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 numerous, e.g. turbomachinery, aeronautical engineering, or scour of bridge piers embedded in river beds.

This flow situation is investigated in the vertical symmetry plane upstream of a cylinder mounted on a flat plate facing an approaching flow (see Fig. 1). This oncoming flow is a fully developed turbulent boundary layer, 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 that blocks the boundary layer at the cylinder and forces its separation; (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 defelction onwards exerting a strong mean velocity gradient, and therefore, a high wall-shear stress. The approaching fluid is dragged downwards by the downflow and likewise deflected in the upstream direction. The approaching boundary layer, however, blocks this upstream pointing flow as well and generates the well-known horseshoe vortex (HV).

This jet-vortex structure characterizes the flow situation and is the main driving force for scour processes in the case of bridge piers due to the resulting high wall-shear stress. Devenport & Simpson (1990) reported that the streamwise velocity component reveals a bi-modal probability density function inside the near-wall jet and underneath the HV. The upstream pointing jet can, therefore, either be 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, this jet breaks and wall-normal eruptions appear, which were described by Schanderl et al. (2017) as flapping of the jet. Corresponding to the dynamics of the jet, the vortex oscillates horizontally and introduces a large amount of turbulent kinetic energy (TKE).

The TKE distribution in the vertical symmetry plane uptream 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.

Brief Review of UFR Studies and Choice of Test Case

We studied the flow around a wall-mounted narrow (D/z0 < 0.7) circular cylinder with infinite height. The flow depth z_0 was 1.5D and the width of the rectangular channel was 11.7D. The investigated Reynolds number was approximately 39,000, the Froude number was in the subcritical region. As inflow condition, we used a fully developed turbulent boundary layer.