CAPILLARY RISE OF LIQUID BETWEEN PLATES WITH A CERTAIN ANGLE UNDER MICROGRAVITY
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摘要: 空间微重力环境中, 由于重力基本消失, 表面张力等次级力发挥主要作用, 流体行为与地面迥异, 因此有必要深入探究微重力环境中的流体行为规律和特征. 板式贮箱利用板式组件在微重力环境中对流体进行管理, 从而为推力器提供不夹气的推进剂, 这对航天器精确进行姿态控制、轨道调整具有重要意义. 板式组件中常包含成一定夹角的平板结构, 比如蓄液叶片之间. 本文研究了微重力环境中成一定角度平板间的表面张力驱动流动问题, 考虑了液体与壁面的动态接触角、对流引起的压力损失、黏滞阻力、液池内弯曲的液面等因素的影响, 推导出了表面张力驱动流动中液体爬升高度的二阶微分方程. 该方程可用四阶Runge−Kutta方法求解. 通过同时考虑两个主导力, 可将流动过程分为三个阶段, 并得到了不同阶段内的爬升高度的近似方程. 本研究建立了6个不同尺寸的计算模型、选用3种不同型号的硅油, 利用有限体积法开展仿真工作, 仿真结果与理论结果吻合良好, 验证了理论解的正确性. 本文的研究结果可为板式贮箱的研制和空间流体管理提供理论依据和数据支撑.
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关键词:
- 微重力 /
- 表面张力驱动流 /
- 成一定夹角的平板 /
- 有限体积法 /
- Runge−Kutta法
Abstract: In space, because the gravity basically disappears and the secondary forces such as surface tension force play a major role, fluid behavior is quite different from that of the ground. Therefore, it is necessary to deeply explore the laws and characteristics of fluid behavior in microgravity environment. The plate-type tank uses plate-type components to manage the fluid in microgravity environment, so as to provide the thruster with gas-free propellant, which is of great significance for the precise attitude control and orbit adjustment of the spacecraft. Plate-type components often include plates with a certain included angle, such as liquid storage blades. The capillary rise of liquid between plates with a certain angle under microgravity is explored in this paper. The influences of the dynamic contact angle between the liquid and the plates wall, the pressure loss caused by convection, the viscous resistance, and the curved liquid surface in the reservoir are all considered. A second order differential equation of the capillary-driven flow is derived, which can be solved with forth-order Runge−Kutta method. By considering two dominant forces at the same time, the flow can be divided into three regions, and approximate equations of climbing height in different regions are obtained. Six kinds of numerical models are created, three kinds of silicone oil is chonsen and Volume of Fluid(VOF) method is used to carry out numerical simulation. Numerical results are in good agreement with theoretical results, which verifies theoretical analysis. This research can be theoretical basis for plate tanks’ design and fluid management in space.-
Key words:
- microgravity /
- capillary driven flow /
- plates with a certain angle /
- VOF /
- Runge−Kutta method
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图 3 板间入口处的等效半球形控制体
Figure 3. Equivalent circular entrance and the control volume around the inlet
图 5 仿真结果侧视图. 液体为10号硅油, a = 2 mm, b = 14 mm, c = 5 mm
Figure 5. Front view of the numerical model as the liquid is SF 10 and a = 2 mm, b = 14 mm, c = 5 mm
图 6 板上液相分布, 红色部分代表液体
Figure 6. Liquid distribution in a plate and the red part represents liquid
表 1 硅油物性参数(25 °C)
Table 1. Liquid properties (25 °C)
Liquid μ/
(kg·m−1·s−1)Ρ/
(kg·m−3)$\sigma $
/(N·m−1)$\nu $
/(mm2·s−1)SF 2 0.001746 873 0.0183 2 SF 5 0.004575 915 0.0197 5 SF 10 0.009350 935 0.0201 10 
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表 2 计算参数
Table 2. Calculation parameters
No. a/mm b/mm c/mm Liquid vmax/(mm·s−1) Remax Oh/10−3 t1/s t2/s 1 2 12 3 SF 2 49.3 215 4.70 0.0743 0.531 2 2 12 3 SF 5 36.7 65.8 11.5 0.0781 0.212 3 2 12 3 SF 10 26.6 23.2 23.1 0.0808 0.106 4 2 12 4 SF 2 41.5 197 4.50 0.0977 0.745 5 2 12 4 SF 5 31.4 59.7 11.1 0.104 0 0.298 6 2 12 4 SF 10 21.9 20.8 22.1 0.110 0 0.149 7 1 14 5 SF 2 45.8 232 4.30 0.0938 0.642 8 1 14 5 SF 10 25.1 25.4 21.4 0.104 0 0.128 9 2 14 5 SF 2 39.2 216 4.20 0.121 0 0.987 10 2 14 5 SF 10 21.2 23.4 20.5 0.138 0 0.197 11 3 14 5 SF 2 33.4 198 4.00 0.154 0 1.350 12 3 14 5 SF 5 25.3 60.1 9.90 0.170 0 0.539 13 3 14 5 SF 10 16.6 20.9 19.8 0.185 0 0.270 14 3 14 4 SF 2 38.9 217 4.10 0.123 0 1.050 15 3 14 4 SF 5 30.0 66.9 10.2 0.134 0 0.419 16 3 14 4 SF 10 21.1 23.5 20.4 0.141 0 0.210
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[1] Washburn EW. The dynamics of capillary flow. Physical Review, 1921, 17(3): 273-283 doi: 10.1103/PhysRev.17.273 [2] Concus P, Finn R. On capillary free surfaces in the absence of gravity. Acta Mathematica, 1974, 132(1): 177-198 [3] Levine S, Reed P, Watson EJ, et al. A theory of the rate of rise of a liquid in a capillary. Journal of Colloid and Interface Science, 1976, 3: 403-419 [4] Stange M, Dreyer M, Rath H. Capillary driven flow in circular cylindrical tubes. Physics of Fluids, 2003, 15(9): 2587-2601 doi: 10.1063/1.1596913 [5] Jiang TS, Oh SG, Slattery JC. Correlation for dynamic contact angle. Journal of Colloid Interface Science, 1979, 69(1): 74-77 doi: 10.1016/0021-9797(79)90081-X [6] Dreyer M, Delgado A, Rath HJ. Capillary rise of liquid between parallel plates under microgravity. Journal of Colloid Interface Science, 1994, 163(1): 158-168 doi: 10.1006/jcis.1994.1092 [7] Weislogel MM, Lichter S. Capillary flow in an interior corner. Journal of Fluid Mechanics, 1998, 373: 349-378 doi: 10.1017/S0022112098002535 [8] Weislogel MM, Nardin CL. Capillary driven flow along interior corners formed by planar walls of varying wettability. Microgravity Science and Technology, 2005, 17(3): 45-55 doi: 10.1007/BF02872087 [9] Chen YK, Weislogel MM, Nardin CL. Capillary driven flows along rounded interior corners. Journal of Fluid Mechanics, 2006, 556: 235-271 [10] Yue BZ, Wang ZL. Numerical study of three-dimensional free surface dynamics. Acta Mechanica Sinica, 2006, 22: 120-125 doi: 10.1007/s10409-006-0100-z [11] Higuera FJ, Medina A, Linan A. Capillary rise of a liquid between two vertical plates making a small angle. Physics of Fluids, 2008, 20(10): 102102 doi: 10.1063/1.3000425 [12] Wolf F, Santos L, Phillippi P. Capillary rise between plates under dynamic conditions. Journal of Colloid and Interface Science, 2010, 344(1): 171-179 doi: 10.1016/j.jcis.2009.12.023 [13] Bolleddula DA, Chen YK, Semerjian B, et al. Compound capillary flows in complex containers: drop tower test results. Microgravity Science and Technology, 2010, 22(4): 475-485 doi: 10.1007/s12217-010-9213-x [14] Wei YX, Chen XQ, Huang YY. Interior corner flow theory and its application to the satellite propellant management device design. Science China-Teconological Sciences, 2011, 54(7): 1849-1854 doi: 10.1007/s11431-011-4374-4 [15] 李永, 赵春章, 潘海林等. 蓄液器在板式贮箱中的应用及性能分析. 宇航学报, 2008, 29(1): 24-28 (Li Yong, Zhao Chunzhang, Pan Hailin, et al. The applications in the vane type tank and performance analysis for the sponge. Journal of Astronautics, 2008, 29(1): 24-28 (in Chinese) doi: 10.3873/j.issn.1000-1328.2008.01.004 [16] 庄保堂, 李永, 潘海林等. 微重力环境下导流叶片流体传输速度的试验研究. 空间控制技术与应用, 2012, 38(6): 1-5 (Zhuang Baotang, Li Yong, Pan Hailin, et al. Experiment investigation on transportation velocity of the fluid on propellant acquisition vanes under microgravity environment. Aerospace Control and Application, 2012, 38(6): 1-5 (in Chinese) doi: 10.3969/j.issn.1674-1579.2012.06.001 [17] 胡齐, 李永, 潘海林等. 微重力环境下大叶片板式贮箱内流体行为的数值仿真与试验验证. 空间控制技术与应用, 2013, 39(2): 58-62 (Hu Qi, Li Yong, Pan Hailin, et al. Numerical simulation and experiment verification of the fluid behaviour in the vane type tank with big vanes in microgravity environment. Aerospace Control and Application, 2013, 39(2): 58-62 (in Chinese) doi: 10.3969/j.issn.1674-1579.2013.02.011 [18] Reyssat E. Capillary bridges between a plane and a cylindrical wall. Journal of Fluid Mechanics, 2015, 773: R1 doi: 10.1017/jfm.2015.233 [19] Wu ZY, Huang YY, Chen XQ, et al. Capillary driven flows along curved interior corners. International journal of multiphase flow, 2018, 109: 14-25 doi: 10.1016/j.ijmultiphaseflow.2018.04.004 [20] Romain C, Fabian D, Michael G, et al. Modeling of capillary-driven flows in axisymmetric geometries. Computers and Fluids, 2019, 178: 132-140 doi: 10.1016/j.compfluid.2018.08.024 [21] Chen ST, Han ZY, Duan L, et al. Experimental and numerical study on capillary flow along deflectors in plate surface tension tanks in microgravity environment. AIP Advances, 2019, 9(2): 025020 doi: 10.1063/1.5083672 [22] Cheng X, Chen Y, Li HR, et al. Investigation on capillary flow in tubes with variable diameters. Journal of Porous and Media, 2019, 22(13): 1627-1638 doi: 10.1615/JPorMedia.2019026774 [23] Chen ST, Ye ZJ, Duan L, et al. Capillary driven flow in oval tubes under microgravity. Physics of Fluids, 2021, 33(3): 032111 doi: 10.1063/5.0040993 -
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