Secondary Motions in Fully Developed Pipe Flow
Secondary motions downstream of pipe curvatures are widely studied for low and moderate Reynolds numbers, where the secondary flows are driven by the centrifugal pressure gradient. For these Reynolds numbers, there exists two cell vortex that is symmetric around the center plane of the pipe known as the Dean motion. However, when the Reynolds number is increased the flow becomes turbulent, and instabilities are introduced to the two-cell structure. These instabilities cause the flow to alternate between a dominating upper cell and lower cell. The two cells coexist in the transition between the modes, Figure 1.
Figure 1The figure shows the instantaneous azimuthal velocity component for Re 18000 at three distinct times. The secondary motion is alternating between a dominant lower and upper cell. The ratio between the curvature of the bend and the radius of the pipe is 1.
Figure 2,The instantaneous vorticity field (left) is compared with the time-averaged vorticity field (right) for Re 18000. Time-averaging reveals the Dean motion, though vorticity levels are considerably weaker.