# UFR 2-02 Description

## Contents

# Flow past cylinder

Underlying Flow Regime 2-02 © copyright ERCOFTAC 2004

# Description

## Preface

The flow past cylinders is an important flow type that occurs in many engineering applications. Although it was detected in only one application challenge (namely in AC4-06), cylindrical structures exposed to flow are basically present in all areas of engineering and in the environment. Often the flow is associated with unsteady vortex shedding and this special feature has a dominant influence on the flow behaviour itself, on the loading of cylindrical structures which is often unsteady and on heat transfer. A wide variety of configurations is possible ranging from infinitely long cylinders in uniform flow normal to the cylinder to cylinders placed in sheared flow like in boundary layers, cylinders at angles to the flow, prismatic or tapered cylinders, various cross-sectional geometries, cylinders having short aspect ratios etc. etc. Here, attention is restricted to infinitely long, prismatic cylinders placed normal to uniform flow and only cylinders with circular and square cross sections are considered; the actual study test case will be the flow around a square cylinder.

## Introduction

The flow past long cylinders exposed to uniform approach flow is an interesting and important test case for CFD calculations because the geometry is simple, but the flow is complex with a rich variety of phenomena occurring. These include thin, separating shear layers, alternating shedding of vortices from the cylinder which are transported downstream, where they retain their identity in a Karman vortex street for a considerable distance, but are eventually broken up and diffused by the turbulent motion. These vortices are predominantly two-dimensional and so is the time- mean flow, but large–scale 3-D structures exist which lead to a modulation of the shedding frequency. The shedding causes unsteady forces on the cylinder which may lead to flow induced vibrations. The approach stagnation flow is basically inviscid and thin laminar boundary layers are formed on the forward faces of the cylinder. The cylinder may have various geometries, but the circular and square shape are the most common ones and will only be considered further. In the case of the square cylinder, the flow separates at the front edges and a flapping shear layer develops on the sides of the cylinder, which is initially laminar but becomes turbulent fairly quickly when the Reynolds number is above 600. In this range, the drag coefficient and dimensionless shedding frequency (Strouhal number) do not depend much on the Reynolds number. In the case of the circular cylinder, the separation point is not fixed but depends on the boundary layer development before separation, which depends on the Reynolds number. For Re > 300 the wake of the cylinder is turbulent and when Re < 1.5 · 10^{5 }the boundary layer remains laminar up to separation. This is called the subcritical region in which the drag coefficient increases with Reynolds number while the Strouhal number is fairly constant. For 1.5 · 10^{5 }< Re < 3.5 · 10^{6} the boundary layer on the cylinder becomes turbulent before separation which thereby moves backwards, the drag is reduced significantly (drag crisis) and the Strouhal number is increased. This is called the transitional region. For Re > 3.5 · 10^{6} the boundary layer on the cylinder is largly turbulent and the strong Reynolds number dependence of drag coefficient and Strouhal number ceases. This is called the super-critical region. Because of the overruling influence of the unsteady vortex shedding, CFD calculations need to be unsteady.

## Review of UFR studies and choice of test case

There have been numerous experimental studies of the flow past circular cylinders, covering a wide range of Reynolds numbers, and the book of Zdravkovich (1997) gives a good overview of the findings. However, in most experiments only global parameters like drag coefficient and Strouhal number were measured and not the details of the flow development. The only detailed phase-resolved measurements of the flow past a circular cylinder were carried out by Cantwell and Coles (1983) at Re = 140.000. The data is available on the CD of the AGARD-AR-345-report (1998). Attempts to calculate this flow with RANS models in unsteady calculations (i.e. basically URANS calculations) were not very successful. LES calculations clearly yielded superior results but also gave rise to some problems for this case, presumably because it was close to the critical Reynolds number. Extensive calculations have been done for a lower Reynolds number of Re = 3.900 with LES but also DNS. The simulations for the two Reynolds numbers are reviewed in Rodi (2002) and LES results for the Re = 3.900 case can be found in the FLOWNET data base.

For the flow past a square cylinder, there are considerably fewer experimental studies then for the flow past the circular one. A brief review is given in the AGARD-AR-345 report. The only experiment with phase–resolved results is that due to Lyn and Rodi (1994) and Lyn et al. (1995) who provided detailed measurements of the flow past a square cylinder at Re = 22.000 obtained with a laser Doppler velocimeter. This flow has been calculated with a wide variety of RANS models (2 D unsteady calculations) and has been used as test case at two LES workshops (Rodi et al. 1995, 1997, Voke 1997), so that numerous LES results are available. Also after the workshops, this flow has been used as test case for LES simulations over and over again. Further, review articles exist summarizing the RANS and LES simulations available (Rodi 1997, 2002) and for all these reasons this flow was chosen as the UFR study test case. Another reason for the choice is that the experiment was carried out in the group of the present author which also performed calculations and hence the experiment was clearly designed for CFD validation.

© copyright ERCOFTAC 2004

Contributors: Wolfgang Rodi - Universität Karlsruhe