The Validity of Morison Equation Extensions

Abstract

Abstract This paper presents results of an experimental work for investigating the hydrodynamic interaction of slender oscillating cylinders, Laboratory tests have been carried out to study wave-current-structure interaction by oscillating a vertical cylinder in the cross-flow and in-line direction with a (steady) flow and/or waves. Inclusion of a wide variety of flow conditions has been an important objective. The present paper deals with results of cylinder oscillations parallel to a current and concentrates on the in-line force component. Validation and suitability of various existing mathematical formulations for describing hydrodynamic interaction have been evaluated for the range of dimensionless parameters included in the laboratory test data. The data refute the independent flow field approach to the prediction of hydrodynamic forces, and it is concluded that a modified form of the Morison equation which also happens to be linear shows promise for the universal prediction of hydrodynamic forces. 1. Introduction Many types of slender marine structures in the offshore industry are affected by hydrodynamic interaction. This interaction must certainly be considered whenever the level of structural motion is not negligible. The present work forms a part of an ongoing study of hydrodynamic interaction of slender cylinders carried out by the Workgroup Offshore Technology of the Deft University of Technology. Tests have been carried out to study flow-structure interaction experimentally by oscillating a vertical cylinder in the cross-flow and in-line direction with a (steady) flow and/or waves (regular and irregular); see table 1. The purpose is to obtain an unbiased set of laboratory measurements of the total interaction between the hydrodynamics (wave and current) on the one hand, and the moving cylinder on the other, Various existing as well as new mathematical formulations for describing this interaction can be evaluated objectively using the data. Details of the experimental program may be found in references I and 2. This paper considers the hydrodynamic interaction with the in-lineoscillation of the cylinder superimposed on a steady towing speed. This is a flow situation similar to that for a cylinder oscillating in a current or a combination of waves and current with a fixed cylinder, 2. Morison Equation Extensions The in-line force arising from the oscillatory flow around slender fixed cylinders is usually represented by the Morison equation: (MATHEMATICAL EQUATION AVAILABLE IN FULL PAPER) where:p is the fluid density,D is the cylinder diameter,u is the flow velocity The hydrodynamic drag and inertia coefficients, CJ and Q, are determined from experimental measurements. The fluid force arising from an oscillating cylinder can also be expressed by a Morion equation by using the added-mass coefficient Ca, instead of inertia coefficient, The added-mass coefficient is generally assumed to be related to the inertia coefficient by: (MATHEMATICAL EQUATION AVAILABLE IN FULL PAPER)