Numerical Study of the Ship Motion in Waves Using the Three-Dimensional Time-Domain Forward-Speed Free-Surface Green Function and a Second-Order Boundary Element Method

2008 ◽  
Author(s):  
D. C. Hong ◽  
S. Y. Hong ◽  
H. G. Sung
Keyword(s):  
Integral Equation ◽  
Free Surface ◽  
Green Function ◽  
Time Domain ◽  
Time Derivative ◽  
Three Dimensional ◽  
Forward Speed ◽  
Surface Green Function ◽  
The Green Function ◽  
The Time Domain

The radiation and diffraction potentials of a ship advancing in waves are calculated in the time-domain using the three-dimensional time-domain forward-speed free-surface Green function and the Green integral equation on the basis of the Neumann-Kelvin linear wave hypothesis. The Green function approximated by Newman for large time is used together with the Green function by Lamb for small time. The time-domain diffraction problem is solved for the time derivative of the potential by using the time derivative of the impulsive incident wave potential represented by using the complementary complex error function. The integral equation for the potential is discretized according to a second-order boundary element method where the collocation points are located inside the panel. It makes it possible to take account of the line integral along the waterline in a rigorous manner. The six-degree-of-freedom motion and memory functions as well as the diffraction impulse response functions of a hemisphere and the Wigley seakeeping model are presented for various Froude numbers. Comparisons of the wave damping and exciting force and moment coefficients for zero forward speed, calculated by using the Fourier transforms of the time-domain results and the frequency-domain coefficients calculated by using the improved Green integral equation which is free of the irregular frequencies, have been shown to be satisfactory. The wave damping coefficients for non-zero forward speed, calculated by using Fourier transforming of the present time-domain results have also been compared to the experimental results and agreement between them has been shown to be good. A simulation of coupled heave-pitch motion of the Wigley seakeeping model advancing in regular head waves of unit amplitude has been carried out.

Influence of the Waterline Integral on the Solution of the Frequency-Domain Forward-Speed Radiation-Diffraction Problem of a Ship Advancing in Waves

2014 ◽  
Author(s):  
D. C. Hong ◽  
S. Y. Hong ◽  
G. J. Lee ◽  
M. S. Shin
Keyword(s):  
Integral Equation ◽  
Free Surface ◽  
Green Function ◽  
Frequency Domain ◽  
Surface Condition ◽  
Numerical Results ◽  
Forward Speed ◽  
Line Integral ◽  
Free Surface Condition ◽  
Surface Green Function

The radiation-diffraction potential of a ship advancing in waves is studied using the three-dimensional frequency-domain forward-speed free-surface Green function (Brard 1948) and the forward-speed Green integral equation (Hong 2000). Numerical solutions are obtained by making use of a second-order inner collocation boundary element method which makes it possible to take account of the line integral along the waterline in a rigorous manner (Hong et al. 2008). The present forward-speed Green integral equation includes not only the usual free surface condition for the potential but also the adjoint free surface condition for the forward-speed free-surface Green function as indicated by Brard (1972). Comparison of the present numerical results of the heave-heave wave damping coefficients and the experimental results for the Wigley ship models I, II and III (Journee 1992) has been presented. These coefficients are compared with those calculated without taking into account of the line integral along the waterline in order to show the forward speed effect represented by the waterline integral when it is properly included in the free-surface Green integral equation. Comparison of the present numerical results and the equivalent time-domain results (Hong et al. 2013) has also been presented.

scholarly journals Computation of Nonlinear Hydrodynamic Loads on Floating Wind Turbines Using Fluid-Impulse Theory

2015 ◽  
Author(s):  
Godine Kok Yan Chan ◽  
Paul D. Sclavounos ◽  
Jason Jonkman ◽  
Gregory Hayman
Keyword(s):  
Free Surface ◽  
Green Function ◽  
Wind Turbines ◽  
Time Domain ◽  
The Body ◽  
Nonlinear Loads ◽  
Frequency Wave ◽  
Linear And Nonlinear ◽  
The Time Domain ◽  
Nonlinear Free Surface

A hydrodynamics computer module was developed to evaluate the linear and nonlinear loads on floating wind turbines using a new fluid-impulse formulation for coupling with the FAST program. The new formulation allows linear and nonlinear loads on floating bodies to be computed in the time domain. It also avoids the computationally intensive evaluation of temporal and spatial gradients of the velocity potential in the Bernoulli equation and the discretization of the nonlinear free surface. The new hydrodynamics module computes linear and nonlinear loads — including hydrostatic, Froude-Krylov, radiation and diffraction, as well as nonlinear effects known to cause ringing, springing, and slow-drift loads — directly in the time domain. The time-domain Green function is used to solve the linear and nonlinear free-surface problems and efficient methods are derived for its computation. The body instantaneous wetted surface is approximated by a panel mesh and the discretization of the free surface is circumvented by using the Green function. The evaluation of the nonlinear loads is based on explicit expressions derived by the fluid-impulse theory, which can be computed efficiently. Computations are presented of the linear and nonlinear loads on the MIT/NREL tension-leg platform. Comparisons were carried out with frequency-domain linear and second-order methods. Emphasis was placed on modeling accuracy of the magnitude of nonlinear low- and high-frequency wave loads in a sea state. Although fluid-impulse theory is applied to floating wind turbines in this paper, the theory is applicable to other offshore platforms as well.

Time-Domain Simulations of Radiation and Diffraction Forces

2010 ◽  
Vol 54 (02) ◽  
pp. 79-94 ◽  
Author(s):  
Xinshu Zhang ◽  
Piotr Bandyk ◽  
Robert F. Beck
Keyword(s):  
Free Surface ◽  
Time Domain ◽  
Three Dimensional ◽  
The Body ◽  
Surface Boundary ◽  
Two Dimensional ◽  
Forward Speed ◽  
Time Step ◽  
Surface Boundary Conditions ◽  
Strip Theory

Large-amplitude, time-domain, wave-body interactions are studied in this paper for problems with forward speed. Both two-dimensional strip theory and three-dimensional computation methods are shown and compared by a number of numerical simulations. In the present approach, an exact body boundary condition and linearized free surface boundary conditions are used. By distributing desingularized sources above the calm water surface and using constant-strength flat panels on the exact body surface, the boundary integral equations are solved numerically at each time step. The strip theory method implements Radial Basis Functions to approximate the longitudinal derivatives of the velocity potential on the body. Once the fluid velocities on the free surface are computed, the free surface elevation and potential are updated by integrating the free surface boundary conditions. After each time step, the body surface and free surface are regrided due to the instantaneous changing wetted body geometry. Extensive results are presented to validate the efficiency of the present methods. These results include the added mass and damping computations for a Wigley III hull and an S-175 hull with forward speed using both two-dimensional and three-dimensional approaches. Exciting forces acting on a Wigley III hull due to regular head seas are obtained and compared using both the fully three-dimensional method and the two-dimensional strip theory. All the computational results are compared with experiments or other numerical solutions.

Numerical Study of Forward-Speed Ship Motion and Added Resistance

2017 ◽  
Author(s):  
D. C. Hong ◽  
T. B. Ha ◽  
K. H. Song
Keyword(s):  
Integral Equation ◽  
Free Surface ◽  
Numerical Study ◽  
Three Dimensional ◽  
The Body ◽  
Experimental Results ◽  
Surface Boundary ◽  
Forward Speed ◽  
Added Resistance ◽  
Following Seas

The added resistance of a ship was calculated using Maruo’s formula [1] involving the three-dimensional Kochin function obtained using the source and normal doublet distribution over the wetted surface of the ship. The density of the doublet distribution was obtained as the solution of the three-dimensional frequency-domain forward-speed Green integral equation containing the exact line integral along the waterline. Numerical results of the Wigley ship models II and III in head seas, obtained by making use of the inner-collocation 9-node second-order boundary element method have been compared with the experimental results reported by Journée [2]. The forward-speed hydrodynamic coefficients of the Wigley models have shown no irregular-frequencylike behavior. The steady disturbance potential due to the constant forward speed of the ship has also been calculated using the Green integral equation associated with the steady forward-speed free-surface Green function since the so-called mj-terms [3] appearing in the body boundary conditions contain the first and second derivatives of the steady potential over the wetted surface of the ship. However, the free-surface boundary condition was kept linear in the present study. The added resistances of the Wigley II and III models in head seas obtained using Maruo’s formula showing acceptable comparison with experimental results, have been presented. The added resistances in following seas obtained using Maruo’s formula have also been presented.

Numerical Study of Large Amplitude Ship Motion With Forward Speed in Severe Seas

2009 ◽  
Author(s):  
D. C. Hong ◽  
H. G. Sung ◽  
S. Y. Hong
Keyword(s):  
Free Surface ◽  
Time Domain ◽  
Large Amplitude ◽  
Numerical Study ◽  
Surface Condition ◽  
Three Dimensional ◽  
Ship Motion ◽  
Forward Speed ◽  
Restoring Force ◽  
Head Waves

A three-dimensional time-domain calculation method is of crucial importance in prediction of ship motion with forward speed in a severe irregular sea. The exact solution of the free surface wave–ship interaction problem is very complicated because of the extremely nonlinear boundary conditions. In this paper, an approximate body nonlinear approach based on the three-dimensional time-domain forward-speed free-surface Green function has been presented. It is a simplified version of the method known as LAMP (Lin and Yue 1990) where the exact body boundary condition is applied on the instantaneous wetted surface of the ship while free-surface condition is linearized. In the present study, the Froude-Krylov force and the hydrostatic restoring force are calculated on the instantaneous wetted surface of the ship while the forces due to the radiation and scattering potentials on the mean wetted surface. The time-domain radiation and scattering potentials have been obtained from a time invariant kernel of integral equations for the potentials. The integral equation for the radiation potential is discretized according to the second-order boundary element method (Hong and Hong. 2008). The diffraction impulse response functions of the Wigley seakeeping model are presented for various Froude numbers. A simulation of coupled heave-pitch motion of the Wigley model advancing in regular head waves of large amplitude has been carried out. Comparisons between the fully linear and the present approximate body nonlinear computations have been made at various Froude numbers.

scholarly journals Hydrodynamic Analysis and Motions of Ship with Forward Speed via a Three-Dimensional Time-Domain Panel Method

2021 ◽  
Vol 9 (1) ◽  
pp. 87
Author(s):  
Peng Zhang ◽  
Teng Zhang ◽  
Xin Wang
Keyword(s):  
Time Domain ◽  
Three Dimensional ◽  
Impulse Response Function ◽  
Panel Method ◽  
Linear Potential ◽  
Forward Speed ◽  
Precise Integration ◽  
Response Function Method ◽  
Surface Green Function ◽  
Linear Potential Theory

A new three-dimensional (3D) time-domain panel method is developed to solve the ship hydrodynamic problem and motions. For an advancing ship with a constant forward speed in regular waves, the ship’s hull can be discretized and processed into a number of quadrilateral panels. Based on Green’s theorem, an analytical expression for Froude–Krylov (F–K) forces evaluation on the quadrilateral panels is derived without accuracy loss. Within the linear potential theory, the transient free surface Green function (TFSGF) is applied to solve the boundary value problem. To improve the efficiency and numerical stability of TFSGF evaluation, a precise integration method with variable parameters setting for extended identity matrix is developed to compute the TFSGF in the computation domain. Then, radiation and diffraction forces can be evaluated by means of the impulse response function method. The Wigley I hull form is taken as a study case, and the computed hydrodynamic coefficients, wave exciting forces, and motions by the present method are compared with previous literature experimental data and prior published results. It manifests that the three-dimensional time-domain panel method proposed in this paper has good accuracy.

Three-Dimensional Large Amplitude Body Motions in Waves

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
Xinshu Zhang ◽  
Robert F. Beck
Keyword(s):  
Free Surface ◽  
Time Domain ◽  
Three Dimensional ◽  
Surface Boundary ◽  
Forward Speed ◽  
Time Step ◽  
Surface Boundary Conditions ◽  
Calm Water ◽  
Wigley Hull ◽  
Constant Strength

Three-dimensional, time-domain, wave-body interactions are studied in this paper for cases with and without forward speed. In the present approach, an exact body boundary condition and linearized free surface boundary conditions are used. By distributing desingularized sources above the calm water surface and using constant-strength flat panels on the exact wetted body surface, the boundary integral equations are numerically solved at each time step. Once the fluid velocities on the free surface are computed, the free surface elevation and potential are updated by integrating the free surface boundary conditions. After each time step, the body surface and free surface are regrided due to the instantaneous wetted body geometry. The desingularized method applied on the free surface produces nonsingular kernels in the integral equations by moving the fundamental singularities a small distance outside of the fluid domain. Constant-strength flat panels are used for bodies with any arbitrary shape. Extensive results are presented to validate the efficiency of the present method. These results include the added mass and damping computations for a hemisphere. The calm water wave resistance for a submerged spheroid and a Wigley hull are also presented. All the computations with forward speed are started from rest and proceeded until a steady state is reached. Finally, the time-domain forced motion results for a modified Wigley hull with forward speed are shown and compared to the experiments for both linear computations and body-exact computations.

Roll Stabilization by Passive Anti-Roll Tanks Using an Improved Model of the Tank-Liquid Motion

2003 ◽  
Vol 9 (7) ◽  
pp. 839-862 ◽  
Author(s):  
Khaled S. Youssef ◽  
Dean T. Mook ◽  
Ali H. Nayfeh ◽  
Saad A. Ragab
Keyword(s):  
Time Domain ◽  
Three Dimensional ◽  
High Amplitude ◽  
Roll Motion ◽  
Nonlinear Phenomena ◽  
Forward Speed ◽  
Liquid Motion ◽  
Pitch Frequency ◽  
The Time Domain ◽  
Improved Model

Roll motion is an undesirable feature of the behavior of a ship in rough seas, and so it is natural to consider ways of reducing it. The most common devices for increasing roll damping are bilge keels. However, the effectiveness of keels is limited, and anti-roll tanks and fins are used when more control is required. Moreover, unlike keels, anti-roll tanks can be used when the ship is not underway. Our objective is to develop design procedures for passive tanks for roll reduction in rough seas. To this end, we develop an improved model of the passive tank-liquid motion in this paper. This tank consists of U-shaped tubes placed side by side along the length of the ship. The equations of six-degrees-of-motion (6DOF) that govern the tank-liquid are coupled with those that govern the 6DOF motion of the ship, and all of the equations are integrated simultaneously in the time domain using the Large Amplitude Motion Program (“LAMP”). LAMP is a three-dimensional time-domain simulation of the motion of ships in waves. The unstabilized and stabilized roll motions of a S60-70 ship with forward speed and beam waves have been analyzed. For high-amplitude waves, the variation of the roll angle with the encounter-wave frequency exhibits typical nonlinear phenomena: a shift in the resonance frequency, multi-valued responses, and jumps. The performance of passive tanks on a S60-70 ship with forward speed is investigated in an irregular sea with different encounter-wave directions. It is found that passive anti-roll tanks tuned in the nonlinear range are very effective in reducing the roll motion. The effect of the tank mass and distribution of tank tubes on the performance of the tank system is studied. Also, it is found that passive anti-roll tanks are very effective in reducing the roll motion in sea state five of a ship whose pitch frequency is nearly twice its roll frequency.

Approximation of Higher-Order Derivatives of the Frequency Domain Free Surface Green Function

2015 ◽  
Author(s):  
Yuyun Shi ◽  
Hui Li ◽  
Zhifu Li ◽  
Huilong Ren
Keyword(s):  
Free Surface ◽  
Green Function ◽  
Frequency Domain ◽  
Higher Order ◽  
Boundary Element Methods ◽  
Source Distribution ◽  
Chebyshev Series ◽  
Surface Green Function ◽  
The Green Function ◽  
Derivatives Of

The higher-order derivatives of the free-surface Green Function are critically important in three-dimensional frequency-domain boundary element methods using mixed dipole-source distribution. To improve the accuracy and efficiency of numerical schemes, the computing domain is divided into five areas. Derivatives in four areas are calculated analytically since the Green function is defined analytically. The 5th area is divided into a number of sub-areas in which truncated Double Chebyshev series are used to approximate the Green function. Unlike the usual way in which the derivatives of Green function are obtained by differentiating the series, we re-approximate the derivatives by new Chebyshev series with new coefficients. Numerical results show that the new series are more accurate, in particular, second order derivatives.

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