EFFECT OF REYNOLDS-NUMBER ON THE EDDY STRUCTURE IN A LID-DRIVEN CAVITY

In this paper we apply a finite volume method, together with a cost-ef fective segregated solution algorithm, to solve for the primitive velo cities and pressure in a set of incompressible Navier-Stokes equations . The well-categorized workshop problem of lid-driven cavity flow is c hosen for this exercise, and results focus on the Reynolds number. Sol utions are given for a depth-to-width aspect ratio of 1:1 and a span-t o width aspect ratio of 3:1. Upon increasing the Reynolds number, the flows in the cavity of interest were found to comprise a transition fr om a strongly two-dimensional character to a truly three-dimensional f low and, subsequently, a bifurcation from a stationary flow pattern to a periodically oscillatory state. Finally, viscous (Tollmien-Schlicht ing) travelling wave instability further induced longitudinal vortices , which are essentially identical to Taylor-Gortler vortices. The obje ctive of this study was to extend our understanding of the time evolut ion of a recirculatory flow pattern against the Reynolds number. The m ain goal was to distinguish the critical Reynolds number at which the presence of a spanwise velocity makes the flow pattern become three-di mensional. Secondly, we intended to learn how and at what Reynolds num ber the onset of instability is generated. (C) 1998 John Wiley & Sons, Ltd.