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.

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

2013 ◽  
Author(s):  
Suresh Rajendran ◽  
Nuno Fonseca ◽  
C. Guedes Soares
Keyword(s):  
Time Domain ◽  
Probability Distributions ◽  
Time Instant ◽  
Green Water ◽  
Cruise Ship ◽  
Short Term ◽  
Numerical Predictions ◽  
Strip Theory ◽  
Radiation Forces ◽  
Linear Radiation

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 nonlinear radiation and diffraction effects on the responses are analyzed by comparing the “fully nonlinear” results with the numerical predictions assuming linear radiation and diffraction forces. The short term nonlinear responses are represented by empirical probability distributions, obtained from time domain simulations, and the quality of the predictions is assessed by comparing with model tests experimental data.

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 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.

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.

Comparison of Spar and Semisubmersible Floater Concepts of Offshore Wind Turbines Using Long-Term Analysis

2015 ◽  
Vol 137 (6) ◽  
Author(s):  
Hasan Bagbanci ◽  
D. Karmakar ◽  
C. Guedes Soares
Keyword(s):  
Wind Turbine ◽  
Wind Turbines ◽  
Transfer Functions ◽  
Probability Distributions ◽  
Offshore Wind ◽  
Short Term ◽  
Offshore Wind Turbines ◽  
Floating Wind Turbine ◽  
Offshore Floating Wind Turbine

The long-term probability distributions of a spar-type and a semisubmersible-type offshore floating wind turbine response are calculated for surge, heave, and pitch motions along with the side-to-side, fore–aft, and yaw tower base bending moments. The transfer functions for surge, heave, and pitch motions for both spar-type and semisubmersible-type floaters are obtained using the fast code and the results are also compared with the results obtained in an experimental study. The long-term predictions of the most probable maximum values of motion amplitudes are used for design purposes, so as to guarantee the safety of the floating wind turbines against overturning in high waves and wind speed. The long-term distribution is carried out using North Atlantic wave data and the short-term floating wind turbine responses are represented using Rayleigh distributions. The transfer functions are used in the procedure to calculate the variances of the short-term responses. The results obtained for both spar-type and semisubmersible-type offshore floating wind turbine are compared, and the study will be helpful in the assessments of the long-term availability and economic performance of the spar-type and semisubmersible-type offshore floating wind turbine.

Strength Performance of Steel Catenary Riser Using Short Term and Long Term Analysis Methodologies

2016 ◽  
Author(s):  
Feng Wang ◽  
Roger Burke ◽  
Anil Sablok ◽  
Kristoffer H. Aronsen ◽  
Oddgeir Dalane
Keyword(s):  
Bending Moment ◽  
Current Profile ◽  
Short Term ◽  
Sea State ◽  
Strength Performance ◽  
Steel Catenary Riser ◽  
Analysis Methodology ◽  
Riser Design ◽  
Term Analysis

Strength performance of a steel catenary riser tied back to a Spar is presented based on long term and short term analysis methodologies. The focus of the study is on response in the riser touch down zone, which is found to be the critical region based on short term analysis results. Short term riser response in design storms is computed based on multiple realizations of computed vessel motions with various return periods. Long term riser response is based on vessel motions for a set of 45,000 sea states, each lasting three hours. The metocean criteria for each sea state is computed based on fifty six years of hindcast wind and wave data. A randomly selected current profile is used in the long term riser analysis for each sea state. Weibull fitting is used to compute the extreme riser response from the response of the 45,000 sea states. Long term analysis results in the touch down zone, including maximum bending moment, minimum effective tension, and maximum utilization using DNV-OS-F201, are compared against those from the short term analysis. The comparison indicates that the short term analysis methodology normally followed in riser design is conservative compared to the more accurate, but computationally more expensive, long term analysis methods. The study also investigates the important role that current plays in the strength performance of the riser in the touch down zone.

Analysis of Ship Structural Loading in a Seaway

1972 ◽  
Vol 9 (02) ◽  
pp. 173-194
Author(s):  
Dan Hoffman
Keyword(s):  
Pressure Distribution ◽  
Phase Relationship ◽  
Bending Moment ◽  
Green Water ◽  
Detailed Structural Analysis ◽  
Transverse Pressure ◽  
Structural Loading ◽  
Wave Induced

The recent advent of the large tanker and bulk carrier has promoted the requirements for more detailed structural analysis of a ship and the reevaluation of theories for calculating the static, quasistatic and dynamic loads. The paper begins with discussion of the methods available to determine the various types of loads expected, their phase relationship, and ways of superimposing them. It then proceeds to the treatment of sea loads based on theoretical and experimental data, and techniques of determining the ship response in a seaway are discussed. The response to regular waves is reviewed with special reference to the determination of pressure distribution on the hull. Statistical ship response, immediate and cumulative over the life of the ship, is demonstrated in relation to the prediction of long-term bending moment trends, and the distribution of the extremes is discussed. Special loading conditions are described with special emphasis on the transverse pressure distribution, dynamic effects due to motion of liquid cargo in tanks, shipping of green water, wave-induced vibrations, slamming pressures and whipping stresses due to various causes. The paper treats the above subjects in a broad manner and no attempt to illustrate the theory in detail is made.

Prediction of Green Water Events on FPSO Vessels

2003 ◽  
Author(s):  
Alexander Fyfe ◽  
Edward Ballard
Keyword(s):  
Probability Distributions ◽  
Green Water ◽  
Design Stage ◽  
Wave Crest ◽  
Peak Period ◽  
Wave Conditions ◽  
Motion Characteristics ◽  
Central North Sea

Most floating vessels experience some sea states, not necessarily extreme storms, which cause large volumes of green water to flow across the deck. Due to the location of safety critical equipment on the deck of FPSOs, the determination of the likely occurrences and the magnitudes of such events are critical to safe design and operation. A method for the determination of green water heights on the deck of an FPSO has been presented in references 1–5. This paper examines the long-term distributions of heights implied by these references and the identification of sea states in which extreme events are likely to occur. The method is based upon the long term distribution of sea states at the intended location, combined with the motion characteristics of the vessel. Freeboard exceedance at the bow and at a point along the side is considered for two typical FPSO configurations. The methodology presented is widely applicable to many locations but wave conditions typical of the Central North Sea are used by way of illustration. The results presented include long term probability distributions of green water height on deck at locations of interest. Relative contributions of each combination of significant wave height and peak period to the probability of the largest single event in a defined return period are determined and discussed. It is shown that the wave conditions most likely to give rise to the most severe green water events are seldom those characterized by the largest wave crest heights. Instead, there exists a complex dependence on characteristic periods associated with vessel motions and on the long-term occurrences of particular sea states. The ability to predict conditions in which the largest green water events are most likely to occur offers the possibility of providing improved operational guidelines for FPSOs, allowing action to be taken to avoid unfavourable loading conditions and/or vessel headings in certain sea conditions. However, it is also shown that it may be difficult to identify some severe green water sea states from normally available forecast data and hence it is important that appropriate provision is made at the design stage.

Random Waves and Capsize Probability Based on Large Amplitude Motion Analysis

2002 ◽  
Author(s):  
Jan O. de Kat ◽  
Dirk-Jan Pinkster ◽  
Kevin A. McTaggart
Keyword(s):  
Time Domain ◽  
Random Waves ◽  
Extreme Wave ◽  
Small Probability ◽  
Safe Operation ◽  
Short Term ◽  
Physical Behavior ◽  
Wind Climate ◽  
Large Amplitude Motion

The objective of this paper is to apply a methodology aimed at the probabilistic capsize assessment of two naval ships: a frigate and a corvette. Use is made of combined knowledge of the wave and wind climate a ship will be exposed to during its lifetime and of the physical behavior of that ship in the various sea states it is likely to encounter. This includes the behavior in extreme wave conditions that have a small probability of occurrence, but which may be critical to the safe operation of a ship. Time domain simulations provide the basis for deriving short-term and long-term statistics for extreme roll angles. The numerical model is capable of predicting the 6 DOF behavior of a steered vessel in wind and waves, including conditions that may lead to broaching and capsizing.

Sensitivity Analysis in Parametric Rolling of a Modern Cruise Ship Using Numerical Simulations in 6-DOF

2020 ◽  
Author(s):  
Bülent Düz
Keyword(s):  
Sensitivity Analysis ◽  
Numerical Simulations ◽  
Time Domain ◽  
Nonlinear Phenomenon ◽  
Cruise Ship ◽  
Parametric Roll ◽  
Parametric Rolling ◽  
Maximum Angle ◽  
Strip Theory ◽  
The Time Domain

Abstract Parametric roll is a nonlinear phenomenon that can result in large roll angles coupled with significant pitch motions. These motions might induce large loads on the ship structure, and compromise the safety of the crew and the cargo. The severity of the motions might reach to such levels that capsizing might occur. In this study sensitivity analysis in parametric rolling of a modern cruise ship is investigated using numerical simulations. Several parameters were considered as sources of uncertainty such as the combined effect of GM and roll radius of gyration, roll damping, ship speed, and fin characteristics. In terms of fin characteristics, fin angle rate and maximum angle, fin area and aspect ratio, and fin gains were investigated. Additionally, the non-ergodicity of parametric roll was studied as well as the effect of simulation duration on the statistics of parametric roll. The simulations were carried out with a hybrid time-domain seakeeping and manoeuvring code. The time-domain code was used in combination with a strip-theory based frequency-domain program in order to calculate diffraction and radiation forces as well as added-mass. The time-domain code was able simulate the dynamic behavior of a steered ship in 6-DOF, where the motions can be large up to the moment of capsize.

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