Flows Around Bodies

Underlying Flow Regime 2-10

Description

Introduction

The flow past finite-height cylinders mounted on a wall is of considerable, practical and fundamental fluid mechanics interest. It has many applications such as flow past cylindrical buildings, stacks or cooling towers, rods in various technical equipment such as fuel or central rods in nuclear power plants, or cylinders used as idealized vegetation roughness elements in atmospheric boundary layers and open channels. The flow is very rich in featuring a variety of phenomena and is particularly complex as it is three-dimensional, highly unsteady and contains several interacting vortex systems. The much studied flow past long cylinders is already quite complex due to the unsteady vortex shedding, but in the case of finite-height cylinders there are in addition end-effects both on the ground side and on the free end. In addition to the Reynolds number, the height-to-diameter-ratio h/D and the relative boundary- layer thickness of the approach flow δ/h are the parameters in the finite-height case.

The sketch provided by Pattenden et al (2005) and reproduced in Fig. 1 gives a good overall impression of the complex 3D flow. The approach flow is in the upper part deflected upwards and then over the top of the cylinder while in the region of the bottom boundary layer the flow is deflected downwards, forming the well-known horseshoe vortex which then wraps around the cylinder and extends with its two legs to the side of the wake. The flow deflected over the top separates at the front edge and a complex flow develops over the free end, with reattachment and owl face behaviour, as described in detail in Palau-Salvador et al (2010). On the side wall of the cylinder, the flow separates at an angle of 70-80° for Reynolds numbers in the subcritical range. Behind the cylinder a wake forms which behaves for larger h/D ratios in the main part like the vortex shedding flow past long cylinders. At small aspect ratios the end effects are considerable. The flow over the top experiences a downwash in this region and impinges eventually on the ground plate. In the mean, vertical vortices along the cylinder are present on either side which bend and join near the top to form the arch vortex that can be seen in Fig. 1. There is an upwash flow on the rear end side walls of the cylinder which separates at the edge of the cylinder top forming a tip vortex springing off this edge. For Reynolds numbers in the sub-critical range the flow is downwards in the center region and upwards outside. The tip vortices turn downwards, widen, decay and interact with the vortices shed from the sides. They then merge with the secondary motion generated by the downwash flow hitting the ground and moving outwards in its vicinity. They also merge with the legs of the horseshoe vortex and finally end up in fairly large trailing vortices as sketched in Fig. 1. The tip vortices interfere with the vortices caused by separation on the cylinder walls and prevent the roll-up of separated shear layers and hence suppress the shedding near the top. The shedding near the ground is not suppressed but is absent when the height-to-diameter ratio is very small, e.g. h/D = 1.

Figure 1. Figure 1. Sketch of flow configuration, from Pattenden et al (2005)

Review of UFR Studies and Choice of Test Case

Over the years many experimental studies of the flow past finite-height cylinders have been carried out, covering a fairly wide range of the main parameters Re, h/D and δ/h and of measurement and visualization techniques. Summaries of the experiments carried out until 2004 are provided in Sumner et al (2004) and in Pattenden et al (2005) and the more recent experimental studies are summarized in Palau-Salvador et al (2010). The latter paper reports on a detailed experimental study with LDV measurements of the mean velocity and Reynolds stress fields for the two aspect ratios h/D = 2.5 and h/D = 5 and Reynolds numbers of the two cases of 43000 and 22000, together with preliminary visualization studies over a somewhat wider range of h/D values. Because of the detailed measurements available, these two cases are taken as the test cases in this UFR.

Palau-Salvador et al (2010) calculated these two cases by LES and these calculations and results will be presented in this UFR. These authors have also reviewed the previous numerical simulations. They noted that employing a steady RANS method for the finite-height cylinder flow allows resolving the mean flow features in reasonable accord with experimental observation, but does of course not allow resolving any details of the unsteady flow behaviour and yields poor agreement about the pressure in the base part after separation. Various LES calculations are also reviewed, some of them for the test cases considered here, but with much coarser numerical resolution, while most LES studies were carried out for different situations, but also generally suffering from insufficient numerical resolution. Frederich et al (2008) report on LES and DES of flow for a situation where h/D = 2 and Re = 200000. They obtained fairly good agreement with experiments for this case but concentrated their study on visualizing the flow structures through various criteria.

In conclusion, the experimental LDV and numerical LES study reported in Palau-Salvador et al (2010) forms the basis of this UFR.

Contributed by: Guillermo Palau-Salvador, Wolfgang Rodi, — Universidad Politecnica de Valencia, Karlsruhe Institute of Technology