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.

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.

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.

Nonlinear Ship Motions in the Time-Domain Using a Body-Exact Strip Theory

2008 ◽  
Author(s):  
Piotr J. Bandyk ◽  
Robert F. Beck
Keyword(s):  
Free Surface ◽  
Boundary Conditions ◽  
Time Domain ◽  
The Body ◽  
Ship Motions ◽  
Surface Boundary ◽  
Theory Approach ◽  
Offshore Structure ◽  
Time Step ◽  
Strip Theory

Modern offshore structure and ship design requires an understanding of responses in large seas. A nonlinear time-domain method may be used to perform computational analyses of these events. To be useful in preliminary design, the method must be computationally efficient and accurate. This paper presents a body-exact strip theory approach to compute wave-body interactions for large amplitude ship motions. The exact body boundary conditions and linearized free surface boundary conditions are used. At each time step, the body surface and free surface are regrided due to the changing wetted body geometry. Numerical and real hull forms are used in the computations. Validation and comparisons of hydrodynamic forces are presented. Selected results are shown illustrating the robustness and capabilities of the body-exact strip theory. Finally, an equation of motion solver is implemented to predict the motions of the vessel in a seaway.

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.

A Forward-Speed Body-Exact Strip Theory

2015 ◽  
Author(s):  
Piotr J. Bandyk ◽  
George S. Hazen
Keyword(s):  
High Frequency ◽  
Numerical Data ◽  
The Body ◽  
Surface Boundary ◽  
Forward Speed ◽  
Rankine Source ◽  
High Frequency Oscillations ◽  
Surface Boundary Conditions ◽  
Strip Theory ◽  
Acceleration Potential

This paper develops an extension to the body-exact strip theory of Bandyk, Beck, and Zhang [1–8], focused on improved prediction of forward-speed effects. One of the known limitations of standard strip theory is the treatment of forward speed terms. The free surface boundary conditions completely neglect the forward speed, which is usually justified by the argument of high-frequency oscillations. The pressure equation on the body includes a speed-dependent term that must computed, most commonly using the Ogilvie-Tuck theorem or numerical approximations. The strip theory variation described here circumvents these deficiencies by applying the 2D+T approach. The model assumes that each two-dimensional frame, in which a boundary value problem (BVP) is solved, remains fixed relative to an earth-fixed frame. The numerical model is based on a time-domain Rankine source method, using the same body-exact approximation as described in earlier work [1]. A suitable acceleration potential BVP is derived. Added mass and damping coefficients are calculated for two Wigley hulls, using the the standard body-exact approach and forward-speed 2D + T variant, and compared to existing model test and numerical data.

Numerical Solution of Body-Exact Problem in the Time Domain

2013 ◽  
Vol 57 (01) ◽  
pp. 13-23
Author(s):  
Wei Qiu ◽  
Hongxuan (Heather) Peng
Keyword(s):  
Free Surface ◽  
Time Domain ◽  
The Body ◽  
Floating Body ◽  
Entire Body ◽  
Surface Boundary ◽  
Time Step ◽  
Submerged Sphere ◽  
Wigley Hull ◽  
The Time Domain

Motions of a floating body in waves are computed in the time domain by solving the body-exact problem with the panel-free method and exact geometry. In the present study, the body boundary condition is imposed on the instantaneous wetted surface exactly at each time step. The free surface boundary is assumed linear so that the time-domain Green function can be applied. The body geometry is represented by NonUniform Rational B-Spline surfaces. At each time step, the instantaneous wetted surface is obtained by trimming the entire body surface. With the panel-free method, the body-exact problems are solved without involving repanelization of the wetted hull surface at each time step. Validation studies have been carried out for a submerged sphere, a flared body, and a Wigley hull. The hydrodynamic forces on the submerged sphere undergoing large-amplitude motion were computed and compared with analytical solutions. For the flared body oscillating in a free surface and the Wigley hull in waves, numerical results were compared with experimental data and solutions by other numerical methods.

scholarly journals Linear pulse structure and signalling in a film flow on an inclined plane

1999 ◽  
Vol 396 ◽  
pp. 37-71 ◽  
Author(s):  
LEONID BREVDO ◽  
PATRICE LAURE ◽  
FREDERIC DIAS ◽  
THOMAS J. BRIDGES
Keyword(s):  
Free Surface ◽  
Saddle Point ◽  
Convective Instability ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Numerical Results ◽  
Navier Stokes ◽  
Surface Boundary ◽  
Navier Stokes Equations ◽  
Surface Boundary Conditions

The film flow down an inclined plane has several features that make it an interesting prototype for studying transition in a shear flow: the basic parallel state is an exact explicit solution of the Navier–Stokes equations; the experimentally observed transition of this flow shows many properties in common with boundary-layer transition; and it has a free surface, leading to more than one class of modes. In this paper, unstable wavepackets – associated with the full Navier–Stokes equations with viscous free-surface boundary conditions – are analysed by using the formalism of absolute and convective instabilities based on the exact Briggs collision criterion for multiple k-roots of D(k, ω) = 0; where k is a wavenumber, ω is a frequency and D(k, ω) is the dispersion relation function.The main results of this paper are threefold. First, we work with the full Navier–Stokes equations with viscous free-surface boundary conditions, rather than a model partial differential equation, and, guided by experiments, explore a large region of the parameter space to see if absolute instability – as predicted by some model equations – is possible. Secondly, our numerical results find only convective instability, in complete agreement with experiments. Thirdly, we find a curious saddle-point bifurcation which affects dramatically the interpretation of the convective instability. This is the first finding of this type of bifurcation in a fluids problem and it may have implications for the analysis of wavepackets in other flows, in particular for three-dimensional instabilities. The numerical results of the wavepacket analysis compare well with the available experimental data, confirming the importance of convective instability for this problem.The numerical results on the position of a dominant saddle point obtained by using the exact collision criterion are also compared to the results based on a steepest-descent method coupled with a continuation procedure for tracking convective instability that until now was considered as reliable. While for two-dimensional instabilities a numerical implementation of the collision criterion is readily available, the only existing numerical procedure for studying three-dimensional wavepackets is based on the tracking technique. For the present flow, the comparison shows a failure of the tracking treatment to recover a subinterval of the interval of unstable ray velocities V whose length constitutes 29% of the length of the entire unstable interval of V. The failure occurs due to a bifurcation of the saddle point, where V is a bifurcation parameter. We argue that this bifurcation of unstable ray velocities should be observable in experiments because of the abrupt increase by a factor of about 5.3 of the wavelength across the wavepacket associated with the appearance of the bifurcating branch. Further implications for experiments including the effect on spatial amplification rate are also discussed.

Development of a Time Domain Boundary Element Method for the Seakeeping Behavior of a Cruise Ship Under Combined Strong Wind and Extreme Irregular Beam Seas

2014 ◽  
Author(s):  
G. D. Gkikas ◽  
F. van Walree
Keyword(s):  
Free Surface ◽  
Time Domain ◽  
Model Tests ◽  
The Body ◽  
Computational Method ◽  
Green Functions ◽  
Strong Wind ◽  
Cruise Ship ◽  
Time Step ◽  
Beam Seas

A computational method for the seakeeping behavior of a cruise ship at zero speed and under severe wind and oblique wave loads is presented. The proposed methodology is a time-domain panel method where the transient Green functions used for the estimation and implementation of the free surface effects on the vessel’s motions are estimated assuming constant low lateral speed, instead of the common practice zero speed influence functions. For the evaluation of the overall hydrodynamic forces, the so called “blended approach” is followed in the sense that the induced hydrodynamic pressures due to the scattering and radiation phenomena are calculated over the linearized position of the body, ignoring any displacements with respect to its mean position, while the hydrostatic and non-linear Froude-Krylov forces are considered at the actual body location and taking into account the free surface elevation at each time step. For the validation of the proposed methodology, heave and roll motions, the drift velocity as well as lateral accelerations of the vessel were investigated for two cases of severe beam seas combined with a constant strong wind load and the results were compared against experimental model tests. The model tests were performed to investigate the vessel’s behavior under extreme weather conditions. The low lateral speed Green functions were estimated for a speed similar to the one that the vessel was expected to drift, an estimation based on the model tests, as well as for the case where the input speed corresponded to the half of the expected speed. Good agreement was presented for both cases, showing that accurate and computationally efficient numerical simulations of the vessel’s motions under severe wind and wave excitations can be obtained by using low lateral speed transient Green functions.

Comparison of Two Base-Potentials for a Slender-Body Method

2012 ◽  
Author(s):  
Mahmoud Alidadi ◽  
Sander Calisal
Keyword(s):  
Three Dimensional ◽  
Slender Body ◽  
Surface Boundary ◽  
Two Dimensional ◽  
Three Dimensional Flow ◽  
Wave Elevation ◽  
Surface Boundary Conditions ◽  
Perturbation Potential ◽  
Order Of Magnitude ◽  
Body Method

The effects of two base-potentials on the accuracy of a slender-body method are studied in this paper. In the formulation for this method which is developed for the slender ships, the velocity potential is decomposed into a base-potential and a perturbation potential. Then using an order of magnitude analysis, the three-dimensional flow problem is simplified into a series of two-dimensional problems for the perturbation potential. These two-dimensional problems are solved with the linearized free surface boundary conditions, using a mixed Eulerian-Lagrangian method. Finally for the two base-potentials, the numerical wave elevation along a Wigleyull are compared with the experimental results.

Computing Large Amplitude Motions of a Floating Offshore Structure in the Time Domain

2008 ◽  
Author(s):  
Wei Qiu ◽  
Hongxuan Peng
Keyword(s):  
Time Domain ◽  
Large Amplitude ◽  
Offshore Structures ◽  
The Body ◽  
Surface Boundary ◽  
Offshore Structure ◽  
Floating Structure ◽  
Time Step ◽  
Large Amplitude Motions ◽  
The Time Domain

Based on the panel-free method, large-amplitude motions of floating offshore structures have been computed by solving the body-exact problem in the time domain using the exact geometry. The body boundary condition is imposed on the instantaneous wetted surface exactly at each time step. The free surface boundary is assumed linear so that the time-domain Green function can be applied. The instantaneous wetted surface is obtained by trimming the entire NURBS surfaces of a floating structure. At each time step, Gaussian points are automatically distributed on the instantaneous wetted surface. The velocity potentials and velocities are computed accurately on the body surface by solving the desingularized integral equations. Nonlinear Froude-Krylov forces are computed on the instantaneous wetted surface under the incident wave profile. Validation studies have been carried out for a Floating Production Storage and Offloading (FPSO) vessel. Computed results were compared with experimental results and solutions by the panel method.

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