Topological flow structures in backward-facing step channels
Journal
Computers and Fluids
Journal Volume
26
Journal Issue
4
Pages
321-337
Date Issued
1997
Author(s)
Abstract
The present paper is intended to solve the steady-state Navier-Stokes equations for different Reynolds numbers. Through out this paper, the incompressible fluid will be considered in three-dimensional channels with different spans. The flow field under investigation was characterized as having a backward-facing step across which a fully-developed three-dimensional channel flow expanded into the channel with an expansion ratio of 1.9432. Numerical solutions for this backward-facing step problem were obtained on the basis of the step height, 0.9423, various spans, taking on values up to 10, and Reynolds numbers as high as 800. Of the different flow conditions that were considered, we elaborate on the flow topology under the conditions of an intermediate Reynolds number, Re = 389, and the largest width of the channel, 10. Following Lighthill [Lighthill, M., Attachment and separation in three-dimensional flow. In Laminar Boundary Layers, Vol. 2(6), ed. L. Rosenhead, II. Oxford University Press, 1963, pp. 72-82.] [1], we apply topology theory, which provides a rigorous mathematical foundation for studying kinematically possible flows. The present computational results, together with the inferred flow topology, reveal details of the flow structure which suggest a mechanism for the development of strongly three-dimensional flow with increasing Reynolds numbers. The computation of 'oil-flow' streamlines improves the visualization of the flow field and helps sketch the complicated flow patterns by clarifying the three-dimensional flow separation just behind the step. The scope of this enhancement to improved visualization of flow structure is also extended to the flow reattachment on the floor as well as the roof recirculatory flow pattern, manifested itself by the upstream separation and downstream reattachment surfaces. Notably addressed is the separation-reattachment phenomenon emanating only from the roof near the two side walls. © 1997 Elsevier Science Ltd.
SDGs
Type
journal article