UFR 3-35 Description

Cylinder-wall junction flow

Front Page

Description

Test Case Studies

Evaluation

Best Practice Advice

References

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 was investigated in 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 downflow approaches the bottom wall, a boundary layer develops along the cylinder resulting in a pressure gradient between the stagnation point S3 (see Fig: Streamlines) and the cylinder-wall junction. 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 studies focus on the scour research, in order to contribute 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 this 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 model performance depends on the time span on which they are based on and a time factor has to be taken into account reducing the error in the scour depth prediction (Baghbadorani et al. 2017).

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. Whereas, the streamwise velocity fluctuations are concentrated at the lower branch of the c-shaped TKE casued by the dynamics of the jet.

In order to provide both numerical and experimental data acquired for the same flow configuration under identical (as good as possible) boundary conditions, we performed a large eddy simulation and a particle image velocimetry experiment. 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.

Fig. 1: Sketch of flow configration

---

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

Front Page

Description

Test Case Studies

Evaluation

Best Practice Advice

References

© copyright ERCOFTAC 2019