Revision as of 12:11, 10 January 2011

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.

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