Can the History Force be Neglected for the Motion of Particles at High Subcritical Reynolds Number Range?

In the present work, the motion of metallic and plastic particles of ۵ mm diameter falling in a quiescent fluid is investigated experimentally. The goal of this investigation is to examine the effect of history force acting on a particle in a range of Reynolds numbers between ۱۰۰۰ and ۵۰۰۰. The instantaneous position of the particle was recorded using a high - speed camera (۵۰۰ to ۱۰۰۰ frames per second). The comparison is made by solving the equation of motion of particle with and without history force based on the Lagrangian approach. The results showed that the combination of gravity, drag and added mass forces are important for simulation of particle motion from the starting point of motion to the wall impact in the range of aforementioned Reynolds numbers. Nevertheless, the predicted trajectories underestimate the experimental observations. In this case, excellent agreement between the measured and predicted particle trajectory was obtained when the history force was included in the governing  equation. Analysis of the results showed, however, the history force in comparison with the other hydrodynamic forces in prediction of the particle motion, from the starting point of motion to the wall  impact has a small effect which is about ۱ to ۴.۳ % and can be ignored. But it has a considerable effect on the bouncing motion of the particle after the first collision, even for the Reynolds numbers up to ۵۰۰۰.

Keywords:

Lagragian Approach , Drag force , Added Mass Force , History Force , Bouncing Motion