In the present study we take a fresh look at a laminar flow evolving into a larger channel through a step configured in a backward-facing format. We conduct steady three-dimensional Navier–Stokes flow analysis in the channel using the step geometry and flow conditions reported by Armaly et al. This allows a direct comparison with the results of physical experiments, thus serving to validate the numerical results computed in the range of 100⩽Re⩽1000. Results show that there is generally excellent agreement between the present results and the experimental data for Re=100 and 389. Fair agreement for Re=1000 is also achieved, except in the streamwise range of 15⩽x⩽25. The main difference stems from the fact that the roof eddy is not extended toward the midspan in the channel with a span width 35 times of the height of the upstream channel. In the present study we also reveal that the flow at the plane of symmetry develops into a two-dimensional-like profile only when the channel width is increased up to 100 times of the upstream step height for the case with Re=800. The present computational results allow the topological features of the flow to be identified using critical point theory. The insight thus gained is useful in revealing a mechanism for the development of an end-wall-induced three-dimensional vortical flow with increasing Reynolds number.

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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 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 -Go ¨rtler 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.

Present computational investigation reports a steady bifurcation phenomenon for three-dimensional flows through a plane-symmetric sudden expansion. When the channel aspect ratio exceeds a critical value, the well-known step height (pitchfork) bifurcation evolves with different symmetry breaking orientations on the left and right sides of the channel and bifurcates in the spanwise direction. For the channel aspect ratio less than the critical value, the originally occurring spanwise bifurcation cannot be stably retained and evolves eventually to a step height bifurcation. Compared to step height bifurcation, the spanwise bifurcation is found to be more difficult to obtain, because the symmetric flow present on the spanwise symmetry plane is unstable in two dimensions. For completeness, an extensive analysis of the observed spanwise bifurcation, covering its transient behavior, dependence on flow Reynolds number, channel aspect ratio, and expansion ratio, is included.

with a primary eddy, downstream and upstream secondary eddies, and possibly meandering Taylor-Gortler longitudinal vortices as the Reynolds number is sufficiently high (see Fig. 1(a)). Previous investigations, however, did not focus much on the end-wall corner vortices other than noting their existence. This motivated us to conduct the present study with an aim to improve our understanding of comer vortices present near the end wall of the lid-driven cavity.We conducted a flow simulation to study the laminar flow in a three-dimensional rectangular cavity. The ratio of cavity depth to width is 1:1, and the span to width aspect ratio (SAR) is 3:1. The governing equations defined on staggered grids were solved in a transient context by using a finite volume method, in conjunction with a segregated solution algorithm. Of the most apparent manifestation of three-dimensional characteristics, we addressed in this study the formation of corner vortices and its role in aiding the transport of fluid flows in the primary eddy and the secondary eddies. /' = 5(/ + Z^) + Re According to the computed errors cast in an L2-norm form for primitive variables, namely (0.55 Downloaded From: http://fluidsengineering.asmedigitalcollection.asme.org/ on 02/26/2014 Terms of Use: http://asme.org/terms