壁面约束对裙带气泡动力学的影响
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摘要
基于流体体积法(volume of fluid,VOF),数值模拟了装满黏性液体的圆柱形汽缸中的裙带气泡的浮升运动,研究了侧壁面约束对裙带气泡浮升动力学的影响.用雷诺数(Re)、韦伯数(We)、长宽比(χ)、裙带厚度(T/d)和裙带长度(L/d)等参数来表征不同约束比条件下(1.1≤Cr≤10)裙带气泡的运动和变形特性,分别在全局参考系和局部参考系下分析了壁面对气泡内外流场的影响.模拟结果显示,当Cr≥8时,裙带气泡的行为特性与在无界流域条件下的情况相当,可视作壁面无关的.当Cr<8时,壁面对裙带气泡的浮升速度和形状演化有显著影响.随着壁面的靠近,裙带气泡受到的阻力增大,造成浮升速度下降.约束比降低使裙带厚度增厚而长度变短直至裙带消失,裙带气泡受挤压而被拉长并逐渐变为椭圆球帽形最后到子弹形.相反,约束比增大时,裙带气泡尾流效应增强,气泡边缘处流场产生明显的循环流动(涡环),促使裙带的形成.研究表明壁面会加剧裙带气泡产生破碎,印证了前人的推断.模拟结果与已有的经验公式吻合良好,分析了前人公式的适用性.
In this work, the confinement effect on the buoyancy-driven, axisymmetric motion of a skirted bubble in a liquid-filled, circular cylinder is numerically studied. The gas and liquid phases are assumed to be isothermal, incompressible and immiscible. The volume of fluid(VOF) method is adopted to simulate the deforming interface between gas and liquid. A confinement ratio range of(1.1≤Cr≤10) is considered. The results reveal that the motion of a skirted bubble under Cr ≥8 resembles that in an infinite medium in terms of both shape and Reynolds number in terminal state.With decreasing Cr, the wall plays a more significant role in determining the motion of the skirted bubble. For the range of Cr < 8, the drag on the bubble increases as Cr decreases, giving rise to the reduction of bubble rising velocity. As for the terminal shape, the skirted bubble is elongated in the axial direction and may evolve to an ellipsoidal cap or a bullet as a result of increasing wall proximity. The sensitivities of the thickness and length of trailing bubble skirts to the confinement ratio are examined. The skirt length reduces with the decrease of Cr, while the skirt thickness increases with decreasing Cr. The details of fluid field are analyzed both in the global reference frame and in a local reference frame moving with the bubble centroid. The wake effect of the skirted bubble is weaken by the increasing wall effect,suppressing the formations of vortex ring and skirt. Bubble break-up is captured under approximate conditions and can be enhanced by decreasing Cr, confirming the deduction in the literature. The present predictions on terminal velocities agree well with results by the correlation in the literature.
In this work, the confinement effect on the buoyancy-driven, axisymmetric motion of a skirted bubble in a liquid-filled, circular cylinder is numerically studied. The gas and liquid phases are assumed to be isothermal, incompressible and immiscible. The volume of fluid(VOF) method is adopted to simulate the deforming interface between gas and liquid. A confinement ratio range of(1.1≤Cr≤10) is considered. The results reveal that the motion of a skirted bubble under Cr ≥8 resembles that in an infinite medium in terms of both shape and Reynolds number in terminal state.With decreasing Cr, the wall plays a more significant role in determining the motion of the skirted bubble. For the range of Cr < 8, the drag on the bubble increases as Cr decreases, giving rise to the reduction of bubble rising velocity. As for the terminal shape, the skirted bubble is elongated in the axial direction and may evolve to an ellipsoidal cap or a bullet as a result of increasing wall proximity. The sensitivities of the thickness and length of trailing bubble skirts to the confinement ratio are examined. The skirt length reduces with the decrease of Cr, while the skirt thickness increases with decreasing Cr. The details of fluid field are analyzed both in the global reference frame and in a local reference frame moving with the bubble centroid. The wake effect of the skirted bubble is weaken by the increasing wall effect,suppressing the formations of vortex ring and skirt. Bubble break-up is captured under approximate conditions and can be enhanced by decreasing Cr, confirming the deduction in the literature. The present predictions on terminal velocities agree well with results by the correlation in the literature.
引文
1 Bhaga D,Weber ME.Bubbles in viscous liquids:shapes,wakes and velocities.J Fluid Mech,1981,105:61
2 Tripathi MK,Sahu KC,Govindarajan R.Dynamics of an initially spherical bubble rising in quiescent liquid.Nat Commun,2015,6:6268
3 Thomson JJ,Newall HF.On the formation of vortex rings by drops falling into liquids,and some allied phenomena.Proc.R.Soc.Lond,1885.39:417-436
4 Shoemaker PD,De Chazal LEM.Dimpled and skirted liquid drops moving through viscous liquid media.Chem Eng Sci,1969,24(4):795-797
5 Wegener PP,Sundel RE,Parlange JY.Spherical cap bubbles rising in liquids.Z Flugwiss,1971,19(8):374
6 Wairegi T.The mechanics of large bubbles and drops moving through extended liquid media.[PhD Thesis].Montreal:McGill University,1974
7 Bhaga D.Bubbles in viscous liquids:shapes,wakes and velocities.[PhD Thesis].Montreal:McGill University,1976
8 Hnat JG,Buckmaster JD.Spherical cap bubbles and skirt formation.Phys Fluids,1976,19(19):182-194
9 Ray B,Prosperetti A.On skirted drops in an immiscible liquid.Chem Eng Sci,2014,108:213-222
10 Davenport WG Richardson FD,Bradshaw AV.Spherical cap bubbles in low density liquids.Chem Eng Sci,1967,22(9):1221-135
11 Wegener PP,Parlange JY.Spherical-cap bubbles.Annu Rev Fluid Mech,1973,5(4):79-100
12 Guthrie RIL,Bradshaw AV.The stability of gas envelopes trailed behind large spherical cap bubbles rising through viscous liquids.Chem Eng Sci,1969,24(5):913-917
13 Lezzi AM,Prosperetti A.The stability of an air film in a liquid flow.J Fluid Mech,1991,226(226):319
14 Ohta M,Sussman M.The buoyancy-driven motion of a single skirted bubble or drop rising through a viscous liquid.Phys Fluids,2012,24(11):112101
15 Sulaiman M,Legendre D.Looking under the skirt of a bubble//Poceedings of the IUTAM Symposium on Bubbly Flows Oaxaca,Mexico,F,2015
16 Mukundakrishnan K,QuanS,Eckmann DM,et al.Numerical study of wall effects on buoyant gas-bubble rise in a liquid-filled finite cylinder.Phys Rev E,2007,76(2):036308
17 Kumar P,Vanka SP.Effects of confinement on bubble dynamics in a square duct.Int J Multiphas Flow,2015,77:32-47
18 Rahmat A,Tofighi N,Yildiz M.The combined effect of electric forces and confinement ratio on the bubble rising.Int J Heat Fluid Fl,2017,65:352-362
19李帅,张阿漫.上浮气泡在壁面处的弹跳特性研究.物理学报,2014,63(5):054705(Li Shuai,Zhang Aman.Study on a rising bubble bouncing near a rigid boundary.Acta Phys Sin,2014,63(5):054705(in Chinese))
20 Zhang AM,Li S,Cui J.Study on splitting of a toroidal bubble near a rigid boundary.Phys Fluids,2015,27(6):062102
21 Liu LT,Yao XL,Zhang AM,et al.Numerical analysis of the jet stage of bubble near a solid wall using a front tracking method.Phys Fluids,2017,29(1):012105
22邱超,张会臣.单个上升空泡撞击顶部壁面的变形和回弹特性研究.机械工程学报,2014,50(9):191-196(Qiu Chao,Zhang Huichen.Deformation and rebound characteristics of single rising bubble impacting against top wall.Journal of Mechanical Engineering,2014,50(9):191-196(in Chinese))
23李维仲,张晓红,董波等.单气泡沿倾斜绝热表面运动特性的LBM方法研究.化工学报,2013,64(11):3940-3948(Li Weizhong,Zhang Xiaohong,Dong Bo,et al.Lattice Boltzmann simulation of moving characteristics of a single bubble rising along inclined adiabatic surface.CIESC Journal,2013,64(11):3940-3948(in Chinese))
24刘云龙,汪玉,张阿漫.有倾角的竖直壁面附近气泡与自由面相互作用研究.物理学报,2013,62(21):214703(Liu Yunlong,Wang Yu,Zhang Aman.The interaction between bubble and free surface near vertical wall with inclination.Acta Phys Sin,2013,62(21):214703(in Chinese))
25鞠花,陈刚,李国栋等.静水中上升气泡沿倾斜壁面的运动特性试验研究.水动力学研究与进展,2011,26(3):327-332(Ju Hua,Chen Gang,Li Guodong,et al.Experimental study on motion behavior of single bubble rising along inclined plane in still water.Chin J Hydrodyn,2011,26(3):327-332(in Chinese))
26 Hirt CW,Nichols BD.Volume of fluid(VOF)method for the dynamics of free boundaries.J Comput Phys,1981,39(1):201-225
27 Youngs DL.Time-dependent Multi-Material Flow with Large Fluid Distortion.New York:Academic Press,1982
28吴应湘,林黎明,钟兴福.带有新型涡激振动抑制罩的圆柱体的水动力特性.力学学报,2016,48(2):307-317(Wu Yingxiang,Lin Liming,Zhong Xingfu.Investigation in hydrodynamics of a circular cylinder with the new suppressing shroud for vortex-induced vibration.Chinese Journal of Theoretical and Applied Mechanics,2016,48(2):307-317(in Chinese))
29张新曙,胡晓峰,尤云祥等.深海多立柱浮式平台涡激运动特性研究.力学学报,2016,48(3):593-598(Zhang Xinshu,Hu Xiaofeng,You Yunxiang,et al.Investigation on the characterisitics of vortex induced motion of a deep sea muti-column floating platform.Chinese Journal of Theoretical and Applied Mechanics,2016,48(3):593-598(in Chinese))
30杜特专,王一伟,黄晨光等.航行体水下发射流固耦合效应分析.力学学报,2017,49(4):782-792(Du Tezhuan,Wang Yiwei,Huang Chenguang,et al.Study on coupling effects of underwater launched vehicle.Chinese Journal of Theoretical and Applied Mechanics,2017,49(4):782-792(in Chinese))
31郝子辉,阎超,周玲.κ-ω-γ模式对转捩影响因素的预测性能研究.力学学报,2015,47(2):215-22(Hao Zihui,Yan Chao,Zhou Ling.Parametric study of aκ-ω-γmodel in predicting hypersonic boundary-layer flow transition.Chinese Journal of Theoretical and Applied Mechanics,2015,47(2):215-222(in Chinese))
32 Clift R,Grace JR,Weber ME.Bubbles,drops,and particles.Academic Press,1978
33黄永念.旋涡结构的湍流统计理论.力学进展,2002,32(4):505-512(Huang Youngnian.ON the statistical vortes structure theory of turbulence.Advances in Mechanics,2002,32(4):505-512(in Chinese))
34 Dijkhuizen W,Van Den Hengel EIV,Deen NG,et al.Numerical investigation of closures for interface forces acting on single airbubbles in water using Volume of Fluid and Front Tracking models.Chem Eng Sci,2005,60(22):6169-6175
35 Balc Zar N,Lehmkuhl O,Jofre L,et al.Level-set simulations of buoyancy-driven motion of single and multiple bubbles.Int J Heat Fluid Fl,2015,56:91-107
2 Tripathi MK,Sahu KC,Govindarajan R.Dynamics of an initially spherical bubble rising in quiescent liquid.Nat Commun,2015,6:6268
3 Thomson JJ,Newall HF.On the formation of vortex rings by drops falling into liquids,and some allied phenomena.Proc.R.Soc.Lond,1885.39:417-436
4 Shoemaker PD,De Chazal LEM.Dimpled and skirted liquid drops moving through viscous liquid media.Chem Eng Sci,1969,24(4):795-797
5 Wegener PP,Sundel RE,Parlange JY.Spherical cap bubbles rising in liquids.Z Flugwiss,1971,19(8):374
6 Wairegi T.The mechanics of large bubbles and drops moving through extended liquid media.[PhD Thesis].Montreal:McGill University,1974
7 Bhaga D.Bubbles in viscous liquids:shapes,wakes and velocities.[PhD Thesis].Montreal:McGill University,1976
8 Hnat JG,Buckmaster JD.Spherical cap bubbles and skirt formation.Phys Fluids,1976,19(19):182-194
9 Ray B,Prosperetti A.On skirted drops in an immiscible liquid.Chem Eng Sci,2014,108:213-222
10 Davenport WG Richardson FD,Bradshaw AV.Spherical cap bubbles in low density liquids.Chem Eng Sci,1967,22(9):1221-135
11 Wegener PP,Parlange JY.Spherical-cap bubbles.Annu Rev Fluid Mech,1973,5(4):79-100
12 Guthrie RIL,Bradshaw AV.The stability of gas envelopes trailed behind large spherical cap bubbles rising through viscous liquids.Chem Eng Sci,1969,24(5):913-917
13 Lezzi AM,Prosperetti A.The stability of an air film in a liquid flow.J Fluid Mech,1991,226(226):319
14 Ohta M,Sussman M.The buoyancy-driven motion of a single skirted bubble or drop rising through a viscous liquid.Phys Fluids,2012,24(11):112101
15 Sulaiman M,Legendre D.Looking under the skirt of a bubble//Poceedings of the IUTAM Symposium on Bubbly Flows Oaxaca,Mexico,F,2015
16 Mukundakrishnan K,QuanS,Eckmann DM,et al.Numerical study of wall effects on buoyant gas-bubble rise in a liquid-filled finite cylinder.Phys Rev E,2007,76(2):036308
17 Kumar P,Vanka SP.Effects of confinement on bubble dynamics in a square duct.Int J Multiphas Flow,2015,77:32-47
18 Rahmat A,Tofighi N,Yildiz M.The combined effect of electric forces and confinement ratio on the bubble rising.Int J Heat Fluid Fl,2017,65:352-362
19李帅,张阿漫.上浮气泡在壁面处的弹跳特性研究.物理学报,2014,63(5):054705(Li Shuai,Zhang Aman.Study on a rising bubble bouncing near a rigid boundary.Acta Phys Sin,2014,63(5):054705(in Chinese))
20 Zhang AM,Li S,Cui J.Study on splitting of a toroidal bubble near a rigid boundary.Phys Fluids,2015,27(6):062102
21 Liu LT,Yao XL,Zhang AM,et al.Numerical analysis of the jet stage of bubble near a solid wall using a front tracking method.Phys Fluids,2017,29(1):012105
22邱超,张会臣.单个上升空泡撞击顶部壁面的变形和回弹特性研究.机械工程学报,2014,50(9):191-196(Qiu Chao,Zhang Huichen.Deformation and rebound characteristics of single rising bubble impacting against top wall.Journal of Mechanical Engineering,2014,50(9):191-196(in Chinese))
23李维仲,张晓红,董波等.单气泡沿倾斜绝热表面运动特性的LBM方法研究.化工学报,2013,64(11):3940-3948(Li Weizhong,Zhang Xiaohong,Dong Bo,et al.Lattice Boltzmann simulation of moving characteristics of a single bubble rising along inclined adiabatic surface.CIESC Journal,2013,64(11):3940-3948(in Chinese))
24刘云龙,汪玉,张阿漫.有倾角的竖直壁面附近气泡与自由面相互作用研究.物理学报,2013,62(21):214703(Liu Yunlong,Wang Yu,Zhang Aman.The interaction between bubble and free surface near vertical wall with inclination.Acta Phys Sin,2013,62(21):214703(in Chinese))
25鞠花,陈刚,李国栋等.静水中上升气泡沿倾斜壁面的运动特性试验研究.水动力学研究与进展,2011,26(3):327-332(Ju Hua,Chen Gang,Li Guodong,et al.Experimental study on motion behavior of single bubble rising along inclined plane in still water.Chin J Hydrodyn,2011,26(3):327-332(in Chinese))
26 Hirt CW,Nichols BD.Volume of fluid(VOF)method for the dynamics of free boundaries.J Comput Phys,1981,39(1):201-225
27 Youngs DL.Time-dependent Multi-Material Flow with Large Fluid Distortion.New York:Academic Press,1982
28吴应湘,林黎明,钟兴福.带有新型涡激振动抑制罩的圆柱体的水动力特性.力学学报,2016,48(2):307-317(Wu Yingxiang,Lin Liming,Zhong Xingfu.Investigation in hydrodynamics of a circular cylinder with the new suppressing shroud for vortex-induced vibration.Chinese Journal of Theoretical and Applied Mechanics,2016,48(2):307-317(in Chinese))
29张新曙,胡晓峰,尤云祥等.深海多立柱浮式平台涡激运动特性研究.力学学报,2016,48(3):593-598(Zhang Xinshu,Hu Xiaofeng,You Yunxiang,et al.Investigation on the characterisitics of vortex induced motion of a deep sea muti-column floating platform.Chinese Journal of Theoretical and Applied Mechanics,2016,48(3):593-598(in Chinese))
30杜特专,王一伟,黄晨光等.航行体水下发射流固耦合效应分析.力学学报,2017,49(4):782-792(Du Tezhuan,Wang Yiwei,Huang Chenguang,et al.Study on coupling effects of underwater launched vehicle.Chinese Journal of Theoretical and Applied Mechanics,2017,49(4):782-792(in Chinese))
31郝子辉,阎超,周玲.κ-ω-γ模式对转捩影响因素的预测性能研究.力学学报,2015,47(2):215-22(Hao Zihui,Yan Chao,Zhou Ling.Parametric study of aκ-ω-γmodel in predicting hypersonic boundary-layer flow transition.Chinese Journal of Theoretical and Applied Mechanics,2015,47(2):215-222(in Chinese))
32 Clift R,Grace JR,Weber ME.Bubbles,drops,and particles.Academic Press,1978
33黄永念.旋涡结构的湍流统计理论.力学进展,2002,32(4):505-512(Huang Youngnian.ON the statistical vortes structure theory of turbulence.Advances in Mechanics,2002,32(4):505-512(in Chinese))
34 Dijkhuizen W,Van Den Hengel EIV,Deen NG,et al.Numerical investigation of closures for interface forces acting on single airbubbles in water using Volume of Fluid and Front Tracking models.Chem Eng Sci,2005,60(22):6169-6175
35 Balc Zar N,Lehmkuhl O,Jofre L,et al.Level-set simulations of buoyancy-driven motion of single and multiple bubbles.Int J Heat Fluid Fl,2015,56:91-107