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 引用本文: 张洋, 陈科, 尤云祥, 任伟. 壁面约束对裙带气泡动力学的影响[J]. 力学学报, 2017, 49(5): 1050-1058.
Zhang Yang, Chen Ke, You Yunxiang, Ren Wei. CONFINEMENT EFFECT ON THE RISING DYNAMICS OF A SKIRTED BUBBLE[J]. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(5): 1050-1058.
 Citation: Zhang Yang, Chen Ke, You Yunxiang, Ren Wei. CONFINEMENT EFFECT ON THE RISING DYNAMICS OF A SKIRTED BUBBLE[J]. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(5): 1050-1058.

## CONFINEMENT EFFECT ON THE RISING DYNAMICS OF A SKIRTED BUBBLE

• 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.

Abstract: 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.

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