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

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.

A Strip Method for Lateral Drift Force of a Semisubmersible

1985 ◽  
Vol 107 (3) ◽  
pp. 329-334
Author(s):  
C. H. Kim ◽  
W. Bao
Keyword(s):  
Experimental Data ◽  
Hydrodynamic Interaction ◽  
Three Dimensional ◽  
Source Distribution ◽  
Regular Waves ◽  
Dimensional Theory ◽  
Lateral Drift ◽  
Drift Force ◽  
Twin Hulls ◽  
Drift Forces

This paper presents the results of an application of a strip technique for the prediction of the lateral drift forces on a semisubmersible platform floating in oblique regular waves. The method employs Maruo’s formula and source distribution technique, without taking account of the hydrodynamic interaction between the twin hulls and columns of the semisubmersible. Overall the strip technique shows a more favorable correlation with the experimental data than the three-dimensional theory. It is, however, premature to conclude that the technique has been fully validated.

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

2000 ◽  
Vol 44 (01) ◽  
pp. 14-32
Author(s):  
Ming-Chung Fang
Keyword(s):  
Steady Flow ◽  
Present Method ◽  
Three Dimensional ◽  
Source Distribution ◽  
Series Expansions ◽  
Ship Motions ◽  
Double Integral ◽  
Flow Potential ◽  
Principal Value ◽  
Good Agreement

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.

Benchmark Tests of Two Body Interaction in Waves

2017 ◽  
Author(s):  
Wei Qiu ◽  
Jean-Marc Rousset ◽  
Heather Peng ◽  
Wei Meng ◽  
Boris Horel
Keyword(s):  
Numerical Solutions ◽  
Ocean Engineering ◽  
Regular Waves ◽  
Towing Tank ◽  
Benchmark Data ◽  
Benchmark Tests ◽  
Wave Basin ◽  
Close Proximity ◽  
Two Bodies ◽  
Drift Forces

As part of the test campaign led by the 27th ITTC Ocean Engineering Committee to produce reliable experimental benchmark data for multiple-body interactions in waves, model tests of two identical models in close proximity were carried out at the towing tank of Memorial University, Canada and at the wave basin of Ecole Centrale de Nantes, France. This paper presents the experimental results for the two bodies in regular waves with various gaps. The experimental data, including motions of two bodies, wave elevations in the gap and drift forces, were compared with numerical solutions based on the potential-flow solution.

A Numerical Investigation Into Hydrodynamic Interaction Coefficients for Multiple Freely Floating Bodies in Waves

2020 ◽  
Author(s):  
Mir Tareque Ali
Keyword(s):  
Hydrodynamic Interaction ◽  
Three Dimensional ◽  
Computer Code ◽  
Source Distribution ◽  
Hydrodynamic Coefficients ◽  
Body System ◽  
Regular Waves ◽  
Floating Bodies ◽  
Interaction Coefficients ◽  
Multi Body

Abstract When two or more bodies are floating in waves in each other’s vicinity, the fluid loading on the separate bodies will be influenced by the presence of the neighboring bodies. The wave loads on each body are affected, because of sheltering or wave-reflection effects due to the presence of surrounding floating body, while additional loads are exerted by the radiated waves, which are produced by the motions of the neighboring bodies. For a multi-body system, it is important to accurately compute the hydrodynamic coefficients and interaction coefficients, since these parameters will be used later to solve the 6xN simultaneous equations to predict the motion responses (where N is the number of freely floating bodies in the multi-body system). This paper aims to investigate the hydrodynamic interaction coefficients for two three dimensional (3-D) bodies floating freely in each other’s vicinity. Since the nature of hydrodynamic interaction is rather complex, it is usually recommended to study this complicated phenomenon using numerically accurate scheme. A computer code developed using 3-D source distribution method which is based on linear three-dimensional potential theory is used and the validation of the computer code has been justified by comparing the present results with that of the published ones for hydrodynamic coefficients and interaction coefficients of two bodies closely floating in regular waves. The calculated results for box-cylinder model are compared with the published results and the agreement is quite satisfactory. Numerical simulations are further conducted for two closely floating rectangular barges of side-by-side position in regular waves. During the computations of hydrodynamic coefficients and interaction coefficients for multi-body model, the separation distance between the floating bodies have been varied. Finally, some conclusions are drawn on the basis of the present analysis.

Interactions of a horizontal flexible membrane with oblique incident waves

1998 ◽  
Vol 367 ◽  
pp. 139-161 ◽  
Author(s):  
I. H. CHO ◽  
M. H. KIM
Keyword(s):  
Eigenfunction Expansion ◽  
Numerical Solutions ◽  
Domain Boundary ◽  
Expansion Method ◽  
Analytic Solutions ◽  
Source Distribution ◽  
Two Dimensional ◽  
Flexible Membrane ◽  
Eigenfunction Expansion Method ◽  
Incident Waves

The interaction of oblique monochromatic incident waves with a horizontal flexible membrane is investigated in the context of two-dimensional linear hydro-elastic theory. First, analytic diffraction and radiation solutions for a submerged impermeable horizontal membrane are obtained using an eigenfunction expansion method. Secondly, a multi-domain boundary element method (BEM) is developed to confirm the analytic solutions. The inner solution based on a discrete membrane dynamic model and simple-source distribution over the entire fluid boundaries is matched to the outer solution based on an eigenfunction expansion. The numerical solutions are in excellent agreement with the analytic solutions. The theoretical prediction was then compared to a series of experiments conducted in a two-dimensional wave tank at Texas A&M University. The measured reflection and transmission coefficients reasonably follow the trend of predicted values. Using the computer program developed, the performance of surface-mounted or submerged horizontal membrane wave barriers is tested with various system parameters and wave characteristics. It is found that the horizontal flexible membrane can be an effective wave barrier if properly designed.

Treatment of Separated Flow in Cascades by a Source Distribution

1976 ◽  
Vol 190 (1) ◽  
pp. 489-501 ◽  
Author(s):  
J. W. Railly
Keyword(s):  
Numerical Solutions ◽  
Three Dimensional ◽  
Sheet Thickness ◽  
Pressure Rise ◽  
Separated Flow ◽  
Leading Edge ◽  
Suction Side ◽  
Source Distribution ◽  
Thickness Variation ◽  
Starting Point

Provided that separation on the blades of a cascade takes place aft of the leading edge, the hypothesis that suction side velocity outside of an enlarged boundary layer remains constant is used as the starting point in a potential flow solution assuming that blades and enlarged bounary layers are thin compared with chord. Representing thickness, boundary layers and wake by a source distribution, an integral equation for the latter is deduced and numerical solutions are found for a nearly two-dimensional rotating radial impeller for various diffusion ratios on the suction side of the blades. The method is valid, incompressible flow for any blade-to-blade surface that is a surface of revolution and in the presence of stream sheet thickness variation. The theory is compared with experiments conducted on a radial impeller and good agreement with velocity distribution and impeller tip pressure rise is shown. Predictions of blade work may be obtained using a shape factor found from the experiment but loss coefficient predictions are too low. The conclusion is drawn that a three-dimensional influence is involved in the displacement growth on the impeller blades.

Hydrodynamic Forces and Motions of a Cylinder Near a Vertical Wall

1992 ◽  
Vol 36 (03) ◽  
pp. 248-254 ◽  
Author(s):  
Edward M. Lewandowski
Keyword(s):  
Vertical Wall ◽  
Finite Depth ◽  
Lateral Force ◽  
Hydrodynamic Forces ◽  
Regular Waves ◽  
Physical Explanation ◽  
Lateral Drift ◽  
The Mean ◽  
Incident Waves ◽  
The Waves

A method for the evaluation of the hydrodynamic forces and moment on a cylinder, located near a vertical wall in water of finite depth, in regular waves, is presented. The method is applied to the simple case of a circular cylinder. The motions of the cylinder and the mean lateral drift force due to the waves are also evaluated. The presence of the wall is shown to have a pronounced effect on the added-mass and damping coefficients of the cylinder in a certain frequency range; the mean lateral force may become negative (directed toward the incident waves) in this range. A simple physical explanation for the results is provided.

Numerical solutions for strain-softening surrounding rock under three-dimensional principal stress condition

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Sheng Yu-ming ◽  
Li Chao ◽  
Xia Ming-yao ◽  
Zou Jin-feng
Keyword(s):  
Finite Element ◽  
Principal Stress ◽  
Stress Condition ◽  
Strain Softening ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Strength Criterion ◽  
Surrounding Rock ◽  
Flow Rule ◽  
Finite Element Software

Abstract In this study, elastoplastic model for the surrounding rock of axisymmetric circular tunnel is investigated under three-dimensional (3D) principal stress states. Novel numerical solutions for strain-softening surrounding rock were first proposed based on the modified 3D Hoek–Brown criterion and the associated flow rule. Under a 3D axisymmetric coordinate system, the distributions for stresses and displacement can be effectively determined on the basis of the redeveloped stress increment approach. The modified 3D Hoek–Brown strength criterion is also embedded into finite element software to characterize the yielding state of surrounding rock based on the modified yield surface and stress renewal algorithm. The Euler implicit constitutive integral algorithm and the consistent tangent stiffness matrix are reconstructed in terms of the 3D Hoek–Brown strength criterion. Therefore, the numerical solutions and finite element method (FEM) models for the deep buried tunnel under 3D principal stress condition are presented, so that the stability analysis of surrounding rock can be conducted in a direct and convenient way. The reliability of the proposed solutions was verified by comparison of the principal stresses obtained by the developed numerical approach and FEM model. From a practical point of view, the proposed approach can also be applied for the determination of ground response curve of the tunnel, which shows a satisfying accuracy compared with the measuring data.

Three-Dimensional Vibration Analysis of Twisted Cylinder With Sectorial Cross Section

2013 ◽  
Vol 80 (2) ◽  
Author(s):  
D. Zhou ◽  
S. H. Lo
Keyword(s):  
Cross Section ◽  
Chebyshev Polynomial ◽  
Numerical Solutions ◽  
Twist Angle ◽  
Ritz Method ◽  
Three Dimensional ◽  
Cylindrical Domain ◽  
Linear Elasticity Theory ◽  
Boundary Functions ◽  
Polynomial Series

The three-dimensional (3D) free vibration of twisted cylinders with sectorial cross section or a radial crack through the height of the cylinder is studied by means of the Chebyshev–Ritz method. The analysis is based on the three-dimensional small strain linear elasticity theory. A simple coordinate transformation is applied to map the twisted cylindrical domain into a normal cylindrical domain. The product of a triplicate Chebyshev polynomial series along with properly defined boundary functions is selected as the admissible functions. An eigenvalue matrix equation can be conveniently derived through a minimization process by the Rayleigh–Ritz method. The boundary functions are devised in such a way that the geometric boundary conditions of the cylinder are automatically satisfied. The excellent property of Chebyshev polynomial series ensures robustness and rapid convergence of the numerical computations. The present study provides a full vibration spectrum for thick twisted cylinders with sectorial cross section, which could not be determined by 1D or 2D models. Highly accurate results presented for the first time are systematically produced, which can serve as a benchmark to calibrate other numerical solutions for twisted cylinders with sectorial cross section. The effects of height-to-radius ratio and twist angle on frequency parameters of cylinders with different subtended angles in the sectorial cross section are discussed in detail.

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