Efficient and Simplified Time Domain Simulation of Nonlinear Responses of Ships in Waves

2003 ◽  
Vol 47 (03) ◽  
pp. 262-273
Author(s):  
XueKang Gu ◽  
JinWei Shen ◽  
Torgeir Moan
Keyword(s):  
Model Test ◽  
Time Domain ◽  
High Efficiency ◽  
Coupling Effect ◽  
Irregular Waves ◽  
Green Water ◽  
Bending Moments ◽  
Strip Theory ◽  
Bow Flare ◽  
Theoretical Results

In this paper, a nonlinear time-domain strip theory is developed to predict nonlinear vertical ship motions and structural responses in severe waves. The effects of bottom impact, bow flare slamming, and green water on bending moments have been simulated. The flexible modes of the ship hull girder are accounted for by a Timoshenko beam theory. To validate the predicted responses, a model test was conducted for a ship with large bow flare and low bending rigidity, in both regular and irregular waves. The agreements between the calculated results and the model test are fairly good. The coupling effect between higher-order harmonic and the whipping components of vertical bending moments are verified by numerical calculations. Comparative studies with test and other theoretical results are also carried out for an S-175 containership with two kinds of bow flare forms. The causes of whipping and the variance in theoretical results are discussed. The good performance and high efficiency will make it possible to use the theory and its code for direct calculation of nonlinear bending moments in a long-term period and to develop a rule formula of design wave loads in the future.

Bending Moments and Shear Forces in Ships Sailing in Irregular Waves

1981 ◽  
Vol 25 (04) ◽  
pp. 243-251
Author(s):  
J. Juncher Jensen ◽  
P. Terndrup Pedersen
Keyword(s):  
Linear Part ◽  
Vertical Motion ◽  
Bending Moment ◽  
Irregular Waves ◽  
Bending Moments ◽  
Shear Forces ◽  
Strip Theory ◽  
Wave Heights ◽  
Exciting Forces ◽  
Wave Induced

This paper presents some results concerning the vertical response of two different ships sailing in regular and irregular waves. One ship is a containership with a relatively small block coefficient and with some bow flare while the other ship is a tanker with a large block coefficient. The wave-induced loads are calculated using a second-order strip theory, derived by a perturbational procedure in which the linear part is identical to the usual strip theory. The additional quadratic terms are determined by taking into account the nonlinearities of the exiting waves, the nonvertical sides of the ship, and, finally, the variations of the hydrodynamic forces during the vertical motion of the ship. The flexibility of the hull is also taken into account. The numerical results show that for the containership a substantial increase in bending moments and shear forces is caused by the quadratic terms. The results also show that for both ships the effect of the hull flexibility (springing) is a fair increase of the variance of the wave-induced midship bending moment. For the tanker the springing is due mainly to exciting forces which are linear with respect to wave heights whereas for the containership the nonlinear exciting forces are of importance.

Response Analysis of a Nonstationary Lowering Operation for an Offshore Wind Turbine Monopile Substructure

2015 ◽  
Vol 137 (5) ◽  
Author(s):  
Lin Li ◽  
Zhen Gao ◽  
Torgeir Moan
Keyword(s):  
Wind Turbine ◽  
Time Domain ◽  
Dynamic Responses ◽  
Offshore Wind ◽  
Irregular Waves ◽  
Offshore Wind Turbine ◽  
Response Analysis ◽  
Steady State Condition ◽  
Strip Theory ◽  
Lifting System

This study addresses numerical modeling and time-domain simulations of the lowering operation for installation of an offshore wind turbine monopile (MP) with a diameter of 5.7 m and examines the nonstationary dynamic responses of the lifting system in irregular waves. Due to the time-varying properties of the system and the resulting nonstationary dynamic responses, numerical simulation of the entire lowering process is challenging to model. For slender structures, strip theory is usually applied to calculate the excitation forces based on Morison's formula with changing draft. However, this method neglects the potential damping of the structure and may overestimate the responses even in relatively long waves. Correct damping is particularly important for the resonance motions of the lifting system. On the other hand, although the traditional panel method takes care of the diffraction and radiation, it is based on steady-state condition and is not valid in the nonstationary situation, as in this case in which the monopile is lowered continuously. Therefore, this paper has two objectives. The first objective is to examine the importance of the diffraction and radiation of the monopile in the current lifting model. The second objective is to develop a new approach to address this behavior more accurately. Based on the strip theory and Morison's formula, the proposed method accounts for the radiation damping of the structure during the lowering process in the time-domain. Comparative studies between different methods are presented, and the differences in response using two types of installation vessel in the numerical model are also investigated.

Wave induced extreme hull girder loads on containerships

2008 ◽  
Author(s):  
J. Juncher Jensen ◽  
Preben Terndrup Pedersen ◽  
Bill Shi ◽  
Sue Wang ◽  
Martin Petricic ◽  
...  
Keyword(s):  
Bending Moments ◽  
Wave Load ◽  
Spreadsheet Program ◽  
Hull Girder ◽  
Conceptual Design Phase ◽  
Strip Theory ◽  
Bow Flare ◽  
Analytical Formulas ◽  
Approximate Wave ◽  
Wave Induced

This paper provides simple but rational procedures for prediction of extreme wave – induced sectional hull girder forces with reasonable engineering accuracy. The procedures take into account main ship hull characteristics such as: length, breadth, draught, block coefficient, bow flare coefficient, forward speed and hull flexibility. The vertical hull girder loads are evaluated for specific operational profiles. Firstly a quadratic strip theory is presented which can give separate predictions for the hogging and sagging bending moments and shear forces and for hull girder loads. Then this procedure is used as a base to derive semi-analytical formulas such that approximate wave load calculations can be performed by a simple spreadsheet program. Due to the few input parameters this procedure can be used to estimate the wave-induced bending moments at the conceptual design phase. Since the procedure is based on rational methods it can be applied for novel single hull ship types not presently covered by the rules of the classification societies or to account for specific operational profiles.

Estimation of hull girder vertical bending moments including non-linear and flexibility effects using closed form expressions

2009 ◽  
Vol 223 (3) ◽  
pp. 377-390 ◽  
Author(s):  
P T Pedersen ◽  
J J Jensen
Keyword(s):  
Closed Form ◽  
Linear Response ◽  
Bending Moment ◽  
Phase Lag ◽  
Bending Moments ◽  
Hull Girder ◽  
Strip Theory ◽  
Non Linear ◽  
Bow Flare ◽  
Wave Induced

A simple but rational procedure for prediction of extreme wave-induced hull girder bending moment in slender mono-hull displacement vessels is presented. The procedure takes into account main ship hull characteristics such as length, breadth, draught, block coefficient, bow flare coefficient, forward speed, and hull flexibility. The wave-induced loads are evaluated for specific operational profiles. Non-linearity in the wave bending moment is modelled using results derived from a second-order strip theory and water entry solutions for wedge-type sections. Hence, bow flare slamming is accounted for through a momentum type of approach. The stochastic properties of this non-linear response are calculated through a monotonic Hermite transformation. In addition, the impulse loading attributable to, for example, bottom slamming or a rapid change in bow flare is included using a modal expansion in the two lowest vertical vibration modes. These whipping vibrations are added to the wave frequency non-linear response, taking into account the rise time of the impulse response as well as the phase lag between the occurrence of the maximum non-linear load and the maximum impulse load. Previous results for the sagging bending moment are validated by comparison with fully non-linear strip theory calculations and supplemented with new closed form results for the hogging bending moment. Focus is on the extreme hull girder hogging bending moment. Owing to the few input parameters, this procedure can be used to estimate the wave-induced bending moments at the conceptual design phase. Another application area is for novel single-hull ship types not presently covered by the rules of the classification societies. As one application example the container ship MSC Napoli is considered. Further validations are needed, however, in order to select proper values of the parameters entering the analytical form of the slamming impulse.

Green Water on FPSO Predicted by a Practical Engineering Method and Validated Against Model Test Data for Irregular Waves

2014 ◽  
Author(s):  
Rafael Vergara Schiller ◽  
Csaba Pâkozdi ◽  
Carl Trygve Stansberg ◽  
Douglas Gustavo Takashi Yuba ◽  
Daniel Fonseca de Carvalho e Silva
Keyword(s):  
Model Test ◽  
Model Tests ◽  
Irregular Waves ◽  
Green Water ◽  
Wave Impact ◽  
Irregular Wave ◽  
Beam Seas ◽  
Practical Engineering ◽  
The University ◽  
Wave Induced

This paper presents a series of numerical analyses performed with the potential theory-based Green Water engineer tool KINEMA3. KINEMA3 was designed to predict wave-induced impact loads on FPSOs in steep irregular waves, and for use in design load analysis. The purpose of the study presented herein is to validate KINEMA3 green water (deck overtopping) predictions in nonlinear irregular waves with results from model tests performed at the TPN (Tanque de Provas Numérico) laboratory at the University of São Paulo, Brazil. Comparisons are made for a selection of irregular wave cases, for two choices of anchoring conditions (free floating vessel and fixed vessel) and for three wave headings (180°, 225° and 270°: head, quartering and beam seas, respectively). KINEMA3 statistical green water predictions present a general good agreement with observations from the TPN model tests for all wave cases, headings and mooring conditions. Overall, observed trends for occurrence of green water and standard deviation/maximum of relative wave height are successfully reproduced by KINEMA3. In agreement with model test results, it is predicted that green water occurs more frequently for a free floating vessel and for beam seas. Additional comparisons between KINEMA3 predictions using different FPSO panel models (low-order and high-order models) present negligible differences with respect to green water estimates. The results presented herein demonstrate the robustness of the tool towards the prediction of green water for variable wave headings and sea states, and highlight the capability of KINEMA3 to be employed as an engineering-like tool for fast and multiple estimates of green water in early design studies. This work is a part of the research project “Green Water and Wave Impact on FPSO” carried out for and in cooperation with PETROBRAS.

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.

Simple Tool for Prediction of Green Water and Bow Flare Slamming on FPSO

2009 ◽  
Author(s):  
Carl Trygve Stansberg ◽  
Kjetil Berget
Keyword(s):  
Water Reservoir ◽  
Software Tool ◽  
Practical Method ◽  
Irregular Waves ◽  
Green Water ◽  
Ship Motions ◽  
Wave Impact ◽  
Bow Flare ◽  
Dam Breaking ◽  
Flare Slamming

A practical method for prediction of green water and wave impact on FPSO’s in steep irregular waves is described. The relative wave elevation and kinematics are found from combining ship motions, wave diffraction and nonlinear irregular waves. Water heights on deck and related velocities are estimated by simple analytical formulas originally derived from dam-breaking theory but modified in this work to take into account a non-zero water velocity input and the effects from a dynamic and finite wave-determined water reservoir. A bulwark is also included. Deckhouse slamming and bow flare slamming loads are computed by simple formulas from the local velocities and, in the latter case, also the relative angle between the water surface and the flare. Verification against more advanced models and to model test data show promising results. The method is being implemented into a simple research-type software tool.

Symmetric Response of a Hydroelastic Scaled Container Ship Model in Regular and Irregular Waves

2014 ◽  
Author(s):  
Sheng Peng ◽  
Pandeli Temarel ◽  
S. S. Bennett ◽  
Weiguo Wu ◽  
Zhengguo Liu ◽  
...  
Keyword(s):  
Full Scale ◽  
Irregular Waves ◽  
Container Ship ◽  
Bending Moments ◽  
Segmented Model ◽  
Numerical Predictions ◽  
Hull Structure ◽  
Strip Theory ◽  
Head Waves ◽  
Wave Induced

Wave-induced vibrations, such as whipping and springing, of container carriers have been attracting much attention because of their effects on hull-girder bending moments and fatigue damage. An investigation has been carried out comparing experimental measurements and numerical predictions of symmetric wave-induced loads (i.e. vertical bending moment) of the latest River-sea link container ship design, LPP = 130 m. The dual mission characteristics, namely rivers and open seas, make this type of ship an extremely interesting type of container carrier, particularly in terms of springing and whipping. A backbone beam segmented model is used in the experiments with the focus on springing- and whipping-induced vertical bending moments, for the model travelling at Fn = 0.21 in regular and long-crested irregular head waves, of 2.5m full-scale height or significant wave height. In addition higher order (harmonics) vertical bending moments (VBM) are also extracted from the experiments. The measurements are taken at amidships and the fore and aft quarters. Numerical predictions, for both the full-scale vessel and segmented model, are obtained using the two-dimensional linear hydroelasticity theories, where the hull structure is idealized as a non-uniform beam and the fluid actions evaluated using strip theory. The measured model test results, in relatively moderate conditions based on a particular area of operation for this low-draught vessel, indicate that nonlinear springing accounts for a significant portion of the total wave-induced bending moments in regular and, to an extent, irregular waves and slamming effects are small due to the operational area selected. The numerical predictions in regular waves show that linear hydroelasticity analysis can only predict similar trends in the variation of the VBM and the resonance peak. On the other hand, in long crested irregular waves the linear hydroelasticity analysis provides peak statistics that are commensurate with the measurements. The numerical predictions were obtained for two variants, having L = LPP and L = 0.9 LPP, the latter corresponding to the length of the backbone.

Experimental and Numerical Extreme Motions and Vertical Bending Moments Induced by Abnormal Waves on a Bulk Carrier

2013 ◽  
Author(s):  
Guillermo Vasquez ◽  
Nuno Fonseca ◽  
Carlos Guedes Soares
Keyword(s):  
Time Domain ◽  
Good Accuracy ◽  
Green Water ◽  
Numerical Code ◽  
Extreme Wave ◽  
Bulk Carrier ◽  
Strip Theory ◽  
Head Waves ◽  
The Time Domain ◽  
Good Agreement

The present investigation focuses on the motions and global structural loads induced by abnormal waves on a bulk carrier. A nonlinear time domain method based on strip theory is used to predict the ship responses. The results are compared with experimental data obtained at the model scale. The time domain hydrodynamic forces are calculated by convolution of linear memory functions, while nonlinear contributions arise from Froude-Krylov forces, hydrostatic forces and shipping of green water. The time domain simulations are compared directly with experimental records from bulk carrier model tests with in head waves for two Froude numbers. Extreme wave conditions (such as the New Year Wave) previously measured at sea during real storms were replicated both at the seakeeping tank and by the numerical code. The comparison analyses show a good agreement between numerical and experimental with good accuracy.

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.

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