Drag in Oscillatory Flow Interpreted From Wake Considerations

SUMMARY The paper presents and evaluates a principle for interpreting forces on bodies in oscillatory flow, based on assuming that the drag coefficient is the same as in stationary flow, provided wake velocities are properly corrected for. The resulting formulae describe general trends correctly, and can in some cases also be used for quantitative calculation of oscillatory flow phenomena. INTRODUCTION For many types of offshore structures drag forces are a major part of the design loads, or they can be of decisive importance to the operational performance of the structures. The drag forces can be due to current, to the orbital motion in the waves, to the oscillatory motions of the structure itself, or to various combinations of these effects. Until now normal design procedures have been based on calculation of drag forces by the wellknown Morison formulation, using drag coefficients determined experimentally for each structure, or taken from empirical data. The present paper introduces and discusses an alternative way of dealing with drag forces in oscillatory flow. It is based on assuming that the drag coefficient itself is the same as in stationary flow, provided the correct relative velocity is applied. This means that the flow velocity has to be corrected for the effect of the wake generated by the previous oscillations. This correction can be done on the basis of momentum considerations and turbulent mixing theory. Based on these principles one can now calculate how drag forces in oscillatory flow are influenced by for instance Keulegan- Carpenter number, geometry of motion pattern, effect of superposed current, effect of interaction between several bodies etc. SCOPE OF INVESTIGATION The scope of the present investigation is:To develop analytical formulae for practical calculations of drag in oscillatory flow based on wake considerations, momentum balance and turbulent mixing theory.To develop computer programs for more extensive calculations.To investigate ranges of applicability of the theory by verification against published experimental data, and by means of new experiments.To discuss possible practical applications of the theory. STATE-OF-THE-ART SURVEY In practical design and analysis of offshore structures the hydrodynamic forces acting on a well submerged, oscillating body are calculated by the Morison formula. (Mathematical equation available in full paper) where the mass coefficient Cm and the drag coefficient Cd depend on:–the geometry of body–the Reynolds number–The Keulegan-Carpenter number. In all practical design and analysis work these dependencies are obtained from experimental data. For the stationary flow case there is a lot of data available from wind tunnel testing of bodies of various geometries, see for instance Refs. 1 and 2. These stationary flow data can also be applied to oscillatory flow in cases of very large Keulegan-Carpenter number. An efficient tool for determining coefficients in oscillatory flow in general is the U-tube. From such experiments there are extensive data available on hydrodynamic coefficients of simple bodies such as two-dimensional cylinders as functions of Rn, Kc, roughness etc., see for instance Ref. 3.