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Numerical simulation of three‐dimensional Couette–Taylor flows
Author(s) -
Liao C.B.,
Jane S.J.,
Young D.L.
Publication year - 1999
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/(sici)1097-0363(19990415)29:7<827::aid-fld819>3.0.co;2-y
Subject(s) - taylor–couette flow , couette flow , flow (mathematics) , mathematics , vortex , taylor series , computer simulation , classical mechanics , mechanics , navier–stokes equations , projection method , mathematical analysis , physics , geometry , compressibility , grating
To investigate the time‐dependent non‐axisymmetric flow between two rotating cylinders, or the so‐called Couette–Taylor problem, a numerical model to solve the three‐dimensional Navier–Stokes equations is established. The projection method is employed to obtain the pressure Poisson equation first. Then the velocity is solved from the equations of motion by using a semi‐implicit finite difference scheme. The numerical solution thus obtained has the accuracy of second‐order in both time and space discretizations. The Couette–Taylor flow patterns are obtained from direct numerical simulation for the states or regimes of steady circular Couette flow, steady Taylor vortices, and their intermediate processes, as well as also the onset of periodic spiral vortices. The present numerical simulation has also confirmed the location of the transitional boundary of the flow states of the experimental study made by Andereck et al. [C.D. Anderek et al. , J. Fluid Mech. , 164 , 155–183 (1986)] Copyright © 1999 John Wiley & Sons, Ltd.