
表 1 影响因素设置
Table 1. Factors setting table
Levels A/mm B/mm C/Pa D/(r/min) E/mm F/mm 1 4 9.5 200000 1000 12 2 2 8 13.5 500000 2000 14 2.6 3 12 17.5 800000 3000 17 3.2 4 16 21.5 1100000 4000 21 4 表 2 正交试验表
Table 2. Orthogonal test table
Test numbers Clearance thickness Sealing gap length Pressure difference Motor speed Clearance diameter Piston stroke Nullcolumn Leakage Sum of evaluation indexes yi 1 1 1 1 1 1 1 1 1.27566E-05 0.99825 2 1 2 2 2 2 2 2 4.06038E-05 0.98505 3 1 3 3 3 3 3 3 1.78506E-04 0.91969 4 1 4 4 4 4 4 4 3.01509E-04 0.86139 5 2 1 1 2 2 3 3 1.25877E-04 0.94463 6 2 2 2 1 1 4 4 1.39146E-04 0.93834 7 2 3 3 4 4 1 1 2.89947E-04 0.86687 8 2 4 4 3 3 2 2 1.01106E-03 0.52507 9 3 1 2 3 4 1 2 9.60161E-04 0.54920 10 3 2 1 4 3 2 1 5.26293E-04 0.75484 11 3 3 4 1 2 3 4 9.09569E-04 0.57318 12 3 4 3 2 1 4 3 4.62742E-04 0.78497 13 4 1 2 4 3 3 4 8.76374E-04 0.58891 14 4 2 1 3 4 4 3 8.34327E-04 0.60884 15 4 3 4 2 1 1 2 1.31809E-03 0.37955 16 4 4 3 1 2 2 1 8.93187E-04 0.58094 17 1 1 4 1 4 2 3 8.39161E-04 0.60655 18 1 2 3 2 3 1 4 6.59262E-05 0.97305 19 1 3 2 3 2 4 1 2.42253E-05 0.99281 20 1 4 1 4 1 3 2 9.06550E-06 1.00000 21 2 1 4 2 3 4 1 1.86725E-03 0.11925 22 2 2 3 1 4 3 2 6.24450E-04 0.70832 23 2 3 2 4 1 2 3 3.42238E-04 0.84208 24 2 4 1 3 2 1 4 6.29290E-05 0.97447 25 3 1 3 3 1 2 4 7.04118E-04 0.67056 26 3 2 4 4 2 1 3 1.02023E-03 0.52073 27 3 3 1 1 3 4 2 2.47633E-04 0.88692 28 3 4 2 2 4 3 1 6.38515E-04 0.70165 29 4 1 3 4 2 4 2 2.11886E-03 0.00000 30 4 2 4 3 1 3 1 1.82858E-03 0.13758 31 4 3 1 2 4 2 4 9.14909E-04 0.57065 32 4 4 2 1 3 1 3 6.08598E-04 0.71583 表 3 极差分析表
Table 3. Range analysis table
Clearance thickness/μm Sealing gap length/mm Pressure difference/Pa Motor speed/(r/min) Clearance diameter/mm Piston stroke/mm T1 7.3368 4.4774 6.7386 6.0083 5.7513 5.9779 T2 5.919 5.6268 6.3139 5.4588 5.5718 5.5358 T3 5.4421 6.0318 5.5044 5.3782 5.4836 5.574 T4 3.5823 6.1443 3.7233 5.4348 5.4735 5.1925 Range R 3.7545 1.667 3.0153 0.63011 0.27787 0.78542 表 4 方差分析表
Table 4. Variance analysis table
Sources of variation Sum of quadratic Degree of freedom Mean squared F value F Critical value Significant test A 0.9013 3 0.3004 18.222 (2.9912;4.6755) Highly significant B 0.2175 3 0.0725 4.3975 (2.9912;4.6755) Significant C 0.6667 3 0.2222 13.4785 (2.9912;4.6755) Highly significant D 0.0324 3 0.0108 0.6559 (2.9912;4.6755) Non-significant E 0.0062 3 0.0021 0.1255 (2.9912;4.6755) Non-significant F 0.0388 3 0.0129 0.7836 (2.9912;4.6755) Non-significant Null column 0.1173 3 0.0391 2.3707 (2.9912;4.6755) Non-significant Error 0.4122 25 0.0165 - - - Sum 1.9802 31 - - - - -
[1] Margaret M, Asantha C, David T, et al. Overview of the Origins Space telescope: science drivers to observatory requirements (Conference Presentation)[C]//Space Telescopes and Instrumentation, 2018: 1-8. [2] Timothy P M, Rishi N P, Jeremy D W, et al. Cryogenic packaging of an optomechanical crystal[J]. Optics Express, 2019, 35: 28782-2871. [3] ZHOUWJ, GAN Z H, ZHANG X, et al. Clearance loss analysis in linear compressor with CFD Method[C]//International Cryocooler Conference, 2010: 353-359. [4] Reed J, Bailey P B, Dadd M W, et al. Motor and thermodynamic losses in linear cryocooler compressors[J]. Aip Conference Proceedings, 2005, 823: 361-368. [5] Bailey P, Dadd M, Stone C, et al. Gas spring losses in linear clearance-seal compressors[C]//International Cryocooler Conference, 2007: 345-353. [6] 陈曦, 武卫东, 周志刚, 等.自由活塞式斯特林制冷机间隙密封技术研究[J].低温与超导, 2008, 36(5): 5-8. https://www.cnki.com.cn/Article/CJFDTOTAL-DWYC200805001.htmCHEN Xi, WU Weidong, ZHOU Zhigang, et al. Study on the clearance seal in free-piston Stirling cooler[J]. Cryogenic & Superconductivity, 2008, 36(5): 5-8. https://www.cnki.com.cn/Article/CJFDTOTAL-DWYC200805001.htm [7] 卢明.间隙密封式伺服液压缸密封特性研究及仿真[D].武汉: 武汉科技大学, 2010.LU Ming. Research and Simulation on The Gap Type Servo Hydraulic Cylinder Seals[D]. Wuhan: Wuhan University of Science and Technology, 2010. [8] 马诗曼, 陈曦, 李静.自由活塞式斯特林制冷机压缩活塞间隙密封泄漏的数值模拟[J].低温工程, 2011, 181(3): 24-28. https://www.cnki.com.cn/Article/CJFDTOTAL-DWGC201103008.htmMA Shiman, CHEN Xi, LI Jing. Numerical simulations of seal leakage of compression piston in free piston Stirling cooler[J]. Cryogenics, 2011, 181(3): 24-28. https://www.cnki.com.cn/Article/CJFDTOTAL-DWGC201103008.htm [9] QI Y X, MENG X Q, MU D F, et al. Study on mechanism and factors affecting the gas leakage through clearance seal at nano-level by molecular dynamics method[J]. Energy, 2016, 102: 252-259. doi: 10.1016/j.energy.2016.02.087