Drag Coefficients of Long Flexible Cylinders
Authors: Vandiver J. Kim 
Published: October 2008

ABSTRACT
In the summer of 1981 a field experiment was conducted investigating the vibration response of long flexible cylinders to vortex shedding in a steady, uniform current. Two basic cylinder types were tested, both 75 feet in length. One cylinder was a cable 1.25 inches in diameter with seven pairs of internal biaxial accelerometers. The second cylinder was a steel pipe, 1.631 inches in diameter, carrying the cable inside. Drag force, current speed, tension, and biaxial acceleration at seven locations were measured. Drag coefficients in excess of 3.0 were measured for both the pipe and the cable under lockin conditions.

INTRODUCTION
Flow induced vibration problems have been confronting engineers for many years. Recent problems encountered at deepwater sites with substantial currents have generated a renewed concern for vortex induced vibration problems. Drilling risers, TLP tension members, suspended pipeline spans, and mooring cables are all subject to vibration related failure.
Considerable experimental work has been conducted on short cylindrical segments under controlled laboratory conditions. Mean drag coefficients as high as 3.0 have been demonstrated with cross flow lockin of spring mounted or driven rigid cylinders. There has been an understandable reluctance on the part of designers to use such high values in design. In fact many engineers find it hard to believe that such high drag coefficients are possible under realistic field conditions with long flexible cylinders.
The purpose of the experiment described in this paper was to measure the flow-induced vibration response of a long flexible cylinder under more realistic, but still uncontrolled, field conditions. These tests were more realistic than laboratory ones, because it was possible to use a cylinder of sufficient length that many different natural modes could be excited. At the same time, reasonably high Reynolds numbers could be achieved.
These tests were controlled in that the flow velocity was uniform over the length of the cylinder, and tension, current and vibration could be easily measured. with substantial effort drag measurements were also made, a task which is at times a challenge even under laboratory conditions.

THE TEST SITE AND INSTRUMENTATION

The Test Site
The site chosen for the experiment was a sandbar located at the mouth of Holbrook Cove near Castine, Maine. This was the same site used for previous experiments during the mid-1970's by Vandiver and Mazel (1,2). At low tide the sandbar was exposed allowing easy access to the test equipment, while at high tide it was covered by about ten feet of water. The test section was oriented normal to the direction of the current which varied from 0 to 2.4 ft/s over the tidal cycle with only small spatial variation over the test section length at any given moment.
The data acquisition station for the experiment was the R/V Edgerton which was chartered from the MIT Sea Grant Program. The Edgerton was moored for the duration of the experiment approximately 300 feet from the sandbar and connected to the instruments on the sandbar by umbilicals.