Wave Forces on Rectangular Cylinders at Low Keulegan-Carpenter Numbers
Authors: Derouich D. Hamel 
Published: October 2008

ABSTRACT
An experimental investigation of fluid loading on large smooth rectangular cylinders of five different aspect ratios was carried out at the Hydrodynamics Laboratory of the University of Glasgow. The cylinders were mounted vertically as surface piercing and horizontally submerged and were subjected to regular waves. The wave force coefficients corresponding to low Keulegan-Carpenter numbers were obtained. The results show that inertia and drag coefficients are dependent of Reynolds and Keulegan-Carpenter numbers and the frequency parameter. It is found that the drag coefficient exhibits large values as KC number approaches zero and then falls sharply as KC number increases within a small range. Inertia and drag coefficients are found to be strongly affected as the cylinders aspect ratios vary. Inertia and drag coefficients are found to be higher for vertical cylinders than those of corresponding horizontal cylinders. The calculated forces using Morison equation through the use of experimentally determined inertia and drag coefficients is found to be in good agreement with the meas-ired forces at low KC numbers.

INTRODUCTION
With the necessity of reducing the capital cost in exploring marginal fields, new offshore structure designs are emerging with non-circular cylindrical members. An offshore platform whose members made of rectangular cross-section cylinders is considered to be economically more viable than the conventional designs with circular cylindrical sections. New generation of semi-submersible drilling rigs and tension-leg platforms whose hulls and legs are conforming to rectangular geometry in cross-section are examples of these new designs. However, the circular cylindrical geometry has always been the sentre of attention in model tests when investigating the fluid loading. While a large amount of fluid loading data for circular cylinders have been accumulated over the years, relatively little is known about the loading on rectangular cylinders. The design of marine structures requires the prediction of wave & current induced forces. The inline force applied on a body immersed in an oscillating fluid is traditionally calculated using the well-known Morison equation. Since its introduction forty years ago, the Morison equation developed by Morison, O'Brien, Johnson and schaaf1 has become widely used and several experimental results have shown that it has enough accuracy for practical applications. The Morison equation gives the in-line force acting on a cylinder as a linear sum of the drag and inertia force components. The in-line force per unit length is expressed as (mathematical equation)(available in full paper) where the hydrodynamic coefficients CD & CM must be determined experimentally. Keulegan & carpenter2 were the pioneers in using the Morison equation to compute forces on submerged horizontal circular cylinders and flat plates placed in the node of a standing wave. They successfully correlated their experimentally determined CM & CD with a period parameter (herein referred as Keulegan-Carpenter KC number) defined as UmT/D. They did not find any significant dependence of these coefficients on Reynolds number. Later Sarpkaya3,4 using his well known Ushaped water oscillation tank generated a large amount of data giving inertia CM, drag CD and lift CL coefficients for circular cylinders. He found that these coefficients were dependent not only on Keulegan Carpenter number but on Reynolds number and roughness of the cylinders as well.