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.

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 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.

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.

Time-Domain Nonlinear Wave Making Simulation of the Catamaran Based on Velocity Potential Boundary Element Method

2010 ◽  
Author(s):  
Dakui Feng ◽  
Xianzhou Wang ◽  
Zhiguo Zhang ◽  
Yanming Guan
Keyword(s):  
Free Surface ◽  
Radiation Condition ◽  
Flow Fields ◽  
Design Stage ◽  
Hydrodynamic Characteristics ◽  
Outer Side ◽  
Surface Boundary ◽  
Computational Domain ◽  
Time Step ◽  
Surface Boundary Conditions

The catamaran is composed of two monohulls, the flow fields between the inner and outer side of each monohull are different, the bodies must be considered as lifting bodies. So it is very important to know the lifting effect on hydrodynamic characteristics of catamaran hull at the preliminary design stage of its hull form. The pressure Kutta condition is imposed on the trailing-surface of the lifting body by determining the dipole distribution, which generates required circulation on the lifting part. The method is based on Green’s second theorem. Rankine Sources and dipoles are placed on boundary surfaces. Time-stepping scheme is adopted to simulate the wave generated by the catamaran with a uniform speed in deep water. The values of the potential and position of the free surface are updated by integrating the nonlinear Lagrangian free surface boundary conditions for every time. A moving computational window is used in the computations by truncating the fluid domain (the free surface) into a computational domain. The grid regeneration scheme is developed to determine the approximate position of the free surface for the next time step. An implicit implement of far field condition is enforced automatically at the truncation boundary of the computational window, Radiation condition is satisfied automatically. The influences on the wave making resistance of the distance between the twin hulls of the Wigley catamaran on the hydrodynamic characteristics are discussed. The numerical results are presented compared with the existing simulation result. The method can be used to simulate the flow fields around the foil near free surface.

Added Wave Resistance Computations Using Desingularized Source and Panel Methods

2015 ◽  
Author(s):  
Xinshu Zhang ◽  
Wei Li ◽  
Yunxiang You
Keyword(s):  
Equations Of Motion ◽  
Three Dimensional ◽  
Wave Resistance ◽  
Boundary Integral ◽  
Time Step ◽  
Panel Methods ◽  
Calm Water ◽  
Constant Strength ◽  
Hull Forms ◽  
Large Amplitude Motion

A three-dimensional time-domain approach has been developed to compute large-amplitude motion response and the second-order added wave resistance for ships traveling in waves. The proposed method is an extension of a well established linear approach developed in a previous paper [1]. The numerical model is developed based on boundary integral equation, which is solved at each time step by distributing desingularized sources above the calm water surface and employing constant-strength panels on body surface. The nonlinear Froude-Krylov and wave diffraction forces are computed. Equations of motion are solved with including the effects of Euler angles. A broad range of different hull forms, including two Wigley hulls, a Series 60 hull, and a S-175 hull, are employed to validate the present computational model. By comparing the obtained numerical results to experiments, it is demonstrated that the present model using double-body basis flow can well predict added wave resistance.

Numerical Study of the Ship Motion in Waves Using the Three-Dimensional Time-Domain Forward-Speed Free-Surface Green Function and a Second-Order Boundary Element Method

2008 ◽  
Author(s):  
D. C. Hong ◽  
S. Y. Hong ◽  
H. G. Sung
Keyword(s):  
Integral Equation ◽  
Free Surface ◽  
Green Function ◽  
Time Domain ◽  
Time Derivative ◽  
Three Dimensional ◽  
Forward Speed ◽  
Surface Green Function ◽  
The Green Function ◽  
The Time Domain

The radiation and diffraction potentials of a ship advancing in waves are calculated in the time-domain using the three-dimensional time-domain forward-speed free-surface Green function and the Green integral equation on the basis of the Neumann-Kelvin linear wave hypothesis. The Green function approximated by Newman for large time is used together with the Green function by Lamb for small time. The time-domain diffraction problem is solved for the time derivative of the potential by using the time derivative of the impulsive incident wave potential represented by using the complementary complex error function. The integral equation for the potential is discretized according to a second-order boundary element method where the collocation points are located inside the panel. It makes it possible to take account of the line integral along the waterline in a rigorous manner. The six-degree-of-freedom motion and memory functions as well as the diffraction impulse response functions of a hemisphere and the Wigley seakeeping model are presented for various Froude numbers. Comparisons of the wave damping and exciting force and moment coefficients for zero forward speed, calculated by using the Fourier transforms of the time-domain results and the frequency-domain coefficients calculated by using the improved Green integral equation which is free of the irregular frequencies, have been shown to be satisfactory. The wave damping coefficients for non-zero forward speed, calculated by using Fourier transforming of the present time-domain results have also been compared to the experimental results and agreement between them has been shown to be good. A simulation of coupled heave-pitch motion of the Wigley seakeeping model advancing in regular head waves of unit amplitude has been carried out.

Numerical Study of Large Amplitude Ship Motion With Forward Speed in Severe Seas

2009 ◽  
Author(s):  
D. C. Hong ◽  
H. G. Sung ◽  
S. Y. Hong
Keyword(s):  
Free Surface ◽  
Time Domain ◽  
Large Amplitude ◽  
Numerical Study ◽  
Surface Condition ◽  
Three Dimensional ◽  
Ship Motion ◽  
Forward Speed ◽  
Restoring Force ◽  
Head Waves

A three-dimensional time-domain calculation method is of crucial importance in prediction of ship motion with forward speed in a severe irregular sea. The exact solution of the free surface wave–ship interaction problem is very complicated because of the extremely nonlinear boundary conditions. In this paper, an approximate body nonlinear approach based on the three-dimensional time-domain forward-speed free-surface Green function has been presented. It is a simplified version of the method known as LAMP (Lin and Yue 1990) where the exact body boundary condition is applied on the instantaneous wetted surface of the ship while free-surface condition is linearized. In the present study, the Froude-Krylov force and the hydrostatic restoring force are calculated on the instantaneous wetted surface of the ship while the forces due to the radiation and scattering potentials on the mean wetted surface. The time-domain radiation and scattering potentials have been obtained from a time invariant kernel of integral equations for the potentials. The integral equation for the radiation potential is discretized according to the second-order boundary element method (Hong and Hong. 2008). The diffraction impulse response functions of the Wigley seakeeping model are presented for various Froude numbers. A simulation of coupled heave-pitch motion of the Wigley model advancing in regular head waves of large amplitude has been carried out. Comparisons between the fully linear and the present approximate body nonlinear computations have been made at various Froude numbers.

Three-Dimensional Forward-Speed Seakeeping Calculation Using FINE/Marine

2016 ◽  
Author(s):  
Limin Chen ◽  
Guanghua He ◽  
Dazheng Wang ◽  
Zihao Zhang
Keyword(s):  
Numerical Model ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Forward Speed ◽  
Ship Waves ◽  
Continuity Equations ◽  
Seakeeping Performance ◽  
Calm Water ◽  
Wigley Hull ◽  
Unsteady Problems

A time-domain seakeeping numerical model based on a computational fluid dynamics (CFD) software FINE/Marine has been developed for nonlinear steady and unsteady viscous flows. Simulation of multi-phase flows around a Wigley hull with forward speed is performed by solving the Reynolds-average Navier-Stokes (RANS) and continuity equations with k-ω (SST-Menter) turbulence model. The water free surface is captured by Blend Reconstruction Interface Capturing Scheme (BRICS). Both steady and unsteady problems including wave-making, radiation and diffraction problems are simulated. Ship waves generated by the Wigley model advancing at a constant forward speed in calm water or incident waves are computed. The numerical results including the wave-making resistance and wave patterns for steady problem, hydrodynamic coefficients and forces for unsteady problems are illustrated and compared with experimental measurements in good agreement. It is confirmed that the present numerical model has the capability of evaluating the seakeeping performance of ships.

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