Study on Hydrodynamics Characteristics of a Single Bubble in Viscoelastic Fluid at Low Weissenberg Numbers
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摘要: 使用VOF法数值研究了气泡在黏弹性流体中的上浮运动，黏弹性模型选用Oldroyd-B模型.在低Weissenberg数(Wi)下，研究了黏性力、松弛时间、表面张力和黏度比对气泡上浮运动的影响.结果表明，当黏性力和弹性力较大(如Ga=2，Wi≥0.5和β=0.2)时，气泡尾部会出现“尾缘尖”现象，“尾缘尖”现象随着弹性的增强和表面张力的减小变得明显；当弹性较弱(如Wi=0.1)时，“尾缘尖”现象消失，气泡呈为帽形；当表面张力较大(如Eo=1)时，气泡呈现为纵向拉长的椭圆形，尾部特征不明显；在黏弹性流体中，表面张力对气泡的影响与在黏性流体中的相似；气泡在上浮过程中，随形状的变化，表现出“持续加速到稳定”和“加速-减速-再加速到稳定”两种上浮形式，在黏弹性流体中，气泡的上浮速度高于在纯黏性流体中的上浮速度；气泡周围的弹性应力与流体的黏度和松弛时间有关，随着黏度的减小和松弛时间的增大，弹性应力作用范围变宽.
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关键词:
- 黏弹性流体 /
- 气泡上浮运动 /
- Oldroyd-B模型 /
- VOF法
Abstract: The VOF method was used to numerically study the upward motion of a single bubble in viscoelastic fluid, and the Oldroyd-B model was applied to describe the fluid viscoelastic property. At low Weissenberg numbers (Wi≤1), the effects of the viscous force, the relaxation time, the surface tension and the viscosity ratio on the rising motion of the bubble were studied. The results show that, under relatively large viscous and elastic forces (such as Ga=2, Wi≥0.5 and β=0.2), the bubble exhibits the phenomenon of "a pointed rear end", and this phenomenon intensifies with the increase of the elasticity and the decrease of the surface tension. Otherwise, under a relatively weak elasticity (such as Wi=0.1), the phenomenon of "a pointed rear end" disappears, and the bubble bears a hat-like shape. For a large surface tension (such as Eo=1), the bubble bears a longitudinally elongated ellipse-like shape without distinct tail features. The effect of the surface tension on the bubble in viscoelastic fluid is like that in viscous fluid. The bubble has 2 types of rising motions, namely, "continuous acceleration" to a stable velocity and "acceleration-deceleration-reacceleration" to a stable velocity, and the bubble rising velocity in viscoelastic fluid is higher than that in pure viscous fluid. The elastic stress around the bubble is influenced by the viscosity and the relaxation time of the fluid, and with the decrease of the fluid viscosity or/and the increase of the relaxation time, the incidence of the elastic stress becomes wide.-
Key words:
- viscoelastic fluid /
- bubble rising motion /
- Oldroyd-B model /
- VOF method
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图 2 网格大小对气泡中心高度和上浮速度的影响
注 为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.
Figure 2. Effects of the grid size on the bubble center height and the center velocity
图 3 时间步长对气泡中心高度和上浮速度的影响
注 为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.
Figure 3. Effects of the time step on the bubble center height and the center velocity
图 6 β=0.2时，气泡形状随Ga数，Wi数和Eo数的变化
Figure 6. Bubble shapes against Ga, Wi and Eo numbers at β=0.2
图 7 Eo=10时，气泡形状随β，Ga数和Wi数的变化
Figure 7. Bubble shapes against β, Ga and Wi numbers at Eo=10
图 8 Wi=1和Ga=2时，聚合物分子对气泡变形的影响
Figure 8. Schematic of effects of polymer molecules on bubble deformation at Wi=1 and Ga=2
图 9 Ga=4和β=0.2时，Wi数和Eo数对气泡上浮速度的影响
Figure 9. Effects of Wi and Eo numbers on the bubble rise velocity at Ga=4 and β=0.2
图 10 Eo=10和β=0.2时，Ga数对气泡上浮速度的影响
Figure 10. Effects of the Ga number on the bubble rise velocity at Eo=10 and β=0.2
图 11 Ga=2和Eo=10时，黏度比β对气泡上浮速度的影响
Figure 11. Effects of viscosity ratio β on the bubble rise velocity at Ga=2 and Eo=10
图 12 Ga=4和β=0.2时，Eo数和Wi数对气泡尾流的影响
Figure 12. Effects of Eo and Wi numbers on the bubble wake at Ga=4 and β=0.2
图 13 Eo=10和β=0.2时，Ga数和Wi数对气泡尾流的影响
Figure 13. Effects of Ga and Wi numbers on the bubble wake at Eo=10 and β=0.2
表 1 计算工况
Table 1. Design of the computation case
Wi β Ga=2 Ga=4 Ga=8 Ga=16 Eo=1 Eo=10 Eo=100 Eo=1 Eo=10 Eo=100 Eo=1 Eo=10 Eo=100 Eo=1 Eo=10 Eo=100 0.1 0.2 √ √ √ √ √ √ √ √ √ √ √ √ 0.5 √ √ √ √ 0.8 √ √ √ √ 0.5 0.2 √ √ √ √ √ √ √ √ √ √ √ √ 0.5 √ √ √ √ 0.8 √ √ √ √ 1 0.2 √ √ √ √ √ √ √ √ √ √ √ √ 0.5 √ √ √ √ 0.8 √ √ √ √ 
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