Morison coefficients for a circular cylinder oscil

Authors: Zhida Yuan Zhenhua Huang

Publish Date: 2015/06/12

Volume: 1, Issue: 4, Pages: 435-444

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Abstract

In this study a set of experimental results for wave forces acting on a cylinder oscillating with dual frequency in still water are reported The experiment was designed to mimic a cylinder slowly oscillating in regular waves with the highfrequency oscillation representing the wave motion and the lowfrequency oscillation the slow drift motion The inline forces acting on the cylinder were analyzed using the independentflow form of Morison’s equation Our experimental results showed that it was not appropriate to simply use in the independentflow form of Morison’s equation the addedmass and drag coefficients obtained for the cylinder oscillating with a single frequency in still water A new dimensionless parameter was introduced to describe each of the wave force coefficients used in the independentflow form of Morison’s equation and empirical expressions for the wave force coefficients were proposed using the new dimensionless parametersWhen studying the responses of offshore structures to ocean waves the wave forces acting on slender members are frequently modeled by Morison’s equation which has been widely used to model wave loadings on cylinders fixed in waves or cylinders oscillating in still water or waves eg Sarpkaya and Storm 1985 Najafian et al 1995 Liu and Bergdahl 1996 DNV 2010 Even though the original Morison’s equation was proposed for regular waves it has been widely used for random waves in practice Najafian et al 1995 Burrows et al 1997 When performing frequencydomain analysis using Morison’s equation the quadratic drag force needs to be linearized eg Gudmestad and Connor 1983 Recent evaluations of the effectiveness of Morison’s equation using the data from two smallscale field tests can be found in Boccotti et al 2012 2013For problems involving two frequencies two forms of Morison’s equation have been proposed 1 the relativevelocity form of Morison’s equation eg Chakrabarti 1987 and 2 the independentflow form of Morison’s equation eg Laya et al 1984 In the relativevelocity form of Morison’s equation which is the most commonly used one the drag force is quadratically related to the velocity difference between the ambient flow and the cylinder In the independentflow form of Morison’s equation which is used less often the total force is the sum of the wave force due to the ambient flow field acting on a fixed cylinder and the force on the cylinder vibrating in an otherwise still waterKoterayama 1984 studied the wave force coefficients for a circular cylinder moving with a constant speed in regular waves the Keulegan–Carpenter numbers for the wave motion ranged from 13 to 100 and the reduced velocity defined by the constant speed and the wave period ranged from 0 to 60 For a circular cylinder oscillating sinusoidally with a very low frequency in regular waves and a cylinder oscillating with dual frequency in still water the ratio of the two frequencies was an integer Koterayama and Nakamura 1988 measured and analyzed the wave forces using the method similar to that of Koterayama 1984 their Keulegan–Carpenter numbers for the wave motion ranged from 11 to 157 and the reduced velocity ranged from 05 to 52 In the data analysis of both Koterayama 1984 and Koterayama and Nakamura 1988 the inline force was first written in terms of the relative velocity form and then a harmonic analysis was applied to the drag force to obtain a drag coefficient for the steady motion and a pair of drag and inertia coefficients for each frequency component All the results were presented as functions of the reduced velocity but the data points were widely scattered in some results Even though the ranges of the Keulegan–Carpenter number and reduced velocity covered a wide range in Koterayama 1984 and Koterayama and Nakamura 1988 but the definitions of the addedmass and drag coefficients used in these two studies are different from those in the independentflow form of Morison’s Equation their drag coefficients include the contributions from nonlinear interactions among different frequenciesAll experiments in this study were conducted in a wave flume located in the Hydraulics Modelling Laboratory in Nanyang Technological University Singapore The wave flume was 055m wide 06m deep and 36m long The model was placed in the middle section of the flume to minimize any possible influence of the two endsThe test section was chemically treated coating to prevent the metal from reacting with water so that its surface was always kept smooth during the experiment We stress that the surface roughness may affect the wave force coefficients Wolfram and Naghipour 1999 The upper dummy section was 300mm long and the length of lower dummy section was adjustable All these three sections were carefully assembled so that their center lines were aligned For the details of this instrumented cylinder model the reader is referred to Yuan and Huang 2010 and Yuan and Huang 2011 who used the same cylindrical force model in their study of hydrodynamic forces on a cylinder fixed in regular waves or oscillating transversely in regular wavesEach individual component in the experimental system was estimated to have a nominal error bound less than 3  Since the overall system error bound cannot be known as a priori the reliability of the test results can only be assured by comparing our force measurements with some theoretical values and experimental data published in the literature

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