雷诺数和界面污染程度对气泡水动力学特性的影响
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摘要
深入研究气泡界面污染程度对气泡水动力学特性的影响,对控制和改善泡状流动中气泡的运动速度和气液界面的传质和传热性能具有重要意义。为此,该文利用停滞帽模型详细研究了不同气泡雷诺数下,球形气泡界面污染程度对气泡界面参数(切向速度、压力、切应力和涡量)及其整体运动特征(尾流和阻力系数)的影响。基于停滞帽模型,通过改变帽角来定量控制气泡界面的污染程度,气泡雷诺数20≤Reb≤200,计算区域为轴对称结构。研究表明,在不同气泡雷诺数下,气泡界面污染程度对气泡水动力学单一物理参量的影响趋势是相似的,且界面参数在帽角处发生了突变;界面污染程度对气泡整体运动特征的影响与气泡雷诺数有关,气泡雷诺数越小,界面污染程度对阻力系数的影响越明显,而尾涡现象越弱。
The bubble flow is extensively encountered in natural and industrial fields. For the majority of bubbly flows, the liquid phase is more or less polluted, which causes the change of the interfacial state of the bubble. The state of the bubble interface has the significant effect on hydrodynamic properties around the bubble. Furthermore, the changed flow field around the bubble directly influences the heat and mass transfer properties between the bubble and the liquid phases too. Therefore, it is necessary to deeply investigate the influence of interface contaminated degree on the dynamic properties of the bubble. In this paper, a bubble with the diameter of d is considered to be suspended in a rectangular region and the fluid flows around it with the velocity of U. As for the size of the region, the distances between the bubble center and the inlet, the outlet and the region wall are 5, 12 and 7 d, respectively. In view of the physical environment of the bubble, the bubble Reynolds number is not lager than 200, and thus the flow structure exhibits the two-dimensional properties. So the axisymmetric field can be used as the computational region, and thus the computational cost can drop greatly. Considering the contaminated degree of the bubble surface, the stagnant cap model is used. With this model, the interface contaminated degree is controlled artificially by changing boundary conditions(such as the interfacial velocity and the tangential stress) directly on the bubble surface. The cap angle, measuring from the rear stagnant point to the front edge of the contaminated interface, is used to describe the interface contaminated degree. In order to understand physical phenomena deeply, the computational cases as many as possible are designed. The cape angles representing the interfacial pollution degree are respectively designated as 0, 15°, 30°, 45°, 60°, 75°, 90°, 105°, 120°, 135°, 150°, 165° and 180°, and the bubble Reynolds numbers are selected as 20, 40, 75, 100, 150 and 200. For the present investigation, the quadrilateral grids are used to discretize the computational field. And the non-uniform grids are used in the radial direction so as to well capture flow properties near the bubble. Thus, the closer to the bubble surface the grids are, the smaller the radial grids size is. Based on the present conditions, it is fully investigated and analyzed on the influence of interfacial contamination degree on interfacial physical parameters(such as the tangential velocity, pressure, tangential stress and vorticity) and overall motion characteristics(such as the wake and drag coefficient) under different bubble Reynolds numbers. The present investigations show that, for any bubble Reynolds number, the influence of interfacial pollution levels on the physical parameters are similar, and the interfacial physical parameters have an abrupt change near the cap angle. The influences of interface contamination levels on the overall motion characteristics of the bubble are related to the bubble Reynolds number. It seems that the smaller the bubble Reynolds number is, the drag coefficient is more sensitive to the interfacial pollution level.
The bubble flow is extensively encountered in natural and industrial fields. For the majority of bubbly flows, the liquid phase is more or less polluted, which causes the change of the interfacial state of the bubble. The state of the bubble interface has the significant effect on hydrodynamic properties around the bubble. Furthermore, the changed flow field around the bubble directly influences the heat and mass transfer properties between the bubble and the liquid phases too. Therefore, it is necessary to deeply investigate the influence of interface contaminated degree on the dynamic properties of the bubble. In this paper, a bubble with the diameter of d is considered to be suspended in a rectangular region and the fluid flows around it with the velocity of U. As for the size of the region, the distances between the bubble center and the inlet, the outlet and the region wall are 5, 12 and 7 d, respectively. In view of the physical environment of the bubble, the bubble Reynolds number is not lager than 200, and thus the flow structure exhibits the two-dimensional properties. So the axisymmetric field can be used as the computational region, and thus the computational cost can drop greatly. Considering the contaminated degree of the bubble surface, the stagnant cap model is used. With this model, the interface contaminated degree is controlled artificially by changing boundary conditions(such as the interfacial velocity and the tangential stress) directly on the bubble surface. The cap angle, measuring from the rear stagnant point to the front edge of the contaminated interface, is used to describe the interface contaminated degree. In order to understand physical phenomena deeply, the computational cases as many as possible are designed. The cape angles representing the interfacial pollution degree are respectively designated as 0, 15°, 30°, 45°, 60°, 75°, 90°, 105°, 120°, 135°, 150°, 165° and 180°, and the bubble Reynolds numbers are selected as 20, 40, 75, 100, 150 and 200. For the present investigation, the quadrilateral grids are used to discretize the computational field. And the non-uniform grids are used in the radial direction so as to well capture flow properties near the bubble. Thus, the closer to the bubble surface the grids are, the smaller the radial grids size is. Based on the present conditions, it is fully investigated and analyzed on the influence of interfacial contamination degree on interfacial physical parameters(such as the tangential velocity, pressure, tangential stress and vorticity) and overall motion characteristics(such as the wake and drag coefficient) under different bubble Reynolds numbers. The present investigations show that, for any bubble Reynolds number, the influence of interfacial pollution levels on the physical parameters are similar, and the interfacial physical parameters have an abrupt change near the cap angle. The influences of interface contamination levels on the overall motion characteristics of the bubble are related to the bubble Reynolds number. It seems that the smaller the bubble Reynolds number is, the drag coefficient is more sensitive to the interfacial pollution level.
引文
[1]Aoyama S,Hayashi K,Hosokawa S,et al.Shapes of single bubbles in infinite stagnant liquids contaminated with surfactant[J].Experimental Thermal and Fluid Science,2018,96:460-469.
[2]Rastello M,MariéJ L,Lance M.Clean versus contaminated bubbles in a solid-body rotating flow[J].Journal of Fluid Mechanics,2017,831:592-617.
[3]Huang J,Saito T.Discussion about the differences in mass transfer,bubble motion and surrounding liquid motion between a contaminated system and a clean system based on consideration of three-dimensional wake structure obtained from LIF visualization[J].Chemical Engineering Science,2017,170:105-115.
[4]Arkhipov V A,Vasenin I M,Usanina A S.Dynamics of bubble rising in the presence of surfactants[J].Fluid Dynamics,2016,51(2):266-274.
[5]Tan Y H,Finch J A.Frother structure-property relationship:Effect of hydroxyl position in alcohols on bubble rise velocity[J].Minerals Engineering,2016,92:1-8.
[6]Tan Y H,Finch J A.Frother structure-property relationship:Effect of alkyl chain length in alcohols and polyglycol ethers on bubble rise velocity[J].Minerals Engineering,2016,95:14-20.
[7]邓丽君,李国胜,曹亦俊,等.浮选起泡剂对气泡兼并行为的影响研究[J].中国矿业大学学报,2017,47(2):410-414.Deng Lijun,Li Guosheng,Cao Yijun,et al.Effect of flotation frothers on bubbles coalescence behavior[J].Journal of China University of Mining&Technology,2017,47(2):410-414.(in Chinese with English abstract)
[8]裴明敬,朱婷婷,杨晶晶,等.环境友好型生物表面活性剂对浮选气泡动力学的影响研究[J].高校化学工程学报,2013,27(6):985-990.Pei Mingjing,Zhu Tingting,Yang Jingjing,et al.Study on effects of environment-friendly biosurfactants on bubble hydrodynamics in flotation column[J].Journal of Chemical Engineering of Chinese Universities,2013,27(6):985-990.(in Chinese with English abstract)
[9]Jarek E,Warszynski P,Krzan M.Influence of different electrolytes on bubble motion in ionic surfactants solutions[J]Colloids and Surfaces A:Physicochemical and Engineering Aspects,2016,505:171-178.
[10]Hayashi K,Tomiyama A.Effects of surfactant on lift coefficients of bubbles in linear shear flows[J].International Journal of Multiphase Flow,2018,99:86-93.
[11]Lu J C,Muradoglu M,Tryggvason G.Effect of insoluble surfactant on turbulent bubbly flows in vertical channels[J].International Journal of Multiphase Flow,2017,95:135-143.
[12]费洋,庞明军.球形气泡界面变化对尾涡性质和尺寸的影响[J].化工学报,2017,68(9):3409-3419.Fei Yang,Pang Mingjun.Influence of interface change for spherical bubble on vortex characteristic and size[J].CIESCJournal,2017,68(9):3409-3419.(in Chinese with English abstract)
[13]Nalajala V S,Kishore N.Motion of partially contaminated bubbles in power-law liquids:Effect of wall retardation[J]International Journal of Mineral Processing,2015,140:8-18.
[14]Fleckenstein S,Bothe D.Simplified modeling of the influence of surfactants on the rise of bubbles in VOF-simulations[J].Chemical Engineering Science,2013102:514-523.
[15]Takagi S,Matsumoto Y.Surfactant effects on bubble motion and bubbly flows[J].Annual Review of Fluid Mechanics2011,43:615-636.
[16]Cuenot B,Magnaudet J,Spennato B.The effects of slightly soluble surfactants on the flow around a spherical bubble[J]Journal of Fluid Mechanics,1997,39:25-53.
[17]Fei Y,Pang M J.The influence of interface contaminated degree on the wake characteristics of a spherical bubble at moderate Reynolds number under the condition of isothermal flow[J].International Journal of Heat and Mass Transfer,2018,121:79-83.
[18]Reddy C R,Kishore N.Wall retardation effects on flow and drag phenomena of confined spherical particles in shear-thickening fluids[J].Industrial&Engineering Chemistry Research,2012,51:16755-16762.
[19]任安禄,李广望,邹建峰.中等雷诺数圆球绕流的数值研究[J].浙江大学学报:工学版,2004,38(5):644-648.Ren Anlu,Li Guangwang,Zou Jianfeng.Numerical study of uniform flow over sphere at intermediate Reynolds numbers[J].Journal of Zhejiang University:Engineering Science,2004,38(5):644-648.(in Chinese with English abstract)
[20]Tomboulides A G,Orszag S A.Numerical investigation of transitional and weak turbulent flow past a sphere[J].Journal of Fluid Mechanics,2000,416:45-73.
[21]Mei R,Klausner J F,Lawrence C J.A note on the history force on a spherical bubble at finite Reynolds number[J]Physics of Fluids,1994,6(1):418-420.
[22]Mei R.History force on a sphere due to a step change in the free-stream velocity[J].International of Journal Multiphase Flow,1993,19:509-525.
[2]Rastello M,MariéJ L,Lance M.Clean versus contaminated bubbles in a solid-body rotating flow[J].Journal of Fluid Mechanics,2017,831:592-617.
[3]Huang J,Saito T.Discussion about the differences in mass transfer,bubble motion and surrounding liquid motion between a contaminated system and a clean system based on consideration of three-dimensional wake structure obtained from LIF visualization[J].Chemical Engineering Science,2017,170:105-115.
[4]Arkhipov V A,Vasenin I M,Usanina A S.Dynamics of bubble rising in the presence of surfactants[J].Fluid Dynamics,2016,51(2):266-274.
[5]Tan Y H,Finch J A.Frother structure-property relationship:Effect of hydroxyl position in alcohols on bubble rise velocity[J].Minerals Engineering,2016,92:1-8.
[6]Tan Y H,Finch J A.Frother structure-property relationship:Effect of alkyl chain length in alcohols and polyglycol ethers on bubble rise velocity[J].Minerals Engineering,2016,95:14-20.
[7]邓丽君,李国胜,曹亦俊,等.浮选起泡剂对气泡兼并行为的影响研究[J].中国矿业大学学报,2017,47(2):410-414.Deng Lijun,Li Guosheng,Cao Yijun,et al.Effect of flotation frothers on bubbles coalescence behavior[J].Journal of China University of Mining&Technology,2017,47(2):410-414.(in Chinese with English abstract)
[8]裴明敬,朱婷婷,杨晶晶,等.环境友好型生物表面活性剂对浮选气泡动力学的影响研究[J].高校化学工程学报,2013,27(6):985-990.Pei Mingjing,Zhu Tingting,Yang Jingjing,et al.Study on effects of environment-friendly biosurfactants on bubble hydrodynamics in flotation column[J].Journal of Chemical Engineering of Chinese Universities,2013,27(6):985-990.(in Chinese with English abstract)
[9]Jarek E,Warszynski P,Krzan M.Influence of different electrolytes on bubble motion in ionic surfactants solutions[J]Colloids and Surfaces A:Physicochemical and Engineering Aspects,2016,505:171-178.
[10]Hayashi K,Tomiyama A.Effects of surfactant on lift coefficients of bubbles in linear shear flows[J].International Journal of Multiphase Flow,2018,99:86-93.
[11]Lu J C,Muradoglu M,Tryggvason G.Effect of insoluble surfactant on turbulent bubbly flows in vertical channels[J].International Journal of Multiphase Flow,2017,95:135-143.
[12]费洋,庞明军.球形气泡界面变化对尾涡性质和尺寸的影响[J].化工学报,2017,68(9):3409-3419.Fei Yang,Pang Mingjun.Influence of interface change for spherical bubble on vortex characteristic and size[J].CIESCJournal,2017,68(9):3409-3419.(in Chinese with English abstract)
[13]Nalajala V S,Kishore N.Motion of partially contaminated bubbles in power-law liquids:Effect of wall retardation[J]International Journal of Mineral Processing,2015,140:8-18.
[14]Fleckenstein S,Bothe D.Simplified modeling of the influence of surfactants on the rise of bubbles in VOF-simulations[J].Chemical Engineering Science,2013102:514-523.
[15]Takagi S,Matsumoto Y.Surfactant effects on bubble motion and bubbly flows[J].Annual Review of Fluid Mechanics2011,43:615-636.
[16]Cuenot B,Magnaudet J,Spennato B.The effects of slightly soluble surfactants on the flow around a spherical bubble[J]Journal of Fluid Mechanics,1997,39:25-53.
[17]Fei Y,Pang M J.The influence of interface contaminated degree on the wake characteristics of a spherical bubble at moderate Reynolds number under the condition of isothermal flow[J].International Journal of Heat and Mass Transfer,2018,121:79-83.
[18]Reddy C R,Kishore N.Wall retardation effects on flow and drag phenomena of confined spherical particles in shear-thickening fluids[J].Industrial&Engineering Chemistry Research,2012,51:16755-16762.
[19]任安禄,李广望,邹建峰.中等雷诺数圆球绕流的数值研究[J].浙江大学学报:工学版,2004,38(5):644-648.Ren Anlu,Li Guangwang,Zou Jianfeng.Numerical study of uniform flow over sphere at intermediate Reynolds numbers[J].Journal of Zhejiang University:Engineering Science,2004,38(5):644-648.(in Chinese with English abstract)
[20]Tomboulides A G,Orszag S A.Numerical investigation of transitional and weak turbulent flow past a sphere[J].Journal of Fluid Mechanics,2000,416:45-73.
[21]Mei R,Klausner J F,Lawrence C J.A note on the history force on a spherical bubble at finite Reynolds number[J]Physics of Fluids,1994,6(1):418-420.
[22]Mei R.History force on a sphere due to a step change in the free-stream velocity[J].International of Journal Multiphase Flow,1993,19:509-525.