University of Illinois Urbana-Champaign

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

Bagchi, Prosenjit; Balachandar, S.

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https://hdl.handle.net/2142/112673

Description

Title
Linearly varying ambient flow past a sphere at finite Reynolds number: part 2 - equation of motion
Author(s)
  • Bagchi, Prosenjit
  • Balachandar, S.
Issue Date
2001-02
Keyword(s)
  • Pseudospectral Methodology
  • Stokes-like Drag
Abstract
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.
Publisher
Department of Theoretical and Applied Mechanics. College of Engineering. University of Illinois at Urbana-Champaign
Series/Report Name or Number
  • TAM R 966
  • 2001-6005
ISSN
0073-5264
Type of Resource
text
Language
eng
Permalink
http://hdl.handle.net/2142/112673
Sponsor(s)/Grant Number(s)
ASCI Center for Simuation of Advanced Rockets
Copyright and License Information
Copyright 2001 Board of Trustees of the University of Illinois

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Technical Reports - Theoretical and Applied Mechanics (TAM) PRIMARY
TAM technical reports include manuscripts intended for publication, theses judged to have general interest, notes prepared for short courses, symposia compiled from outstanding undergraduate projects, and reports prepared for research-sponsoring agencies.