NUMERICAL STUDY ON THE ROTATION OF AN ELLIPTICAL PARTICLE IN SHEAR FLOW
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摘要: 研究颗粒在流体剪切作用下的运动特性是理解和预测颗粒悬浮流流动行为的关键.当流体的惯性不能忽略时，颗粒的运动往往变得非常复杂.本文采用格子Boltzmann方法对中等雷诺数下椭圆颗粒在剪切流中的旋转运动进行了模拟.首先，研究了雷诺数（0 < Re≤170）的影响，结果表明当雷诺数低于临界值时，颗粒以周期性的方式旋转，角速度最小时对应的长轴方向随着雷诺数的增大而逐渐远离水平方向，而且这一倾角与雷诺数呈分段线性关系；当雷诺数大于临界值时，椭圆形颗粒最终保持静止状态，且静止时的转角与雷诺数呈幂函数关系，雷诺数越大，转角越小，椭圆的长轴越远离水平位置.其次，研究了椭圆颗粒的长短轴之比α（1≤α≤10）的影响，结果表明颗粒旋转的周期与α呈幂函数关系，α越大，颗粒旋转周期越小.此外，当α超过临界值时，颗粒也在水平位置附近保持静止状态，此时的转角与α也呈幂函数关系，α越大，转角越小.研究还发现，当雷诺数较大时椭圆颗粒在旋转过程中会产生过冲现象.
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关键词:
- 格子Boltzmann方法 /
- 剪切流 /
- 椭圆颗粒 /
- 旋转
Abstract: A thorough understanding of the behavior of particles freely suspended in a shear flow is fundamentally important for understanding and predicting flow behavior of particle suspensions. The motion of particles is very complex when the fluid inertia is taken into account. In the present study, the lattice Boltzmann method has been used to simulate the rotation of an elliptical particle in simple shear flow at intermediate Reynolds numbers. Firstly, the effect of the Reynolds number (0 < Re≤170) has been studied. Results show that the particle rotates periodically when Re is smaller than a critical value. The orientation of the particle at which the particle has its minimum angular velocity decreases as Re increases, which has a piecewise linear relationship with Re. Moreover, the rotation period has a power-law relationship with Re. The larger Re is, the larger the rotation period is. However, when Re is greater than the critical value, the elliptical particle will reach a steady state. Results show that the final orientation of the elliptical particle has a power-law relationship with Re for the steady state. The larger Re is, the smaller the orientation is. Secondly, the effect of the ratio of major axis/minor axis α (1≤α≤10) has also been studied. It shows that there is also a power-law relationship between the rotation period and α. The larger the value of α is, the smaller the rotation period is. Similarly, when α is greater than a critical value, the elliptical particle does not rotate. The final orientation of the elliptical particle has a power-law relationship with α. The larger the value of α is, the smaller the orientation is. Furthermore, it also shows that the overshoot is observed when the elliptical particle is rotating if Re is larger enough.-
Key words:
- lattice Boltzmann method /
- shear flow /
- elliptical particle /
- rotation
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图 2 椭圆形颗粒在剪切流中的运动示意图
Figure 2. Schematic of an elliptical particle subjected to simple shear flow
图 4 不同雷诺数下椭圆颗粒的旋转周期的对比
Figure 4. The period of the rotation of the elliptical particle at differentReynolds number
图 5 不同雷诺数下椭圆颗粒旋转的角度和角速度
Figure 5. The orientation and rotation velocity of the elliptical particle atdifferent Reynolds numbers
图 6 椭圆颗粒转速最小时对应的转角
Figure 6. The orientation of the elliptical particle when its rotation velocityis smallest
图 7 不同雷诺数下椭圆颗粒在剪切流中的旋转周期
Figure 7. The period of the rotation of elliptical particle at differentReynolds number
图 8 椭圆转角$\theta=0.94 \pi $时不同雷诺数下的流线结构及压力分布
Figure 8. The streamlines and pressure for $ \theta=0.94 \pi $ at different Reynoldsnumbers
图 9 椭圆颗粒静止时不同雷诺数下的流线结构和压力分布
Figure 9. The streamlines and pressure at different Reynolds numbers when theparticle becomes stationary
图 10 不同雷诺数下椭圆颗粒倾角随时间的变化
Figure 10. Time history of orientation of elliptical particle for differentReynolds numbers
图 11 不同雷诺数下椭圆颗粒角速度随时间的变化
Figure 11. Time history of rotational velocity of elliptical for differentReynolds numbers
图 12 不同雷诺数下椭圆颗粒的最终倾角
Figure 12. Final orientation of elliptical particle at different Reynoldsnumbers
图 13 不同$\alpha $对应的椭圆颗粒旋转角度和角速度的变化
Figure 13. The orientation and rotational velocity of elliptical particle fordifferent $\alpha $
图 14 雷诺数分别为5和10对应的周期与$\alpha $的关系
Figure 14. The period of the rotation of elliptical particle fordifferent $ \alpha $ at $Re=5$ and 10, respectively
图 15 $Re=10$时不同长短轴之比对应的流线结构及压力分布
Figure 15. The streamlines and pressure for different $\alpha $ at $Re=10$
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