Drag Forces on Oscillating Cylinders in a Uniform Flow
Authors: Kato Minoru , Abe Toru , Tamiya Masaru , Kumakiri Tadashi 
Published: June 2014

ABSTRACT
This paper describes the drag coefficients of cylinders oscillated in both in-line and transverse directions to a uniform flow. The drag coefficients CD have been obtained experimentally over a wide range of oscillating frequencies, amplitude and flow velocities for the cylinders of various diameters under simulated practical offshore conditions.
The boundary between the regions, where CD=l and CD&lt;l, are clearly established by employing the Keulegan-Carpenter number and the Reduced Velocity as dimensionless numbers. These numbers also describe CD variation within the region of rapid CD value decrease. Recommendations are offered for determining CD values in order to predict the dynamic response of risers under actual offshore conditions.

INTRODUCTION
In recent years, the increasing exploitation of ocean fossil resources has required the use of various offshore cylindrical structures. These structures are subject to harsh environmental conditions such as waves, currents and wind forces in the ocean. Especially on risers, these forces cause high stress and large deflection. Therefore, it is very important to accurately estimate these fluid forces.
The authors have been engaged in thedevelopment of the re-entry/completion risers and the automatic positioning system for water depths over 300 meters, as part of a national research project. Thrusters are fitted to the bottom end of the riser string to position the riser over the subsea wellhead, for the purpose of guideline-less and diver-less re-entry operations. In designing the riser and its positioning system, which is excited by the additional thruster's force, the precise estimation of the fluid forces, especially the drag forces acting as damping forces, is most important in order to predict with certainty the dynamic response of the risers.
Numerous studies have investigated the fluid forces acting on stationary cylinders in an oscillating fluid or oscillating cylinders in a still fluid (1) (2) (3). In addition, the fluid forces exerted on oscillating cylinders in a uniform flow have been reported by Mercier(4), Sarpkaya(S), and Bernitsas(6). The results obtained by Mercier(4) generally agreed with those obtained by Keulegan-Carpenter(7) regarding the drag coefficient Go in a still fluid, although Mercier did not consider the influence of surface waves, which should not be neglected, upon the measured data in a uniform flow. Sarpkaya(S) represented useful experimental data, but the experimental regions were restricted as compared with the practical offshore conditions. Bernitsas(6) measured the fluid forces on oscillating cylinders in any direction to a uniform stream, but his results provided incomplete information on the variations of the drag coefficients CD' As mentioned above, unfortunately, useful CD values for practical offshore conditions have not been obtained.
The purpose of this study is to obtain useful CD values over a wide range of offshore conditions. In our research, the fluid forces exerted on a circular cylinder which was oscillated sinusoidally in both in-line and transverse directions to a uniform flow were measured experimentally under various conditions of frequency, amplitude and uniform-flow velocity. New expressions are proposed for the drag coefficients CD used in the equations of the drag forces, which act on cylinders as damping forces.