The Effect of the Steady Flow Potential on the Motions of a Moving Ship in Waves

A three-dimensional method to analyze the motions of a ship running in waves is presented, including the effects of the steady-flow potential. Basically, the general formulations are based on the source distribution technique by which the ship hull surface is regarded as the assembly of many panels. The present study includes three algorithms for treating the corresponding Green function:the Hess & Smith algorithm for the part of simple source I/r,the complex plane contour integral of the Shen & Farell algorithm for the double integral of steady flow, andthe series expansions of the Telste & Noblesse algorithm for the Cauchy principal value integral of unsteady flow. The study reveals that the effect of steady flow on ship motions is generally small, but it still cannot be neglected in some cases, especially for the ship running in oblique waves. The effect also depends on the fore-aft configuration of the ship. The results predicted by the present method are found to be in fairly good agreement with existing experiments and other theories.

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Calculation and Analysis of Components of Added Resistance of Ships in Waves

10.5957/wmtc-2015-100 ◽

2015 ◽

Author(s):

Hong Liang ◽

Zhu Chuan ◽

Miao Ping

Keyword(s):

Frequency Domain ◽

Present Method ◽

Three Dimensional ◽

Wave Resistance ◽

Source Distribution ◽

Ship Motions ◽

Hydrodynamic Coefficients ◽

Added Resistance ◽

Distribution Method ◽

Different Types

Ship motions and its hydrodynamic coefficients are solved by three dimensional frequency domain potential theories with a translating and pulsating source distribution method. Furthermore, components of added wave resistance of ships advancing in waves due to the radiation and diffraction waves are obtained respectively. Added wave resistances of Wigley III hull and S175 containership with various forward speeds are carried out and analyzed in frequency domain. The numerical results are validated for the models by comparing them with experimental data. Its percentage of components of the total ship added wave resistance varying with frequency is investigated and discussed. The present method provides a rapid and efficient approach to predict added resistance of different types of ships in waves.

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The Prediction of the Added Resistance for the Trimaran Ship With Different Side Hull Arrangements in Waves

Journal of Ship Research ◽

10.5957/jsr.2009.53.4.227 ◽

2009 ◽

Vol 53 (04) ◽

pp. 227-235

Author(s):

Ming-Chung Fang ◽

Yi-Chin Wu ◽

Deng-Kai Hu ◽

Zi-Yi Lee

Keyword(s):

Steady State ◽

Steady Flow ◽

Three Dimensional ◽

Prediction Method ◽

Source Distribution ◽

Added Resistance ◽

Distribution Method ◽

Related Data ◽

Head Waves ◽

Flow Potential

In this paper, a second-order steady-state approach and a three-dimensional pulsating source distribution method are applied to derive the added resistance on a trimaran ship advancing in waves. The added resistance treated here is the secondorder steady-state hydrodynamic force, which can be expressed as products of the ship-motion responses, the radiation potential, diffraction potential, and the incident wave potential, and all related velocity potentials are in three-dimensional form. The steady flow potential is also included in the motion response calculation to investigate its effect on the added resistance. In order to validate the prediction method, the experiments for measuring the added resistance of a trimaran model in head waves were also handled in a National Cheng Kung University (NCKU) towing tank, and the related data are adopted to compare with the theoretical results. The comparisons show that the prediction results obtained in the paper generally agree well with experimental data; the validity of the prediction method applied here can be regarded as acceptable, and the effect of the steady flow potential on the added resistance of the trimaran ship can be neglected.

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3D Vibration Analysis of Hermetic Capsules by Using Ritz Method

International Journal of Structural Stability and Dynamics ◽

10.1142/s0219455417500407 ◽

2017 ◽

Vol 17 (03) ◽

pp. 1750040

Author(s):

Jae-Hoon Kang

Keyword(s):

Eigenvalue Problem ◽

Free Vibration ◽

Vibration Analysis ◽

Legendre Polynomials ◽

Present Method ◽

Ritz Method ◽

Three Dimensional ◽

Dynamic Equations ◽

Vibration Frequencies ◽

Good Agreement

A three-dimensional (3D) method of analysis is presented for determining the free vibration frequencies of a hermetic capsule comprising a cylinder closed with hemi-ellipsoidal caps at both ends. Unlike conventional shell theories, which are mathematically 2D, the present method is based upon the 3D dynamic equations of elasticity. Displacement components [Formula: see text], [Formula: see text], and [Formula: see text] in the radial, circumferential, and axial directions, respectively, are taken to be periodic in [Formula: see text] and in time, and the Legendre polynomials in the r and z directions instead of ordinary ones. Potential (strain) and kinetic energies of the hermetic capsule are formulated, and the Ritz method is used to solve the eigenvalue problem, thereby yielding upper bound values of the frequencies. As the degree of the Legendre polynomials is increased, frequencies converge to the exact values. Typical convergence studies are carried out for the first five frequencies. The frequencies from the present 3D method are in good agreement with those obtained from other 3D approach and 2D shell theories proposed by previous researchers.

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Motion Prediction of the Ship With Sloshing Tanks

Volume 4: Ocean Engineering; Ocean Renewable Energy; Ocean Space Utilization, Parts A and B ◽

10.1115/omae2009-80118 ◽

2009 ◽

Author(s):

Kang Zou ◽

Quan-ming Miao ◽

Ren-qing Zhu

Keyword(s):

Time Domain ◽

Three Dimensional ◽

Panel Method ◽

Ship Motion ◽

Motion Prediction ◽

Ship Motions ◽

Motion Responses ◽

Motion Problem ◽

Good Agreement

Sloshing flow in ship tanks is excited by ship motions, but it affects the ship motions in reverse. This paper focuses on the motion responses of the ship in waves with consideration of coupled effects with sloshing in tanks. A three-dimensional panel method in time-domain is applied to solve the ship motion problem, and the sloshing tanks are solved by commercial CFD software simultaneously. Experiments were carried out on a SL175 ship and good agreement is obtained.

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Hydrodynamic Analysis of Trimaran Vessels

Polish Maritime Research ◽

10.2478/v10012-007-0046-5 ◽

2008 ◽

Vol 15 (1) ◽

pp. 11-18 ◽

Cited By ~ 8

Author(s):

M. Javanmardi ◽

E. Jahanbakhsh ◽

M. Seif ◽

H. Sayyaadi

Keyword(s):

Present Method ◽

Three Dimensional ◽

Solution Algorithm ◽

Body Motion ◽

Hydrodynamic Resistance ◽

Hydrodynamic Behavior ◽

Hydrodynamic Analysis ◽

Hydrodynamic Simulations ◽

Two Phases ◽

Good Agreement

Hydrodynamic Analysis of Trimaran Vessels Trimaran vessels are developed for different applications and hydrodynamic behavior of such vessels is different than usual mono-hulls. In this paper hydrodynamic resistance and maneuvering of a trimaran with Wigley body form are investigated. The effects of outriggers position in four different longitudinal and two transverse locations are studied. For hydrodynamic simulations a CFD code has been developed and used. This code is capable for simulating three dimensional, time dependent, two phases, viscous flow coupled with rigid body motion. Formulation and solution algorithm are described in detail. Different case studies have been performance and numerical results have shown good agreement with experimental data. Based on resistance and maneuvering simulation of the trimaran vessels different conclusion are made. The results show that positions of outriggers have great effect on resistance and maneuverability of trimaran. The present method can be further employed to investigate other hydrodynamic qualities of trimaran vessels.

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Numerical Study of a Conjecture in the Self-avoiding Random Walk Problem

Australian Journal of Physics ◽

10.1071/ph730207 ◽

1973 ◽

Vol 26 (2) ◽

pp. 207 ◽

Cited By ~ 11

Author(s):

AJ Guitmann ◽

MF Sykes

Keyword(s):

Random Walk ◽

Numerical Study ◽

Three Dimensional ◽

The Self ◽

Series Expansions ◽

Honeycomb Lattice ◽

Exact Inequality ◽

Good Agreement

It has been conjectured that the sum of the critical attritions p. and v of a selfavoiding random walk on a triangular and a honeycomb lattice respectively should be precisely six. Estimates of the critical attrition obtained from the analysis of exact series expansions support this conjecture. Assuming the conjecture, estimates of the two critical attritions are made and found to be in good agreement with those obtained by other methods. The exact inequality v2 ~ p.2/(1 + p.) is proved, and it is shown that an analogous inequality applies to a pair of three-dimensional lattices.

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On Three-Dimensional Solutions of Drift Forces and Moments Between Two Ships in Waves

Journal of Ship Research ◽

10.5957/jsr.2002.46.4.280 ◽

2002 ◽

Vol 46 (04) ◽

pp. 280-288

Author(s):

Ming-Chung Fang ◽

Gung-Rong Chen

Keyword(s):

Numerical Solutions ◽

Three Dimensional ◽

Source Distribution ◽

Regular Waves ◽

Lateral Drift ◽

Expansion Technique ◽

Present Technique ◽

Principal Value ◽

Incident Waves ◽

Drift Forces

A far-held approach solving the lateral drift forces and moments between two ships in regular waves is adopted. The velocity potentials for diffraction and radiation based on a 3-D-source distribution technique are obtained. Using the Telste & Noblesse algorithm with a series expansion technique for the principal value integral solves the numerical solutions for corresponding Green functions and their derivatives. One pair of ship models is used for numerical calculations and a 2-D method based on the near-held approach is also included for comparisons. Generally the results obtained by the present technique indicate that the interaction effects between two ships have a profound influence on the drift forces and moments, and the direction of incident waves plays an important role. The results also show that the values predicted by the 2-D method are always very much overestimated because of the trapping energy between two ships. Therefore, the 3-D method prediction model developed here is regarded as more physically reasonable than the 2-D one.

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Three-Dimensional Rotational Flow in Transonic Turbomachines: Part II—Full Three-Dimensional Flow in CAS Rotor Obtained by Using a Number of S1 and S2 Stream Filaments

Journal of Turbomachinery ◽

10.1115/1.2927997 ◽

1992 ◽

Vol 114 (1) ◽

pp. 50-60

Author(s):

Wu Chung-Hua ◽

Zhao Xiaolu ◽

Qin Lisen

Keyword(s):

Transonic Flow ◽

Present Method ◽

Three Dimensional ◽

Flow Fields ◽

Rotational Flow ◽

Three Dimensional Flow ◽

Measured Velocity ◽

Dimensional Flow ◽

Iterative Calculation ◽

Good Agreement

The general theory for three-dimensional flow in subsonic and supersonic turbo-machines has recently been extended to transonic turbomachines. In this paper, which is Part II of the study, quasi- and full three-dimensional solutions of the transonic flow in the CAS rotor are presented. The solutions are obtained by iterative calculation between a number of S1 stream filaments and, respectively, a central S2m Stream filament and a number of S2 stream filaments. Relatively simple methods developed recently for solving the transonic flow along S1 and S2 stream filaments are used in the calculation. The three-dimensional flow fields in the CAS rotor obtained by the present method are presented in detail with special emphasis on the converging process for the configuration of the S1 and S2 stream filaments. The three-dimensional flow fields obtained in the quasi- and full three-dimensional solutions are quite similar, but the former gives a lower peak Mack number and a smaller circumferential variation in Mach number than the latter. A comparison between the theoretical solution and the Laser-2-Focus measurement shows that the character of the transonic flow including the three-dimensional shock structure is in good agreement, but the measured velocity is slightly higher than the calculated one over most of the flow field.

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Three-Dimensional Investigation of the Stokes Eigenmodes in Hollow Circular Cylinder

Advances in Acoustics and Vibration ◽

10.1155/2013/857821 ◽

2013 ◽

Vol 2013 ◽

pp. 1-15

Author(s):

Adil El Baroudi ◽

Fulgence Razafimahery

Keyword(s):

Present Method ◽

Numerical Solutions ◽

Three Dimensional ◽

Finite Depth ◽

Navier Stokes ◽

Navier Stokes Equation ◽

Element Analysis ◽

Fluid Medium ◽

Stokes Eigenmodes ◽

Good Agreement

This paper studies the influence of boundary conditions on a fluid medium of finite depth. We determine the frequencies and the modal shapes of the fluid. The fluid is assumed to be incompressible and viscous. A potential technique is used to obtain in three-dimensional cylindrical coordinates a general solution for a problem. The method consists in solving analytically partial differential equations obtained from the linearized Navier-Stokes equation. A finite element analysis is also used to check the validity of the present method. The results from the proposed method are in good agreement with numerical solutions. The effect of the fluid thickness on the Stokes eigenmodes is also investigated. It is found that frequencies are strongly influenced.

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