New Methods to Solve High Order Potential Used in Calculating Non-Linear Wave Loads

2006 ◽  
Author(s):  
Yasunori Nihei ◽  
Weiguang Bao ◽  
Takeshi Kinoshita
Keyword(s):  
Perturbation Expansion ◽  
Low Frequency ◽  
The Body ◽  
Body Motion ◽  
Moving Frame ◽  
Linear Wave ◽  
Wave Loads ◽  
Wave Drift ◽  
Non Linear ◽  
Low Frequency Motion

In the present study, non-linear wave loads such as the wave-drift force, wave-drift damping and wave-drift added mass, acting on the body is considered based on the potential theory. To investigate non-linear wave loads, consistent perturbation expansion by means of two small parameters, i.e. the incident wave slope and the low frequency body motion, is performed on a moving frame (body-fixed) coordinate system. To avoid complicated free surface integrals as much as possible, new approach for the higher order potential in the interaction problem of low frequency motion and waves is suggested in the present work. Instead of integrals, derivative operators are defined to obtain special solutions efficiently.

Non-Linear Wave Forces Acting on a Body of Arbitrary Shape Slowly Oscillating in Waves

2005 ◽  
Author(s):  
Yasunori Nihei ◽  
Takeshi Kinoshita ◽  
Weiguang Bao
Keyword(s):  
Low Frequency ◽  
The Body ◽  
Coordinate Frame ◽  
Wave Forces ◽  
Linear Wave ◽  
Wave Loads ◽  
Low Frequency Oscillation ◽  
Wave Drift ◽  
Non Linear ◽  
Low Frequency Motion

In the present study, non-linear wave loads such as the wave drift force, wave drift damping and wave drift added mass, acting on a moored body is evaluated based on the potential theory. The body is oscillating at a low frequency under the non-linear excitation of waves. The problem of interaction between the low-frequency oscillation of the body and ambient wave fields is considered. A moving coordinate frame following the low frequency motion is adopted. Two small parameters, which measure the wave slope and the frequency of slow oscillations (compared with the wave frequency) respectively, are used in the perturbation analysis. So obtained boundary value problems for each order of potentials are solved by means of the hybrid method. The fluid domain is divided into two regions by an virtual circular cylinder surrounding the body. Different approaches, i.e. boundary element method and eigen-function expansion, are applied to these two regions. Calculated nonlinear wave loads are compared to the semi-analytical results to validate the present method.

Nonlinear Wave Loads Acting on Cylinder Array Slowly Oscillating in Diffraction and Radiation Wave Fields

2005 ◽  
Author(s):  
Weiguang Bao ◽  
Takeshi Kinoshita ◽  
Motoki Yoshida
Keyword(s):  
Nonlinear Wave ◽  
Perturbation Expansion ◽  
Low Frequency ◽  
Added Mass ◽  
Wave Loads ◽  
Wave Fields ◽  
Wave Drift ◽  
Cylinder Array ◽  
Radiation Wave ◽  
Low Frequency Motion

The problem of a circular cylinder array slowly oscillating in both diffraction and radiation wave fields is considered in the present work. As a result of the interaction between the wave fields and the low-frequency motion, nonlinear wave loads may be separated into the so-called wave-drift added mass and damping. They are force components proportional to the square of the wave amplitude but in phase of the acceleration and velocity of the low-frequency motion respectively. The frequency of the slow oscillation is assumed to be much smaller than the wave frequency. Perturbation expansion based on two time scales and two small parameters is performed to the order to include the effects of the acceleration of the low-frequency motion. Solutions to these higher order potentials are suggested in the present work. Wave loads including the wave drift added mass and damping are evaluated by the integration of the hydrodynamic pressure over the instantaneous wetted body surface.

Non-Linear Wave Loads Acting on Obliquely Slowly Advancing Platform

2009 ◽  
Author(s):  
Yasunori Nihei ◽  
Sota Sugimoto ◽  
Takashi Tsubogo ◽  
Weiguang Bao ◽  
Takeshi Kinoshita
Keyword(s):  
Boundary Value Problems ◽  
Potential Theory ◽  
Boundary Value ◽  
The Body ◽  
Linear Wave ◽  
Wave Loads ◽  
Forward Speed ◽  
Wave Drift ◽  
Non Linear ◽  
Drift Force

It is necessary to evaluate wave drift force for ships advancing obliquely. There are some approaches, for instance the strip method, solving the Navier-Stokes equation directly in the fluid domain (CFD), potential theory and so on. In the present study, the non-linear wave loads acting on the ship with constant oblique forward speed is considered based on the potential theory. Consistent perturbation expansion based on two parameters, i.e. the incident wave slope and the ratio of the forward speed compared to the phase velocity of the waves, is performed on a moving frame (body-fixed) coordinate system to simplify the problem. So obtained boundary value problems for each order of potentials is solved by means of the hybrid method. The fluid domain is divided into two regions by an artificial circular cylinder surrounding the body. The potential in the inner region is expressed by an integral over the boundary surface with a Rankin source as its Green function while it is expressed in the eigen function expansion for the outer region. Consequently, the boundary value problems can be solved efficiently. In the present paper, the authors will discuss the effects of the obliquely advancing on the wave drift force in a diffraction wave field up to the order proportional to the advancing speed. An ellipsoid model is used in the calculation and the wave drift force is evaluated for various Froude number.

Nonlinear Wave Loads Affected by the Low-Frequency Oscillations in the Horizontal Plane

2003 ◽  
Author(s):  
Takeshi Kinoshita ◽  
Weiguang Bao
Keyword(s):  
Nonlinear Wave ◽  
Perturbation Expansion ◽  
Low Frequency ◽  
Hydrodynamic Pressure ◽  
Wave Loads ◽  
Slow Oscillations ◽  
Low Frequency Oscillations ◽  
Wave Drift ◽  
Small Parameters ◽  
Wave Drift Damping

To investigate the effects of the low-frequency oscillations on the nonlinear wave loads, the interaction of the low-frequency oscillations with the ambient wave fields is considered. The frequency of the slow oscillations is assumed to be much smaller than the wave frequency. Perturbation expansion based on two small parameters, i.e. the incident wave amplitude and the low frequency, is performed to simplify the problem. Nonlinear wave loads including the wave drift damping and wave drift added mass are evaluated by the integration of the hydrodynamic pressure over the instantaneous wetted body surface. The problem is solved for a uniform circular cylinder by means of the Green’s theorem and semi-analytical solutions are presented. The far field conditions for each order of potentials are proposed to ensure the existence of a unique solution. The restriction on the validation of the solutions is discussed.

Wave-Drift Added Mass of a Cylinder Array Free to Respond to the Incident Waves

2002 ◽  
Author(s):  
Takeshi Kinoshita ◽  
Weiguang Bao ◽  
Motoki Yoshida ◽  
Kazuko Ishibashi
Keyword(s):  
Perturbation Expansion ◽  
Low Frequency ◽  
Hydrodynamic Pressure ◽  
Added Mass ◽  
Floating Body ◽  
Wave Loads ◽  
Alternative Source ◽  
Wave Drift ◽  
Cylinder Array ◽  
Incident Waves

Conventional linear added mass and damping can be obtained when a floating body is forced to oscillate in the calm water. However, with the presence of the incident waves, there exists an alternative source of added mass and damping caused by the nonlinear interactions between waves and low-frequency oscillations. Proportional to the square of the wave amplitude, they are called the wave drift added mass and the wave drift damping. The problem of a circular cylinder array slowly oscillating in both diffraction and radiation wave fields is considered in the present work. The frequency of the low-frequency oscillation is assumed to be much smaller than the wave frequency. Perturbation expansion based on two time scales is performed to simplify the problem. Wave loads including the wave drift added mass are formulated by integration of the hydrodynamic pressure over the instantaneous wetted body surface.

A Parametric Study of Low-Frequency Damping of Mooring System

2014 ◽  
Author(s):  
Minglu Chen ◽  
Shan Huang ◽  
Nigel Baltrop ◽  
Ji Chunyan ◽  
Liangbi Li
Keyword(s):  
Low Frequency ◽  
Structure Design ◽  
The Body ◽  
Body Motion ◽  
Mooring Line ◽  
Offshore Structure ◽  
Frequency Oscillation ◽  
Low Frequency Oscillation ◽  
Line System ◽  
Irregular Wave

Mooring line damping plays an important role to the body motion of moored floating platforms. Meanwhile, it can also make contributions to optimize the mooring line system. Accurate assessment of mooring line damping is thus an essential issue for offshore structure design. However, it is difficult to determine the mooring line damping based on theoretical methods. This study considers the parameters which have impact on mooring-induced damping. In the paper, applying Morison formula to calculate the drag and initial force on the mooring line, its dynamic response is computed in the time domain. The energy dissipation of the mooring line due to the viscosity was used to calculate mooring-induced damping. A mooring line is performed with low-frequency oscillation only, the low-frequency oscillation superimposed with regular and irregular wave-frequency motions. In addition, the influences of current velocity, mooring line pretension and different water depths are taken into account.

A Joint Numerical and Experimental Study of a Surging Point Absorbing Wave Energy Converter (WRASPA)

2009 ◽  
Author(s):  
Majid A. Bhinder ◽  
Clive G. Mingham ◽  
Derek M. Causon ◽  
Mohammad T. Rahmati ◽  
George A. Aggidis ◽  
...  
Keyword(s):  
Wave Energy ◽  
Informed Choice ◽  
Wave Energy Converter ◽  
Body Motion ◽  
Numerical Dissipation ◽  
Small Scale ◽  
Linear Wave ◽  
Energy Converter ◽  
Non Linear ◽  
Experimental Project

This paper presents the findings from using several commercial computational fluid dynamics codes in a joint numerical and experimental project to simulate WRASPA, a new wave energy converter (WEC) device. A series of fully 3D non-linear simulations of WRASPA are presented. Three commercial codes STAR-CCM, CFX and FLOW-3D are considered for simulating the WRASPA device and final results are presented based on the use of Flow-3D. Results are validated by comparison to experimental data obtained from small scale tank tests undertaken at Lancaster University (LU). The primary aim of the project is to use numerical simulation to optimize the collector geometry for power production over a range of likely wave climates. A secondary aim is to evaluate the ability of commercial codes to simulate rigid body motion in linear and non-linear wave climates in order to choose the optimal code with respect to compute speed and ease of problem setup. Issues relating to the ability of a code in terms of numerical dissipation of waves, wave absorption, wave breaking, grid generation and moving bodies will all be discussed. The findings of this paper serve as a basis for an informed choice of commercial package for such simulations. However the capability of these commercial codes is increasing with every new release.

scholarly journals Analytical Model of Wave Loads and Motion Responses for a Floating Breakwater System with Attached Dual Porous Side Walls

2018 ◽  
Vol 2018 ◽  
pp. 1-14
Author(s):  
Weiliang Qiao ◽  
Keh-Han Wang ◽  
Wenqi Duan ◽  
Yuqing Sun
Keyword(s):  
Analytical Model ◽  
Dynamic Responses ◽  
Body Motion ◽  
Linear Wave ◽  
Wave Loads ◽  
Vertical Side ◽  
Damping Coefficients ◽  
Floating Breakwater ◽  
Exciting Forces ◽  
Porous Walls

A set of two-dimensional analytical solutions considering the effects of diffraction and radiation are presented in this study to investigate the hydrodynamic interaction between an incident linear wave and a proposed floating breakwater system consisting of a rectangular-shaped body and two attached vertical side porous walls in an infinite fluid domain with finite water depth. The Matched Eigenfunction Expansion Method (MEEM) for multiple fluid domains is applied to derive theoretically the velocity potentials and associated unknown coefficients for wave diffraction and body motion induced radiation in each subdomain. Also, the exciting forces, as well as the added mass and damping coefficients for the floating breakwater system under the surge, heave, and pitching motions, are formulated. The displacements of breakwater motions are determined by solving the equation of motion. As a verification of the analytical model, the present solutions of the limiting cases in terms of exciting forces, moments, added masses, and damping coefficients are found to be well matched with other published numerical results. Additionally, the hydrodynamic performances and the dynamic responses in terms of Response Amplitude Operators (RAOs) of the proposed floating breakwater system are evaluated versus various dimensionless variables, such as wavelength and porous-effect parameter. The results show that the attached porous walls with selected porous properties are observed to have the advantages of reducing wave impacts on the floating breakwater system and at the same time its dynamic responses are also noticeably improved.

Generation of surf beat by non-linear wave interactions

1971 ◽  
Vol 49 (1) ◽  
pp. 1-20 ◽  
Author(s):  
Brent Gallagher
Keyword(s):  
Gravity Waves ◽  
Numerical Evaluation ◽  
Low Frequency ◽  
Linear Wave ◽  
Transfer Energy ◽  
Wave Interactions ◽  
Frequency Spectra ◽  
Non Linear ◽  
Linear Interactions ◽  
Low Frequency Waves

Non-linear interactions among wind-generated gravity waves transfer energy to low frequency waves in a coastal zone. A transfer function is derived for a straight coastline of constant bottom slope. This model is applied to three actual cases, and numerical evaluation of the energy transfer produces low frequency spectra which are compared with observations.

scholarly journals Numerical Simulation of Fully Nonlinear Interaction Between Regular and Irregular Waves and a 2D Floating Body

2019 ◽  
Author(s):  
Haoran Li ◽  
Erin E. Bachynski
Keyword(s):  
Numerical Results ◽  
The Body ◽  
Body Motion ◽  
Irregular Waves ◽  
Floating Body ◽  
Computational Time ◽  
Wave Loads ◽  
Nonlinear Loads ◽  
Fully Nonlinear ◽  
Irregular Wave

Abstract A fully nonlinear Navier-Stokes/VOF numerical wave tank, developed within the open-source CFD toolbox OpenFOAM, is used to investigate the response of a moored 2D floating body to nonlinear wave loads. The waveDyMFoam solver, developed by extending the interDyMFoam solver of the OpenFOAM library with the waves2Foam package, is applied. Furthermore, a simple linear spring is implemented to constrain the body motion. An efficient domain decomposition strategy is applied to reduce the computational time of irregular wave cases. The numerical results are compared against the results from potential flow theory. Numerical results highlight the coupling between surge and pitch motion and the presence of nonlinear loads and responses. Some minor numerical disturbance occurs when the maximum body motion response is achieved.

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