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Vortical Structures in Channel Flows with a Backward-Facing Step

The aim of this study was to conduct a detailed numerical analysis of steady-state Navier-Stokes equations to broaden our knowledge of the vortical flow structure in the channel. The problem considered is that of the laminar flow of an incompressible fluid through a straight channel with a backward-facing step. This step is configured as having an expansion ratio of γ = 1.9423 in channels with different channel widths of B. Finite volume solutions for this backward-facing step problem were obtained on the basis of different span ratios, B/h = 2, 4, 6, 10, and Reynolds numbers, Re = 100, 389, and 800. In this study, we elaborate on the case of Re = 389 due to lack of space. Inspired by the success of Lighthill who proposed a method with a rigorous mathematical foundation for studying kinematically possible flows, we apply the topology theory to analyze the computed three-dimensional vector field. The inferred 'oil-flow' streamlines improve visualization of the flow field and help sketch the complicated flow patterns by clarifying the three-dimensional flow separation just behind the step, the formation of secondary eddies in the transverse plane, and recirculating bubbles attached to the roof of the channel. Notably addressed is the separation-reattachment phenomenon that emanates only from the roof near the two end walls.