Interaction of trailing vortices in the wake of a wall-mounted rectangular cylinder

Abstract

Numerical simulations are performed to investigate three-dimensional unsteady vortex-vortex and vortex-surface interactions in the near field of a wall-mounted rectangular cylinder placed inside a channel. The generation mechanism of the upstream and the trailing vortices from the topologically important critical points and their near-wall evolution pattern have been examined in detail. In the upstream region, a laminar necklace vortex system formed around the junction between the rectangular block (cylinder) and the flat channel floor. A sequence of streamwise vortical rollers dominated the downstream interaction region, and they exhibited strong unsteady vortex-surface interaction. Streamwise vortices which formed upstream of the obstacle exhibited quadrupole structure with the dominant pair being central downwash, whereas those lifting the flow behind the obstacle were of predominantly central upwash. Notably, at some downstream location, the near-wall wake structure was observed to locally disappear due to mutual interaction and annihilation by opposite strength vortices on either side of the wake centerline. During the entire course of unsteady flow evolution, such a disappearance of the wake remained closely associated with local contraction of the limiting streamlines on the channel floor, the development of a pair of topologically important floor critical points (saddles), and the presence of a near-wall node on the vertical symmetry plane. The dominance of inward transverse flow toward these saddles together with flow evolution from the downstream node on the vertical symmetry plane were found to be particularly responsible for facilitating the local interaction of various vortices of opposite strength, leading to significant vorticity cancellation in the region. Moreover, the basic source of the wake vortices and their nature of evolution behind the cylinder were also investigated here, and they were found to be fundamentally different from what one usually observes in the near-wake of a transverse jet. However, the growth of a pair of vertically lifting vortices from the spiraling shear layer nodes just behind the downstream edge of the cylinder base was detected in this flow configuration also.

Structure of wake of a sharp-edged bluff body in a shallow channel flow

“…It should be noted here that the nature of the foci changes from stable, inward spiraling to unstable, outward spiraling from the near-bed to the near-surface location. The existence of the stable, inward spiraling focus was also reported by Akilli and Rockwell (2002), and Sau et al (2003). In the present study, the foci and the saddle points continues to exist at the mid-depth and near-surface locations.…”

Simple diffusion hopping model with convection

“…The wake region is typified by the presence of a recirculation flow consisting of vortex flow patterns. Similar vortices have also been observed for particle flux around wallmounted cubic obstacles in flow channels [52][53][54][55][56], around geographical mountains or hills [57], around islands in shallow water [58,59], and airflows around buildings [60,61]. In this case study we examine the effect of a particle flux with varying Re on the velocity field in the vicinity of a square obstacle of side l placed at the center of a flow channel.…”

Flow evolution of an internal solitary wave generated by gravity collapse

“…Therefore, the general mass continuity equation and Navier-Stokes equations are utilized to simulation the flow problem. These governing equations [16][17][18][19] are written as follows: …”

“…The numerical method employed here is an improved version of the VOF method of Hirt and Nichols [20], in which a second-order central difference scheme is used to discretize the continuity equation, pressure gradient, and diffusion terms. The convective terms are discretized using QUICK scheme of third-order accuracy (e.g., Sau et al, [16,17]). A semi-implicit method is adopted to evaluate the temporal terms while coupling between pressure and velocities remains implicit.…”

“…The boundary conditions at both sides of x and the bottom z are specified as a smooth non-slip walls. The upper z for the free-surface displacement F (0 ≤ F ≤ 1) is captured using the volume of fluid (VOF) method [16]. This method is established following the principle of conservation of material transport.…”