Surface Roughness Effects on Vortex-Induced Vibration of Cylindrical Structures at Critical and Supercritical Reynolds Numbers
Authors: Allen D.W. , Henning D.L. 
Published: October 2008

Abstract
Experiments examining the effect of surface roughness on vortex-induced vibration (VIV) and drag of flexible cylinders at critical and supercritical Reynolds numbers have been conducted. Four levels of surface roughness were tested for their effect on VIV and drag of a circular cylinder that was 20 diameters upstream of a downstream cylinder (i.e. effectively an isolated cylinder). The rougher cylinders experienced vibrations of up to 3rd mode (in transverse bending). A surprising discovery was that the smooth cylinder experienced low drag and virtually no VIV as the boundary layers became turbulent in the critical Reynolds number range.

Introduction and Background
The study of flow separation and vortex shedding past a circular (or approximately circular) cylinder has a long history. Simple observation of flow past a vertical stick or reed in a stream indicates that man has probably observed this phenomenon well before recorded history. Similarly, vortexinduced vibration (VIV), which results when something free to move experiences vortex shedding, has an equally long history. The vibration felt when attempting to move one's arm through the water as fast as possible is evidence that VIV was also observed in antiquity.
A parameter that strongly influences flow past a circular cylinder is the Reynolds number (Re), which represents the ratio of the convective forces to the diffusive forces, defined as Re=V*D/?. Another important parameter, for the purposes of this paper, is the surface roughness k/D, where k is the average "peak to trough" height of the surface protrusions.
Figure 1 illustrates the basics of flow past a circular cylinder. As the fluid approaches the cylinder, a thin boundary layer (exaggerated in the figure for illustration purposes) forms on each side of the cylinder (shown on only one side). The fluid closest to the cylinder wall is impeded by friction on the cylinder's surface, hence the region between the wall and where the velocity is close to that of the free stream is known as the boundary layer. As the boundary layer fluid proceeds around the cylinder surface, the retardation of the fluid near the surface eventually causes it to come to a halt, thereby resulting in separation of the boundary layer into a "shear layer". Because the outer fluid in the shear layer is moving faster than the inner fluid of the shear layer, the layer rolls up into a vortex. For Reynolds numbers larger than about 40, the vortex pattern is unstable, and thus there is an alternating vortex street that is shed from the cylinder.
Numerous studies have been made of flow past a stationary circular cylinder, most of these with air as the flowing fluid1–6. These studies have covered Reynolds numbers well exceeding 1×107. Figure 2 illustrates the general relationship that these studies have found between drag coefficient (defined as Cd = Fd/(0.5*?*V2*D*L) and Reynolds number for flow past a stationary cylinder. This figure shows that, at a Reynolds number of about 1×105 (the "critical" Reynolds number range), the drag coefficient diminishes dramatically, a phenomenon known as the "drag crisis". This corresponds to a change in the boundary layers from laminar to turbulent.