# Abstr:Flow past cylinder

## Flows Around Bodies

### Underlying Flow Regime 2-02

#### Abstract

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.

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 x 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 x 10^{5} < Re < 3.5 x 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 x 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.

*Contributors: Wolfgang Rodi - Universität Karlsruhe*

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