Drag Coefficients of a Long Flexible Circular Cylinder with Wake Interference

Drag coefficients of the downstream cylinder in a tandem arrangement of two models aligned with the flow are shown in this work. The models. which experienced vortex-induced vibrations with wake inteiference. had an external diameter of 16 mm and a total length of 1.5 m giving an aspect ratio of about 94. More than 400 runs were carried out in a water flume with only the lower 40% of the models exposed to the current. The flow speed was varied up to 0.75 mls giving Reynolds numbers in the range from 1200 to 12000. A supporting structure. where the models were attached. allowed changes in the centre to centre distances and in the applied top tensions. Separations {~f up to 4 diameters were tested with tension variations from 15 to lION. Reduced velocities based on the fundamental natural frequency reached values up to 16. The mass ratio of the models was around 1.8 and the combined mass-damping parameter about 0.05. NOMENCLATURE Cd Drag coefficient ex In-line curvature c y Cross-flow curvature D External diameter EA Axial Stiffness EI Flexural Stiffness EI* Modified flexural stiffness fl Fundamental natural frequency in water fx In-line force distribution Fx Total in-line force 277 L Length L/ D Aspect ratio L., Submerged Length m Mass m* Mass ratio (m* +CA)I; Combined mass-damping parameter Re Reynolds number S Centre to centre distance 7; Top Tension V Flow speed VI Reduced velocity based on fl Ws Submerged weight W Point load at mid point x In-line displacements XM In-line deflection at mid point y Cross-flow displacements p Water density I; Damping ratio INTRODUCTION Knowledge about the hydrodynamic forces acting on flexible circular cylinders responding to vortex-induced vibrations (VIV) is fundamental for the design of offshore structures. Insitu measurements are always difficult and instrumentation is most of the times not designed to resolve completely the response of such structures. Most of the field data comes from accelerometers and hydrodynamic forcing is rarely reported. In contrast, Copyright © 2009 by ASME some prediction tools used by the industry arc based on measurements and hence. they rely on the quality of the measurements available. Even though excellent reviews on VIV have been reported [I]. [2]. [3]. [4J. [51 and 16], data showing drag forces on flexible cylinders is scarce and even more when there is wake interference between several bluff bodies. A recent benchmarking exercise I7J in which several CFD and empirical prediction tools were used to simulate the response of a single long flexible cylinder, reported significant differences between the predicted response and that measured in laboratory experiments [8]. There is still the need for data showing force coefficients of different arrangements of flexible circular cylinders. The drag coefficients exhibited by long flexible cylinders are considerably larger than those typical of stationary or flexibly mounted rigid cylinders and this large values of drag coeflicient are related to large amplitude responses. Large values of drag coefficient were reported in towing experiments with long flexible cylinders and related to large amplitude motions in [9]. In another experiment with a very high aspect ratio cylinder [10], drag coefficients between 1.5 and 2.7 depending on the response experienced by the model were also reported. Similar values to those reported in those two studies, were observed in recent experimental work carried out in a large laboratory facility [8], where it was shown how the drag coefficients increased monotonically with values between I and 2.8, inside clearly defined mode related lock-in branches. Offshore flexible structures such as marine deep water risers and mooring lines are more often found arranged in groups than solitary. In contrast, most of the studies in the past years have been focused into solitary flexibly mounted rigid or flexible circular cylinders. There is no data published showing drag coefficients of long flexible cylinders in tandem or other arrangements of several bodies when vibrating at high mode numbers, and this situation is of especial interest because of its practical implications in offshore design. The design of models and the facilities needed to accomplish multi-mode vortex-induced vibration experiments with wake interference in tandem or other arrangements, is certainly challenging. Keeping realistic mechanical characteristics in relatively small facilities is very difficult. Resolving high mode motion requires a large number of sensors and without it, the information one can obtain from the structure is very limited. Measuring hydrodynamic forces is also very challenging and this is the reason why the data available is very limited. Vortex-induced vibrations, galloping and combinations of both types of response were observed in experiments [11] with a flexibly mounted rigid cylinder immersed in the wake of an stationary one with the same dimensions. Different configurations of side-by-side, staggered and tandem arrangements of flexible cantilevers of circular cross section have also been studied in a wind tunnel [12]. In the recent years, several authors have performed experiments to study vortex and wake induced vibrations 278 of tandem arrangements of rigid cylinders 1131 and [14]. In this work. two long flexible circular cylinders have been used and the drag coefficients acting on the trailing one. with wake interference, arc shown when responding in its first structural mode. The drag coefficients are calculated indirectly from the measured displacements. The dynamic response of the cylinder model used as the trailing one. but in a single circular cylinder arrangement has also been reported [15] and [16], together with the drag coefficients 117]), which appear compared with the results in this paper. EXPERIMENT DETAILS The set up in Figures I and 2 illustrates an aluminium supporting structure which was used to place the cylinder models in the water ft.ume at the department of Aeronautics of Imperial College London.