Power Extraction from Water Waves

1976 ◽  
Vol 20 (02) ◽  
pp. 63-66 ◽  
Author(s):  
Chiang C. Mei
Keyword(s):  
Water Waves ◽  
Degrees Of Freedom ◽  
Vertical Axis ◽  
Horizontal Cylinder ◽  
The Body ◽  
Floating Body ◽  
Maximum Efficiency ◽  
Viscous Effects ◽  
Two Degrees Of Freedom ◽  
Power Extraction

Salter has demonstrated experimentally that a horizontal cylinder in the free surface of water can be a device to extract energy from the incident waves. This paper proposes a design which is based on the idea of a tethered-float breakwater, and gives the theoretical design criteria for maximum power extraction from a general floating cylinder with one or two degrees of freedom. It is shown that the rate of energy extraction must be equal to the rate of radiation damping and that the floating body must be made to resonate then for a body with one degree of freedom, the maximum efficiency at a given frequency can be at leastone half if the body is symmetrical about a vertical axis, and greater for an asymmetrical body. For a body with two degrees of freedom, all the wave power can be extracted. Hydrodynamical aspects of the controlled motion are examined. Viscous effects are ignored.

Analysis of the First Order and Slowly Varying Motions of an Axisymmetric Floating Body in Bichromatic Waves

2013 ◽  
Vol 135 (1) ◽  
Author(s):  
João Pessoa ◽  
Nuno Fonseca ◽  
C. Guedes Soares
Keyword(s):  
Vertical Cylinder ◽  
Vertical Axis ◽  
Second Order ◽  
The Body ◽  
Floating Body ◽  
Drift Motion ◽  
First Order ◽  
Motion Responses ◽  
Simple Geometry ◽  
Good Agreement

The paper presents an experimental and numerical investigation on the motions of a floating body of simple geometry subjected to harmonic and biharmonic waves. The experiments were carried out in three different water depths representing shallow and deep water. The body is axisymmetric about the vertical axis, like a vertical cylinder with a rounded bottom, and it is kept in place with a soft mooring system. The experimental results include the first order motion responses, the steady drift motion offset in regular waves and the slowly varying motions due to second order interaction in biharmonic waves. The hydrodynamic problem is solved numerically with a second order boundary element method. The results show a good agreement of the numerical calculations with the experiments.

Drift Forces on a Floating Body of Simple Geometry Due to Second Order Interactions Between Pairs of Harmonics With Different Frequencies

2009 ◽  
Author(s):  
Joa˜o Pessoa ◽  
Nuno Fonseca ◽  
C. Guedes Soares
Keyword(s):  
Vertical Cylinder ◽  
Vertical Axis ◽  
Second Order ◽  
The Body ◽  
Floating Body ◽  
Order Problem ◽  
Simple Geometry ◽  
The Mean ◽  
Order Quantities ◽  
Drift Forces

The paper presents an investigation of the slowly varying second order drift forces on a floating body of simple geometry. The body is axis-symmetric about the vertical axis, like a vertical cylinder with a rounded bottom and a ratio of diameter to draft of 3.25. The hydrodynamic problem is solved with a second order boundary element method. The second order problem is due to interactions between pairs of incident harmonic waves with different frequencies, therefore the calculations are carried out for several difference frequencies with the mean frequency covering the whole frequency range of interest. Results include the surge drift force and pitch drift moment. The results are presented in several stages in order to assess the influence of different phenomena contributing to the global second order responses. Firstly the body is restrained and secondly it is free to move at the wave frequency. The second order results include the contribution associated with quadratic products of first order quantities, the total second order force, and the contribution associated to the free surface forcing.

Theoretical Study of the Water Entry of a Body in Waves: Application to Safety of Occupants in Free-Fall Lifeboats

2009 ◽  
Author(s):  
Thomas Sauder ◽  
Se´bastien Fouques
Keyword(s):  
Water Waves ◽  
Degrees Of Freedom ◽  
Mass Matrix ◽  
Free Fall ◽  
Theoretical Method ◽  
Emergency Evacuation ◽  
Momentum Conservation ◽  
The Body ◽  
Water Impact ◽  
The Impact

The safety of occupants in free-fall lifeboats (FFL) during water impact is addressed. The first part of the paper describes a theoretical method developed to predict the trajectory in six degrees of freedom of a body entering water waves. Slamming forces and moments are computed, based on momentum conservation, long wave approximation and a von Karman type of approach. The added mass matrix of the body is evaluated for impact conditions by a boundary element method. The second part of the paper focuses on the application of the method to free-fall lifeboats, which are used for emergency evacuation of oil platforms or ships. Acceleration loads on FFL occupants during water impact are dependent on numerous parameters, especially the hull shape, the mass distribution, the wave heading relative to the lifeboat, and the impact point on the wave surface. Assessing operational limits of FFL by means of model tests only has therefore been costly and time consuming. This issue is addressed here by applying the theoretical method described in the first part. The model has been validated for FFL through extensive model testing in calm water and regular waves, and statistical estimates of acceleration levels for lifeboat occupants, as well as acceleration time series were obtained that can be used as inputs to numerical human response models.

A Numerical Investigation of the Response of an Elastically Mounted Rigid Cylinder With Two Degrees of Freedom

2010 ◽  
Author(s):  
Bruno C. Ferreira ◽  
Marcelo A. Vitola ◽  
Juan B. V. Wanderley ◽  
Sergio H. Sphaier ◽  
Carlos A. Levi
Keyword(s):  
Experimental Data ◽  
Phase Angle ◽  
Degrees Of Freedom ◽  
Stokes Equations ◽  
Lift Coefficient ◽  
The Body ◽  
Curvilinear Coordinates ◽  
Two Degrees Of Freedom ◽  
Conservative Scheme ◽  
Rigid Cylinder

The vortex induced vibration (VIV) on a circular cylinder is investigated by the numerical solution of the Reynolds average Navier-Stokes equations. An upwind and Total Variation Diminishing (TVD) conservative scheme is used to solve the governing equations written in curvilinear coordinates and the k–ε turbulence model is used to simulate the turbulent flow in the wake of the body. The cylinder is supported by a spring and a damper and free to vibrate in the transverse and in-line directions. In previous work, numerical results for the amplitude of oscillation, vortex shedding frequency, and phase angle between lift and displacement were compared to experimental data obtained from Khalak and Williamson (1996) to validate the code for VIV simulations in the transverse direction. In the present work, results are obtained for phase angle, amplitude, frequency, and lift coefficient and compared to experimental data from Jauvtis and Williamson (2003) for an elastically mounted rigid cylinder with two degrees of freedom. Differences in the amplitude of oscillation between experimental and numerical data were observed for both direction. It seems that the fluid flow memory effect is an important aspect that should be taken in consideration on numerical simulation to reproduce the experimental results for VIV with 2DOF as pointed out by Moe and Wu [1].

Shape Effects on Viscous Damping and Motion of Heaving Cylinders1

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
Ronald W. Yeung ◽  
Yichen Jiang
Keyword(s):  
Fluid Motion ◽  
Vortex Method ◽  
The Body ◽  
Floating Body ◽  
Navier Stokes ◽  
Inviscid Fluid ◽  
Fluid Viscosity ◽  
Viscous Damping ◽  
Viscous Effects ◽  
Shape Effects

Fluid viscosity is known to influence hydrodynamic forces on a floating body in motion, particularly when the motion amplitude is large and the body is of bluff shape. While traditionally these hydrodynamic force or force coefficients have been predicted by inviscid-fluid theory, much recent advances had taken place in the inclusion of viscous effects. Sophisticated Reynolds-Averaged Navier–Stokes (RANS) software are increasingly popular. However, they are often too elaborate for a systematic study of various parameters, geometry or frequency, where many runs with extensive data grid generation are needed. The Free-Surface Random-Vortex Method (FSRVM) developed at UC Berkeley in the early 2000 offers a middle-ground alternative, by which the viscous-fluid motion can be modeled by allowing vorticity generation be either turned on or turned off. The heavily validated FSRVM methodology is applied in this paper to examine how the draft-to-beam ratio and the shaping details of two-dimensional cylinders can alter the added inertia and viscous damping properties. A collection of four shapes is studied, varying from rectangles with sharp bilge corners to a reversed-curvature wedge shape. For these shapes, basic hydrodynamic properties are examined, with the effects of viscosity considered. With the use of these hydrodynamic coefficients, the motion response of the cylinders in waves is also investigated. The sources of viscous damping are clarified.

Experimental and Numerical Study of the Depth Effect on the First Order and Slowly Varying Motions of a Floating Body in Bichromatic Waves

2010 ◽  
Author(s):  
Joa˜o Pessoa ◽  
Nuno Fonseca ◽  
C. Guedes Soares
Keyword(s):  
Numerical Study ◽  
Vertical Cylinder ◽  
Vertical Axis ◽  
Second Order ◽  
The Body ◽  
Floating Body ◽  
Harmonic Waves ◽  
Depth Effect ◽  
Drift Motion ◽  
First Order

The paper presents an experimental and numerical investigation on the motions of a floating body of simple geometry subjected to harmonic and bi-harmonic waves. The experiments were carried out in three different water depths representing shallow and deep water. The body is axis-symmetric about the vertical axis, like a vertical cylinder with a rounded bottom, and it is kept in place with a soft mooring system. The experimental results include the first order motion responses, the steady drift motion offset in regular waves and the slowly varying motions due to second order interaction in bi-harmonic waves. The hydrodynamic problem is solved numerically with a second order boundary element method. The results show a good agreement of the numerical calculations with the experiments.

scholarly journals WAVE-INDUCED OSCILLATIONS OF SMALL MOORED VESSELS

1966 ◽  
Vol 1 (10) ◽  
pp. 70 ◽  
Author(s):  
Fredric Raichlen
Keyword(s):  
Water Waves ◽  
Wave Length ◽  
Standing Waves ◽  
The Body ◽  
Viscous Effects ◽  
Response Curves ◽  
Near Resonance ◽  
Spring System ◽  
Reflecting Surface ◽  
Wave Induced

This study deals with the motions of a neutrally buoyant rectangular parallelpiped moored by a linear spring system m standing waves. The results show that a linear theory which considers the response of the body as a smgle-degree-of-freedom oscillator adequately describes the surge motion for standing waves ranging from shallow-water waves to deep-water waves and for ratios of body length to wave length of from 0.1 to 1 5. It was found that the response curves for surge motion become more selective with respect to frequency in the vicinity of resonance as the distance of the body from a reflecting surface increases. Therefore, coupling this with viscous effects, which are more important near resonance, it is possible to reduce the effect of resonance considerably for a moored body with a particular natural frequency by choosing the proper mooring location in its standing wave environment. This has possible application in the planning of berthing facilities in marinas.

Drift Motion of Floating Bodies Under the Action of Green Water

2021 ◽  
Author(s):  
Sasan Tavakoli ◽  
Luofeng Huang ◽  
Alexander V. Babanin
Keyword(s):  
Numerical Simulations ◽  
Water Waves ◽  
The Body ◽  
Green Water ◽  
Floating Body ◽  
Floating Bodies ◽  
Drift Motion ◽  
Upper Deck ◽  
Steep Waves ◽  
The Impact

Abstract Numerical simulations are peformed to model the dynamic motions of a free floating body exposed to water waves. The solid body has low freeboard and draft, and its upper deck can be washed by the steep waves. Thus, the green water phenomenon occurs as large waves interact with the floating body. The aim of the research is to improve the understanding of the green water emerging above the upper deck of a floating plate. A thin floating body with barriers is also modeled. For the case of the body equipped with barriers, no green water occurs. Green water has been seen to affect the wave field and the dynamic motions of the plate. It is observed that when water can wash the upper surface of the floating object, drift speed is slightly decreased as a proportion of the energy of waves is dissipated above the body. Water waves are seen to impact the upper surface of the thin floating body as the green water flows over its upper deck. Furthermore, water is seen to impact the plate as its front edge re-enters the water. The first water impact only occurs when the floating body is not equipped with any barrier. By sampling the numerical simulations, it is observed that the non-dimensional value of the impact pressure, resulting from the green water, is larger for the case of smaller wavelength.

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