Cylinder-wall junction flow

Underlying Flow Regime 3-35

Description

Introduction

Flow around bluff bodies such as circular cylinders is among the basic flow configurations yet not fully understood. The field of application of this configuration is broad, e.g. turbomachinery, aeronautical engineering, or scour of bridge piers embedded in river beds.

This flow situation was investigated in the vertical symmetry plane upstream of a cylinder mounted on a flat plate. The oncoming flow is a fully-developed turbulent open-channel flow, and due to the deceleration by the obstacle an adverse pressure gradient occurs in the main flow direction. The blockage of the body leads to a deflection of the flow in vertical direction downwards to the cylinder-wall junction. Therefore, a vertical pressure gradient occurs as well, which transports high-momentum fluid from the top to the bottom part. While the downflow approaches the bottom plate, a boundary layer develops at the flow facing edge of the cylinder. When the downflow impinges at the bottom plate it is deflected in all directions: (i) towards the cylinder rolling up to a small-scale foot-vortex; (ii) in the spanwise direction around the cylinder; and (iii) in the upstream direction forming a wall-parallel jet (Dargahi 1989). This jet accelerates from the point of deflection onwards and exerts large shear stress on the bottom wall. Some parts of the down-flow that are deflected in the upstream direction are not contributing to this jet but are blocked by the approaching flow causing a coil-up: the well-known horseshoe vortex (HV) (Baker 1980)).

Brief Review of UFR Studies and Choice of Test Case

This jet-vortex interaction is the characterizing feature of the cylinder-wall junction flow, and therefore, in the focus of numerous studies in the past. Since the configuration of a body-wall junction is of various interests, the backgrounds and motives of these studies differ likewise. Many focus on the scour research for predicting the depth of a scour hole such as Laursen & Toch (1956), Melville & Raudkivi (1977), Roulund et al. (2005), Ettema et. al (2006), and Link et al. (2008) just to mention a few.

Dargahi (1989), Sumer et al. (1993), , Escauriaza & Sotiropoulos (2011), Apsilidis et al. (2015), and Schanderl et al. (2017) studied the flow around a circular cylinder while focussing on the horseshoe vortex system and its turbulence structure. According to Simpson (2001), the geometrical shape of the body plays a minor role and the flow filed does not significantly change. Therefore, the work of Devenport & Simpson (1990) and Paik et al. (2007) are mentioned here as well, who studied the flow around a wing body and observed similar mechanisms than it is the case for an cylinder, for example. Furthermore, the observations of the dynamics of the wall-parallel jet showing a bi-modal probability density function of the streamwise velocity component goes back to Devenport & Simpson (1990). They found the upstream pointing jet to be either in the back-flow or the zero-flow mode. The first describes a strong wall-parallel flow in the upstream direction in which the wall-parallel velocity component dominates the flow. In the zero-flow mode, the jet breaks and erupts the fluid away from the wall. Corresponding to the dynamics of the jet, the vortex oscillates horizontally which generates large levels of turbulent kinetic energy (TKE).

The TKE distribution in the vertical symmetry plane upstream of a cylinder has a characteristic c-shaped distribution (Paik et al., 2007; Escauriaza & Sotiropoulos, 2011; Kirkil & Constantinescu, 2015; Apsilidis et al., 2015; Schanderl & Manhart, 2016). The horizontal oscillations of the HV cause mainly wall-normal fluctuations in the region of the vortex itself. Whereas, the streamwise velocity fluctuations are concentrated at the lower branch of the c-shaped TKE casued by the dynamics of the jet.

We studied the flow around a wall-mounted slender ( $D/z_{0}<0.7$ ) circular cylinder with infinite height. The flow depth was $z_{0}=1.5D$ and the width of the rectangular channel was $11.7D$ . The investigated Reynolds number was approximately $Re_{D}={\frac {u_{\mathrm {b} }D}{\nu }}=39,000$ , the Froude number was in the subcritical region. As inflow condition we applied a fully-developed open-channel flow.