Chiang, T.P.T.P.ChiangSheu, W.H.W.H.SheuHwang, R.R.R.R.HwangTONY W. H. SHEU2020-01-172020-01-17199802712091https://scholars.lib.ntu.edu.tw/handle/123456789/451828In 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 ratio 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.Instabilites; Lid-driven cavity; Taylor Görtler-like vorticesAspect ratio; Computational fluid dynamics; Finite volume method; Flow patterns; Navier Stokes equations; Reynolds number; Transition flow; Viscous flow; Eddy structure; Taylor-Gortler vortex flow; Vortex flow; cavity; eddy; instability; Reynolds number; vortex; eddies; instability; Reynolds number; vorticesjournal article10.1002/(SICI)1097-0363(19980315)26:5<5572-s2.0-0032029321https://www.scopus.com/inward/record.uri?eid=2-s2.0-0032029321&doi=10.1002%2f%28SICI%291097-0363%2819980315%2926%3a5%3c557%3a%3aAID-FLD638%3e3.0.CO%3b2-R&partnerID=40&md5=13d220004f03030545f0f3877f3b38c0