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Effect of Reynolds number on the eddy structure in a lid‐driven cavity
Author(s) -
Chiang T. P.,
Sheu W. H.,
Hwang Robert R.
Publication year - 1998
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(19980315)26:5<557::aid-fld638>3.0.co;2-r
Subject(s) - reynolds number , mechanics , hele shaw flow , mathematics , vortex , instability , flow (mathematics) , magnetic reynolds number , bifurcation , physics , classical mechanics , geometry , turbulence , nonlinear system , quantum mechanics
In this paper we apply a finite volume method, together with a cost‐effective segregated solution algorithm, to solve for the primitive velocities and pressure in a set of incompressible Navier–Stokes equations. The well‐categorized workshop problem of lid‐driven cavity flow is chosen for this exercise, and results focus on the Reynolds number. Solutions are given for a depth‐to‐width aspect ration of 1:1 and a span‐to width aspect ratio of 3:1. Upon increasing the Reynolds number, the flows in the cavity of interest were found to comprise a transition from a strongly two‐dimensional character to a truly three‐dimensional flow and, subsequently, a bifurcation from a stationary flow pattern to a periodically oscillatory state. Finally, viscous (Tollmien–Schlichting) travelling wave instability further induced longitudinal vortices, which are essentially identical to Taylor–Görtler vortices. The objective of this study was to extend our understanding of the time evolution of a recirculatory flow pattern against the Reynolds number. The main goal was to distinguish the critical Reynolds number at which the presence of a spanwise velocity makes the flow pattern become three‐dimensional. Secondly, we intended to learn how and at what Reynolds number the onset of instability is generated. © 1998 John Wiley & Sons, Ltd.