Cylinder-wall junction flow

Underlying Flow Regime 3-35

Description

Introduction

Flows around bluff bodies such as circular cylinders are among the basic flow configurations which are not yet 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 is highly three-dimensional. The presented data, however, are restricted to the vertical symmetry plane upstream of a circular cylinder mounted on a flat plate. The oncoming flow is 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 approaching boundary layer causes a vertical pressure gradient at the cylinder front that leads to a downward deflection of the flow towards the cylinder-wall junction transporting high-momentum fluid. While the down-flow approaches the bottom wall, a boundary layer develops along the cylinder resulting in a pressure gradient between the stagnation point S3 (see Fig. 6) and the cylinder-wall junction. The down-flow impinges at the bottom plate at stagnation point S3 and is deflected in all directions: (i) towards the cylinder rolling up to a corner vortex V3; (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 a 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 form a main vortex: the well-known horseshoe vortex (V1) (Baker 1980). The saddle point S1 devides the fluid entrained into the main vortex from the one contributing to the near-wall jet.

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 was therefore in the focus of numerous studies in the past. Since the configuration of a body-wall junction is of interest in various fields, the backgrounds and motivations of these studies differ likewise. Many studies focus on scour research related to the daunting task of 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. Since the bed erosion is a highly complex process, the corresponding models vary widely in predicting the final scour depth at the cylinder front (Roulund et al. 2005; Pfleger 2011). Furthermore, the effect of time plays a major role when extrapolating empirical models for estimating the equilibrium scour depth. Baghbadorani et al. 2017 observed that common scour models underpredicted the equilibrium scour depth by at least $29\%$ and therefore suggest to take a time factor into account to reduce this error.

Dargahi (1989), Escauriaza & Sotiropoulos (2011), Apsilidis et al. (2015), and Schanderl et al. (2017), for example, studied the flow around a circular cylinder while focussing on the turbulence structure of the horseshoe vortex system. This system consists of a set of vortices that interact with each other and the number of individual vortices that appear depends on the cylinder Reynolds number ( $Re_{D}$ ) (Escauriaza & Sotiropoulos 2011).

According to Simpson (2001), the geometry of the body plays a minor role and the flow field does not significantly change for different body shapes. Therefore, the work of Martinuzzi & Tropea (1993), Devenport & Simpson (1990) and Paik et al. (2007) are mentioned here as well, who studied the flow around a prismatic or a wing body and observed mechanisms similar to those of a 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 generating 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. On the other hand, the streamwise velocity fluctuations are concentrated at the lower branch of the c-shaped TKE and are caused by the dynamics of the jet.

The current contribution is based on the work reported in the publications listed at the beginning of the Test Case Studies section.

Contributed by: Ulrich Jenssen, Wolfgang Schanderl, Michael Manhart — Technical University Munich