Three-Dimensional Structure of Laminar Flow through a Square Sudden Expansion Channel (Vortex Structure of the Recirculation Zone)

Three-dimensional numerical predictions are presented for a laminar flow through a square channel with a sudden expansion of area ratio 4 : 1 in the range of Reynolds numbers Re = 20 to 700, using an Open Source CFD Toolbox (OpenFOAM). In particular, the vortex structure in the recirculation zone behind the sudden expansion was examined from the fluid particle trajectory based on Lagrangian method. The results showed that the main flow diverged through the expansion, and at the constant x section, the flow vector of the duct centerline is directed towards the wall in the vertical plane, while the secondary flow vector of the duct corner is directed toward the centerline in the diagonal plane. So that, the overall regular flow structure consisted of the eight regions that is 1/8 part of the flow field surrounded by two diagonal plane, vertical plane, horizontal plane and peripheral wall. The results of the particle trajectory in the 1/8 area clarifies that the fluid particles enter into the recirculation zone behind the sudden expansion from upstream diagonal corner, and move toward spanwise direction with helical motions, and then they flow out to the downstream region near the lower wall. It seems that the helical type vortex is formed. Moreover, the other particles have been recirculated accompany with longitudinal small scale vortex motion inside the helical type vortex. We call it the ring type vortex. These structures could not be explained by two-dimensional flow structure and showed the characteristics of three-dimensional vortices.