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本文针对毫米量级的上浮气泡在壁面处的弹跳现象进行数值研究. 基于势流方法求解气泡的运动，同时考虑气泡的表面张力作用. 在伯努利方程中，对气泡与壁面之间水膜中因黏性引起的压力梯度进行修正，开发相应的计算程序，计算值与实验值符合良好. 从气泡弹跳的基本现象入手，研究了特征参数对气泡弹跳过程的动态特性以及最终平衡形态的影响. 发现随着泡在撞击壁面之前上浮距离增大，气泡回弹距离和弹跳周期增加，但是当上浮距离增加到一定程度后将不会影响气泡的弹跳特性；表面张力是影响气泡弹跳特性的重要因素，气泡的弹跳周期随其增大逐渐减小，但回弹距离却呈现先增后减的规律；最后，影响气泡最终平衡形态的主要因素是气泡的浮力参数与韦伯数.Some numerical studies were carried out on micrometer-sized rising bubble bouncing near a rigid boundary. Taking surface tension into consideration, the bubble motion could be solved using the potential flow theory. A correction should be made in Bernoulli equation because the pressure gradient was caused by the viscosity between the bubble and the wall. The numerical result agree well with the experimental data. Based on the fundamental phenomenon, we have studied the influence of characteristic parameter on bubble bouncing behavior, and the balanced shape due to the action of the wall. With the increase of the rising distance of the bubble, the distance of the bubble bouncing downward and the period of bouncing would increase. However, they would not change obviously when the rising distance is large enough. Surface tension has great effect on the dynamic behavior of the bubble. The bouncing period decreases when surface tension becomes large, but the bouncing distance will have an increase before it gradually decreases. Finally, the balanced shape of the bubble due to the wall effect can be mainly controlled by buoyance parameter and the Weber number.
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Keywords:
- bubble /
- wall /
- bouncing /
- boundary integral method
[1] Duineveld P C 1998 Appl. Sci. Res. 58 409
[2] Zhang A M, Ni B Y, Song B Y 2010 Appl. Math. and Mech. 31 449
[3] Tsao H K, Koch D 1997 Phys. Fluids 9 44
[4] Malysa K, Krasowska M, Krzan M 2005 Adv. Colloid. Interface. Sci. 114-115 205
[5] Toshiyuki S, Masao W, Tohru F 2005 Chem. Eng. Sci. 60 5372
[6] Wang H, Zhang Z Y, Yang Y M 2008 Chin. Phys. B 17 3847
[7] Wang H, Zhang Z Y, Yang Y M 2010 Chin. Phys. B 19 026801
[8] Klaseboer E, Manic R, Khoo B C, Chan D Y C 2011 Eng. Anal. Bound. Elem. 35 489
[9] Shopov P J, Minev P D, Bazhlekov I B, Zapryanov Z D 1990 J. Fluid Mech. 219 241
[10] Canot E, Davoust L, Hammoumi M E, Lachkar D 2003 Theoret. Comput. Fluid Dynamics 17 51
[11] Zhang A M, Yao X L 2008 Acta Phys. Sin. 57 1662(in Chinese)[张阿漫, 姚熊亮 2008 物理学报 57 1662]
[12] Liu Y L, Wang Y, Zhang A M 2013 Acta Phys. Sin. 62 214703 (in Chinese) [刘云龙, 汪玉, 张阿漫2013物理学报 62 214703]
[13] Newman J N 1977 Marine Hydrodynamics (1st Ed.) (London: MIT Press) p131
[14] Wang Q X, Teo K S, Khoo B C 1996 Theoret. Comput. Fluid Dynamics 8 73
[15] Best J P 1993 J. Fluid Mech. 251 79
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[1] Duineveld P C 1998 Appl. Sci. Res. 58 409
[2] Zhang A M, Ni B Y, Song B Y 2010 Appl. Math. and Mech. 31 449
[3] Tsao H K, Koch D 1997 Phys. Fluids 9 44
[4] Malysa K, Krasowska M, Krzan M 2005 Adv. Colloid. Interface. Sci. 114-115 205
[5] Toshiyuki S, Masao W, Tohru F 2005 Chem. Eng. Sci. 60 5372
[6] Wang H, Zhang Z Y, Yang Y M 2008 Chin. Phys. B 17 3847
[7] Wang H, Zhang Z Y, Yang Y M 2010 Chin. Phys. B 19 026801
[8] Klaseboer E, Manic R, Khoo B C, Chan D Y C 2011 Eng. Anal. Bound. Elem. 35 489
[9] Shopov P J, Minev P D, Bazhlekov I B, Zapryanov Z D 1990 J. Fluid Mech. 219 241
[10] Canot E, Davoust L, Hammoumi M E, Lachkar D 2003 Theoret. Comput. Fluid Dynamics 17 51
[11] Zhang A M, Yao X L 2008 Acta Phys. Sin. 57 1662(in Chinese)[张阿漫, 姚熊亮 2008 物理学报 57 1662]
[12] Liu Y L, Wang Y, Zhang A M 2013 Acta Phys. Sin. 62 214703 (in Chinese) [刘云龙, 汪玉, 张阿漫2013物理学报 62 214703]
[13] Newman J N 1977 Marine Hydrodynamics (1st Ed.) (London: MIT Press) p131
[14] Wang Q X, Teo K S, Khoo B C 1996 Theoret. Comput. Fluid Dynamics 8 73
[15] Best J P 1993 J. Fluid Mech. 251 79
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