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.

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 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 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.

Evaluation of non-linear wave forces on a fixed body by the higher-order boundary element method

2000 ◽  
Vol 214 (6) ◽  
pp. 825-839 ◽  
Author(s):  
H G Sung ◽  
S Y Hong ◽  
H S Choi
Keyword(s):  
Diffraction Problem ◽  
Radiation Condition ◽  
Wave Force ◽  
The Body ◽  
Wave Forces ◽  
Linear Wave ◽  
Algebraic Equations ◽  
Regular Elements ◽  
Linear Algebraic Equations ◽  
Non Linear

A numerical method is developed to evaluate non-linear waves diffracted by a fixed body and the resulting wave force acting on it. The entire boundary and all the variables are discretized by means of isoparametric biquadratic elements. To resolve the difficulty of describing the flow in the intersection region with regular elements, discontinuous elements are introduced. The generalized minimal residual (GMRES) algorithm is implemented to solve the reduced linear algebraic equations. Non-linearity of the free surface is integrated accurately in time by the fourth-order Runge-Kutta method with minimum truncation error. A new numerical radiation condition for non-linear diffraction is suggested, which resolves accurate non-linear diffraction around the body. Non-linear diffraction problem of a bottom-mounted circular cylinder is exemplified. The non-linear wave used by Rienecker and Fenton is chosen as the incident wave field. Based on the numerical results, it is believed that the present method is quite promising.

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.

Analysis of Semi-Submersible Under Combined High Waves and Current Conditions Compared With Model Tests

2018 ◽  
Author(s):  
Limin Yang ◽  
Arne Nestegård ◽  
Erik Falkenberg
Keyword(s):  
Simulation Model ◽  
Low Frequency ◽  
Model Tests ◽  
Wave Forces ◽  
Viscous Effects ◽  
Numerical Predictions ◽  
Wave Drift ◽  
Zero Current ◽  
Frequency Excitation ◽  
Wave Drift Forces

Viscous effects on the low-frequency excitation force on column based platforms are significant in extreme waves. The wave drift force as calculated by a zero-current potential flow radiation/diffraction code becomes negligible for such waves. In the present study, the effect of current and viscous contributions on the slowly varying wave forces are adjusted by a formula developed in the Exwave JIP, see e.g. [1], which is validated against model test results. This paper presents numerical predictions of low frequency horizontal motions of a semi-submersible in combined high waves and current condition. In the simulation model, frequency dependent wave drift forces from radiation/diffraction code are modified by the formula. Static current forces and viscous damping are modelled by the drag term in Morison load formula using relative velocity between current and floater and with force coefficients as recommended by DNVGL-RP-C205 [2]. Low frequency surge responses calculated by the simulation model are compared with model tests for waves only and for combined collinear and noncollinear wave and current conditions.

scholarly journals ACCURATE PREDICTION OF NON-LINEAR WAVE FORCES: PART II (RESPONDING CYLINDER)

1998 ◽  
Vol 12 (3) ◽  
pp. 487-498 ◽  
Author(s):  
S.A. Billings ◽  
P.K. Stansby ◽  
A.K. Swain ◽  
M. Baker
Keyword(s):  
Accurate Prediction ◽  
Wave Forces ◽  
Linear Wave ◽  
Non Linear

Study on the Motions and Stress of Immersing Tunnel Element under Wave Actions

2013 ◽  
Vol 328 ◽  
pp. 614-622
Author(s):  
Hong Da Shi ◽  
Shui Yu Li ◽  
Dong Wang
Keyword(s):  
Large Scale ◽  
Three Dimensional ◽  
Diffraction Theory ◽  
Wave Force ◽  
Source Distribution ◽  
Wave Forces ◽  
Linear Wave ◽  
Wave Loads ◽  
Distribution Method ◽  
Motion Responses

The dynamic characteristics of large-scale tunnel element are very important for the process of immersion. In the paper, the motions and stress of the element under wave actions were studied. The linear wave diffraction theory and the three-dimensional source distribution method were applied to calculate the wave loads and motion responses of the tunnel element under different incident wave conditions. In the study, there have no cable on the element. On the basis of the above theories, the stress and the motions of the element were studied. The first order wave forces and the second order wave force were deduced, and the motions equation was made.

Calculation of Wave Forces Acting on a Cylinder With a Porous Plate Fixed Inside

2009 ◽  
Author(s):  
Weiguang Bao ◽  
Fenfang Zhao ◽  
Takeshi Kinoshita
Keyword(s):  
Body Surface ◽  
Porous Body ◽  
Porous Plate ◽  
Wave Theory ◽  
Wave Forces ◽  
Linear Wave ◽  
Normal Velocity ◽  
Wave Loads ◽  
Eigen Values ◽  
Eigen Function

To evaluate wave forces and to estimate the motion of breakwater, a circular cylinder is investigated based on the linear wave theory in the present work. The cylinder possesses a porous sidewall, an impermeable bottom and a horizontal porous plate inside that is fixed in the cylinder to work as obstruct and make wave dissipation more effectively. To simplify the problem, the Darcy’s fine-pore model is applied to the boundary condition on the porous body surface. The boundary value problem is solved by means of the eigen-function expansion approach. The fluid domain is divided into three regions and different eigen-function series are used. The so-called dispersion relation for the region inside the cylinder is quite different from a conventional one due to the existence of the porous plate. It leads to eigen values of complex number. To obtain solutions for the radiation problems, particular solution should be constructed to take account of the normal velocity appearing on the porous boundary. The wave loads are evaluated by integrating the pressure difference on two sides of the wetted body surface. The theoretical works are in good consistence with the experimental results. The Haskind relations are examined for the porous body. It is found that the damping coefficient consists of two parts. In addition to the component of conventional wave-radiating damping, exists a second component caused by the porous effects.

Viscous Drift Force and Motion Analysis of Semi-Submersible in Storm Sea States Compared With Model Tests

2017 ◽  
Author(s):  
Limin Yang ◽  
Erik Falkenberg ◽  
Arne Nestegård ◽  
Jørn Birknes-Berg
Keyword(s):  
Frequency Response ◽  
Potential Flow ◽  
Low Frequency ◽  
Model Tests ◽  
Viscous Drag ◽  
Wave Forces ◽  
Linear Wave ◽  
Wave Excitation ◽  
Frequency Wave ◽  
Drift Force

Standard analysis models applied for motions of moored floaters are based on potential flow perturbation methods with wave frequency response governed by first order wave forces and low-frequency response governed by second-order difference frequency wave forces. These models have been shown to have limitations in extreme sea states where nonlinear wave excitation and viscous drag forces above still water level may dominate. This effect is particularly visible for the low frequency excitation since the potential flow contribution goes to zero for long waves. In the present study non-linear wave excitation and viscous drag contributions on a semi-submersible is modelled by Morison’s load formula since the columns and pontoons are slender elements. A numerical simulation model is developed using SIMO [6], in which viscous forces and damping are included by the drag term of Morison equation and with drag coefficients recommended from DNV-RP-C205 [1]. Low frequency surge responses calculated by the combined potential flow drift forces and viscous drag from Morison load model are compared with model tests for waves only and for combined wave and current conditions. A simplified formula for current and viscous effects on wave drift force, generalized to non-collinear conditions is presented and compared with model test results.

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