Simulation Of Irregular Waves Research Articles

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°.

Development of model-based and model-free reactive control scheme: considering copper loss and movable-floater-displacement constraint for a wave energy converter

The utilization of wave energy is expected since ocean wave energy has a high potential. The improvement of the feasibility of wave energy converters requires control that maximizes the electric output energy, including the copper loss under a displacement constraint. Several model-based and model-free reactive controls have been developed. Although model-based reactive control attains high performance, it struggles to deal with modeling errors and forecasting wave excitation forces. On the other hand, the model-free reactive control can adapt to dynamic modeling, including modeling errors; however, it requires a vast amount of learning data and considerable time and effort to consider the displacement constraint. Model-based and model-free reactive controls each have advantages and disadvantages. Combined model-based and model-free reactive controls are desirable to freely switch between the model-based and model-free reactive controls based on various ocean situations. In this study, two equivalent model-based and model-free reactive controls that can consider the copper loss and displacement constraints without forecasting the wave excitation forces were proposed. The model-free reactive control was compared with the model-based reactive control and a conventional control using numerical simulations in irregular waves. The results of the simulation show that the proposed model-based reactive control achieves superior performance compared to that of the conventional control. The proposed model-free reactive control achieved comparable performance to that of the proposed model-based reactive control under various wave conditions. Moreover, the proposed model-free reactive control decreased the required training trials. The development of the two equivalent control schemes will lead to the proposal of combined model-based and model-free reactive controls in the future.

Turning circle tests with system-based simulations in irregular waves including wave drift and propeller side forces

Controlled motion in seas require mathematical modeling of ship motions under external disturbances. Waves are one of the most influential factors that undermine ship control. In this study, we investigate the maneuvering ability of the benchmark Japan Bulk Carrier (JBC) in calm water and in waves. Turning circle tests are conducted via system-based analysis and direct CFD method in calm water condition. Comparison of system-based analysis with experiments and direct CFD method have shown to be satisfactory. After validation of the mathematical model, empirical relations are used to include the ship drift in irregular wave conditions. Two different cases are considered. The first one is with constant significant wave height and changing wave angles. The second case is with constant wave angle but different significant wave height. The ship drift was observed to be in the direction of wave propagation, growing larger with increasing wave height. The maneuvering indices with changing wave directions were graphed and it revealed the maneuvering capability of JBC under the disturbance of waves.

Numerical Evaluation of Climate Scatter Performance of a Cycloidal Wave Energy Converter

Ocean waves offer an uninterrupted, rich resource of globally available renewable energy. However, because of their high cost and low power production, commercial wave energy converters are not operational at present. In this paper, we numerically evaluated the performance of a novel feedback-controlled lift-based cycloidal wave energy converter (CycWEC) at various sea states of the Humboldt Bay wave climate. The device comprised of two hydrofoils attached eccentrically to a shaft at a radius, submerged at a distance under the ocean surface. The pitch of the blades was feedback-controlled based on estimation of the incoming wave. The simulations were performed for regular waves and irregular waves approximated with a JONSWAP spectrum. Climate data from Humboldt Bay, CA was used to estimate the yearly power generation. The results underline the importance of a well-tuned control algorithm to maximize the annual energy production. The estimated annual energy production of the CycWEC was 3000MWh from regular wave simulations and 1800MWh from irregular wave simulations, showing that it can be a commercially viable means of electricity production from ocean waves.

Numerical study of swell impact on seakeeping performance of surface combatant

The complex sea states with the co-occurrence of swell and wind-sea conditions represent threats to sailing vessels. This study presents the computational fluid dynamics (CFD) simulations for a surface combatant model advancing in mixed seas combined with the swell and wind-sea components, aimed at estimating the swell impact on ship seakeeping performance. An in-house unsteady Reynolds-averaged Navier–Stokes solver coupled with an overset grid approach is applied to the numerical predictions, along with the assessment study for the model advancing in calm water and harmonic wave group based on the existed model tests, indicating the CFD results agree well with the experimental data. Irregular wave simulations are then conducted for the model advancing in head seas combined with different swell and wind-sea components. Comparisons of ship seakeeping behaviors for wind-sea dominated, energy equivalent, and swell dominated mixed seas are carried out with the statistical assessment and frequency analysis. Overall, both the heave and pitch amplitudes are larger as the ship is advancing in swell dominated sea than those in the other two seas. The ship motions are also predicted in wind sea and it indicates that the ship encounters the larger heave motion in mixed seas compared with that in wind sea.

Simulation stage-based seabed pre-trenching technique for steel catenary riser touchdown fatigue analysis

ABSTRACT The development of seabed trench by the steel catenary riser (SCR) touch-down zone (TDZ) in its early life can be caused by installation loads, direct hydrodynamic loads, and vessel first and second-order motions on the SCR. This paper presents a numerical technique by which pre-trench can be initiated for fatigue response calculations during SCR detailed design analysis. Examples are presented to demonstrate the new approach and how the SCR fatigue response can be calculated in the presence of the created pre-trench. The SCR (after the pre-trenching process) is allowed to respond to the vessel first order six degrees of freedom motions about its nominal position in the presence of the created pre-trench. As demonstrated in this paper, the pre-trenching technique makes it possible to conduct a full time-domain, irregular wave simulations of the SCR in the presence of a pre-trench created using the hysteretic non-linear pipe soil interaction mode.

CFD Research on the Hydrodynamic Performance of Submarine Sailing near the Free Surface with Long-Crested Waves

The simulations of submarine sailing near the free surface with long-crested waves have been conducted in this study using an in-house viscous URANS solver with an overset grid approach. First, the verification and validation procedures were performed to evaluate the reliability, with the results showing that the generation of irregular waves is adequately accurate and the results of total resistance are in good agreement with EFD. Next, three different submerged depths ranging from 1.1D to 3.3D were selected and the corresponding conditions of submarine sailing near calm water were simulated, the results of which were then compared with each other to investigate the influence of irregular waves and submerged depths. The simulations of the model near calm water at different submerged depths demonstrated that the free surface will cause increasing resistance, lift, and bow-up moments of the model, and this influence decreases dramatically with greater submerged depths. The results of the irregular wave simulations showed that irregular waves cause considerable fluctuations of hydrodynamic force and moments, and that this influence remains even at a deeper submerged depth, which can complicate the control strategies of the submarine. The response spectrum of hydrodynamic forces and moments showed slight amplitudes in the high-frequency region, and the model showed less sensitivity to high-frequency excitations.

Motion of Floating Caisson with Extended Bottom Slab under Regular and Irregular Waves

Floating caissons may oscillate primarily due to ocean waves during towing operations. Reducing the oscillation based on the extension part (footing) of the bottom slab of the caissons can efficiently increase the safety of towing maneuvers. However, the influence of the footing length on the motion of floating caissons has not been adequately studied. This study investigates this topic through hydraulic model experiments and numerical simulations. Experimental results for regular waves show that the rotational motion (pitch) of the caisson around the wave crest direction increases owing to resonance. This suggests that the pitch could be reduced by designing caissons, such that resonance may be prevented along the footing length. In the numerical simulations of irregular waves, the Fourier amplitudes of the heave and pitch show that the footings amplify their low-frequency components and reduce their high-frequency components. Furthermore, the significant total amplitudes of the heave and pitch show a different trend from that of the regular waves observed in the hydraulic model experiments. This suggests that it is essential to examine the motion of a caisson under irregular waves when assessing the effect of footings in an actual marine environment.

WaveMIMO Methodology: Numerical Wave Generation of a Realistic Sea State

This paper presents a methodology that allows the numerical simulation of realistic sea waves, called WaveMIMO methodology, which is based on the imposition of transient discrete data as prescribed velocity on a finite volume computational model developed in Fluent software. These transient data are obtained by using the spectral wave model TOMAWAC, where the wave spectrum is converted into a series of free surface elevations treated and processed as wave propagation velocities in the horizontal (x) and vertical (z) directions. The processed discrete transient data of wave propagation velocity are imposed as boundary conditions of a wave channel in Fluent, allowing the numerical simulation of irregular waves with realistic characteristics. From a case study that reproduces the sea state occurring on March 31st, 2014, in Ingleses Beach, in the city of Florianopolis, state of Santa Catarina, Brazil, it was concluded that the WaveMIMO methodology can properly reproduce realistic conditions of a sea state. In sequence, the proposed methodology was employed to numerically simulate the incidence of irregular realistic waves over an oscillating water column (OWC) wave energy converter (WEC). From these results, the WaveMIMO methodology has proved to be a promising technique to numerically analyze the fluid-dynamic behavior of WECs subjected to irregular waves of realistic sea state on any coastal region where the device can be installed.

Wave overtopping flow striking a human body on the crest of an impermeable sloped seawall. Part II: Numerical modelling

The present paper is the second of two companion papers on the investigations of wave overtopping flow striking a cylinder, which is the schematisation of a human body, on the crest of an impermeable sloped seawall with a deep foreshore. This paper numerically examines the detailed characteristics of the overtopping flow and the force on the cylinder in-line with the flow direction by using a volume-of-fluid (VOF) based Reynolds-Averaged Navier-Stokes (RANS) model. The numerical model is successfully validated against the experimental data on the wave overtopping flow depth and the inline force on the cylinder. The characteristics of the overtopping flow velocity are analysed using the validated numerical model. It is observed that the maximum depth-averaged flow velocity usually occurs before the maximum flow depth during an overtopping event, and decay of the overtopping velocity is much slower than the flow depth along the seawall crest. For plunging-breaker cases, the overtopping force on the cylinder usually comprises a cycle of a first impact peak, a main peak and a secondary peak. However, for surging-breaker cases, it is largely dominated by the main peak. The first impact peak is due to the impact of the tip of the overtopping flow on the cylinder, which usually has a higher flow velocity than the main stream. The main peak is generated by the asymmetric pressure distribution around the cylinder, which co-occurs with the maximum local momentum flux of the overtopping flow. As the force decreases after the main peak, there sometimes exists a secondary peak, which is formed by the complex free surface motion locally behind the cylinder. Additional numerical experiments are presented to demonstrate the applicability of a simple maximum force predictor developed in Part I. A prototype-scale simulation of irregular waves overtopping a sloped seawall is conducted to obtain the maximum force. The predictor also gives the maximum force in a wave-by-wave manner using the incident wave condition. These two approaches produce very similar estimates, suggesting that the predictor can be used for engineering applications.

Higher-order Spectral Method for Regular and Irregular Wave Simulations

In this study, a nonlinear wave simulation code is developed using a higher-order spectral (HOS) method. The HOS method is very efficient because it can determine the solution of the boundary value problem using fast Fourier transform (FFT) without matrix operation. Based on the HOS order, the vertical velocity of the free surface boundary was estimated and applied to the nonlinear free surface boundary condition. Time integration was carried out using the fourth order Runge–Kutta method, which is known to be stable for nonlinear free-surface problems. Numerical stability against the aliasing effect was guaranteed by using the zero-padding method. In addition to simulating the initial wave field distribution, a nonlinear adjusted region for wave generation and a damping region for wave absorption were introduced for wave generation simulation. To validate the developed simulation code, the adjusted simulation was carried out and its results were compared to the eighth order Stokes theory. Long-time simulations were carried out on the irregular wave field distribution, and nonlinear wave propagation characteristics were observed from the results of the simulations. Nonlinear adjusted and damping regions were introduced to implement a numerical wave tank that successfully generated nonlinear regular waves. According to the variation in the mean wave steepness, irregular wave simulations were carried out in the numerical wave tank. The simulation results indicated an increase in the nonlinear interaction between the wave components, which was numerically verified as the mean wave steepness. The results of this study demonstrate that the HOS method is an accurate and efficient method for predicting the nonlinear interaction between waves, which increases with wave steepness.

Short-term Prediction of Output Power and Constrained Optimal Control for Point-Absorber Type Wave-Energy Converters with Linear Generators

This paper addresses the issue of a control subject to physical constraints, involving an energy maximization for wave energy converters with a linear generator. Previous approaches to this problem including model predictive control (MPC) have currently some challenges. The conventional control methods, on the other hand, to be able to estimate the performance of wave energy converters are required in practice. In this study, casual constrained optimal control based on the short-term prediction method is proposed. A novel short-term prediction method of both satisfying with maximum output-power and limited heave amplitudes using the energy spectrum method is shown in this paper. Maximizing estimated output power subject to making the estimated amplitude smaller than motion limitation realizes maximizing output power under the heave-motion limitation. To confirm the accuracy of the short-term prediction method and the performance of the proposed control method, the output power is compared with the output power obtained from other control methods through the frequency and time domain simulations in irregular waves. The results show that the short-term prediction method is useful, and the proposed method can maximize output power under the heave-motion limitation.

Time-domain simulation of a slack-moored floating oscillating water column and validation with physical model tests

The development of devices for extracting wave energy from the ocean is largely supported by numerical models, as they allow the simulation of different configurations without the large costs of tank testing. From the different available options, time-domain models offer a very good combination between accuracy, flexibility and computational time. They allow the incorporation of non-linearities from power take-off systems, mooring lines, sophisticated control techniques and other relevant hydrodynamic effects. In this paper, we present a time-domain model to simulate the dynamics and power performance of a slack-moored Spar-buoy OWC (Oscillating Water Column) wave energy converter. The model considers linear hydrodynamics, mean drift forces, viscous drag effects and air compressibility inside the OWC chamber. The mooring system is simulated using a quasi-static approach. The floating structure is defined as a rigid body with six degrees of freedom, whereas the OWC free surface is assumed flat. The converter motion and power extraction from regular and irregular wave simulations are compared with experimental results from small-scale model tests in a wave channel. Numerical results show good agreement with experimental data except when parametric resonance is observed and near the channel cut-off frequencies.

A generating and absorbing boundary condition for dispersive waves in detailed simulations of free-surface flow interaction with marine structures

The boundaries of numerical domains for free-surface wave simulations with marine structures generate spurious wave reflection if no special measures are taken to prevent it. The common way to prevent reflection is to use dissipation zones at the cost of increased computational effort. On many occasions, the size of the dissipation area is considerably larger than the area of interest where wave interaction with the structure takes place. Our objective is to derive a local absorbing boundary condition that has equal performance to a dissipation zone with lower computational cost. The boundary condition is designed for irregular free-surface wave simulations in numerical methods that resolve the vertical dimension with multiple cells. It is for a range of phase velocities, meaning that the reflection coefficient per wave component is lower than a chosen value, say 2%, over a range of values for the dimensionless wave number kh. This is accomplished by extending the Sommerfeld boundary condition with an approximation of the linear dispersion relation in terms of kh, in combination with vertical derivatives of the solution variables. For this article, the boundary condition is extended with a non-zero right-hand side in order to prevent wave reflection, while, at the same time, at the same boundary, generating waves that propagate into the domain. Results of irregular wave simulations are shown to correspond to the analytical reflection coefficient for a range of wave numbers, and to have similar performance to a dissipation zone at a lower cost.

Lifetimes of Rogue Wave Events in Direct Numerical Simulations of Deep-Water Irregular Sea Waves

The issue of rogue wave lifetimes is addressed in this study, which helps to detail the general picture of this dangerous oceanic phenomenon. The direct numerical simulations of irregular wave ensembles are performed to obtain the complete accurate data on the rogue wave occurrence and evolution. Purely collinear wave systems, moderately crested, and short-crested sea states have been simulated by means of the high-order spectral method for the potential Euler equations. As rogue waves are transient and poorly reflect the physical effects, we join instant abnormally high waves in close locations and close time moments to new objects, rogue events, which helps to retrieve the abnormal occurrences more stably and more consistently from the physical point of view. The rogue event lifetime probability distributions are calculated based on the simulated wave data. They show the distinctive difference between rough sea states with small directional bandwidth on one part, and small-amplitude sea states and short-crested states on the other part. The former support long-living rogue wave patterns (the corresponding probability distributions have heavy tails), though the latter possess exponential probability distributions of rogue event lifetimes and generally produce much shorter rogue wave events.

Comparison of Numerical Solutions by TVD Schemes in Simulations of Irregular Waves Propagating over a Submerged Shoal Using FUNWAVE-TVD Numerical Model

Comparison of Numerical Solutions by TVD Schemes in Simulations of Irregular Waves Propagating over a Submerged Shoal Using FUNWAVE-TVD Numerical Model

A framework for efficient irregular wave simulations using Higher Order Spectral method coupled with viscous two phase model

In this paper a framework for efficient irregular wave simulations using Higher Order Spectral method coupled with fully nonlinear viscous, two-phase Computational Fluid Dynamics (CFD) model is presented. CFD model is based on solution decomposition via Spectral Wave Explicit Navier–Stokes Equation method, allowing efficient coupling with arbitrary potential flow solutions. Higher Order Spectrum is a pseudo-spectral, potential flow method for solving nonlinear free surface boundary conditions up to an arbitrary order of nonlinearity. It is capable of efficient long time nonlinear propagation of arbitrary input wave spectra, which can be used to obtain realistic extreme waves. To facilitate the coupling strategy, Higher Order Spectrum method is implemented in foam-extend alongside the CFD model. Validation of the Higher Order Spectrum method is performed on three test cases including monochromatic and irregular wave fields. Additionally, the coupling between Higher Order Spectrum and CFD is validated on three hour irregular wave propagation. Finally, a simulation of a 3D extreme wave encountering a full scale container ship is shown.

Investigation of the Bottom-Slope Dependence of the Nonlinear Wave Evolution toward Breaking Using SWASH

Filipot, J.-F., 2016. Investigation of the bottom-slope dependence of the nonlinear wave evolution toward breaking using SWASH. Numerical simulations of irregular waves propagating over planar beaches with slopes varying from 1 to 10% are performed with the Simulating WAves till SHore (SWASH) model. As reported in observational studies, waves shoaling over steep (mild) slopes break in shallower (deeper) water. The bottom slope is found to influence the cumulative contribution of the triad wave interactions to the wave spectrum. The triad contribution affects wave skewness and wave asymmetry at breaking point. This consolidates findings reported in previous field studies and has significant implications for coastal applications.

Simulation of Irregular Waves in a Numerical Wave Tank

Abstract The time domain boundary element method was utilized to simulate the propagation of the irregular waves in a numerical wave tank. The problem was solved in a time-marching scheme, upon the irregular waves being fed through the inflow boundary, in which the theoretical solution was obtained from the wave energy spectrum. The open boundary condition was modeled by the multi transmitting formula (MTF), in which the phase velocity was calculated according to the Sommerfeld’s condition. The velocity potential and wave elevation were directly obtained by integrating the free surface condition twice, with respect to time. The accuracy of the developed numerical scheme was verified by simulating the propagation of irregular waves. The numerical results show good agreements with the analytical solutions, which prove that the proposed scheme is a promising way to the simulation of wave-body interactions.

Simulation of irregular waves over submerged obstacle on a NURBS potential numerical wave tank

In this paper, a fully non-linear three-dimensional Numerical Wave Tank (NWT) is developed for studying propagation and scattering of non-linear random sea wave over bottom submerged bars. The simulation of fully non-linear free-surface is based on Non-Uniform Rational B-Spline formulation (NURBS) as a novel approach and Mixed Eulerian-Lagrangian method (MEL). High-order boundary integral equation is used to solve the Laplace equation in the Eulerian frame. To update the free-surface, time marching approach including material node method and fourth order Runge-Kutta time integration scheme is used. To obtain appropriate numerical solutions for wave propagation problem, damping zone is set at the downstream. Also, the NURBS approximation is employed to evaluate the velocity of the free-surface particles. Propagation of regular and irregular waves in a NWT is investigated and compared with the available experimental and numerical data. Transmission of the random sea wave over submerged bars is also compared with the experimental and prior numerical studies.