Prediction of Wave-Induced Motions and Loads of Ships With Forward Speed by Matching Method

2020 ◽  
Author(s):  
Hui Li ◽  
Baoli Deng ◽  
Chunlei Liu ◽  
Jian Zou ◽  
Huilong Ren
Keyword(s):  
Green Function ◽  
Exterior Domain ◽  
Boundary Integral ◽  
Control Surface ◽  
Source Distribution ◽  
Forward Speed ◽  
Matching Method ◽  
Distribution Method ◽  
Interior Domain ◽  
Wave Induced

Abstract A novel matching method has been developed to solve the wave-induced motions and loads of ships with forward speed. The fluid domain is divided into two subdomains by a cylindrical control surface: an interior domain and an exterior domain. Unlike the conventional domain decomposition strategy, the control surface is meshless in present method, on which the physical quantities are expanded into Fourier-Laguerre series. Based on forward speed Green function, the source distribution method is adopted to solve the exterior domain. The calculations of boundary integral equation about forward speed Green function over the control surface are performed analytically, and the solution of exterior domain provides a Dirichlet-to-Neumann (DN) relation on the control surface. In the interior domain, the boundary value problem is solved by Rankine source method. In order to be consistent with exterior solution, the control surface is kept meshless. The ship hull is discretized into constant panels. The free-surface is discretized into cubic B-splines to represent the high-order derivatives of velocity potential precisely. Then, the DN relation is used to close the equation system established in the interior domain. Comparisons with known experimental measurements show that the calculations achieve good accuracy. Furthermore, the influences of numerical method used in the exterior domain are described.

Zero Speed Rankine-Kelvin Hybrid Method With a Cylinder Control Surface

2015 ◽  
Author(s):  
Hui Li ◽  
Hao Lizhu ◽  
Huilong Ren ◽  
Xiaobo Chen
Keyword(s):  
Free Surface ◽  
Green Function ◽  
Hybrid Method ◽  
Exterior Domain ◽  
Control Surface ◽  
Surface Boundary ◽  
Rankine Source ◽  
Free Surface Boundary Condition ◽  
Interior Domain ◽  
The Green Function

The solution of hydrodynamic problem with forward speed still has some well-known problems such as high oscillation and slow convergence of the wave term when using a moving and oscillating source as the Green function. Recently, Ten and Chen (2010) has come up with a new method to benefit the merits of both the Rankine source and moving and oscillating source by taking a hemisphere as the control surface which separates the fluid region into two domains, but some troubles have been induced in the process of solution. Therefore, in this paper, a cylindrical surface instead of a hemisphere is selected to be the control surface to make the solution easy, and in this method, the control surface isn’t divided into panels. In the interior domain near the ship, the Rankin Green function is used to simplify the calculation. In the exterior domain some distance from the ship, there is no panels representing the free surface by using the Green function which satisfy the free surface boundary condition. The whole fluid region matches by the condition that the velocity potentials and their normal derivatives in the interior domain and exterior domain are equal on the control surface separately. In this paper, we have validated the Rankine-Kelvin hybrid method is applicable by adopting it to solve the zero speed problem in this work.

Prediction of Wave-Induced Motions and Loads of Ships With Forward Speed by Matching Method

2021 ◽  
Author(s):  
Hui Li ◽  
Baoli Deng ◽  
Chunlei Liu ◽  
Jian Zou ◽  
Huilong Ren
Keyword(s):  
Forward Speed ◽  
Matching Method ◽  
Wave Induced

Efficient Methods for Hydroelastic Analysis of Very Large Floating Structures

1993 ◽  
Vol 37 (01) ◽  
pp. 58-76 ◽  
Author(s):  
R. C. Ertekin ◽  
H. R. Riggs ◽  
X. L. Che ◽  
S. X. Du
Keyword(s):  
Green Function ◽  
Function Method ◽  
Source Distribution ◽  
Fluid Loading ◽  
Floating Structure ◽  
Distribution Method ◽  
Green Function Method ◽  
Structural Deformations ◽  
Hydroelastic Analysis ◽  
The Green Function

The linear hydroelastic response of a very large floating structure (VLFS) consisting of multiple modules is studied theoretically, following a review of the past work on hydroelasticity in fluid-structure interaction. The 3-dimensional Green function method and Morison's equation approach are used to determine the fluid loading in conjunction with two different hydroelastic models. The first method uses a rigid module, flexible connector model in which the hydrodynamic interaction between rigid modules is taken into account. The double composite source distribution method, which is a numerically efficient implementation of the Green function method that exploits double symmetry of the structure in the longitudinal and lateral directions, is used to reduce computations. In the second method, fully elastic modules are considered. In this approach, the fluid loading is obtained by Morison's equation, and the structure is modeled by frame finite elements. The predictions for the rigid-body motions and structural deformations, as well as module-connector loads, obtained by the two different methods are compared. The proposed methods of hydroelasticity have been used to predict the response of a 16-module VLFS, 100 m by 1600 m. Both methods are sufficiently efficient to allow the analysis of even larger VLFS.

A New Slender-Ship Theory Valid for all Oscillatory Frequencies and Forward Speeds

2013 ◽  
Author(s):  
Masashi Kashiwagi ◽  
Xin Wang
Keyword(s):  
Green Function ◽  
Present Theory ◽  
Added Mass ◽  
Source Distribution ◽  
Unified Theory ◽  
Forward Speed ◽  
Radiation Problem ◽  
Damping Coefficients ◽  
Radiation Wave ◽  
The Green Function

A new theory is presented for the radiation problem of heave and pitch of a slender ship advancing at arbitrary forward speed. The theory has no restriction on the order of forward speed and oscillation frequency. The general inner solution is constructed by the source distribution with Green function over the ship’s hull surface plus a line distribution along the ship’s centerline on the free surface with the radiation-wave related residue part of the Green function. By matching the inner solution with the outer solution, the source strengths on both hull surface and line distribution can be obtained. Numerical results of the added-mass and damping coefficients based on the present theory are shown for two modified Wigley models and compared with the unified theory and experiment results.

scholarly journals Motion Simulation of a Fine Shaped Vessel at Hiron Point in the Bay of Bengal

1970 ◽  
Vol 2 (2) ◽  
pp. 25-40
Author(s):  
M Rafiqul Islam ◽  
Md Munir Hassan ◽  
Md Sdaiqul Baree
Keyword(s):  
Mathematical Model ◽  
Bay Of Bengal ◽  
Wave Spectrum ◽  
Research Work ◽  
Irregular Waves ◽  
Source Distribution ◽  
Forward Speed ◽  
Distribution Method ◽  
Hydrodynamic Behaviour ◽  
Speed Effect

The hydrodynamic behaviour of a fast fine vessel is of great importance than that of a fuller vessel as the fast fine vessels are engaged for important operations. Moreover with the advent of modern computers, in ship hydrodynamics, 3-D source distribution method is gaining much popularity and normally applied for blocky hull. But in the case of finer hull, examples are rare especially considering forward speed effect. With these views in mind, in the present research work, effort has been given to develop a mathematical model for fine shape vessel to predict and simulate her motions in irregular waves. A computer program has been developed on the basis of mathematical model and to examine the validity of the developed program, results for hydrodynamic coefficient and motions of a series 60 ship have been compared with Gerristma's experimental results and with the results based on other codes. After validation of the program, simulation of motions of an existing the fine shape ship has been carried out at Hiron point of the Bay of Bengal by utilizing hydrodynamic coefficients and wave exciting forces and moments obtained in regular waves and a new wave spectrum formula based on wave data at the concerned location. On the basis of the results presented, it may be concluded that the developed model based on 3-D distribution technique can be applied for prediction of motion of fine shape ship with forward speed effect. Moreover limitations of operation of the vessel have been demonstrated at various combinations of significant wave heights and speeds. doi:10.3329/jname.v2i2.1870  Journal of Naval Architecture and Marine Engineering 2(2005) 25-40

The Computation of Higher Order Derivatives of Velocity Potential Based on B Spline Function

2016 ◽  
Author(s):  
Hui Li ◽  
Hao Lizhu ◽  
Huilong Ren ◽  
Xiao-bo Chen ◽  
Fang Li
Keyword(s):  
Free Surface ◽  
Velocity Potential ◽  
Numerical Solutions ◽  
Second Order ◽  
Control Surface ◽  
Cylinder Surface ◽  
Matching Method ◽  
B Spline ◽  
Interior Domain ◽  
Derivatives Of

When solving the forward speed hydrodynamic problem in frequency domain adopting the matching method with a meshless cylinder surface as the control surface, the simple Green function is used in the interior domain. To tackle the integration containing the first and second order derivatives of velocity potential on free surface about x, a method in which the velocity potential on the free surface and its derivatives are fitted by the cubic B spline is given, and the regular wave is chosen as the incident wave, and the theory solutions of its velocity potential and the first and second order derivatives about x are compared to the numerical solutions get from the cubic B spline.

Shallow-Water Effect on the Motions of Three-Dimensional Bodies in Waves

1987 ◽  
Vol 31 (01) ◽  
pp. 34-40
Author(s):  
Hideichi Endo
Keyword(s):  
Green Function ◽  
Shallow Water ◽  
Three Dimensional ◽  
Source Distribution ◽  
Linear Wave ◽  
Water Effect ◽  
Surface Source ◽  
Distribution Method ◽  
The Green Function ◽  
Shallow Water Effect

The motions of three-dimensional bodies of arbitrary shape freely floating in waves in shallow water are studied. The wave loads on and hydrodynamic forces of a rigid body are calculated by applying the surface source distribution method (Green's function method) in the framework of linear wave potential theory. Special attention is paid to the numerical evaluation of the Green function for finite water depth; namely, an improper integral containing a singularity in the Green function is obtained by Gauss-Laguerre quadrature, and the ∫1 lr* ds term obtained is by numerical quadrature. Computational results of wave exciting forces, hydrodynamic coefficients, and motions of freely floating structures in shallow and deep water are compared with those obtained in the literature. Furthermore, the shallow-water effect on the motions of a large structure is examined.

scholarly journals Computation of ship responses in waves using panel method

1970 ◽  
Vol 1 (1) ◽  
pp. 35-46 ◽  
Author(s):  
MN Islam ◽  
MR Islam ◽  
MS Baree
Keyword(s):  
Green Function ◽  
Degrees Of Freedom ◽  
Velocity Potential ◽  
Panel Method ◽  
Numerical Code ◽  
Source Distribution ◽  
Forward Speed ◽  
Six Degrees Of Freedom ◽  
Marine Engineering ◽  
Speed Effect

Hydrodynamic coefficients, Forces / Moments and Motions of a ship moving with a mean forward speed in six degrees of freedom are computed using Panel Method. In this study, an existing numerical model without speed consideration was modified by incorporating the speed parameters. Appropriate Green function was used to calculate the concern velocity potential. The accuracy of the developed numerical code employing the Panel Method has been validated by comparing the result with known/published results of a series 60 ship available in the literature. Based on the results presented in the paper, it can be concluded that the developed model is able to predict the responses of the ship with forward speed effect. Keywords: Motions, Green function, 3D Source distribution.   doi: 10.3329/jname.v1i1.2037 Journal of Naval Architecture and Marine Engineering 1(2004) 35-46

On modified Green functions in exterior problems for the Helmholtz equation

1982 ◽  
Vol 383 (1785) ◽  
pp. 313-332 ◽  
Keyword(s):  
Integral Equation ◽  
Green Function ◽  
Helmholtz Equation ◽  
Least Squares ◽  
Present Note ◽  
Boundary Integral ◽  
Green Functions ◽  
Exterior Problems ◽  
The Green Function ◽  
Definition Of

The question of non-uniqueness in boundary integral equation formu­lations of exterior problems for the Helmholtz equation has recently been resolved with the use of additional radiating multipoles in the definition of the Green function. The present note shows how this modification may be included in a rigorous formalism and presents an explicit choice of co­efficients of the added terms that is optimal in the sense of minimizing the least-squares difference between the modified and exact Green functions.

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.

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