Lift Estimate and Response Analysis of Vertical Pipes Subjected to Regular Waves

Abstract

It has been pointed out that under same KC number condition the lift force acting on a vertical pipe in regular wave can exceed the force acting in the wave progressing direction. In this study a model for the lift force is presented, and using this model dynamical response of pipes are calculated employing a analysis program of under water line structure. And these results are compared with those of experiments. The model is consist of two formulae, the first formula expresses two alternation of lift force acting on a element of the pipe during one cycle of wave elevation and the other one expresses three alternation of lift force.fL2=1/2ρDCLV2n× (VN-vN) /|n× (VN-vN) |sgn (dH/dt) f (H) fL3=1/2ρDCLV2 n× (VN-vN) /|n× (VN-vN) |sgn (H-Hmax√3/2) sgn (H+Hmax√3/2) g(H)Here ρ represents the fluid density, and D is the diameter of the element, V denotes the velocity of fluid particle, and CL represents lift force coefficient, n is unit vector parallel to the axis of element, VN and vN represent components of fluid particle velocity and element velocity normal to the element axis respectively. And sgn is a sign function and take its value +1 and -1 according to positive and negative of its argument value respectively. 1/2ρDCLV2 represents the amplitude of lift force, and the following functions detect the crest, the maximum slope position and the definite height position of free surface elevation, f and g are smooth functions and their maximum values are unity. CL values used here were determined experimentally as to the solid pipes. As a result next conclusions are obtained.(1) Using the first formula, the predicted displacements of the bottom end are in good coincidence with experimental result especially in case of resonance. The results, obtained using the second formulae, didn't show good coincidence with the those of experiment, but the resonance similar to the experiment were observed.(2) CL calculated from the measured lift force, increased in case of the resonance, but the calculated displacement, using the fixed CL value obtained through experiments with solid pipes, were in good agreement with the experimental results. Therefore, major part of increase in CL in case of resonance could be explained as a result of dynamic magnification.