Short-crested Irregular Waves Research Articles

Experimental reproduction of inhomogeneous fjord waves

Waves in coastal areas and fjords can present inhomogeneities that affect the responses of very large floating structures. However, spatial inhomogeneities of waves are usually not included in model testing. In this paper, the feasibility of generating inhomogeneous wave conditions in an Ocean basin is investigated. For that purpose, a fast linear numerical model of a basin of constant depth is applied, and an optimization method is presented, that allows to find the control signal for the multiflap wavemaker. Comparisons with experiments in SINTEF’s Ocean basin demonstrate the validity of the method for generating simple monochromatic synthetic waves, as well as short-crested irregular waves representing realistic conditions in Sulafjorden.

A numerical study of added resistance performance and hydrodynamics of KCS hull in oblique regular waves and estimation of resistance in short-crested irregular waves through spectral method

Research on multidirectional waves is increasing as studies on added resistance advance. In this study, the added resistance of the multidirectional regular waves of the KCS hull was estimated by numerical analysis. The direction of the grid was changed according to the heading angle to consider waves in multiple directions. In addition, the method in which the entire domain moved along the movement of the hull was used without using the overset method to minimize the numerical errors. The added resistance and motion RAOs for each angle and the flow characteristics were compared to support the results. For fluid dynamics, time-averaged stern dynamics pressure, boundary layer, and nominal wake for each heading angle were compared, and differences compared to calm water were also reviewed. Based on the bow quartering sea condition analysis results, the added resistance in long-crested and short-crested irregular wave conditions was estimated using the spectral method. The JONSWAP spectrum was used as the target wave spectrum, and the cos-power type was considered the directional spreading function.

Analysis of FPSO Motion Response under Different Wave Spectra

A variety of floating structures at sea play a vital role in the exploitation and utilization of marine resources. The study about interactions between waves and structures is necessary for the impact of the harsh marine environment on the motion and service life of structures. Currently, most studies about the seakeeping of structures are based on simplified regular waves. Because the regular waves do not truly restore the actual wave conditions at sea, the simulation of irregular waves has great practical importance to the study of interactions between waves and structures. Based on the potential flow theory and high-order boundary element method (HOBEM), a Fortran code is developed in this paper and named as SWBI (Solver for Wave–Body Interactions). This program consists of the following two parts: a time–domain numerical model about interactions between waves and 3D structures is based on weakly nonlinear method, and a numerical model about simulation of the nonlinear regular waves, the long-crested irregular waves, and the short-crested irregular waves. This Fortran code is used to simulate the motion of Floating Production Storage and Offloading (FPSO) under three different ocean wave spectra (including ITTC two-parameters spectrum, JONSWAP spectrum and the most likely spectral form of Ochi-Hubble) and found that: To a certain extent, the difference in the motion of FPSO under different wave spectra have a connection with different type of wave, sea conditions and incident angle. The difference in roll of FPSO is quite significant in short-crested irregular waves. The range of FPOS’s roll under the JONSWAP spectrum is the largest when the incident angle is 30°, and range of FPOS’s roll under the most likely spectral form of Ochi-Hubble is the largest when the incident angle is 90°.

Probabilistic estimation of the large heel due to broaching associated with surf-riding for a ship in short-crested irregular waves and its experimental validation

The International Maritime Organization started using a numerical simulation to quantify the probability of a ship's stability failure as a direct stability assessment for broaching associated with surf-riding. Some of the authors proposed a critical wave method to estimate such probability, and its numerical verification and experimental validation in long-crested irregular stern-quartering waves were already published. The remaining issue is numerically verifying and experimentally validating the methodology applied to short-crested irregular stern-quartering waves. The work described in this paper is an attempt to resolve this remaining issue by executing numerical simulation and a free-running model experiment in both short-crested and long-crested irregular waves. The subject ship used in this work is an ocean research ship similar to the one lost in actual stern-quartering waves with higher speed, which was used in our previous study in regular waves. The experimental results indicate that the direct counting in the numerical simulation shows stochastically sufficient agreement with the model experiment, and the critical wave method provides reasonably conservative estimates even in short-crested irregular waves.

CFD investigation on the hydrodynamic loads and motions when ship maneuvers in regular and irregular waves

To explore and predict the ship maneuverability in the regular and irregular waves, the zigzag tests, the turning tests, and the course-keeping tests for the model-scale S175 containership under various wave conditions are simulated. The simulations are performed using a structured overset Unsteady Reynolds Averaged Navier-Stokes (URANS) solver with a moving grid. A body force method is adopted to predict the propeller forces. The simulation results are validated by the free-running experiments with satisfactory accuracy, which indicates that the present simulation strategy is effective and reliable. The hydrodynamic loads on the hull and the rudder together with the ship motion characteristics during the maneuvers in waves are obtained. It is concluded that the ship motions and hydrodynamic loads increase with the increase of the wavelength when the wave height is kept constant. The variation trends and magnitudes for low-frequency components of the self-propulsion factors in waves are similar to those in the calm water condition except obvious high-frequency fluctuations due to the wave effect. For the zigzag tests under the long-crested and short-crested irregular waves, the time histories of the yaw and rudder angle are similar. For the turning tests, the amplitude of roll motion in waves is much larger compared with that of the zigzag tests under the same wave condition, and the drift of the trajectory due to the wave is obvious. The current course keeping simulation can be an alternative tool to predict course keeping maneuvers in waves. Furthermore, flow visualizations are presented for providing a better understanding of the wave effect on free-running ship maneuvers.

A practical direct URANS CFD approach for the speed loss and propulsion performance evaluation in short-crested irregular head waves

This paper employed a direct URANS CFD based approach to investigate the speed loss and waterjet performance for a waterjet-propelled trimaran in short-crested head waves. Firstly, a reasonable quantity of linear superposed regular waves was validated to simulate the realistic ocean wave adopted on the ITTC directional wave spectrum. Then the wave parameters were applied to the URANS CFD simulations, to avoid the wave reflection due to structures and to narrow the simulation domain, the Euler Overlay Method (EOM) based wave forcing zone was defined in the outer domain, the time history of the wave elevation and the wave patterns matched well with the theoretical results. Moreover, by employing the PID-controller and Body-Force method, the 1/30 scale waterjet-propelled trimaran free-running numerical model was validated through the trimaran model tests. Eventually, the free-running simulations in short-crested head waves of the trimaran were performed considering the effects of sea state, traveling speed, and wind, respectively. The added resistance in short-crested waves was mainly caused by the pitch and heave variation, and lead to the speed loss and waterjet performance deterioration. Notable, the wind-induced speed loss could account for nearly one half of the total while the wind speed exceeds the vessel speed. The proposed approach of direct evaluating the traveling and propulsion performance in short-crested waves shows reasonable results and practical value.

Estimation of full-scale ship manoeuvrability in adverse weather using free-running model test

The ship manoeuvrability in actual seas with both wind and waves, especially in adverse weather conditions, for a full-scale tanker with different maximum available power of the engine is studied. It is directly evaluated based on the result of a free-running model test (FRMT) under a course-keeping manoeuvre in long-crested and short-crested irregular waves of Beaufort scale force (BF) 7–10. The FRMT combines rudder effectiveness and speed correction considering the operational limit of an engine, and a wind load simulator, both of which were previously proposed by the authors. Therefore, not only the effect of waves but also effect of wind, rudder effectiveness of the full-scale ship, and the engine limit for continuous operation are considered in the FRMT. To validate the reliability of the direct evaluation method in FRMT and the measured data in irregular waves of large amplitude, the time-averaged manoeuvring motion of the FRMT at BF 9 is compared with ship manoeuvring motion under steady equilibrium conditions estimated using numerical simulation based on a modular mathematical model. The wave drift forces and moment in the simulation are determined on the basis of the results of the captive model test in regular waves, which is carried out using the same tanker model before the FRMT, so that we can eliminate the estimation errors in the manoeuvring motion caused by the imprecision in the wave drift forces as much as possible. The comparison shows the FRMT results acceptably agree with the simulation results, although a discrepancy is observed in the rudder angle in beam seas for the tanker with a low engine output. Further, FRMT data themselves show that full-scale rudder effectiveness, operational limit of an engine, and the engine with lower power cause the ship speed to decrease and the drift angle and the rudder angle to increase in head, bow, or beam seas because of the difference in the propeller rotational speed in each model control condition. In addition, it was clarified that operational limit of an engine also affects the significant single amplitudes of the fluctuating components of them and the oscillatory ship motion. Next, the authors assess the manoeuvring limit in adverse weather by comparing the FRMT data of the time-averaged values of the longitudinal ship speed, as well as the drift and rudder angles in short-crested irregular waves at BF 7–10 with their thresholds. The assessment clarifies that the tanker becomes unmanoeuvrable at BF 9–10 and in head, bow, or beam seas owing to a lack of sufficient advancing speed. However, the limit is not attributable to the drift or rudder angle, although the lower-power engine worsens the course-keeping ability owing to the decrease in the ship speed and the increase in the drift and rudder angles. Furthermore, the tanker is manoeuvrable in any wind and waves directions at BF 8, which is defined as adverse weather conditions for this subject ship in the interim guideline (IMO, 2013). It indicates that the tanker has sufficient margin of the engine power to keep manoeuvrability in adverse weather conditions. In summary, these findings reflect the possibility that FRMT can replace numerical simulation as a direct evaluation method of full-scale ship manoeuvring motion and limits in adverse weather.

Study of ship turning in irregular waves

This paper presents the turning test results of ships having a rudder angle of $$\pm 35^\circ$$ in short-crested irregular waves using ship models of a tanker (KVLCC2) and a container ship (KCS). The tests were performed in head waves at the time of approaching with the significant wave height 4.5 m for KVLCC2 and 3.0 m for KCS at full-scale. Turning indices such as the advance $$A_D$$ and tactical diameter $$D_T$$ , and drifting parameters during turning such as the drifting distance $$H_D$$ and drifting direction $$\mu _D$$ are used to characterize the ship turning in waves. With a decrease in the approach speed of the ships sailing in the same wave condition, $$A_D$$ decreases but $$D_T$$ does not change significantly. With a decrease in the approach speed, both $$H_D$$ and $$\mu _D$$ increase significantly, and the tendency of the ship drifting to the rudder execution point in space becomes remarkable. Although a variation in the turning trajectories which may be introduced due to the slowly varying second-order wave forces acting on the ship models is observed, its influence on turning is negligible in view of practical purposes. In addition, theoretical formulas for $$H_D$$ and $$\mu _D$$ were derived on the assumptions of small rudder angle, small maneuvering motions and small wave-induced steady forces. The calculation results using these formulas roughly agree with the turning test results. The formulas newly derived are useful for a better understanding of the wave-induced drift motion of ships during turning.

Direct Stability Assessment for excessive acceleration failure mode and validation by model test

Abstract The excessive acceleration is one of five stability failure modes for intact stability being discussed at IMO. The trial calculation for Direct Stability Assessment (DSA) and the model test have been carried out to verify two prediction methods of ship motions in the short-crested irregular waves for DSA. The ship motions in the short-crested irregular waves calculated by the linear superposition of frequency responses and the time domain simulation agree well with the results of the model test. Using experimentally validated prediction method and wave scatter table of North Atlantic, the long term probabilities have been calculated and the results obtained by two prediction methods become closer to each other. DSA evaluated by using the long-term failure probabilities obtained by two prediction methods are same.

Wake Effect Assessment in Long- and Short-Crested Seas of Heaving-Point Absorber and Oscillating Wave Surge WEC Arrays

In the recent years, the potential impact of wave energy converter (WEC) arrays on the surrounding wave field has been studied using both phase-averaging and phase-resolving wave propagation models. Obtaining understanding of this impact is important because it may affect other users in the sea or on the coastline. However, in these models a parametrization of the WEC power absorption is often adopted. This may lead to an overestimation or underestimation of the overall WEC array power absorption, and thus to an unrealistic estimation of the potential WEC array impact. WEC array power absorption is a result of energy extraction from the incoming waves, and thus wave height decrease is generally observed downwave at large distances (the so-called “wake” or “far-field” effects). Moreover, the power absorption depends on the mutual interactions between the WECs of an array (the so-called “near field” effects). To deal with the limitations posed by wave propagation models, coupled models of recent years, which are nesting wave-structure interaction solvers into wave propagation models, have been used. Wave-structure interaction solvers can generally provide detailed hydrodynamic information around the WECs and a more realistic representation of wave power absorption. Coupled models have shown a lower WEC array impact in terms of wake effects compared to wave propagation models. However, all studies to date in which coupled models are employed have been performed using idealized long-crested waves. Ocean waves propagate with a certain directional spreading that affects the redistribution of wave energy in the lee of WEC arrays, and thus gaining insight wake effect for irregular short-crested sea states is crucial. In our research, a new methodology is introduced for the assessment of WEC array wake effects for realistic sea states. A coupled model is developed between the wave-structure interaction solver NEMOH and the wave propagation model MILDwave. A parametric study is performed showing a comparison between WEC array wake effects for regular, long-crested irregular, and short-crested irregular waves. For this investigation, a nine heaving-point absorber array is used for which the wave height reduction is found to be up to 8% lower at 1.0 km downwave the WEC array when changing from long-crested to short-crested irregular waves. Also, an oscillating wave surge WEC array is simulated and the overestimation of the wake effects in this case is up to 5%. These differences in wake effects between different wave types indicates the need to consider short-crested irregular waves to avoid overestimating the WEC array potential impacts. The MILDwave-NEMOH coupled model has proven to be a reliable numerical tool, with an efficient computational effort for simulating the wake effects of two different WEC arrays under the action of a range of different sea states.

Real-Time Simulation of a Rescue Ship Maneuvering in Short-Crested Irregular Waves

Research on the mathematical model and the real-time simulation of the ship motion is investigated. An equation of three degrees of freedom (DOF) nonlinear maneuvering motion is established by means of the unified model in short-crested irregular waves in deep water. The resistance and propulsion dynamics are modeled by the classical methods as well as forces and moments of the rudder and the viscous crossflow. The three-dimensional boundary element method (BEM) using Green function source is adopted to solve the boundary value problem (BVP) in the frequency domain. The added mass and potential damping coefficients are calculated by Cummins method, and the mean wave drift forces by far-field formulas along with numerical verifications. After that, the turning motions of two ships (a rescue ship NHJ111 and the Mariner) in calm water are performed, and the relative error is approximately 7% by comparing calculated results with the experimental data. The maneuvering motion of the Mariner in short-crested irregular waves is then carried out. The turning trajectory, surge speed, and drift forces agree well with the theoretical results in regular waves. Finally, the synchronous interpolation method with two-thread double-timer is conceived. The real-time maneuvering simulation of NHJ111 using the validated model is then realized. The developed method can lay the foundation for fast computations of predicting the rescue ship motions in waves.

A comprehensive study on ship motion and load responses in short-crested irregular waves

Wave-induced ship motion and load responses are usually investigated on the assumption that the incident waves are long-crested. The realistic sea waves are however short-crested irregular waves. Real practice reveals that the ship motion and load responses induced by short-crested waves are different from those induced by long-crested waves. This paper aims to conduct a comprehensive study on ship motions and loads in different wave fields. For this purpose, comparative studies by small-scale model towing tank test and large-scale model sea trial are conducted to experimentally identify the difference between ship motions and loads in long-crested and short-crested irregular waves. Moreover, the influences of directional spreading function of short-crested waves on ship motions and loads are analyzed by numerical seakeeping calculation. The results and conclusions obtained from this study are of great significance for the further extrapolation and estimation of ship motions and loads in short-crested waves based on long-crested wave response results.

MODELLING OF WAVE ATTENUATION INDUCED BY MULTI-PURPOSE FLOATING STRUCTURES USED FOR POWER SUPPLY AND COASTAL PROTECTION

Experiments have been performed in the Shallow Water Wave Basin of DHI (Horsholm, Denmark) within the EU FP7 Hydralab Programme, on large farms of up to 25 heaving point absorber type Wave Energy Converters (WECs). For a range of geometric lay-out configurations and wave conditions (regular, polychromatic, long- and short-crested irregular waves), WEC response and modification of the wave field have been measured to provide data for the understanding of WEC farm interactions and for the evaluation of farm interaction numerical models. A first extensive wave farm database is established. The experimental arrangement and the obtained database are presented, as well as results for wave height attenuation downwave of the farms. For long-crested irregular waves, up to 18.1 % and 20.8 % reduction in significant wave height is observed downwave of the 5x5-WEC rectilinear and staggered farm, respectively. Wave height attenuation is expected to be larger, since in practical wave farm applications WECs will be controlled to extract a large amount of power from the waves, and therefore the array will cause larger wave height dissipation. These findings present the ability to combine the harvesting of energy from sea waves with coastal defence systems, resulting in cost reduction for both applications when WECs operate as multi-purpose devices.

Stochastic hydroelastic analysis of a very large floating structure using pseudo-excitation method

This paper is concerned with the linear hydroelastic response of a pontoon-type very large floating structure (VLFS) in short-crested irregular waves. The linear potential theory is employed for the analysis of VLFS in frequency domain. To decouple the fluid–structure interaction, the higher-order boundary element method (HOBEM) combined with the finite element method (FEM) is adopted. VLFS is modeled as a Mindlin plate, and the mode superposition method is used to reduce the dimension of dynamic equations. The pseudo-excitation method (PEM) is adopted to analyze the stationary stochastic response of the floating structure. The efficiency of this new calculation scheme with the application of PEM is investigated in comparison with the conventional method for stochastic response by analyzing the computational complexity theoretically. Finally, the new calculation scheme is validated by comparing with the experimental data as well as the existing numerical results calculated in the conventional way. In addition, the efficiency of the present numerical approach is also testified which indicates that the proposed numerical scheme is time-saving.

Wave Basin Experiments with Large Wave Energy Converter Arrays to Study Interactions between the Converters and Effects on Other Users in the Sea and the Coastal Area

Experiments have been performed in the Shallow Water Wave Basin of DHI (Hørsholm, Denmark), on large arrays of up to 25 heaving point absorber type Wave Energy Converters (WECs), for a range of geometric layout configurations and wave conditions. WEC response and modifications of the wave field are measured to provide data for understanding WEC array interactions and to evaluate array interaction numerical models. Each WEC consists of a buoy with a diameter of 0.315 m and power take-off (PTO) is modeled by realizing friction based energy dissipation through damping of the WEC’s motion. Wave gauges are located within and around the WEC array. Wave conditions studied include regular, polychromatic, long- and short-crested irregular waves. A rectilinear arrangement of WEC support structures is employed such that several array configurations can be studied. In this paper, the experimental arrangement and the obtained database are presented. Also, results for wave height attenuation downwave a rectilinear array of 25 heaving WECs are presented, for the case of irregular waves. Up to 16.3% and 18.1% (long-crested) and 11.2% and 18.1% (short-crested waves) reduction in significant wave height is observed downwave the WEC array, for the radiated wave field only and for the combination of incident-diffracted-radiated (perturbed) wave field, respectively. Using spectra at different locations within and around the array, the wave field modifications are presented and discussed.

Irregular wave transformation in the nearshore zone: experimental investigations and comparison with a higher order Boussinesq model

A non-linear wave propagation model, based on the higher order depth-integrated Boussinesq-type equations for breaking and non-breaking waves, was applied to predict irregular wave transformation in two horizontal dimensions. A new source function, adapted for the proposed equations, is introduced inside the computational domain, to generate the desired short-crested waves. The dissipation due to the roller is introduced in the momentum equation in order to simulate wave breaking. Bottom friction and sub-grid turbulent processes are also introduced in the model. At the open boundaries a damping layer is applied together with a radiation boundary condition. Model results are compared with experimental measurements, containing tests with normal or oblique to the shore long- and short-crested irregular waves. The comparisons show that the model is able to simulate successfully the non-linear evolution of a unidirectional or a multidirectional wave filed in the nearshore zone, under the effects of refraction, shoaling, and breaking.

斜め追波中におけるコンテナ船の転覆と波の多方向性との関係

In order to investigate capsizing in quartering and following seas, numerical simulations of the rolling motion were systematically carried out for a container ship sailing in short-crested irregular waves, e.g., directional spectrum waves. The obtained results are summarized as follows : (1) Low cycle resonance occurs for a container ship even in short-crested irregular waves. (2) The heading angle from the wave principal direction reduces danger of ship capsizing. (3) The short-crestedness of waves also reduces danger.

Homogeneity of Directional Irregular Waves with Side-Wall Reflections

For model experiments of nonlinear behaviors of a ship running in realistic ocean environment, it is necessary to generate short-crested irregular waves that have a specified and stationary directional spectrum in a model basin. However, the measurements of the waves generated by the double-summation method with side-wall reflections indicated that the variance of wave elevation is not stationary in space. Therefore, the authors carried out comprehensive numerical experiments to compare the double-summation method and single-summation one both with side-wall reflections. As a result, it is concluded that single-summation method even with side-wall reflections can be regarded as practically stationary in space but the double-summation method cannot.

Deterministic wave model for short-crested ocean waves: Part I. Theory and numerical scheme

A directional hybrid wave model (DHWM) has been developed for deterministic prediction of short-crested irregular ocean waves. In using the DHWM, a measured wave field is first decomposed into its free-wave components based on as few as three point measurements. Then the wave properties are predicted in the vicinity of the measurements based on the decomposed free-wave components. Effects of nonlinear interactions among the free-wave components up to second order in wave steepness are considered in both decomposition and prediction. While the prediction scheme is straightforward, the decomposition scheme is innovative and accomplished through an iterative process involving three major steps. The extended maximum likelihood method is employed to determine the directional wave spreading; the initial phases of directional free-wave components are determined using a least-square fitting scheme; and nonlinear effects are computed using both conventional and phase modulation methods to achieve fast convergence. The free-wave components are obtained after the nonlinear effects being decoupled from the measurements. Variety of numerical tests have been conducted, indicating that the DHWM is convergent and reliable.

On Statistical Properties of Wave Amplitudes in Stormy Sea

A method to estimate the statistical properties of non-linear short-crested irregular waves without any limitation regarding the directional spreading or the spectral band width is presented which is based on the secondary interaction theory of surface waves. It is shown that the statistical problem can be reduced to that of finding the eigenvalues and the eigenvectors of two real symmetric matrices and the probability density functions of surface elevation can be obtained using the so-called Saddle Points Method. Numerical investigations regarding the effect of shortcrestedness on the statistics of wave amplitudes are performed. And the method is also used to analyze full-scale data measured in stormy sea states and is shown to be a powerful tool for the estimation of the statistical properties of the directional sea.