TOPOLOGICAL FLOW STRUCTURES IN BACKWARD-FACING STEP CHANNELS

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 character ized as having a backward-facing step across which a fully-developed t hree-dimensional channel flow expanded into the channel with an expans ion ratio of 1.9432. Numerical solutions for this backward-facing step problem were obtained on the basis of the step height, 0.9423, variou s spans, taking on values up to 10, and Reynolds numbers as high as 80 0. Of the different Bow conditions that were considered, we elaborate on the Bow topology under the conditions of an intermediate Reynolds n umber, Re = 389, and the largest width of the channel, 10. Following L ighthill [Lighthill, M., Attachment and separation in three-dimensiona l flow. In Laminar Boundary Layers, Vol. 2(6), ed. L. Rosenhead, II. O xford University Press, 1963, pp. 72-82.] [1], we apply topology theor y, which provides a rigorous mathematical foundation for studying kine matically 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-dimens ional flow with increasing Reynolds numbers. The computation of 'oil-f low' streamlines improves the visualization of the flow field and help s sketch the complicated flow patterns by clarifying the three-dimensi onal flow separation just behind the step. The scope of this enhanceme nt 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-reattachmen t phenomenon emanating only from the roof near the two side waits. (C) 1997 Elsevier Science Ltd.