基于扩散界面法的较大气泡上升过程数值模拟
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摘要
基于扩散界面法和有限元法,对较大气泡在上升阶段的形态和速度进行了模拟,结果与实验吻合较好,说明该方法能准确地模拟气泡的运动特性。利用该模型,对初始直径不同的较大气泡上升过程中的形态、速度和振荡随时间变化的规律进行了分析。并分析了14mm直径的气泡在不同尺寸通道中上升过程的形态、速度的变化规律。结果表明:气泡的稳定形态随着气泡初始直径的增大由椭球形变为球帽形,且达到稳定形状的时间更长。气泡初始直径越大,气泡的顶端速度越快,并稍有波动。而气泡的底端速度开始快速增大使气泡向内凹陷,随后回落并在气泡顶端速度上下振荡。气泡上升通道越窄,气泡达到稳定形态的时间越长,顶端速度越小,气泡的高宽比越大。
Based on the diffusion interface method and the finite element method,the shape and velocity of the larger bubble during the rising process were simulated.The results agree well with the experiments of the references.It is indicated that the diffusion interface method can correctly simulate the motion characteristics of the bubble.By using this model,the shape,velocity and oscillation of bubbles with different initial diameters were analyzed during the rising process.Moreover,the variations of shape and velocity of the bubble with diameter of 14 mm in rising process with different sizes of channel were also studied.The results show that with the increase of the initial diameter it takes more time to get the stable shape of the bubble from the ellipsoid to the spherical cap type.The larger the initial diameter bubble is,the greater the top velocity of the bubble is.The bottom velocity of the bubble increases rapidly at very beginningso that the bottom of the bubble is inward depression,then the bottom velocity falls back and shocks around the top velocity of the bubble.As the bubble rises in a smaller size channel,the top velocity of the bubble decreases,the height/width ratio increases and longer time is needed to get the stable shape.
Based on the diffusion interface method and the finite element method,the shape and velocity of the larger bubble during the rising process were simulated.The results agree well with the experiments of the references.It is indicated that the diffusion interface method can correctly simulate the motion characteristics of the bubble.By using this model,the shape,velocity and oscillation of bubbles with different initial diameters were analyzed during the rising process.Moreover,the variations of shape and velocity of the bubble with diameter of 14 mm in rising process with different sizes of channel were also studied.The results show that with the increase of the initial diameter it takes more time to get the stable shape of the bubble from the ellipsoid to the spherical cap type.The larger the initial diameter bubble is,the greater the top velocity of the bubble is.The bottom velocity of the bubble increases rapidly at very beginningso that the bottom of the bubble is inward depression,then the bottom velocity falls back and shocks around the top velocity of the bubble.As the bubble rises in a smaller size channel,the top velocity of the bubble decreases,the height/width ratio increases and longer time is needed to get the stable shape.
引文
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[3]ALBADAWI A,DONOGHUE D B,ROBINSON A J,et al.Influence of surface tension implementation in volume of fluid and coupled volume of fluid with level set methods for bubble growth and detachment[J].International Journal of Multiphase Flow,2013,53:11-28.
[4]左娟莉,田文喜,秋穗正,等.液态金属内单个气泡上升行为的MPS法数值模拟[J].原子能科学技术,2011,45(12):1 449-1 455.ZUO Juanli,TIAN Wenxi,QIU Suizheng,et al.Numerical simulation on single bubble rising behavior in liquid metal using moving particle semiimplicit method[J].Atomic Energy Science and Technology,2011,45(12):1 449-1 455(in Chinese).
[5]YUE P,JAMES J F,CHUN L,et al.A diffuse-interface method of simulating two-phase flows of complex fluids[J].Journal of Fluid Mechanics,2004,515:293-317.
[6]ERIK T K,SONG P,LOWENGRUB J,et al.A diffuse-interface method for two-phase flows with soluble surfactants[J].Journal of Computational Physics,2011,230(2):375-393.
[7]任秀,王锦程,杨玉娟,等.纯物质晶界结构及运动的晶体相场法模拟[J].物理学报,2010,59(5):3 595-3 600.REN Xiu,WANG Jincheng,YANG Yujuan,et al.Simulation of the structure and motion of grain boundary in pure substances by phase field crystal model[J].Acta Physica Sinica,2010,59(5):3 595-3 600(in Chinese).
[8]van der WAALS J D.The thermodynamic theory of capillarity under the hypothesis of a continuous variation of density[J].Journal of Statistical Physics,1979,20(2):200-244.
[9]YUE P,ZHOU C,FENG J J,et al.Phase-field simulations of interfacial dynamics in viscoelastic fluids using finite elements with adaptive meshing[J].Journal of Computational Physics,2006,219(1):47-67.
[10]FRANCESCO M,LUCA M,CARLO M C.Diffuse interface modeling of a radial vapor bubble collapse[J].Journal of Physics:Conference Series,2015,656(1):12028.
[11]CAHN J W,HILLIARD J E.Free energy of a nonuniform system,Ⅰ:Interfacial free energy[J].Journal of Chemical Physics,1958,28(2):258-267.
[12]BHAGAT D,WEBER M E.Bubbles in viscous liquids:Shapes,wakes and velocities[J].Department of Chemical Engineering,1981,105:61-85.
[13]TOMIYAMA A,KATAOKA I,ZUN I,et al.Drag coefficients of single bubbles under normal and micro gravity conditions[J].JSME International Journal,1998,41(2):472-479.