On equation of discrete solid particles' motion in arbitrary flow field and its properties

Abstract

The forces on rigid particles moving in relation to fluid having been studied and the equation of modifications of their expressions under different flow conditions discussed, a general form of equation for discrete particles' motion in arbitrary flow field is obtained. The mathematical features of the linear form of the equation are clarified and analytical solution of the linearized equation is gotten by means of Laplace transform. According to above theoretical results, the effects of particles' properties on its motion in several typicalflow field are studied, with some meaningful conclusions being reached.

An Oil Wear Particles Inline Optical Sensor Based on Motion Characteristics for Rotating Machines Condition Monitoring

“…Jeffrey et al investigated the motion of particles in a laminar vertical pipe experimentally and discovered that the motion of rigid spherical particles suspended in a viscous liquid was consistent with the Segre and Silberberg effect [25]. Huang et al studied the motion of particles in an arbitrary flow field and found that the diameter and density of particles played an important role in the relative motion of liquid-solid two-phase flow; the larger the diameter and density of the particles, the greater the relative velocity of the two phases, and the effect of particle density is greater than the effect of particle diameter [26]. Choi et al analyzed the influence of particles of different sizes, shapes, and densities on particle motion, using the PTV (particle tracking velocimetry) technique.…”

“…The force environment of the model was analyzed following the BBO equation for particle motion in a viscous fluid by Oseen. [29] and the equation of motion for discrete particles in an arbitrary flow field by Huang et al [26]: a solid particle of diameter d P and density ρ P , placed in the tube cross-section at z = 0 (see Figure 2), at time t = 0. When t > 0, it started to move in the z-axis direction under gravity.…”

A Lumped Particle Modeling Framework for Simulating Particle Transport in Fluids

“…We will, however, for simplicity use the term "BBO-like" in this paper. The omitted terms can be important in some applications [35], but are not relevant for the particle sizes considered in this paper.…”