Vortical flow over a 3-D backward-facing step

Numerical simulations of Navier-Stokes equations were performed for incompressible Navier-Stokes flow inside a channel. The flow field under investigation was characterized as having a backward-facing step, with an expansion ratio gamma = H/h = 1.9423, over which a fully developed channel flow is suddenly expanded into the channel with a channel width, B, to upstream channel height, h, ratio B/h = 2, 4, 6, and 10. Numerical solutions for this backward-facing step problem were obtained on the basis of span ratios and Reynolds numbers. For the Reynolds numbers considered, Re = 100, 389, 800, we elaborate on the changes in the flow topology according to solutions computed at Re = 389. We use topology theory as a guide to studying flows that are kinematically possible. This theory is mathematically rigorous and helps find critical points, from which we can sketch complicated flow patterns by clarifying the three-dimensional flow separation just behind the step and the flow reattachment on the downstream roof. Clearly visible on the roof of the channel is the separation-reattachment flow feature. Notably addressed is that separated flow on the roof is only confined to regions near the two side walls and does not extend over the whole span. The onset of a near-wad pair of counterrotating vortices is associated with the presence of closed separation-reattachment bubbles. They are visible at transverse planes, just upstream of termination of the roof recirculation bubble, near the two end walls.