Linearly varying ambient flow past a sphere at finite Reynolds number: part 2 - equation of motion

The focus of this paper is to investigate the effects of spatially nonuniform ambient flow on the equation of motion of a particle at a finite particle Reynolds number, Re, in the range 10 to 300. Numerical simulations based on pseudospectral methodology are carried out to solve unsteady three-dimensional flow field around a spherical particle which is either held stationary or allowed to move freely under hydrodynamic forces. The total force on the particle is written as a sum of different contributions, namely, inertial, steady viscous and transient viscous forces . The effect of inertial forces is isolated by monitoring the rapid changes in the drag and lift forces in response to a rapid acceleration of the ambient flow. It is shown that the inertial forces arising due to convective as well as temporal acceleration follow the inviscid result even at finite Reynolds numbers. We then consider simulation results for a stationary particle subjected to steady straining flows . It is shown that the steady viscous forces under nonuniform ambient conditions cannot be adequately represented by the standard parameterization in terms of the particle Reynolds number alone. A generalized representation for the steady viscous force on a sphere subjected to linearly varying flows is presented. The limiting behavior of this representation is examined in low Reynolds number limit and at finite Re. Such a representation together with the inertial forces provide an improved parameterization of force. The accuracy of the improved parameterization is tested against the exact results obtained from direct numerical simulations of a freely moving particle in straining flows. Different contributions to the improved parameterization, such as , the Stokes-like drag, effect of fluid and particle accelerations and history force are compared.ASCI Center for Simuation of Advanced Rocket