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Boundary layers, wakes and other shear layers
Published in Bernard S. Massey, John Ward-Smith, Mechanics of Fluids, 2018
Bernard S. Massey, John Ward-Smith
The drag coefficient for a three-dimensional body varies in a similar way to that for a two-dimensional body. However, for a sphere or other body with axial symmetry, the vortex street and the associated alternating forces observed with a two-dimensional body do not occur. Instead of a pair of vortices, a vortex ring is produced. This first forms at Re ≏ 10 (for a sphere) and moves further from the body as Re increases. For 200 < Re < 2000, the vortex ring may be unstable and move downstream, its place immediately being taken by a new ring. Such movements, however, do not occur at a definite frequency, and the body does not vibrate.
Numerical study of a symmetric submerged spatial hydraulic jump
Published in Journal of Hydraulic Research, 2020
Vimaldoss Jesudhas, Ram Balachandar, Tirupati Bolisetti
The statistical approach in analysing turbulent flows provides useful results for engineering applications. However, from a fluid mechanics perspective, it is imperative to identify the size, shape and dynamics of organized structures present in the flow. These structures are unique to the flow field and can be used to describe the internal structure of turbulence within the flow. The vortical structures in the symmetric SSHJ flow field were educed using the criterion (Jeong & Hussain, 1995). This vortex identification technique uses dynamic considerations (pressure minimum) to identify vortices. The tensor has real eigenvalues, where and are the strain and rotational tensors. If these values are ordered as , then denotes a region of vorticity. Fig. 10a and b show the instantaneous iso-surface for in the initial region of the symmetric SSHJ coloured by the contours of y-vorticity and z-vorticity, respectively. The iso-surface captures the rectangular vortex rings shed from the conduit opening. These rectangular vortex rings stretch and tend deform into a circular shape as they move downstream of the conduit opening. The ring deformation is caused by the velocity-pressure differential between the edges and faces of the rectangular vortex ring (Ghasemi, Roussinova, Barron, & Balachandar, 2016). The two sides of the rectangular vortex ring are counter-rotating with predominant y-vorticity as observed in Fig. 10a. It must be noted that, since the bed restricts the motion of the rectangular vortex ring in the bottom, the stretching and deformation happens on the sides and the top of the rectangular vortex ring. The stretching causes the sides of the vortex rings to turn upward and become z-vortical (Fig. 10b). As the vortex ring moves further downstream, the shear between the wall jet and rollers cause it to break-up. Smaller vortical structures are also generated in the shear layer. Due to this, the developing region of symmetric SSHJ is composed of smaller vortex worm like structures as shown in Fig. 10c. This is important as the energy dissipation occurs through the smaller scales. While the criteria provides a qualitative interpretation, the search for pressure minima is not always a sufficient criterion for the presence of a vortex. A more quantitative statistical technique, i.e. POD, was used to further validate the presence of these organized structures.