Wave Forces on Pipes Near the Ocean Bottom

Abstract

ABSTRACT Where wake effects are negligible potential flow calculations predict well the lift and added mass forces acting on pipelines near the ocean floor when subjected to time dependent flows. Wake effects have a significant influence on the flow conditions and measured frequencies of vortex shedding can predict the drag force acting on the cylinder. The Strouhal number is a function of the gap below the cylinder. The added mass coefficient is much larger when the cylinder is near the boundary than when it is a free stream. INTRODUCTION Vertical and horizontal hydrodynamic forces on pipes near the ocean bottom are influenced by pipe roughness, ambient turbulence, angle of skew, number and grouping of pipes, formation and collapse 'of the wake, the proximity of the free surface and the proximity of the bottom. Most of these topics have received little attention as to quantifying their effects for engineering purposes. However, a fund of knowledge is growing for smooth circular cylinders near the bottom away from the influence of the free surface. Let the non-dimensional gap below the cylinder be designated as shown in Fig. l. We consider waves with crests parallel to the cylinder center line. The free surface does not influence the forces 'acting on the cylinder if ?> 4, (3). The importance of on the lift force is treated analytically in (2, 3, 7,8,9, 10, 11) for potential flow calculations, substantiated with laboratory results. Some influences from the free surface was presented by Chakraborti and Cotter (9), and Grace discussed the importance of the period parameter (9). The influence of groups of nearby cylinders has also been treated analytically (11). The wake, however, exerts a significant modification to the hydrodynamic forces (1, 2, 3, 4, 5, 6, 7). This paper focuses on the importance of wake modifications for time varying flows. The conditions when potential flow theory can be used will be indicated. In general the wake formation is not in phase with the ambient fluid velocities, and therefore the drag force is not in phase with the ambient velocity. This can influence the value of added mass coefficients derived from laboratory data, which are ordinarily determined at a time in the records when the ambient velocity is presumed to be zero. DEVELOPMENT It is well known that some fluid flows in nature can be described with potential flow theory. The beginning instants in impulsive flows, converging flows, and other acceleration conditions when a wake formation has not occurred, are applicable examples. When a wave passes a cylinder as herein considered, the total particle motions in the region of the cylinder may be relatively small and the wake may not have time to form before the flow reverses in the usual sense.