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Proceedings Papers

#### Use of a Rectangular Liquid-Filled Bottom-Mounted Distensible Device to Harness Nearshore Wave Power

Paper presented at the The Twenty-second International Offshore and Polar Engineering Conference, June 17–22, 2012

Paper Number: ISOPE-I-12-111

... ABSTRACT The present work aims to find out the applicability of the bulge concept used in the Anaconda (

**Chaplin**et al., 2011) on a possible seabed version. The tested model is a long rectangular duct covered with an elastic membrane and placed on the seabed, parallel to wave propagation...
Abstract

ABSTRACT The present work aims to find out the applicability of the bulge concept used in the Anaconda (Chaplin et al., 2011) on a possible seabed version. The tested model is a long rectangular duct covered with an elastic membrane and placed on the seabed, parallel to wave propagation. The tension in the membrane and its submergence can be varied by pressurising the system. Two configurations were tested: one with closed ends and one with a Power Take-Off system. Measurements were made of pressure in the duct, membrane displacement and capture width and are compared with a theoretical 1D model. INTRODUCTION This study started with the recent developments of the Anaconda which is a new way of extracting energy from ocean waves, based on bulge waves travelling along a distensible rubber tube (Chaplin et al., 2011), filled with water, oriented in the direction of wave travel and anchored head to waves. Oscillations in pressure beneath the waves generate travelling bulges in the tube. The bulge waves grow in the down-wave direction, converting wave energy into internal oscillatory flow that can be used to drive a turbine. The up-wave end of the tube is closed. Tuning is achieved by matching the speed of free bulge waves (a function of the tube's material properties and geometry) to the phase speed of water waves. A common example of the propagation of waves through fluid-filled tubes is that of blood flow in arteries. Most Wave Energy Converters (WECs) face problems with connection to the seabed, survivability in severe weather conditions and adaptation to surrounding activities (ships, fishing industry, whales migration). This is why the focus of the present paper is on a seabed version of the Anaconda, leading to a bottom-mounted distensible device set in shallow waters. The model studied is a duct filled with water and closed on the top with the elastic membrane.

Proceedings Papers

Paper presented at the The Twentieth International Offshore and Polar Engineering Conference, June 20–25, 2010

Paper Number: ISOPE-I-10-639

... numerical solution are first introduced. Then we present two applications, first for the prescribed motion of a submerged body in a wave field (including the case of a fixed cylinder, such as in

**Chaplin's**(1984) experiments), and then for a freely-moving body in waves. In the first application, we consider...
Abstract

ABSTRACT The purpose of this work is to develop advanced numerical tools for modeling two-way fully nonlinear interactions of ocean surface waves (irregular waves in the general situation) with a submerged structure undergoing large amplitude motion. The final aim is to apply these models to simulating the behavior of a point-absorber-type Wave Energy Converter (WEC). In our modeling approach, an existing twodimensional Numerical Wave Tank (NWT), based on potential flow theory, is extended to include a submerged horizontal cylinder of arbitrary cross-section. The mathematical problem and related numerical solution are first introduced. Then we present two applications, first for the prescribed motion of a submerged body in a wave field (including the case of a fixed cylinder, such as in Chaplin's (1984) experiments), and then for a freely-moving body in waves. In the first application, we consider the forced oscillations of a circular cylinder, either in the vertical direction or in a circular motion (with comparison to the theoretical results of Wu (1993)). In the second application, dynamical equations describing the body motion are solved simultaneously with the hydrodynamic problem, which requires correctly representing the coupling forces between both mechanical and hydrodynamic problems. This is illustrated by preliminary simulations for the free motion in periodic waves of an idealized WEC; these results are favorably compared to a linear model. INTRODUCTION In recent years there has been a renewed interest in using ocean renewable energy and, in particular, wave energy. To do so, many types of Wave Energy Converters (WECs) have been proposed, and some constructed and tested. Some types of so-called point-absorber WEC are based on harvesting the wave-induced motion of oscillating submerged bodies (see, e.g., the CETO system; Mann et al., 2007). These bodies can be quite close to the free surface and may undergo large amplitude motion.

Proceedings Papers

Paper presented at the The Nineteenth International Offshore and Polar Engineering Conference, July 21–26, 2009

Paper Number: ISOPE-I-09-510

...Semi-Empirical Modeling for Seawater Corrosion of Wire Rope E. Fontaine a, R. Armstrong a, A. Potts a R.E. Melchers b, C.R.

**Chaplin**c, M. François d a AMOG Consulting, Melbourne, VIC, Australia b University of Newcastle, NSW, Australia c University of Reading, Berkshire, UK d Bureau Veritas, La...
Abstract

The paper proposes a semi-empirical model for the seawater corrosion of six strand wire rope. The model includes the local effects of water temperature, oxygen concentration, flow velocity, together with the location of the wire within the internal rope structure and the zone location along the rope. The analytical formulation of the model is sustained by physical considerations and calibration of the model parameters is performed against a large set of experimental results available in the literature. INTRODUCTION Steel wire rope and chain have been used for mooring floating offshore production systems since their introduction nearly 30 years ago. A recent survey (2006) prepared for the Health and Safety Executive (HSE) of past and presently operating FPS units has shown that serious incidents have occurred in the past, including loss of station. The survey has also shown that even for more up-to-date designs, deterioration of certain areas of the mooring systems may be more rapid than expected. In the majority of systems, unless fully sheathed in plastic, the life of the rope is typically less than that of the installation. This requires a policy of life prediction, inspection and replacement. For long term integrity, it is vital that wear and corrosion are correctly accounted for in the design and selection process of wire rope and chains. The present study focuses attention on corrosion modeling of wire rope. CORROSION DESIGN GUIDANCE The American Petroleum Institute (API RP 2SK) and Det Norske Veritas (DNV-OS-E301) give recommendations for life expectancy of different constructions in terms of corrosion resistance. As shown in Table 1,(Refer to the full paper) both require all wires to be galvanized though neither make reference to the different weights of galvanizing available. API, DNV, Bureau Veritas (BV-NI-493), and the International Organization for Standardization (ISO 1990–7) all identify corrosion protection measures (galvanizing, lubricant as blocking compound, sheathing, zinc anode wires) and all draw attention to the need for special protection adjacent to terminations including additional anodes and electrical isolation of the rope, and the socket.

Proceedings Papers

Paper presented at the The Nineteenth International Offshore and Polar Engineering Conference, July 21–26, 2009

Paper Number: ISOPE-I-09-028

... waves are generated based on the mechanism of wave focusing in a 2D numerical wave tank. wavelet spectrum focus point

**chaplin**wave force mechanism vertical cylinder wavelet transform wave elevation time series frequency freak wave equation wave tank wavelet transform analysis...
Abstract

In this paper, to disclose the ringing mechanism, properties of numerical simulated freak waves and the response of small diameter vertical cylinder are analyzed by using wavelet transform analysis. Freak waves are generated based on the mechanism of wave focusing in a 2D numerical wave tank. The nonlinear properties of freak waves are analyzed by using wavelet analysis method. It is showed that in the evolution process of freak waves, besides wave energy convergence due to wave focusing, high frequency energy is generated due to wave-wave nonlinear interaction. And high frequency components of freak waves are discussed. The ringing mechanism is disclosed through the spatial and temporal transformation of wave energy and the spectrum of cylinder response by using wavelet transform analysis. INTRODUCTION With the development of harbor, coastal and offshore engineering, more and more coastal and offshore structures are being or will be constructed in deep water. These offshore structures may encounter rough sea climate when freak waves act on the offshore structures and may induce high frequency resonance response - ringing. In this paper, to disclose the ringing mechanism, properties of numerical simulated freak waves and the response of small diameter vertical cylinder are analyzed by using wavelet transform analysis. Freak waves are highly transient and non-linear. Therefore it is not genuine to analyze such waves with the classical Fourier analysis, as it is actually a linear as well as a stationary method. So the alternative method of Wavelet analysis is used to analyze the numerical simulated freak waves and the ringing response of vertical cylinder in this paper. Some fundamental theory and function of continuous wavelet transformation were introduced in the first part of the paper. Freak waves are generated based on the mechanism of wave focusing in a 2D numerical wave tank.

Proceedings Papers

Paper presented at the The Seventeenth International Offshore and Polar Engineering Conference, July 1–6, 2007

Paper Number: ISOPE-I-07-082

... incident wave interaction amplitude coefficient harmonic component experimental result wave length submerged circular cylinder

**chaplin**numerical result cylinder reflection simulation submerged cylinder frequency Nonlinear Wave Diffraction by a Fixed Submerged Circular Cylinder in Deep...
Abstract

This paper presents an experimental and numerical study of the two-dimensional wave diffraction by a fixed horizontal-axis submerged circular cylinder. The objective of the paper is to report and validate the results from the fully non-linear two-dimensional boundary-element method code CANAL and to assess the capability of the physical wave flume and the measurement methodology to study this type of problem. Two test cases are presented, both in deep-water conditions. The cylinder axis submergence is 1.5 r ( r being the cylinder radius) for the first case, and 3 r for the second case, the later corresponding to the experimental study presented in the paper. A discretization convergence evaluation is also presented for the second case. The good agreement between the numerical and the experimental results proves that this numerical model is capable to simulate accurately this type of problems. INTRODUCTION The interaction between a horizontal submerged cylinder and regular surface waves has been studied analytically, experimentally and numerically by many authors. The great variety of available good quality studies makes it a good choice for testing numerical codes and experimental techniques. The study of the interaction between fully submerged bodies and surface waves is of long-standing interest to many offshore engineering applications, namely submerged breakwaters and some wave energy devices. Unlike surface-piercing bodies, which are exposed to extreme forces originated by severe free-surface wave motions, completely submerged bodies may produce the desirable reflective properties with less demanding structural designs. The presence of a submerged obstacle near the free surface may originate a reflected wave and a modified transmitted wave. The properties of the transmitted and the reflected waves are dependent of the relation between the incident wave characteristics (amplitude and frequency) and the obstacle properties (shape, characteristic dimension and submergence depth).

Proceedings Papers

Paper presented at the The Fourteenth International Offshore and Polar Engineering Conference, May 23–28, 2004

Paper Number: ISOPE-I-04-262

... refinement (Contento et al., 2001). In generation of freak wave, we referred to the experimental condition in

**Chaplin**(1996) to generate freak waves. The experimental wave tank was 18m long, 0.75m wide with water depth 0.525m. There are 34=freqN different wave components with frequencies if equally spaced...
Abstract

ABSTRACT To identify the mechanism of ringing of offshore structures, non-linear loads on vertical small diameter cylinder in freak waves, which are generated in a two-dimensional BEM-based numerical wave tank, were calculated and analyzed in this paper. Numerical study demonstrated that the loads on vertical small diameter cylinder under the action of freak waves were highly nonlinear and impulsive, and they contained high frequency components. The analysis of numerical calculation results indicated that the non-linear loads on vertical cylinders under the action of freak waves may be one of the mechanisms of ringing of offshore structures. INTRODUCTION The study of Natvig (1994) indicated that ringing response of vertical cylinder and tether of Tension Leg Platforms, TLPs, were induced by highly nonlinear and asymmetric freak waves. So it is a key problem to identify the wave force that may induce the ringing of structures and the structures responses to wave force in the study of ringing of offshore structures. In the study of wave forces on structures, the structures are classified into two types, large scale structures and small scale structures based on whether the scale of structures affect the wave motion evidently or not. Many offshore platforms are supported by vertical cylinders. In routine design, the diagnostic scale, i. e. diameter of vertical cylinder and tether of TLPs, D, is about 20m, while in the severe sea state the wave height and wave length are about 10m and 200~400m respectively. Then the ratio of structures characteristic scale and the wave scale is D L < 0.2, so the structures can be regard as small diameter structures. To study the mechanism of ringing of offshore structure theoretically, only the response of the vertical small diameter cylinder due to the freak wave in medium water depth is carried out in this paper.

Proceedings Papers

Paper presented at the The Thirteenth International Offshore and Polar Engineering Conference, May 25–30, 2003

Paper Number: ISOPE-I-03-023

... Eulerian-Lagrangian (MEL) time marching scheme, and boundary element method (BEM). Wave deformation and wave forces on submerged single and dual cylinders are calculated using the NWT. The computed mean, 1st, 2nd, and 3rd order wave forces on a single submerged cylinder are compared with those of

**Chaplin**s...
Abstract

ABSTRACT A 2D fully nonlinear NWT is developed based on the potential theory, mixed Eulerian-Lagrangian (MEL) time marching scheme, and boundary element method (BEM). Wave deformation and wave forces on submerged single and dual cylinders are calculated using the NWT. The computed mean, 1st, 2nd, and 3rd order wave forces on a single submerged cylinder are compared with those of Chaplin's experiment, Ogilvie's 2nd-order theory, and another nonlinear computation called high-order spectral method. The computed mean, 2nd and 3rd harmonic forces agree well with lab measurement but there exists noticeable discrepancy in the 1st-order wave forces as KC number increases, which can be contributed to viscous effects (clock-wise circulation around the body). An independently developed 2D viscous NWT confirmed this speculation. The NWT simulations for submerged dual cylinders show that the interaction effects can be significant when the gap is small. In particular, the higher-harmonic forces on the rear cylinder can be greatly increased due to already-deformed incident waves by the front cylinder. The potential NWT results for dual cylinders are also compared with those including viscous effects. INTRODUCTION Nonlinear waves usually have higher/sharper crest and lower/flatter trough compared to sinusoidal waves and their interactions with various shapes of body can be significantly different from those of linear theory. The interactions of such nonlinear waves with fixed structures are of vital importance in various ocean engineering applications. For instance, the resulting forces and kinematics by fully nonlinear simulations can be significantly amplified when compared with linear theory. In this paper, a 2D fully nonlinear NWT is developed based on the potential theory, mixed Eulerian-Lagrangian (MEL) time marching scheme (Runge-Kutta 4th-order), and boundary element method (BEM). The use of fully nonlinear free-surface time-stepping method for 2D waves by MEL technique was first introduced by Longuet Higgins and Cokelet (1976).

Proceedings Papers

Paper presented at the The Eleventh International Offshore and Polar Engineering Conference, June 17–22, 2001

Paper Number: ISOPE-I-01-275

... a series of multipole potentials, and Ogilvie (1963).expanded Dean's solution and derived the second-order time-independent force. circular cylinder interaction order solution reflection coefficient variation artificial intelligence amplitude cylinder computation

**chaplin**boundary...
Abstract

ABSTRACT Non-linear irrotational two-dimensional wave-body interactions are investigated using an indirect Desingularised Boundary Integral Equation Method with fully non-linear free-surface boundary conditions. A fully implicit multi-point method is used for the time-integration, and the model is applied to the interactions of regular waves with a horizontal circular cylinder. There has been no sign of saw-tooth instabilities. The incident waves are modelled explicitly, and efficient sponge layers are used to damp out the computed scattered waves at each end of the domain. Numerical convergence and mass and energy conservation are demonstrated. Excellent agreement is observed between the present results and those from experiments, analytical solutions, and other numerical models. Particular attention is given to wave reflections in deep and finite water depths, and to some unexpected wave conditions on the lee side of the cylinder. INTRODUCTION The problem of waves diffracted by a submerged horizontal cylinder whose axis is parallel with the wave crests is one that is of both industrial and intrinsic interest. The existence of linear and second order analytical solutions, numerical solutions to various orders, and a range of good quality data also make it an attractive subject on which to test new codes and those that use novel techniques. Dean (1948) gave the first solution to the linear diffraction problem of a horizontal restrained circular cylinder beneath monochromatic waves in deep water. Dean showed the remarkable facts that to this approximation the reflection from the cylinder is zero and that the only effect of the cylinder on the waves is a change in their phase. Expressions for the first order forces on the cylinder were obtained by Ursell (1950), using a series of multipole potentials, and Ogilvie (1963).expanded Dean's solution and derived the second-order time-independent force.

Proceedings Papers

Paper presented at the The Eleventh International Offshore and Polar Engineering Conference, June 17–22, 2001

Paper Number: ISOPE-I-01-286

... interaction potential theory cylinder outer domain grid system

**chaplin**simulation ogilvie upstream oil & gas circular cylinder submerged circular cylinder resolution submerged body force component computational domain experiment accuracy Proceedings of the Eleventh (2001) International...
Abstract

ABSTRACT A 2D viscous NWT (Numerical Wave Tank) code based on Navier- Stokes equations by a multi-block FDM/FVM hybrid method has been developed to investigate the interactions of fully nonlinear regular waves with stationary two-dimensional bodies. The CFD code is applied to the case of submerged circular cylinder and extensively tested against published computational and experimental results. The multi-block hybrid method uses rectangular-grid-structured FDM (Finite Difference Method) at far field and body-fitted-coordinatestructured FVM (Finite Volume Method) in the near field. The two solutions are matched in a narrow overlap region assuring the continuity of pressure and velocities. The fully nonlinear free-surface conditions are satisfied through a density-function equation. The NWT is able to reproduce with high accuracy the nonlinear interactions of free-surface viscous flows around arbitrary 2D bodies as long as the turbulence phenomena are not important. The flow simulations for a submerged circular cylinder are able to reproduce, through advanced computer graphics software, various interesting features observed in the physical experiments for a variety of KC (Keulegan Carpenter) numbers. The developed computer program is proved to be robust and efficient in simulating more complicated flow problems including multiple bodies and bodies in motion. INTRODUCTION The oil companies or offshore industries rely in most cases on subsea pipelines or risers to transport gas and oil from ocean grounds to land or surface platforms. Therefore, they have to ensure that these slender structures are resistant and stable while undergoing the hydrodynamic forces induced by currents and waves. In this regard, it is very important to accurately predict the hydrodynamic forces (inertia, drag and lift) and better understand the physics of nonlinear unsteady viscous flows around such members, and their interactions with the neighboring structures. Indeed, the oscillatory forces may cause fatigue problems and lead to local damages.

Proceedings Papers

Paper presented at the The Ninth International Offshore and Polar Engineering Conference, May 30–June 4, 1999

Paper Number: ISOPE-I-99-226

... & gas

**chaplin**japan keulegan carpenter number ikeda amplitude coefficient Proceedings of the Ninth (1999) International Offshore and Polar Engineering Conference Brest, France, May 30-June 4, 1999 Copyright © 1999 by The International Society of Offshore and Polar Engineers ISBN 1-880653-39-7...
Abstract

ABSTRACT: This paper presents a brief review of recent research into a few examples from a wide range of problems that are concerned with the effects of viscosity on forces and responses of offshore structures and floating bodies. Particular attention is given to viscous damping of high frequency oscillations of cylindrical elements of an offshore structure, the effects of secondary flow around a horizontal cylinder beneath waves at low Keulegan Carpenter numbers, and the viscous damping of ship motions. Also some recent conclusions concerned with forces in waves in the Morison regime are summarised. Some prediction methods of viscous damping for wave-frequency and lowfrequency motions of a semi-submersible and viscous roll damping for ships are introduced, and recent studies in this field are reviewed. INTRODUCTION Wave forces on fixed structures and the forces and motion of floating bodies are influenced to various degrees by viscosity. In some cases the presence of viscosity makes a radical difference to the flow, in others its effects are apparently localised. Its practical importance is not confined to the former however, since for example viscous damping is derived from shear flow in the boundary layer, or from small-scale vortex shedding from sharp-edged or curved surfaces. But because it involves severe analytical and numerical problems, and because laboratory measurements are notoriously subject to scale effects, our understanding of the effects of viscosity on offshore structures and floating bodies has in many respects lagged behind that of other aspects of fluid/structure interaction. This paper aims to provide a brief review of a few of the problems and of recent related research. For many purposes, wave loading on structures that are composed of members which are essentially bluff bodies can conveniently be divided into four regimes.

Proceedings Papers

Paper presented at the The Eighth International Offshore and Polar Engineering Conference, May 24–29, 1998

Paper Number: ISOPE-I-98-135

... a newly proposed model. In addition, the question of size effects as regards the axial fatigue performance of spiral strands will be addressed in some detail. Finally, the proposed S-N curves are compared with others recommended by API,

**Chaplin**, and Tilly, which are the ones that are currently most...
Abstract

ABSTRACT The paper presents newly developed S-N curves which take the construction details of large diameter (i.e. realistic) spiral strands into account, and also cater for the effects of end terminations. The proposed S-N curves are based on extensive theoretical parametric studies using a newly proposed model. In addition, the question of size effects as regards the axial fatigue performance of spiral strands will be addressed in some detail. Finally, the proposed S-N curves are compared with others recommended by API, Chaplin, and Tilly, which are the ones that are currently most commonly referred to, and it is shown that, in certain cases, these S·N curves may provide unconservative results. INTRODUCTION The safety of the many deep-water platform concepts is, among other considerations, strongly dependent on the reliability of the anchoring systems which should have a high level of integrity and whose costs of installation and replacement are very high. Steel cables are used for mooring certain types of offshore platforms such as semi-submersibles, guyed towers, etc., and are proposed as elements of mooring systems of wave energy devices. The loading spectrum on the individual mooring lines is obviously very complex: it depends mainly upon the type of structure, its location, and type of mooring system adopted. The most significant aspects of the service conditions are long lives (in excess of perhaps twenty years) and the random nature of imposed loading. Permanent immersion of most of the cable in sea water is another important consideration. Cable design and manufacture is often considered to be an art rather than a science. The limits of validity of present design and calculating routines, largely based on commercial experience, are far from clear and it is an area where the rule of thumb reigns supreme.

Proceedings Papers

Paper presented at the The Seventh International Offshore and Polar Engineering Conference, May 25–30, 1997

Paper Number: ISOPE-I-97-305

... by

**Chaplin**(1984), with respect to purely inviscid models. amplitude vorticity circulation viscosity interaction free surface profile free surface equation loading evolution fluid mech viscous effect navier-stoke equation vorticity field**chaplin**cylinder diffusion vortex method...
Abstract

ABSTRACT The laminar flow about a circular cylinder beneath a Stokes waves train is numerically investigated. An efficient grid free algorithm is developed by coupling an accurate boundary integral equation method for computing the velocity field with a viscous vortex method for solving the Navier Stokes equations near the body. The problem of generating the incident wave system is effectively circumvented by means of a perturbation formulation which assumes the Stokes wave solution as the base flow. Forβ ≈ 500 and Kc = Ο(1) the systematic comparison with the available experimental values for the Fourier components of the loading is presented. An overall good agreement is observed, even for the added inertia coefficient which is known to be largely affected by viscous effects. INTRODUCTION The flow of an incompressible viscous fluid about a circular cylinder beneath a regular Stokes wave train is a typical problem of marine structures hydrodynamics. When the relevant wavelengths are comparable with the characteristic dimension of the body, the hydrodynamic loads are quantitatively dominated by the momentum exchange between the wave and the body. Consistently, it is widely accepted that the nonlinear potential flow theory effectively describes the force on the structure. In fact, the experimental analysis confirms that the vertical mean value of the hydrodynamic force and of both the second and third harmonics of the fluctuating components are well explained in terms of the inviscid wave diffraction in agreement with the predictions of weakly or fully nonlinear models (Ogilvie, 1963, Vada, 1987 and Liu et. al., 1992). However, the potential theory fails to capture exhaustively the entire phenomenon. Actually, a significant reduction in the amplitude of the fundamental harmonic of the loading is emphasized by Chaplin (1984), with respect to purely inviscid models.

Proceedings Papers

Paper presented at the The Fifth International Offshore and Polar Engineering Conference, June 11–16, 1995

Paper Number: ISOPE-I-95-132

...

**chaplin**upstream oil & gas wire rope axial fatigue wire fracture spiral strand loading prediction fatigue life strand Proceedings of the Fifth (1995) IntemtJliolUll Offshore and Polar Engineering Conference The Hague, The Netherlands, June 11-16, 1995 Copyright © 1995...
Abstract

ABSTRACT: Fairly recently, a theoretical model for predicting axial fatigue life of multi-layered spiral strands from first principles was reported by the second author. The theoretical predictions were based on an extension of a previously reported orthotropic sheet model, and the theory could predict the strand axial fatigue life to first outer (or inner) wire fracture both at the fixed end and away from the terminations (i.e. in the free field). Some experimental data from other sources provided very encouraging support for the theoretical predictions for strands with outer diameters ranging from 39 to 51mm. Some large-scale experimental results on Spiral strands with diameters up to 127mm were recently obtained by others. The purpose of the present paper is to report the correlations between these test data and theoretical predictions which has been found to be very encouraging, providing further support for the theoretical model. Moreover, it has previously been argued that with proper design. of end terminations, it is possible to design test specimens in which (under axial fatigue loading) wire fractures occur away from the ends thus enabling one to apply the test data on laboratory specimens directly to the much longer cables in the actual structures. The present reported results throw some light on the plausibility of such suggestions and identify possible practical limitations of such approaches. INTRODUCTION Steel cables are used for mooring certain types of offshore platforms such as semi-submersibles, guyed towers, etc., and are proposed as elements of mooring systems of wave energy devices. Permanent immersion of most of the cable in sea water is another important consideration. In the past, the only reliable source of information on the steel cable (wire rope and/or spiral strand) fatigue characteristics has been laboratory tests on cable specimens which can be very costly and time consuming.

Proceedings Papers

Paper presented at the The Fifth International Offshore and Polar Engineering Conference, June 11–16, 1995

Paper Number: ISOPE-I-95-227

... that there is difference between the hydrodynamic coefficients in a planar flow and a wavy flow. After that,

**Chaplin**(1984a, 1984b) reported that the inertia force coefficient at the low KC decreases due to the circulating flow that is induced around a cylinder because of a non-linear boundary layer effect...
Abstract

ABSTRACT: The wave forces acting on a circular, a square and a rectangular cylinders are examined together with the visualized flow about the cylinders. The inertia force coefficient of the every cylinder decreases with the increasing Keulegan-Carpenter number. The secondary flow induced around the cylinder is exposed from the path lines of ambient flow. The lift force calculated from the circulation can explain the decrement of the inertia force well. INTRODUCTION It is important to estimate wave forces correctly to design offshore structures. The force experienced by cylinders has been a matter of vital interest and the usual practice has been to represent this force by Morison's equation (Morison et al. 1950), where the viscous effect plays an important role. In this equation, a wave force is divided into the inertia force and the drag force and their empirical hydrodynamic coefficients are named as the inertia force coefficient and the drag coefficient. Many efforts have been paid to the choice of the coefficients. Those hydrodynamic coefficients of a circular cylinder in a planar oscillatory flow such as a vertical pile in a wave are studied well and explained in detail by, for example, Sarpkaya and Isaacson (1981). In the case of a horizontal cylinder in a wave, a particle of an ambient flow of a cylinder draws a circular orbit, which is called as a wavy flow hereafter. Koterayama and Tasiro (1978) found out from their experiment of a wide range of Keulegan-Carpenter number KC that there is difference between the hydrodynamic coefficients in a planar flow and a wavy flow. After that, Chaplin (1984a, 1984b) reported that the inertia force coefficient at the low KC decreases due to the circulating flow that is induced around a cylinder because of a non-linear boundary layer effect.

Proceedings Papers

Paper presented at the The Fifth International Offshore and Polar Engineering Conference, June 11–16, 1995

Paper Number: ISOPE-I-95-224

... prediction mean water level short-crested wave splash zone sleeve 6 vertical cylinder

**chaplin**cylinder loading Loading on a Vertical Cylinder Near Mean Water Level in Long- and Short-Crested Waves Kesavan Subbiah and John R.**Chaplin**Dept. of Civil Engineering, City University London, United...
Abstract

ABSTRACT: This paper presents the results of an experimental investigation on wave forces on a vertical cylinder in the splash zone. The cylinder was subjected to long- and short-crested waves corresponding to JONSWAP spectra, and sectional loads were measured on force sleeves up to mean water level. Ambient particle velocities were measured by means of perforated ball velocity meters whose performance in intermittent flow was checked with reference to a Laser Doppler Anemometer. Maximum Keulegan-Carpenter numbers were about 24, and maximum Reynolds numbers about 8.5 × 104. Analysis of the measurements concentrated on determining the effect of wave directionality on loading at mean water level. Comparison with earlier results for the submerged part of the cylinder suggests that in the splash zone directionality leads to stronger attenuation of loading than at lower elevations. The changes in loading are rather greater than those predicted by Dean's (1977) hybrid theory. INTRODUCTION Predictions of wave forces on cylinders in the splash zone are subject to uncertainties associated with both the particle kinematics and the loading mechanism. Wave forces on offshore structures above trough level may make significant contributions to the total shear force and overturning moment, but little information is available on how they can be computed with confidence. In studying the loading on a cylinder in this region, experimental problems arise through the difficulty of measuring particle velocities in the intermittent flow, where wave theories are not likely to be very accurate even in long-crested waves. Tørum (1989) measured forces in the splash zone on a vertical cylinder in regular waves over the Keulegan-Carpenter number range 10–55. Drag and inertia coefficients were obtained using second order Stokes wave theory, and elevations above mean water level were normalised in the form of a Froude number.

Proceedings Papers

Paper presented at the The Fourth International Offshore and Polar Engineering Conference, April 10–15, 1994

Paper Number: ISOPE-I-94-212

... is applied to the wavelets the reductions will be 85% and 72%, respectively, whereas the reductions will be 93% and 87%, respectively, if a cos 6 spreading is applied. force maxima force ratio wave field

**chaplin**wave force experiment spectrum standard deviation resultant force cylinder...
Abstract

ABSTRACT In this paper the results from physical experiments with an instrumented cylinder conducted in laboratory environments are presented. The primary aim of the study has been to investigate the effect from wave directionality on the local and depth integrated maximum wave forces on a smooth vertical cylinder. The experiments were carried out using a newly designed cylinder instrumented with miniature pressure transducers. As expected the experiments show a significant reduction of the in-line and resultant wave forces in directional waves compared to unidirectional waves with equal spectral properties. The observed reductions are nearly constant below mean water level but increase rapidly above mean water level. The transverse wave forces are generally increased in directional waves. INTRODUCTION It is a generally adopted fact that the wave forces m irregular directional (short crested) waves are smaller than in a unidirectional waves with equal spectral properties the effect is a consequence of the directional spreading of energy m a short crested sea. Consider a simple example where two wavelets are travelling in perpendicular directions Let the wavelets have equal phase, frequency and amplitude Measured by a wave gauge the surface formed by the two wavelets will be identical to the surface formed by one regular wave with twice the amplitude but phase and frequency as one of the wavelets By superposition of the kinematics in the two wavelets. It is evident that the horizontal particle velocity and acceleration will be equal to 1/√2 times those in this corresponding regular wave. The force on a cylinder calculated by the Monson equation will therefore be reduced by the factor 1/√2 for the inertia term and 1/√2 for the quadratic drag term When a cos 2 spreading is applied to the wavelets the reductions will be 85% and 72%, respectively, whereas the reductions will be 93% and 87%, respectively, if a cos 6 spreading is applied.

Proceedings Papers

Paper presented at the The Second International Offshore and Polar Engineering Conference, June 14–19, 1992

Paper Number: ISOPE-I-92-270

... describes some initial analysis of measurements of local forces on a vertical: cylinder in unidirectional waves. The experiments were carried out as part of a programme (described fully by Irani,

**Chaplin**and Subbiah, 1992) which was aimed at the more complex (and much less well-researched) problem...
Abstract

ABSTRACT This paper presents results from an experimental investigation on the loading on a rigid slender vertical circular cylinder in unidirectional regular and irregular waves. The ambient flow was measured directly, so that the derived results would not be subject to additional uncertainties associated with the use of wave theories. Reynolds numbers were in the range 10 4 to 7 × 10 4 and Keulegan-Carpenter numbers 1 to 20. Morison drag, inertia and lift coefficients are computed from forces measured at one force sleeve and compared with data obtained at the same Reynolds and Keulegan Carpenter numbers, but under uniform flow conditions in a U-tube. In regular waves, the present results show the importance of the non-uniformity of wave-induced flow, and in irregular waves it is clear that the loading is much influenced by the history of the flow. INTRODUCTION This paper describes some initial analysis of measurements of local forces on a vertical: cylinder in unidirectional waves. The experiments were carried out as part of a programme (described fully by Irani, Chaplin and Subbiah, 1992) which was aimed at the more complex (and much less well-researched) problem of Morison loading in multidirectional waves. For reference purposes however, a comprehensive series of measurements was made first in regular and irregular unidirectional waves; it is some of these that form the basis of the present paper. These measurements are of interest in their own right. First, because particular emphasis was placed throughout the test programme on obtaining good quality measurements of the particle kinematics at the cylinder's location, thus avoiding the need to rely on wave theories in the derivation of force coefficients. Second, measurements of local forces in waves are to be found in only a few references (e.g. Bullock, 1983; Chakrabarti, 1980), and then usually only in regular waves.

Proceedings Papers

Paper presented at the The Second International Offshore and Polar Engineering Conference, June 14–19, 1992

Paper Number: ISOPE-I-92-232

.... Amongst the most notable works is that of Dold and Peregrine (1985). paddle motion numerical wave tank horizontal velocity

**chaplin**wave flume equation prediction mean horizontal velocity two-dimensional numerical wave tank trough good agreement stoke wave theory tank monochromatic...
Abstract

ABSTRACT A two-dimensional numerical wave tank has been developed using a boundary integral scheme. Waves are generated by a hinged "wave-maker" at one end of the "wave flume" and they are absorbed by a "damper" at the other end. In deep water, the wave forms are solely determined by the motion of the wave-maker. A single-frequency sinusoidal motion of the paddle results in a steady progressive wave of the same frequency. Starting from the still-water condition, the first few waves are seen to disappear as they travel towards the other end of the tank, which is exactly what happens in a real wave flume. Comparisons between Stokes wave kinematics and that of monochromatic waves generated in the numerical wave tank have been carried out and the results are in good agreement with experimental observations. 1 INTRODUCTION With its unique advantages over laboratory methods, computer modelling has long been used for a wide spectrum of scientific and engineering applications. The introduction of more and more advanced computer systems, such as parallel and vector computers, have made it possible to implement some computational methods which were once beyond our capacity. In the field of offshore and coastal engineering, a wide range of numerical methods have been developed throughout the years in an attempt to understand the mechanism of natural waves. Many of these methods, such as those of Dommermuth and Vue (1987) and Creamer et al (1989), deal with waves of moderate steepness. The model of Longuet-Higgins and Cokelet (1976) was the first successful example in simulating steep overturning gravity waves. The boundary integral method they used has since been pursued and great effort has been given to improving the numerical stability and efficiency when implementing the method. Amongst the most notable works is that of Dold and Peregrine (1985).