A Numerical Calculation of Hydrodynamic Forces on a Seagoing Ship by 3-D Source Technique With Forward Speed

2004 ◽  
Author(s):  
Yoshiyiki Inoue ◽  
Md. Kamruzzaman
Keyword(s):  
Free Surface ◽  
Velocity Potential ◽  
Hydrodynamic Forces ◽  
The Body ◽  
Source Distribution ◽  
Accurate Estimation ◽  
Forward Speed ◽  
Surface Ship ◽  
Wave Patterns ◽  
Wigley Hull

In this paper, the hydrodynamic forces of a surface ship advancing in waves at constant forward speed are numerically calculated by using the 3-D source distribution techniques. The paper also deals with the numerical calculations of free surface flow around an advancing ship in calm water as well as in waves. The body boundary condition is linearised about the undisturbed position of the body and the free surface condition is linearised about the mean water surface. The potential is represented by a distribution of sources over the surface of the ship and its waterline. The problem is solved by the method of singularities distributed over the hull surface. Hess & Smith method is used to obtain the density of these singularities. The numerical solution of the surface ship case is approximately obtained by considering the hull as a position of plane polygonal elements, bearing a constant singularity distribution. The velocity potential of any particular point in the free surface around the moving hull is determined by using the 3-D Green function with forward speed which satisfies the boundary conditions for a pulsating source in the fluid. Contours of wave patterns around moving surface ships are calculated from the velocity potential. The numerical accuracy of the computer code is firstly checked by calculating the velocity potential of a translating, pulsating unit source with arbitrary frequency and forward speed. Free surface wave patterns generated by a Wigley hull advancing with steady forward speed are calculated by using this code. Some corresponding hydrodynamic coefficients of heave and pitch modes for the Wigley hull has been calculated. Exciting forces and motion amplitudes are also investigated. The numerical result of this code is validated by comparing the calculated results with the experimental ones and those calculated by other methods. From the comparison, the results predicted by the present calculations are found in fairly good agreement with the experiment. Finally, the effects of motion amplitude on the free surface elevation are analyzed. These will be helpful for the accurate estimation of sea keeping problems for a ship advancing in waves.

Lifting Effects for Wave Resistance or Sea-Keeping Calculations

2002 ◽  
Author(s):  
Jean Philippe Boin ◽  
Michel Guilbaud ◽  
Malick Ba
Keyword(s):  
Free Surface ◽  
Green Function ◽  
Surface Condition ◽  
The Body ◽  
Source Distribution ◽  
Diffraction Radiation ◽  
First Order ◽  
Wigley Hull ◽  
The Green Function ◽  
Sailing Boat

We present the introduction of lifting effects in a code of calculation [1–3] based on a first order panel method using the diffraction-radiation with forward speed Green function satisfying a linearised free-surface condition and the radiation one. A mixed formulation has been used with a source distribution on the hull and a doublet one on the plane of symmetry and the wake of lifting parts of the body, leading to an integral equation derived from the 3 rd Green identity. The Green function and its derivatives are not computed but are directly integrated on elementary panels, segments or semi-infinite strips. Results are presented for semi-submerged ellipsoid, rectangular surface-piercing bodies, Wigley hull, Series 60 ship, sailing boat and military 5415 hull. Global forces, moments but also free surface elevations are compared with the results of other methods and with measurements, either in steady or in unsteady flows in the frequency domain.

Hydrodynamic Forces on a Marine Riser: A Velocity-Potential Method

1982 ◽  
Vol 104 (1) ◽  
pp. 53-57 ◽  
Author(s):  
J. S. Chung
Keyword(s):  
Free Surface ◽  
Velocity Potential ◽  
Potential Method ◽  
Hydrodynamic Forces ◽  
Marine Riser ◽  
Morison Equation ◽  
Wave Damping ◽  
Drag Forces ◽  
Vessel Motion ◽  
Semi Empirical

A linear equation is mathematically derived for hydrodynamic forces on a marine riser under effects of free surface and floating-vessel motion using a velocity-potential method. It accounts for inertia and wave damping forces, including the force caused by riser motion, and empirically includes the drag force caused by viscosity. The equation, when reduced to a simpler form, is basically identical to the semi-empirical Morison equation for the inertia and drag forces. Theoretical validity of the simpler equation and the Morison equation is discussed. Previously, practical, semi-empirical force equations on the riser have been suggested, ignoring the effects of the free surface and the wave damping. The equations in current practice are compared with the present simpler equation.

Three-Dimensional Large Amplitude Body Motions in Waves

2007 ◽  
Author(s):  
Xinshu Zhang ◽  
Robert F. Beck
Keyword(s):  
Free Surface ◽  
Three Dimensional ◽  
Surface Boundary ◽  
Forward Speed ◽  
Time Step ◽  
Surface Boundary Conditions ◽  
Submerged Body ◽  
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 panels on the exact submerged body surface, the boundary integral equations are solved numerically 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 changing submerged body geometry. The desingularized method applied on the free surface produces non-singular kernels in the integral equations by moving the fundamental singularities a small distance outside of the fluid domain. Constant strength 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 proceed 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 with the experiments for both linear computations and body-exact computations.

scholarly journals Splash formation at the nose of a smoothly curved body in a stream

1999 ◽  
Vol 40 (4) ◽  
pp. 421-436 ◽  
Author(s):  
E. O. Tuck ◽  
S. T. Simakov
Keyword(s):  
Integral Equation ◽  
Free Surface ◽  
Velocity Potential ◽  
Integral Form ◽  
The Body ◽  
Front Face ◽  
Separation Condition ◽  
Polygonal Approximation ◽  
Side Condition ◽  
Two Dimensional Flow

AbstractIn two-dimensional flow past a body close to a free surface, the upwardly diverted portion may separate to form a splash. We model the nose of such a body by a semi-infinite obstacle of finite draft with a smoothly curved front face. This problem leads to a nonlinear integral equation with a side condition, a separation condition and an integral constraint requiring the far-upstream free surface to be asymptotically plane. The integral equation, called Villat's equation, connects a natural parametrisation of the curved front face with the parametrisation by the velocity potential near the body. The side condition fixes the position of the separation point, whereas the separation condition, known as the Brillouin-Villat condition, imposes a continuity relation to be satisfied at separation. For the described flow we derive the Brillouin-Villat condition in integral form and give a numerical solution to the problem using a polygonal approximation to the front face.

The hydrodynamic forces on a submerged sphere moving in a circular path

1990 ◽  
Vol 428 (1874) ◽  
pp. 215-227 ◽  
Keyword(s):  
Green Function ◽  
Body Surface ◽  
Velocity Potential ◽  
Surface Condition ◽  
Hydrodynamic Forces ◽  
Constant Angular Velocity ◽  
The Body ◽  
Circular Path ◽  
Legendre Functions ◽  
Submerged Sphere

Analytical solutions for various hydrodynamic problems are briefly reviewed. The case of a submerged sphere moving in a circular path at constant angular velocity is then analysed based on the linearized velocity potential theory. The potential is expressed by means of a Green function and a distribution of sources over the body surface, written in terms of Legendre functions. The coefficients in the series of the Legendre functions are obtained by imposing the body surface condition. Figures are provided showing the hydrodynamic forces on the sphere.

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.

Radiation and diffraction of second-order surface waves by floating bodies

1988 ◽  
Vol 196 ◽  
pp. 65-91 ◽  
Author(s):  
P. D. Sclavounos
Keyword(s):  
Free Surface ◽  
Linear Problem ◽  
Velocity Potential ◽  
Surface Condition ◽  
Second Order ◽  
The Body ◽  
Green Functions ◽  
Floating Bodies ◽  
Free Surface Condition ◽  
Body Boundary

The paper studies the radiation and diffraction by floating bodies of deep-water bichromatic and bidirectional surface waves subject to the second-order free-surface condition. A theory is developed for the evaluation of the second-order velocity potential and wave forces valid for bodies of arbitrary geometry, which does not involve the evaluation of integrals over the free surface or require an increased accuracy in the solution of the linear problem. Explicit sum- and difference-frequency ‘Green functions’ are derived for the radiation and diffraction problems, obtained from the solution of initial-value problems that ensure they satisfy the proper radiation condition at infinity. The second-order velocity potential is expressed as the sum of a particular and a homogeneous component. The former satisfies the non-homogeneous free-surface condition and is expressed explicitly in terms of the second-order Green functions. The latter is subject to the homogeneous free-surface condition and enforces the body boundary condition by the solution of a linear problem. An analysis is carried out of the singular behaviour of the second-order potential near the intersection of the body boundary with the free surface.

scholarly journals Wave forces on three-dimensional floating bodies with small forward speed

1991 ◽  
Vol 227 ◽  
pp. 135-160 ◽  
Author(s):  
Jan Nossen ◽  
John Grue ◽  
Enok Palm
Keyword(s):  
Velocity Potential ◽  
The Body ◽  
Wave Forces ◽  
Forward Speed ◽  
Floating Bodies ◽  
Wave Drift ◽  
Exciting Forces ◽  
Wave Exciting Forces ◽  
Wave Drift Damping ◽  
The Mean

A boundary-integral method is developed for computing first-order and mean second-order wave forces on floating bodies with small forward speed in three dimensions. The method is based on applying Green's theorem and linearizing the Green function and velocity potential in the forward speed. The velocity potential on the wetted body surface is then given as the solution of two sets of integral equations with unknowns only on the body. The equations contain no water-line integral, and the free-surface integral decays rapidly. The Timman-Newman symmetry relations for the added mass and damping coefficients are extended to the case when the double-body flow around the body is included in the free-surface condition. The linear wave exciting forces are found both by pressure integration and by a generalized far-field form of the Haskind relations. The mean drift force is found by far-field analysis. All the derivations are made for an arbitrary wave heading. A boundary-element program utilizing the new method has been developed. Numerical results and convergence tests are presented for several body geometries. It is found that the wave exciting forces and the mean drift forces are most influenced by a small forward speed. Values of the wave drift damping coefficient are computed. It is found that interference phenomena may lead to negative wave drift damping for bodies of complicated shape.

Radiation and diffraction of water waves by a submerged sphere at forward speed

1988 ◽  
Vol 417 (1853) ◽  
pp. 433-461 ◽  
Keyword(s):  
Water Waves ◽  
Velocity Potential ◽  
Surface Condition ◽  
Wave Resistance ◽  
The Body ◽  
Legendre Functions ◽  
Forward Speed ◽  
Submerged Sphere ◽  
Exciting Forces ◽  
Similar Equation

A submerged sphere advancing in regular deep-water waves at constant forward speed is analysed by linearized potential theory. A distribution of sources over the surface of the sphere is expanded into a series of Legendre functions, by extension of the method used by Farell ( J . Ship Res . 17, 1 (1973)) in analysing the wave resistance on a submerged spheroid. The equations governing the velocity potential are satisfied by use of the appropriate Green function and by choosing the coefficients in the series of Legendre functions such that the body surface condition is satisfied. Numerical results are obtained for the wave resistance, hydrodynamic coefficients and exciting forces on the sphere. Some theoretical aspects of a body advancing in waves are also discussed. The far-field equation of Newman ( J . Ship Res . 5, 44 (1961)) for calculation of the damping coefficients is extended, and a similar equation for the exciting forces is derived.

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