Wall Effects on a Sphere Falling in Quiescent Power Law Fluids in Cylindrical Tubes
Wall Effects on a Sphere Falling in Quiescent Power Law Fluids in Cylindrical Tubes
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DOI：
10.1021/ie900176y
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发表时间：
2009-06-17
影响因子：
4.2
通讯作者：
Chhabra, Rajendra P.
中科院分区：
文献类型：
--
作者：
Song, Daoyun;Gupta, Rakesh K.;Chhabra, Rajendra P.
本文用数值方法研究了有限边界对圆柱形容器中静止幂律流体中球体所受阻力的影响。特别是，动量方程已在以下范围内的条件下数值求解：球雷诺数，1-100;幂律指数，0.2-1;和球管直径比，0-0.5。由于由下落的球体引起的流体的回流以及接近球体的速度场的相应变化，有限边界的存在导致作用在下落的球体上的阻力增加，从而减缓其下降。然而，这种影响在低雷诺数下比在高雷诺数下更显著。类似地，由于壁引起的附加阻力随着限制程度的增加而增加，即，球管直径比。总的来说，在其他条件相同的情况下，幂律流体的壁面效应不如牛顿流体严重。此外，限制壁还影响流动分离的开始以及随后的再循环区域的尺寸。目前的数值预测与文献中的实验结果是一致的。
The effect of finite boundaries on the drag experienced by a sphere settling in quiescent power law fluids in cylindrical vessels has been investigated numerically. In particular, the momentum equations have been solved numerically over the following ranges of conditions: sphere Reynolds number, 1-100; power law index, 0.2-1; and sphere-to-tube diameter ratio, 0-0.5. Due to the backflow of the fluid caused by a falling sphere and the corresponding changes in the velocity field close to the sphere, the presence of finite boundaries leads to an increase in the drag force acting on a falling sphere thereby slowing its descent. The effect, however, is more significant at low Reynolds numbers than at high Reynolds numbers. Similarly, the additional drag due to the walls increases with the increasing degree of confinement, i.e., the sphere-to-tube diameter ratio. Overall, all else being equal, the wall effect is less severe in power law fluids than in Newtonian fluids. Furthermore, the confining walls also influence the onset of flow separation and subsequently the size of the recirculation region. The present numerical predictions are consistent with the experimental results available in the literature.