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自由汇流旋涡形成过程中有抽吸现象发生, 是一个比较复杂的气液两相耦合过程, 其中所涉及的Ekman层耦合及演化机理具有重要的科研价值与实际意义. 针对上述问题, 提出了一种自由汇流旋涡Ekman抽吸演化机理建模与分析方法. 基于多相流体体积VOF模型与湍动能-耗散(k-ε)模型, 建立了面向汇流旋涡Ekman抽吸演化的两相动力学模型. 基于上述模型, 分析初始转动速度分量、排流量与Ekman抽吸过程的内在联系, 并揭示相关流场分布规律. 研究结果表明: 初始扰动不同, 汇流旋涡的吸气孔、抽气孔距离容器底面边界的高度保持不变; 初始扰动加强, 吸气阶段转速增加, Ekman边界层厚度及抽吸高度增加, 抽吸、贯穿阶段Ekman抽吸现象减弱; 初始扰动恒定, Ekman抽吸高度保持不变, 与排流量变化无关. 研究结果可为自由汇流旋涡形成机理方面的研究提供有益参考, 也可为冶金、化工领域的旋涡抑制控制提供技术支持.The suction-extraction phenomenon occurs in the formation process of free sink vortex (bathtub vortex), and it is a complex gas-liquid coupling matter. The Ekman layer coupling and its evolution mechanism involved in the above matter possess important scientific value and practical engineering significance. To address the above issue, a modeling and analytical method for the Ekman suction-extraction evolution mechanism of free sink vortex is proposed.#br#Based on the multiphase volume of fluid model and turbulent kinetic energy-dissipation (k-ε) model, a gas-liquid two-phase fluid dynamic model for free sink vortex Ekman suction-extraction is set up. Considering the rotating and shearing characteristics of sink vortex, a two-phase surface is reconstructed by piecewise linear interface construction method. Based on the above models, the internal relations between initial rotation velocity component, drainage capacity and Ekman suction-extraction are investigated, and the corresponding flow field profile regularities are revealed.#br#According to the results of a series of numerical instances, some regularities are obtained as follows. 1) If the initial velocity disturbance is variable, the distances of the suction and extraction holes from the container bottom both keep constant. In the suction stage, the suction hole is located at a fixed position above the container bottom surface, and the extraction hole is in the plane of the bottom surface. 2) If the initial disturbance is enhanced, the rotation velocity of the suction stage increases, and the suction and extraction heights and Ekman layer thickness become larger, while Ekman suction-extraction intensities of suction, extraction and penetration stages turn weaker. 3) If the initial disturbance is invariable, the heights of Ekman suction and extraction remain unchanged, and are independent of drainage capacity. 4) The small-scale vortexes separated from the large-scale ones in the bottom corner of container take on a phenomenon of flow around by a right-angle, which is caused by the viscosity of Ekman boundary layer and the potential flow of the sink hole. 5) Considering the stream line profiles of suction and extraction stages, the dispersion of stream lines keeps constant with the time going by, and the stream lines near the central region of vortex tend to be converged by increasing the gas-liquid coupling.#br#In general, the results can offer useful reference to the research work of free sink vortex formation mechanism, and provide technical supports for vortex suppression control of the areas of metallurgy pouring, chemistry separation and hydraulic drainage. The subsequent researches of the fractal based sink vortex evolution mechanism and lattice Boltzmann based phase surface tracing will be carried out.
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Keywords:
- free sink vortex /
- Ekman boundary layer /
- Ekman suction-extraction /
- volume of fluid
[1] Tan D P, Zhang L B 2014 Sensor. Actuat. B-Chem. 202 1257
[2] Ji S M, Weng X X, Tan D P 2012 Acta. Phys. Sin. 61 010205 (in Chinese) [计时鸣, 翁晓星, 谭大鹏 2012 61 010205]
[3] Mazzaferro G M, Piva M, Ferro S P 2004 Ironmak. Steelmak. 31 503
[4] Ji S M, Xiao F Q, Tan D P 2010 Sci. China Technol. Sci. 53 2867
[5] Gai J, Xia Z H, Cai Q D 2015 Chin. Phys. B 24 104701
[6] Koria S C, Kanth U 1994 Steel Res. 65 8
[7] Santos F, Gomez-Gesteira M, deCastro M, Alvarez I 2012 Cont. Shelf. Res. 34 79
[8] Chen G J, Zhang Y J, Yang Y S 2013 Chin. Phys. B 22 124703
[9] Chen J L, Xu F, Tan D P, Shen Z, Zhang L B, Ai Q L 2015 Appl. Energ. 141 106
[10] Tan D P, Ji S M, Li P Y, Pan X H 2010 Sci. China Technol. Sci. 53 2378
[11] Tan D P, Li P Y, Ji Y X, Wen D H, Li C 2013 IEEE T. Ind. Electron. 60 4702
[12] Li C, Ji S M, Tan D P 2013 IEEE T. Power Electron. 28 408
[13] Tan D P, Ji S M, Jin M S 2013 IEEE T. Educ. 56 268
[14] Tan D P, Li P Y, Pan X H 2009 J. Iron Steel Res. Int. 16 1
[15] Zhang L, Huang S X, Du H D 2015 Pure Appl. Geophys. 172 2831
[16] Han Y Q, Zhong Z, Wang Y F, Du H D 2013 Acta. Phys. Sin. 62 049201 (in Chinese) [韩月琪, 钟中, 王云峰, 杜华栋 2013 62 049201]
[17] Wang Y F, Gu C M, Zhang X H, Wang Y S, Han Y Q, Wang Y F 2014 Acta. Phys. Sin. 63 240202 (in Chinese) [王云峰, 顾成明, 张晓辉, 王雨顺, 韩月琪, 王耘锋 2014 63 240202]
[18] Lundgren T S 1985 J. Fluid Mech. 155 381
[19] Andersen A, Bohr T, Stenum B, Rasmussen J J, Lautrup B 2003 Phys. Rev. Lett. 91 104502
[20] Andersen A, Bohr T, Stenum B, Rasmussen J J, Lautrup B 2006 J. Fluid Mech. 556 121
[21] Zhao Z Y, Gu Z L, Yu Y Z, Li Y, Feng X 2003 J XiAn Commun. Univ. 37 85 (in Chinese) [赵永志, 顾兆林, 郁永章, 李云, 冯霄 2003 西安交通大学学报 37 85]
[22] Osher S, Sethian J A 1988 J. Comput. Phys. 79 12
[23] Tan D P, Ji S M, Fu Y Z 2015 Int. J. Adv. Manuf. Tech. (Published online, DOI: 10.1007/s00170-015-8044-8)
[24] Li C, Ji S M, Tan D P 2012 Int. J. Adv. Manuf. Tech. 61 975
[25] Shapiro A H 1962 Nature 196 1080
[26] Jeong J T 2012 Theor. Comp. Fulid. Dyn. 26 93
[27] Ma W, Liu J, Wang B 2009 Wear 266 1072
[28] Zhao Z Y, Gu Z L, Yu Y Z, Feng X 2002 J. Hydraul. Eng-Asce. 12 1 (in Chinese) [赵永志, 顾兆林, 郁永章, 冯霄 2002 水利学报 12 1]
[29] Lewellen W S 1962 J. Fluid Mech. 14 420
[30] Batchelor G K 1967 An Introduction to Fluid Dynamics (Massachusetts: Cambridge University Press)
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[1] Tan D P, Zhang L B 2014 Sensor. Actuat. B-Chem. 202 1257
[2] Ji S M, Weng X X, Tan D P 2012 Acta. Phys. Sin. 61 010205 (in Chinese) [计时鸣, 翁晓星, 谭大鹏 2012 61 010205]
[3] Mazzaferro G M, Piva M, Ferro S P 2004 Ironmak. Steelmak. 31 503
[4] Ji S M, Xiao F Q, Tan D P 2010 Sci. China Technol. Sci. 53 2867
[5] Gai J, Xia Z H, Cai Q D 2015 Chin. Phys. B 24 104701
[6] Koria S C, Kanth U 1994 Steel Res. 65 8
[7] Santos F, Gomez-Gesteira M, deCastro M, Alvarez I 2012 Cont. Shelf. Res. 34 79
[8] Chen G J, Zhang Y J, Yang Y S 2013 Chin. Phys. B 22 124703
[9] Chen J L, Xu F, Tan D P, Shen Z, Zhang L B, Ai Q L 2015 Appl. Energ. 141 106
[10] Tan D P, Ji S M, Li P Y, Pan X H 2010 Sci. China Technol. Sci. 53 2378
[11] Tan D P, Li P Y, Ji Y X, Wen D H, Li C 2013 IEEE T. Ind. Electron. 60 4702
[12] Li C, Ji S M, Tan D P 2013 IEEE T. Power Electron. 28 408
[13] Tan D P, Ji S M, Jin M S 2013 IEEE T. Educ. 56 268
[14] Tan D P, Li P Y, Pan X H 2009 J. Iron Steel Res. Int. 16 1
[15] Zhang L, Huang S X, Du H D 2015 Pure Appl. Geophys. 172 2831
[16] Han Y Q, Zhong Z, Wang Y F, Du H D 2013 Acta. Phys. Sin. 62 049201 (in Chinese) [韩月琪, 钟中, 王云峰, 杜华栋 2013 62 049201]
[17] Wang Y F, Gu C M, Zhang X H, Wang Y S, Han Y Q, Wang Y F 2014 Acta. Phys. Sin. 63 240202 (in Chinese) [王云峰, 顾成明, 张晓辉, 王雨顺, 韩月琪, 王耘锋 2014 63 240202]
[18] Lundgren T S 1985 J. Fluid Mech. 155 381
[19] Andersen A, Bohr T, Stenum B, Rasmussen J J, Lautrup B 2003 Phys. Rev. Lett. 91 104502
[20] Andersen A, Bohr T, Stenum B, Rasmussen J J, Lautrup B 2006 J. Fluid Mech. 556 121
[21] Zhao Z Y, Gu Z L, Yu Y Z, Li Y, Feng X 2003 J XiAn Commun. Univ. 37 85 (in Chinese) [赵永志, 顾兆林, 郁永章, 李云, 冯霄 2003 西安交通大学学报 37 85]
[22] Osher S, Sethian J A 1988 J. Comput. Phys. 79 12
[23] Tan D P, Ji S M, Fu Y Z 2015 Int. J. Adv. Manuf. Tech. (Published online, DOI: 10.1007/s00170-015-8044-8)
[24] Li C, Ji S M, Tan D P 2012 Int. J. Adv. Manuf. Tech. 61 975
[25] Shapiro A H 1962 Nature 196 1080
[26] Jeong J T 2012 Theor. Comp. Fulid. Dyn. 26 93
[27] Ma W, Liu J, Wang B 2009 Wear 266 1072
[28] Zhao Z Y, Gu Z L, Yu Y Z, Feng X 2002 J. Hydraul. Eng-Asce. 12 1 (in Chinese) [赵永志, 顾兆林, 郁永章, 冯霄 2002 水利学报 12 1]
[29] Lewellen W S 1962 J. Fluid Mech. 14 420
[30] Batchelor G K 1967 An Introduction to Fluid Dynamics (Massachusetts: Cambridge University Press)
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