Short Term Distribution of Loads Acting on a Cruise Vessel in Extreme Seas Using a Body Nonlinear Time Domain With Second Order Froude-Krylov Pressure

2015 ◽  
Author(s):  
Suresh Rajendran ◽  
Nuno Fonseca ◽  
C. Guedes Soares
Keyword(s):  
Free Surface ◽  
Time Domain ◽  
Surface Condition ◽  
Bending Moment ◽  
The Body ◽  
Short Term ◽  
Weakly Nonlinear ◽  
Strip Theory ◽  
Vertical Bending Moment ◽  
Nonlinear Time Domain

Short term probability distribution of the vertical bending moment acting on a cruise vessel in extreme seas is calculated using a body nonlinear time domain method based on strip theory. The hydrodynamic forces are calculated for the exact wetted surface area under the incident wave profile. The incident potential satisfies the weakly nonlinear free surface condition based on the Stokes expansion. The disturbance potential satisfies the linear free surface and body boundary conditions. Certain practical engineering techniques are employed for the calculation of the body nonlinear forces. The statistics and the probability of distribution of the numerical vertical bending moment are compared with the experimental results measured in the wave tank.

Prediction of Ship Responses in Large Amplitude Waves Using a Body Nonlinear Time Domain Method With 2nd Order Froude-Krylov Pressure

2014 ◽  
Author(s):  
Suresh Rajendran ◽  
Nuno Fonseca ◽  
C. Guedes Soares
Keyword(s):  
Surface Area ◽  
Time Domain ◽  
Time Instant ◽  
The Body ◽  
Regular Waves ◽  
Time Step ◽  
Strip Theory ◽  
Practical Engineering ◽  
Wetted Surface Area ◽  
Nonlinear Time Domain

The paper analyzes the effect of 2nd order waves on the vertical ship responses in extreme seas. The numerical simulations are carried out using a body nonlinear time domain code based on strip theory. The radiation, diffraction, Froude-krylov and hydrostatic forces are calculated for the exact wetted surface area of the ship for each time step. A practical engineering approach is followed to calculate the body nonlinear radiation and diffraction forces. First order Froude Krylov pressures are replaced with a second order model for the present study. The 2nd order Froude-Krylov pressures are integrated upto the exact wetted surface area for each time instant. The ship responses in regular waves with varying steepness are analyzed. Finally, the vertical ship responses are compared with the responses in design waves measured in the wave tank.

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.

Influence of Whipping on Long-term Vertical Bending Moment

2004 ◽  
Vol 48 (04) ◽  
pp. 261-272
Author(s):  
Gro Sagli Baarholm ◽  
Jørgen Juncher Jensen
Keyword(s):  
Nonlinear Response ◽  
Extreme Values ◽  
Bending Moment ◽  
Sea Waves ◽  
Short Term ◽  
Strip Theory ◽  
Long Time ◽  
Wave Induced ◽  
Vertical Bending Moment

This paper is concerned with estimating the response value corresponding to a long return period, say 20 years. Time domain simulation is required to obtain the nonlinear response, and long time series are required to limit the statistical uncertainty in the simulations. It is crucial to introduce ways to improve the efficiency in the calculation. A method to determine the long-term extremes by considering only a few short-term sea states is applied. Long-term extreme values are estimated using a set of sea states that have a certain probability of occurrence, known as the contour line approach. Effect of whipping is included by assuming that the whipping and wave-induced responses are independent, but the effect of correlation of the long-term extreme value is also studied. Numerical calculations are performed using a nonlinear, hydroelastic strip theory as suggested by Xia et al (1998). Results are presented for the S-175 containership (ITTC 1983) in head sea waves. The analysis shows that whipping increases the vertical bending moment and that the correlation is significant.

Time-Domain Analysis of Large-Amplitude Vertical Ship Motions and Wave Loads

1998 ◽  
Vol 42 (02) ◽  
pp. 139-153 ◽  
Author(s):  
N. Fonseca ◽  
C. Guedes Soares
Keyword(s):  
Free Surface ◽  
Time Domain ◽  
Large Amplitude ◽  
Surface Condition ◽  
Memory Effects ◽  
Wave Loads ◽  
Strip Theory ◽  
Large Amplitude Motions ◽  
Free Surface Oscillations ◽  
The Time Domain

The vertical motions and wave induced loads on ships with forward speed are studied in the time domain, considering non-linear effects associated with large amplitude motions and hull flare shape. The method is based on a strip theory, using singularities distributed on the cross sections which satisfy the linear free surface condition. The solution is obtained in the time domain using convolution to account for the memory effects related to the free surface oscillations. In this way the linear radiation forces are represented in terms of impulse response functions, infinite frequency added masses and radiation restoring coefficients. The diffraction forces associated with incident wave scattering are linear. The hydrostatic and Froude-Krylov forces are evaluated over the instantaneous wetted surface of the hull to account for the large amplitude motions and hull flare. The radiation contribution for wave loads is also obtained in the time domain using convolution to account for the memory effects related to the free surface oscillations. Results of motions and wave loads for the S175 container ship are presented and analyzed. The results from the present method are compared with linear results.

Time Domain Comparison With Experiments for Ship Motions and Structural Loads on a Container Ship in Abnormal Waves

2011 ◽  
Author(s):  
Suresh Rajendran ◽  
Nuno Fonseca ◽  
C. Guedes Soares ◽  
Gu¨nther F. Clauss ◽  
Marco Klein
Keyword(s):  
Time Domain ◽  
Bending Moment ◽  
Green Water ◽  
Ship Motions ◽  
Container Ship ◽  
Wave Elevation ◽  
Strip Theory ◽  
The Time Domain ◽  
Vertical Bending Moment ◽  
Comparison With Experiments

The paper presents experimental results from model tests with a containership advancing in abnormal wave conditions and comparisons with numerical simulations. A nonlinear time domain method based on strip theory is used for the calculation of vertical ship responses induced by abnormal waves. This code combines the linear diffraction and radiation forces with dominant nonlinear forces associated with vertical response arising from Froude-Krylov forces, hydrostatic forces and shipping of green water. The time domain simulations are compared directly with experimental records from tests with a model of a container ship in deterministic waves for a range of Froude numbers. Extreme sea conditions were replicated by the reproduction of realistic abnormal waves like the New Year Wave and abnormal wave from North Alwyn. Head sea condition is considered and the comparisons include the wave elevation, the vertical motions of the ship and the vertical bending moment at midship.

Analysis of Vertical Bending Moment on an Ultra Large Containership Induced by Extreme Head Seas

2014 ◽  
Author(s):  
Suresh Rajendran ◽  
Nuno Fonseca ◽  
C. Guedes Soares
Keyword(s):  
Rigid Body ◽  
Bending Moment ◽  
Variable Stiffness ◽  
The Body ◽  
Experimental Results ◽  
Irregular Waves ◽  
Time Step ◽  
Strip Theory ◽  
Vertical Bending Moment ◽  
Body Response

This paper discusses the numerical analysis of an ultra large containership model in severe head seas. A body nonlinear time domain code based on the strip theory is used for the calculation of the rigid body response of the vessel. The radiation, diffraction, Froude-krylov and hydrostatic forces are calculated for the exact wetted surface area of the ship at each time step. A practical engineering approach is followed to calculate the body nonlinear radiation and diffraction forces. The numerical vertical bending moment is compared with the experimental results. The experiment was conducted on a flexible model in both regular and irregular waves. The model comprised six segments that were joined with an aluminum backbone of variable stiffness characteristics in order to replicate the hydroelastic behavior of the real ship. The model was tested for two ship speeds, 15 and 22 knots. For the first three harmonic values of the vertical bending moment, a good agreement between the numerical and the experimental results are found. However, higher harmonics significantly contributed to the total experimental vertical bending moment, in regular waves with 8m wave height and a ship speed of 15 knots. Similarly, the value of the fourth harmonic was 32% of the first harmonic values when the ship encountered a 5m regular wave with 22 knots speed. On comparison of the rigid body response in irregular seas, the hydroelastic loads resulted in 49% increase in the maximum value of the vertical bending moment.

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.

Estimation of Short-and Long-Term Probability Distributions of Wave-Induced Loads Acting on a Cruise Vessel in Extreme Seas

2017 ◽  
Vol 140 (2) ◽  
Author(s):  
Suresh Rajendran ◽  
Nuno Fonseca ◽  
C. Guedes Soares
Keyword(s):  
Time Domain ◽  
International Association ◽  
Probability Distributions ◽  
Bending Moment ◽  
Green Water ◽  
Cruise Ship ◽  
Short Term ◽  
Strip Theory ◽  
Radiation Forces

A time domain code based on strip theory is applied to calculate the probability distributions of relative motions and bending moments of a cruise ship in a set of extreme seas. The code includes two levels of complexity. The simpler one combines linear radiation and diffraction forces with nonlinear Froude–Krylov forces, hydrostatic forces, and shipping of green water on the bow. Cummins formulation is used to represent the radiation forces. The second approach is a generalization of the first one and, although the formulation is based on the linear assumption (of the radiation forces), the effects of body nonlinearity are considered by a simplified method: the memory functions, infinite frequency added masses, and the radiation restoring coefficients are assessed at each time instant as function of the instantaneous wetted surface. A similar procedure is used to calculate the diffraction forces. The code is used to analyze the responses of a cruise ship in a set of extreme sea conditions. The short-term nonlinear responses are represented by empirical probability distributions, obtained from the nonlinear time domain simulations, and the quality of the predictions is assessed by comparing with model tests experimental data. Finally, the long-term value of the bending moment is calculated from the short-term distribution of the nonlinear loads in a few extreme sea states selected based on coefficient of contribution method, and the results are compared with the International Association of Classification Societies (IACS) rule bending moment.

scholarly journals Bilge Keel Induced Roll Damping of an FPSO With Sponsons

2016 ◽  
Author(s):  
Babak Ommani ◽  
Nuno Fonseca ◽  
Trygve Kristiansen ◽  
Christopher Hutchison ◽  
Hanne Bakksjø
Keyword(s):  
Free Surface ◽  
Two Dimensions ◽  
The Body ◽  
Proximity Effects ◽  
Roll Damping ◽  
Damping Coefficients ◽  
Free Decay ◽  
Strip Theory ◽  
Decay Tests ◽  
Bilge Keel

The bilge keel induced roll damping of an FPSO with sponsons is investigated numerically and experimentally. The influence of the bilge keel size, on the roll damping is studied. Free decay tests of a three-dimensional ship model, for three different bilge keel sizes are used to determine roll damping coefficients. The dependency of the quadratic roll damping coefficient to the bilge keel height and the vertical location of the rotation center is studied using CFD. A Navier-Stokes solver based on the Finite Volume Method is adopted for solving the laminar flow of incompressible water around a section of the FPSO undergoing forced roll oscillations in two-dimensions. The free-surface condition is linearized by neglecting the nonlinear free-surface terms and the influence of viscous stresses in the free surface zone, while the body-boundary condition is exact. An averaged center of rotation is estimated by comparing the results of the numerical calculations and the free decay tests. The obtained two-dimensional damping coefficients are extrapolated to 3D by use of strip theory argumentations and compared with the experimental results. It is shown that this simplified approach can be used for evaluating the bilge keel induced roll damping with efficiency, considering unconventional ship shapes and free-surface proximity effects.

scholarly journals Computation of Nonlinear Hydrodynamic Loads on Floating Wind Turbines Using Fluid-Impulse Theory

2015 ◽  
Author(s):  
Godine Kok Yan Chan ◽  
Paul D. Sclavounos ◽  
Jason Jonkman ◽  
Gregory Hayman
Keyword(s):  
Free Surface ◽  
Green Function ◽  
Wind Turbines ◽  
Time Domain ◽  
The Body ◽  
Nonlinear Loads ◽  
Frequency Wave ◽  
Linear And Nonlinear ◽  
The Time Domain ◽  
Nonlinear Free Surface

A hydrodynamics computer module was developed to evaluate the linear and nonlinear loads on floating wind turbines using a new fluid-impulse formulation for coupling with the FAST program. The new formulation allows linear and nonlinear loads on floating bodies to be computed in the time domain. It also avoids the computationally intensive evaluation of temporal and spatial gradients of the velocity potential in the Bernoulli equation and the discretization of the nonlinear free surface. The new hydrodynamics module computes linear and nonlinear loads — including hydrostatic, Froude-Krylov, radiation and diffraction, as well as nonlinear effects known to cause ringing, springing, and slow-drift loads — directly in the time domain. The time-domain Green function is used to solve the linear and nonlinear free-surface problems and efficient methods are derived for its computation. The body instantaneous wetted surface is approximated by a panel mesh and the discretization of the free surface is circumvented by using the Green function. The evaluation of the nonlinear loads is based on explicit expressions derived by the fluid-impulse theory, which can be computed efficiently. Computations are presented of the linear and nonlinear loads on the MIT/NREL tension-leg platform. Comparisons were carried out with frequency-domain linear and second-order methods. Emphasis was placed on modeling accuracy of the magnitude of nonlinear low- and high-frequency wave loads in a sea state. Although fluid-impulse theory is applied to floating wind turbines in this paper, the theory is applicable to other offshore platforms as well.

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