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Numerical analysis of the rotating viscous flow approaching a solid sphere
Author(s) -
Wang YanXing,
Lu XiYun,
Zhuang LiXian
Publication year - 2004
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.683
Subject(s) - inviscid flow , reynolds number , rossby number , mechanics , hele shaw flow , physics , flow (mathematics) , classical mechanics , taylor–couette flow , stokes flow , potential flow around a circular cylinder , mathematics , turbulence
A numerical simulation is performed to investigate the flow induced by a sphere moving along the axis of a rotating cylindrical container filled with the viscous fluid. Three‐dimensional incompressible Navier–Stokes equations are solved using a finite element method. The objective of this study is to examine the feature of waves generated by the Coriolis force at moderate Rossby numbers and that to what extent the Taylor–Proudman theorem is valid for the viscous rotating flow at small Rossby number and large Reynolds number. Calculations have been undertaken at the Rossby numbers ( R o ) of 1 and 0.02 and the Reynolds numbers ( R e ) of 200 and 500. When R o =O (1), inertia waves are exhibited in the rotating flow past a sphere. The effects of the Reynolds number and the ratio of the radius of the sphere and that of the rotating cylinder on the flow structure are examined. When R o ≪ 1, as predicted by the Taylor–Proudman theorem for inviscid flow, the so‐called ‘Taylor column’ is also generated in the viscous fluid flow after an evolutionary course of vortical flow structures. The initial evolution and final formation of the ‘Taylor column’ are exhibited. According to the present calculation, it has been verified that major theoretical statement about the rotating flow of the inviscid fluid may still approximately predict the rotating flow structure of the viscous fluid in a certain regime of the Reynolds number. Copyright © 2004 John Wiley & Sons, Ltd.