Flow past a cylinder close to a free surface

Abstract

Two-dimensional flow past a cylinder close to a free surface at a Reynolds number of 180 is numerically investigated. The wake behaviour for Froude numbers between 0.0 and 0.7 and for gap ratios between 0.1 and 5.0 is examined. For low Froude numbers, where the surface deformation is minimal, the simulations reveal that this problem shares many features in common with flow past a cylinder close to a no-slip wall. This suggests that the flow is largely governed by geometrical constraints in the low Froude number limit. At Froude numbers in excess of 0.3-0.4, surface deformation becomes substantial. This can be traced to increases in the local Froude number to unity or higher in the gap between the cylinder and the surface. In turn, this is associated with supercritical to subcritical transitions in the near wake resulting in localised free-surface sharpening and wave breaking. Since surface vorticity is directly related to surface curvature, such high surface deformation results in significant surface vorticity, which can diffuse and then convect into the main flow altering the development of Strouhal vortices from the top shear layer, affecting wake skewness and suppressing the absolute instability. The variations of parameters such as Strouhal number and formation length are provided for Froude numbers spanning the critical range. At larger Froude numbers good agreement is obtained with recently published experimental investigations. The previously-seen metastable wake states are observed to occur for similar system parameters to the experiments despite the difference in Reynolds numbers by a factor of about 40. The wake state switching appears to be controlled by a feedback loop. Important elements of the feedback loop include the cyclic generation and suppression of the absolute instability of the wake, and the role of surface vorticity and vortices formed from the bottom shear layer in controlling vortex formation from the top shear layer. The proposed mechanism is presented. Shedding ceases at very small gap ratios (∼ 0.1 − 0.2). This behaviour can be explained in terms of the fluid flux through the gap, vorticity diffusion into the surface and opposite-signed surface vorticity from the strong surface deformation.

Vorticity generation and conservation for two-dimensional interfaces and boundaries

“…The original motivation for this article arose from the conundrum presented by the problem of the flow past a submerged circular cylinder (Sheridan, Lin & Rockwell 1997;Reichl, Hourigan & Thompson 2005;Bozkaya et al 2011). As the gap between the cylinder and the free surface decreases, the vorticity strongly shed from the top surface of the cylinder remarkably, and rapidly, disappears in the wake, leaving vorticity of only one sign in the flow (see figure 1).…”

“…Conservation of vorticity/circulation Part of the motivation for this article is the observation, in free-surface flows, that vorticity can seem to disappear (e.g. in the wake of a circular cylinder close to a free surface (Sheridan et al 1997;Reichl et al 2005)). Some authors have appeared comfortable with the notion that the total vorticity (circulation) need not be conserved (Rood 1994;Wu & Wu 1996), whilst others have included the vortex sheet at the free surface for conservation of circulation (Lundgren & Koumoutsakos 1999).…”

The effect of slip distribution on flow past a circular cylinder

“…This software has been proven to perform with high accuracy on similar fluid mechanical problems. Examples include Taylor vortex flow (Deng et al, 2006), flow past a static or rotating circular cylinder (Gillies, 1998;Padrino and Joseph, 2006), flow past a cylinder close to a free surface (Reichl et al, 2005), and laminar flow on structured surfaces (Ou et al, 2007). The numerical results are often validated, e.g., with experimental measurements (Gillies, 1998) and alternative simulation methods (Mittal and Kumar, 2003).…”

Codimension three bifurcation of streamline patterns close to a no-slip wall: A topological description of boundary layer eruption

“…In dynamic stall of an unsteady airfoil, the vortex created at the leading edge plays a key role in generating the transition to separated flow [8,9]. A vortex wake created by the flow around a bluff body may interact with a wall or a free surface and give rise to secondary vortices [10,11,12,13]. This is also the case when vortices, solid bodies or jets impinge directly on a wall [14,15,16,17].…”