Oblique Seas Research Articles

Experimental investigations on extreme bow-flare slamming loads of 10,000-TEU containership

Bow-flare slamming is issue that must be considered in ship design because it affects the local strength and fatigue life of a ship. In this paper, the experimental study of the spatial distribution of slamming load was conducted, which acts on the bow flares of ultra-large containerships. For a model test, 10,000 TEU container ship model with 1/60-scale ratio divided into six segments was applied. Fifteen force sensors were placed on the bow flare surface to measure slamming load. The slamming loads were measured in regular and irregular waves at various ship speeds, wave lengths, wave heights, and heading angles. In a regular wave test, the slamming load was larger in oblique sea than in head sea because the relative angle of the wave and bow flare is smaller in oblique sea. In an irregular wave test, extremely large slamming loads were measured at the centre line at the bow, which is influenced by the horizontal relative velocity such as the ship speed and surge. In an analysis of the slamming load of the ship, the direction of wave and forward speed of the ship should be carefully considered. These are difficult to consider in 2D analysis.

Oblique wave scattering by double porous structures

The linear wave scattering by double submerged structures of different structural parameters in oblique sea is investigated by use of eigenfunction expansion method. The important hydrodynamical scattering quantities such as reflection, transmission and dissipation coefficients are obtained and analyzed to examine the effects of various wave and structural parameters. As a special case, the computational results are validated for their accuracy by comparing with known results in the literature in case of single structure. The study reveals that a significant amount of wave energy dissipated in case of double structures as compared to that in the presence of single structure. Moreover, the energy dissipation is found to be independent of relative spacing between the two structures.

A Semi-Analytical Method for the PDFs of A Ship Rolling in Random Oblique Waves

The PDFs (probability density functions) and probability of a ship rolling under the random parametric and forced excitations were studied by a semi-analytical method. The rolling motion equation of the ship in random oblique waves was established. The righting arm obtained by the numerical simulation was approximately fitted by an analytical function. The irregular waves were decomposed into two Gauss stationary random processes, and the CARMA (2, 1) model was used to fit the spectral density function of parametric and forced excitations. The stochastic energy envelope averaging method was used to solve the PDFs and the probability. The validity of the semi-analytical method was verified by the Monte Carlo method. The C11 ship was taken as an example, and the influences of the system parameters on the PDFs and probability were analyzed. The results show that the probability of ship rolling is affected by the characteristic wave height, wave length, and the heading angle. In order to provide proper advice for the ship's manoeuvring, the parametric excitations should be considered appropriately when the ship navigates in the oblique seas.

Wave radiation and diffraction by a floating rectangular structure with an opening at its bottom in oblique seas

The radiation and the diffraction of linear waves by a rectangular structure with an opening at its bottom floating in oblique seas of finite depth are investigated. Analytical expressions for the radiated potentials and the diffracted potential are obtained by use of the method of separation of variables and the eigenfunction expansion method, with the unknown coefficients being determined by the boundary conditions and the matching requirement on the interface. The hydrodynamic coefficients and the wave excitation forces are verified using the symmetry properties of coupled hydrodynamic coefficients and one specific example investigated previously. By use of the present analytical-numerical solution, the influences of the angle of incidence, the width of the opening on the wave forces and the hydrodynamic coefficients are investigated. It is also found that in the oblique sea the external excitation frequency that can lead to the resonance of a rectangular tank depends on the wave direction and the wave number of the incident wave.

URANS predictions of wave induced loads and motions on ships in regular head and oblique waves at zero forward speed

The paper presents predictions on the hydrodynamics of a conceptual floating liquefied natural gas (FLNG) and a liquefied natural gas (LNG) carrier in regular head and oblique sea waves using an unsteady Reynolds-Averaged Navier–Stokes (URANS) solver. Initially, a verification and validation study is performed on estimating the numerical uncertainties in the presented URANS simulations. Using the verified numerical setup, ship hydrodynamic properties including wave induced loads as well as ship motion responses are investigated for different wave conditions. The computed time history results are decomposed by Fourier Series to estimate the wave load and ship motion transfer functions. These results show good correlation with predictions from model tests and potential flow calculations. From the computations, it is observed when increasing the wave length, wave diffraction around the ship becomes less profound and the water depth starts to influence the transfer functions. Full scale computations in head and oblique sea waves are also presented and compared with model scale predictions for investigating possible scale effects. The differences are found to be close to the numerical uncertainties, indicating minor influences of scale effects on the prediction of wave loads and ship motion responses for the tested cases.

Numerical investigation of wave-induced vibrations and their effect on the fatigue damage of container ships

Wave-induced vibrations of the ship hull girder consist of springing when it is associated with a resonance phenomenon, and whipping when it is caused by a transient impact loading due to wave slamming. This paper presents a new approach to predict the wave-induced vibrations and their contributions to fatigue damage of container ships. The seakeeping, whipping, springing and elastic modes calculations are coupled in every time step. According to the design characteristics of large container ships the existing methods are modified, air cushion effect and flow separation are considered in the slamming calculation, symmetric and asymmetric vibration modes equations are applied to predict the springing response in head seas and oblique seas. Based on rain flow counting method, spectral-based analysis method is used to calculate the additional fatigue damage due to springing and whipping.

Estimation of added resistance and ship speed loss in a seaway

The prediction of the added resistance and attainable ship speed under actual weather conditions is essential to evaluate the true ship performance in operating conditions and assess environmental impact. In this study, a reliable methodology is proposed to estimate the ship speed loss of the S175 container ship in specific sea conditions of wind and waves. Firstly, the numerical simulations are performed to predict the added resistance and ship motions in regular head and oblique seas using three different methods; a 2-D and 3-D potential flow method and a Computational Fluid Dynamics (CFD) with an Unsteady Reynolds-Averaged Navier-Stokes (URANS) approach. Simulations of various wave conditions are compared with the available experimental data and these are used in a validation study. Secondly, following the validation study in regular waves, the ship speed loss is estimated using the developed methodology by calculating the resistance in calm water and the added resistance due to wind and irregular waves, taking into account relevant wave parameters and wind speed corresponding to the Beaufort scale, and results are compared with simulation results obtained by other researchers. Finally, the effect of the variation in ship speed and therefore the ship speed loss is investigated. This study shows the capabilities of the 2-D and 3-D potential methods and CFD to calculate the added resistance and ship motions in regular waves in various wave headings. It also demonstrates that the proposed methodology can estimate the impacts on the ship operating speed and the required sea margin in irregular seas.

Interaction of oblique waves and a rectangular structure with an opening near a vertical wall

With the method of separation of variables and the eigenfunction expansion employed, an analytical solution is presented for the radiation and diffraction of a rectangular structure with an opening near a vertical wall in oblique seas, in which the unknown coefficients are determined by the boundary conditions and matching requirement on the interface. The effects of the width of the opening and the angle of incidence on the hydrodynamic characteristics of a rectangular structure with an opening near a vertical wall are mainly studied. The comparisons of the calculation results with wall-present and with wall-absent are also made. The results indicate that the variation trends of the heave added mass and excitation force with wall-present are almost the same as those with wall-absent, and that the peak values in the former case are obviously larger than those in the latter due to the reflection of the vertical wall.

Seakeeping Performance of Series 60 Ships

The seakeeping performance in terms of added resistance in head and oblique seas of five series 60 ships, parent form, have been evaluated analytically. The results are presented in tabular forms as function of principal particulars of ship, Froude Number, wave heading and the seaway. Some comparisons of the results obtained analytically have been made with that obtained from seakeeping tables of Grigoropoulos et. al. [2].

Design safety margin of a 10,000 TEU container ship through ultimate hull girder load combination analysis

Assessment of the ultimate longitudinal strength of hull girders under combined waveloads can be of particular importance especially for ships with large deck openings and low torsional rigidity. In such cases the horizontal and torsional moments may approach or exceed the vertical bending moment when a vessel progresses in oblique seas. This paper presents a direct calculation methodology for the evaluation of the ultimate strength of a 10,000 TEU container ship by considering the combined effects of structural non-linearities and steady state wave induced dynamic loads on a mid ship section cargo hold. The strength is evaluated deterministically using non-linear nite element analysis. The design extreme values of principal global wave-induced load components and their combinations in irregular seaways are predicted using a cross-spectral method together with short-term and long-term statistical formulations. Consequently, the margin of safety between the ultimate capacity and the maximum expected moment is established.

Global Structure Strength Analysis of SWATH Based on Direct Calculate Method

The stress concentration of SWATH’s cross-deck structure is serious and the problem of its structure strength appears particularly important. In this paper, A 3-D global element model of SWATH was built, the design Loads, load cases and boundary conditions were studied. on the base of that, the structure response analysis was completed. The result show that the global ship’s stress is small in all load cases of head seas and oblique seas, and the bulkheads have serious stress concentration phenomenon in beam seas.The result can offer the reference for SWATH’s design and development.

Maximum wave power absorption by slender bodies of arbitrary cross sections in oblique seas

Published results for the maximum wave power absorption by slender bodies subjected to vertical deformations are extended. To this end, a more general form of the Kochin function is derived for floating or submerged slender bodies of arbitrary (asymmetric) cross sections undergoing vertical or horizontal deformations. The Kochin function allows a determination of the theoretical maximum wave power absorption in oblique seas. It is shown that in beam seas, two-dimensional limits can be recovered when the slender body length tends to infinity. This establishes a formal continuity in behavior from attenuators (head seas) to terminators (beam seas). The wavelike vertical and horizontal deformations of a flexible body, as well as the hinge motions of an articulated raft are also considered in oblique seas. In the former case, results suggest an equivalence between the maximum absorption width of bodies with symmetric cross sections and two degrees of freedom, and that of bodies with optimal cross sections and one degree of freedom. Overall, the potential for significant wave power absorption from horizontal motions is also demonstrated.

Nonlinear effects from wave-induced maximum vertical bending moment on a flexible ultra-large containership model in severe head and oblique seas

Vertical bending moment (VBM) is of crucial importance in ensuring the survival of vessels in rough seas. With regard to conventional vessels, wave-induced maximum VBM is normally considered to be experienced in head seas. It is conservative to determine the extreme VBM based on either numerical simulations or model tests in long-crested head seas. Extensive model tests have been conducted in head seas with focus on the nonlinear vertical responses in severe seas, and the measured results were compared with numerical calculations for validation. Unexpected phenomena, however, were observed during the model tests of an ultra-large containership. The maximum sagging and hogging VBMs were encountered in oblique seas. Furthermore, the significant wave height used in oblique seas was even smaller than that used in head seas. The nonlinear vertical load effects in oblique seas require further investigations for this particular vessel. Limited experimental results in oblique seas have been reported, in which the lateral responses were always more concerned than the vertical responses. Up to now, rare systematic comparisons of the nonlinear vertical responses between head and oblique seas have been published, especially when the hydroelastic effects are also accounted for. A 13000-TEU ultra-large containership model, which was designed by Hyundai Heavy Industries (HHI), has been tested in the towing tank and the ocean basin at the Marintek center in Trondheim. The experimental results in regular waves are first compared between head and oblique seas. The statistical characteristics of the VBM amidships under nineteen irregular wave conditions are then investigated. Next, the extreme hogging and sagging VBMs are compared under different wave conditions with focus on the extreme hogging VBMs. At the end of the paper, the uncertainties in the experiments are discussed.

Wave Spectrum Based Fatigue Analysis for Mediterranean Sea, Black Sea and Aegean Sea

In this study, wave spectrum based fatigue analyses are studied for Turkey's adjacent coastal seas by using Maestro finite element analyzing software. Palmgren-Miner's method is used to obtain the fatigue safe life time. Palmgren-Miner's method was selected for the fatigue analyses because of its good acceptance of data from almost all classification societies such as Germanischer Lloyd, the American Bureau of Shipping, Det Norske Veritas, etc. The maximum stress regions of the structures are obtained by using finite element analyses, and the results are compared with the endurance limit of the W<TEX>$\ddot{o}$</TEX>hler diagram of AA5059 H321 aluminum alloy. The wave characteristics table given in this article is used to obtain the number of cycles for each sea condition. By using the wave characteristics table, the wave lengths, wave speeds, and cycles are obtained. This study is performed to estimate the lifetimes of a semi-swath type coast guard boat and/or commercial yacht projects, which are produced by using AA5059 H321 aluminum alloy, under different sea environment conditions. Fatigue examinations are performed for both head seas and oblique seas.

Wave-Induced Motions of Gas Cat: A Novel Catamaran for Gas Processing and Offloading

The preliminary development of the novel concept of using a large catamaran, known as Gas Cat, as a floating natural gas processing and offloading facility is outlined. The proposed system is based on two ship-shaped hulls joined by a spanning superstructure. For off-loading purposes a carrier may dock with or be tethered to the catamaran. A concept design has been developed based on two retrofitted VLCCs allowing for the processing and storage of 1 × 106 bbls of condensate and approximately 240,000 m3 of liquefied natural gas. A key aspect of the development of this concept is the accurate estimation of the motions of the catamaran in a variety of operational scenarios. Model experiments were conducted in the Model Test Basin of the Australian Maritime College using a 1:78 scale model of two full-form hulls converted into a catamaran configuration. Tests were conducted in head, beam, and oblique seas for two hull spacings and a range of wave heights. The experimental results show that for the range of wave conditions tested good linearity of the motions can be expected with respect to wave height. An increase in demihull separation was found to significantly reduce the sway, heave, and roll motions in beam seas. However, a change in demihull separation had little influence on the motions in oblique seas. A change in heading angle from head seas to beam seas significantly increased the sway, heave, and roll motions while reducing pitch motions. Bow quartering seas were seen to be the worst heading angle for yaw. The results from the experiments allowed the expected motions of the Gas Cat to be determined in extreme weather conditions.

Experimental investigation into wave-induced design loads on a large moored catamaran

A new concept uses a large catamaran, Gas Cat, as a floating natural gas processing, storage and offloading facility. The concept design of the vessel is based on two retrofitted very large crude carriers allowing for the processing and storage of 1 million bbls of condensate and approximately 240,000 m3 of liquid natural gas. Key to the development of this concept is the accurate estimation of the wave-induced cross-demi-hull loads experienced by the catamaran in a variety of operational scenarios. Model experiments were conducted in the model test basin of the Australian Maritime College using a 1:78 scale model of two full-form hulls, converted into a catamaran configuration, to measure the wave-induced forces and moments. Tests were conducted in head, beam and oblique seas for two hull spacings and a range of wave heights. The experimental results show that for the range of wave conditions tested, good linearity of the forces and moments can be expected with respect to wave height. This allows the results to be used to determine expected loads for a range of wave conditions. Changes in demi-hull separation were found to have little influence on the measured cross-demi-hull loads. Forces and moments were the least for the head sea condition; therefore, in order to minimise the wave-induced loads on the vessel, it is recommended that it be allowed to weathervane with the prevailing swell direction. The forces and moments which may be expected in Timor Sea 10,000-year return storm conditions have been estimated based on the model results. These provide valuable data for the preliminary design of an appropriate structural configuration for the vessel.

Experimental investigation of hull girder vibrations of a flexible backbone model in bending and torsion

Although the coupled horizontal–torsional vibrations of open ships have been investigated numerically for decades, the available experimental data in oblique seas seem rare. Model tests, considering natural frequencies of bending and torsional modes, have been conducted by the Centre for Ships and Ocean Structures (CeSOS) in the towing tank and ocean basin. A flexible backbone model was designed with five cut-outs on the top side of the aluminum beam to realize approximately torsional stiffness as well as vertical and horizontal bending stiffness. This paper mainly deals with measured bending and torsional vibrations in regular and irregular waves. The damping ratios, mode shapes, and modal moments were derived from experimental data, and a numerical model based on modal superimposition is established according to the measured hydroelastic properties. Some time-domain simulations are carried out considering the structural characteristics, and compared with measured results. The test data in regular waves are presented to show the possible factors of influence on the vibrations. The effect of bending and torsional vibrations on the extreme response values in irregular waves is estimated. The uncertainties in the experiments are discussed and conclusions are presented at the end of this paper.

Experimental and Numerical Study of Wave-Induced Load Effects of Open Ships in Oblique Seas

Open ships inherently possess low torsional rigidity because of their open deck structural configuration. Some of the structural failures for open ships are caused by wave-induced torsional moment in combination with other load components in oblique seas. Relatively few experimental results about horizontal bending and torsional moments in oblique seas have been published, however. Further, test data for vertical shear force and vertical bending moment in oblique seas are quite scarce. A backbone model has been recently tested by the Center for Ships and Ocean Structures (CeSOS) in the towing tank and ocean basin at the Marine Technology Center. The model consists of 15 box-shaped segments, in addition to bow and stern segments, which are interconnected by an aluminum beam on the top. Model tests in oblique seas without forward speed were first carried out to provide basic comparisons. Tests in head and oblique seas with speeds were then conducted in regular waves. Irregular wave tests were also carried out to assess the spectral responses and peak distributions of cross-sectional load effects. Load effects at 7 longitudinal positions were measured through strain gauges, including vertical shear force (VSF), vertical bending moment (VBM), horizontal bending moment (HBM), and torsional moment (TM). The motivation of this paper is to perform a benchmark study by comparing numerical predictions of different computer codes with these test results. The uncertainties in the experiments and the computer codes are discussed, and conclusions are presented at the end of this paper.

Evaluation of Effects of Wave-induced Vibrations on Fatigue Damage of Large Ships

Low frequency response to normal wave loads and high frequency response due to wave-induced vibrations coexist in the ship's structural loads. This paper addresses the effect of the wave-induced vibrations on long-term fatigue damage in various types of ships. A bulk carrier, a VLCC, and a container carrier are employed as subject ships. A weakly nonlinear method proposed by one of the authors is employed for evaluating the load effects. Slamming loads are separately implemented by using momentum theory.The whole ship is represented by using shell FE model. The calculations are performed for various short-term sea states. Stress cycles are counted by using Rainflow counting method. Then, long-term fatigue damage is evaluated by using the Palmgren-Miner rule. A series of sensitivity analysis is also performed to clarify the characteristics of the fatigue damage by the wave-induced vibrations in oblique seas as well as in head seas. It is shown that the amount of the increase in fatigue damage depends on the wave load characteristics of the ships in waves as well as the structural properties such as natural frequencies of flexible mode.

Numerical analysis and validation of weakly nonlinear ship motions and structural loads on a modern containership

This paper aims to validate a numerical seakeeping code based on a 3D Rankine panel method by comparing its results with experimental data. Particularly, the motion response and hull-girder loads on a real modern ship, a 6500 TEU containership, are considered in this validation study. The method of solution is a 3D Rankine panel method which adopts B-spline basis function in the time domain. The numerical code is based on the weakly nonlinear scheme which considers nonlinear Froude–Krylov and restoring forces. The main focus of this study is given to investigate the nonlinear characteristics of wave-induced loads, and to validate this present scheme for industrial use in the range of low Froude number. The comparisons show that the nonlinear motions and hull-girder loads, computed by the present numerical code, have good overall agreements with experimental results. It is found that, for the better accuracy of computational results, particularly at extreme waves in oblique seas, the careful treatment of soft-spring (or compatible) system is recommended to the control of non-restoring motions such as surge, sway, and yaw.