The Basset-Boussinesq-Oseen (BBO) equation can be used for most flows to trace the motion of a particle, but in a centrifugal pump, among the forces that act on the particles, one should also include those due to the impeller rotation, as additional effects. This paper firstly reviews various approximations of the BBO equation for the motion of dispersion particles in a viscous fluid. Then based on the motion equation for particles in low Reynolds number centrifugal pumps, a formula for calculating the tracking characteristics of tracer particles is deduced through the Fourier integral transformation. After that the deviations of the particle motion from the fluid motion, as predicted by the various approximations, are discussed and compared. At last, with an emphasis on the Particle Image Velocimetry (PIV) results, the tracking characteristics of particles are estimated. Also, advantages and disadvantages of different tracer particles are discussed and suitable tracer particles for application in PIV studies for flow fields in centrifugal pumps are suggested.

中文翻译：

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示踪颗粒在离心泵中的运动及其跟踪特性

Basset-Boussinesq-Oseen（BBO）方程可用于大多数流动，以追踪颗粒的运动，但在离心泵中，作用在颗粒上的力中还应包括由于叶轮旋转而产生的力，作为附加效果。本文首先回顾了BBO方程对粘性流体中分散颗粒运动的各种近似。然后根据低雷诺数离心泵中颗粒的运动方程，通过傅立叶积分变换推导了示踪剂颗粒的跟踪特性的计算公式。之后，讨论并比较了由各种近似值预测的粒子运动与流体运动之间的偏差。最后，重点介绍粒子图像测速（PIV）结果，估计粒子的跟踪特性。此外，讨论了不同示踪剂颗粒的优缺点，并提出了适用于离心泵流场PIV研究的合适示踪剂颗粒。