Multi-bubble motion behavior of electric field based on phase field model
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摘要
By coupling the phase field model with the continuity equation of incompressible fluid, Navier–Stokes equation,electric field equation, and other governing equations, a multi-field coupling model for multi-bubble coalescence in a viscous fluids is established. The phase field method is used to capture the two-phase interface. The motion and coalescence of a pair of coaxial bubbles under an external uniform electric field and the effects of different electric field strengths on the interaction and coalescence of rising bubbles are studied. The results show that the uniform electric field accelerates the collision and coalescence process of double bubbles in the fluid, and increases the rising velocity of the coalesced bubble.The electric field with an intensity of E = 2 kV/mm is reduced about 2 times compared with that without electric field in coalescence time. When the electric field strength is strong(E ≥ 1 kV/mm), the coalesced bubble will rupture before it rises to the top of the calculation area, and the time of the bubble rupturing also decreases with the increase of the electric field strength. The phase field method is compared with the simulation results of Lattice Boltzmann Method(LBM), and the shape of bubble obtained by the two methods is in good agreement, which verifies the correctness of the calculation model.
By coupling the phase field model with the continuity equation of incompressible fluid, Navier–Stokes equation,electric field equation, and other governing equations, a multi-field coupling model for multi-bubble coalescence in a viscous fluids is established. The phase field method is used to capture the two-phase interface. The motion and coalescence of a pair of coaxial bubbles under an external uniform electric field and the effects of different electric field strengths on the interaction and coalescence of rising bubbles are studied. The results show that the uniform electric field accelerates the collision and coalescence process of double bubbles in the fluid, and increases the rising velocity of the coalesced bubble.The electric field with an intensity of E = 2 kV/mm is reduced about 2 times compared with that without electric field in coalescence time. When the electric field strength is strong(E ≥ 1 kV/mm), the coalesced bubble will rupture before it rises to the top of the calculation area, and the time of the bubble rupturing also decreases with the increase of the electric field strength. The phase field method is compared with the simulation results of Lattice Boltzmann Method(LBM), and the shape of bubble obtained by the two methods is in good agreement, which verifies the correctness of the calculation model.
By coupling the phase field model with the continuity equation of incompressible fluid, Navier–Stokes equation,electric field equation, and other governing equations, a multi-field coupling model for multi-bubble coalescence in a viscous fluids is established. The phase field method is used to capture the two-phase interface. The motion and coalescence of a pair of coaxial bubbles under an external uniform electric field and the effects of different electric field strengths on the interaction and coalescence of rising bubbles are studied. The results show that the uniform electric field accelerates the collision and coalescence process of double bubbles in the fluid, and increases the rising velocity of the coalesced bubble.The electric field with an intensity of E = 2 kV/mm is reduced about 2 times compared with that without electric field in coalescence time. When the electric field strength is strong(E ≥ 1 kV/mm), the coalesced bubble will rupture before it rises to the top of the calculation area, and the time of the bubble rupturing also decreases with the increase of the electric field strength. The phase field method is compared with the simulation results of Lattice Boltzmann Method(LBM), and the shape of bubble obtained by the two methods is in good agreement, which verifies the correctness of the calculation model.
引文
[1] Zhang A M and Yao X L 2008 Chin.Phys. B 17 927
[2] Clift R, Grace J R and Weber M E 1978 Bubbles, Drops, and Particles(New York:Academic Press)
[3] Kirkpatrick R D and Lockett M J 1974 Chem. Eng. Sci. 29 2363
[4] Zhang S J and Wu C J 2011 J. Hydrodyn 23 89
[5] Annal, M V S, Deen N G and Kuipers J A M 2005 Chem. Eng. Sci. 602999
[6] Cheng M, Hua J S and Lou J 2010 Comput. Fluid. 39 260
[7] Li S B, Xu S, Fan J G and Huang S Y 2017 J. Shenyang. Inst. Aerona Eng. 34 63
[8] Lv Y Q 2016 Numerical Research on Bubble Merging and its Motion in Shear Flow(MS Thesis)(Hangzhou:China Jiliang University)(in Chinese)
[9] Hadidi A and Jalali-Vahid D 2016 Theor. Comput. Fluid. Dyn 30 165
[10] Hirt C W and Nichols B D 1981 J. Comput. Phys. 39 201
[11] Abbassi W, Besbes S, Elhajem M, Aissia H B and Champagne J Y 2018Comput. Fluids 161 47
[12] Osher S and Sethian J A 1988 J. Comput. Phys. 79 12
[13] Nagrath S, Jansen K E and Jr R T L 2005 C Omput. Method. Appl. M194 4565
[14] Jacqmin D 1999 J. Comput. Phys. 155 96
[15] Yang Q Z, Li B Q, Shao J Y and Ding Y C 2014 Int. J. Heat Mass.Tran. 78 820
[16] Zhang Q Y, Sun D K, Zhang Y F and Zhu M F 2016 Chin. Phys. B 25066401
[17] Chen S and Doolen G D 1998 Ann. Rev. Fluid. Mech. 30 329
[18] Yue P T, Zhou C F, Jams J, Feng J J and Ollivier-Gooch C F 2006 J.Comput. Phys. 219 47
[19] Wang L L, Li G J, Tian H and Ye Y H 2011 J. Xi'an JiaoTong Univ. 4565
[20] Ding H, Spelt P D M and Shu C 2007 J. Comput. Phys. 226 2078
[21] Liang M, Li Q, Wang K S, Liu J Y and Chen J Q 2014 Ciesc. J. 65 843
[22] Allen P H G and Karayiannis T G 1995 Heat Recov. Syst. Chp. 15 389
[2] Clift R, Grace J R and Weber M E 1978 Bubbles, Drops, and Particles(New York:Academic Press)
[3] Kirkpatrick R D and Lockett M J 1974 Chem. Eng. Sci. 29 2363
[4] Zhang S J and Wu C J 2011 J. Hydrodyn 23 89
[5] Annal, M V S, Deen N G and Kuipers J A M 2005 Chem. Eng. Sci. 602999
[6] Cheng M, Hua J S and Lou J 2010 Comput. Fluid. 39 260
[7] Li S B, Xu S, Fan J G and Huang S Y 2017 J. Shenyang. Inst. Aerona Eng. 34 63
[8] Lv Y Q 2016 Numerical Research on Bubble Merging and its Motion in Shear Flow(MS Thesis)(Hangzhou:China Jiliang University)(in Chinese)
[9] Hadidi A and Jalali-Vahid D 2016 Theor. Comput. Fluid. Dyn 30 165
[10] Hirt C W and Nichols B D 1981 J. Comput. Phys. 39 201
[11] Abbassi W, Besbes S, Elhajem M, Aissia H B and Champagne J Y 2018Comput. Fluids 161 47
[12] Osher S and Sethian J A 1988 J. Comput. Phys. 79 12
[13] Nagrath S, Jansen K E and Jr R T L 2005 C Omput. Method. Appl. M194 4565
[14] Jacqmin D 1999 J. Comput. Phys. 155 96
[15] Yang Q Z, Li B Q, Shao J Y and Ding Y C 2014 Int. J. Heat Mass.Tran. 78 820
[16] Zhang Q Y, Sun D K, Zhang Y F and Zhu M F 2016 Chin. Phys. B 25066401
[17] Chen S and Doolen G D 1998 Ann. Rev. Fluid. Mech. 30 329
[18] Yue P T, Zhou C F, Jams J, Feng J J and Ollivier-Gooch C F 2006 J.Comput. Phys. 219 47
[19] Wang L L, Li G J, Tian H and Ye Y H 2011 J. Xi'an JiaoTong Univ. 4565
[20] Ding H, Spelt P D M and Shu C 2007 J. Comput. Phys. 226 2078
[21] Liang M, Li Q, Wang K S, Liu J Y and Chen J Q 2014 Ciesc. J. 65 843
[22] Allen P H G and Karayiannis T G 1995 Heat Recov. Syst. Chp. 15 389