# UFR 2-10 Description

## 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.

## 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*

© copyright ERCOFTAC 2011