Numerical Wave Tank Research Articles

Analysis of various algorithms for optimizing the wave energy converters associated with a sloped wall-type breakwater

The optimal arrangement of multiple wave energy converters (WECs) is an important topic that can greatly affect the efficiency of ocean energy extraction. This study used various algorithms to optimize multiple heaving-buoy-type hemispherical WEC associated with a sloped wall-type breakwater. To this end, a calculation framework linking a three-dimensional frequency-domain numerical wave tank (FR-NWT) based on the Rankin panel method and an optimization algorithm was established. The fitness function for optimization was set to the power efficiency of WEC. The algorithms used were a genetic algorithm, simulated annealing algorithm, particle swarm optimization algorithm (PSO), and advanced PSO algorithm. Under irregular wave conditions, optimization of the spacing between each WEC, the distance between the WEC and the breakwater, the diameter and draft of the WEC, the bottom length and slope angle of the breakwater were performed. The results of the advanced PSO algorithm were consistent and did not converge to local maxima. The excellence of the advanced PSO algorithm in this study was demonstrated.

A viscous numerical wave tank based on immersed-boundary generalized harmonic polynomial cell (IB-GHPC) method: Accuracy, validation and application

A viscous numerical wave tank based on immersed-boundary generalized harmonic polynomial cell (IB-GHPC) method: Accuracy, validation and application

Hydrodynamic responses of a reversed L type floating breakwater integrated with a wave energy converter impacted by extreme waves

This research studies the hydrodynamic responses of a reversed L type floating breakwater integrated with a wave energy converter moored by a vertical pile in extreme sea states and intermediate water depth in a numerical wave tank based Navier-Stokes equations. Three wave-type representations (solitary, regular, and focus waves) of the same wave state are considered. The surface wave elevation, heave motion, wave force, impulse, wave moment on the mooring pile, moment of impulse, pressure distribution and flow field are investigated and compared. The comparison shows that different waves yield to diverse peak hydrodynamic responses. Largest wave force and moment are found in the regular wave condition, while largest heave motion, impulse and moment of impulse are obtained for the solitary wave. The pressure distribution on the bottom of the floater under the solitary wave shows a distinct character from the two others. The effect of the PTO damping parameter with the focus on the maximum wave force and moment is discussed and it is revealed that there exists an optimal PTO damping force for which the minimum wave force on the floater is obtained. This study therefore gains an insight into the hydrodynamic responses under different extreme waves.

Investigation of the Spiral Wave Generation and Propagation on a Numerical Circular Wave Tank Model

A two-phase incompressible flow model in three-dimensional cylindrical coordinates is applied for oblique wave generation in a numerical circular wave tank. The governing equations are discretized by a finite volume method, and a mass source function is added to reproduce oblique waves through a spiral wave generator positioned at the center of the tank. The volume of fluid method is implemented to track the free surfaces between the air and fluid, and the zonal embedded grid system is adopted to obtain a grid-independent solution in the cylindrical coordinates. A permeable, circumferentially sloping topography (1:7), similar to a natural beach profile, is set up for investigating wave propagation and other characteristics. The simulation and physical experimental results are compared, which show a good agreement in randomly selected water surface elevation profiles and wave heights under the same wave and sloping conditions. The spiral waves are reproduced and propagated in a phenomenon similar to that observed in the physical experiment. The results also show that the wave-breaking positions differ in different wave conditions and suggest a relationship with cross-shore and longshore velocity distribution in terms of incident wave heights and wave-breaking positions in different wave periods on the same sloping topography. Furthermore, this model can be used to investigate the mechanism of longshore current generation and the influences of beach slope on the generated wave propagation in a sloping topography.

Experimental and numerical investigation on anti-rolling performance of a DP semi-submersible platform based on thruster group biasing

For semi-submersible platforms equipped with dynamic positioning (DP) system, which has a small water-plane area and low metacentric height, roll motion will be affected by the lateral control force of the thrusters, causing a larger roll amplitude. In view of this problem, present paper proposes a thrust allocation method based on thruster group biasing. The thruster axial forces in group counteract each other while the normal force directions are opposite to form an anti-rolling moment, so that the roll damping can be enhanced without affecting the positioning performance in the horizontal plane. The roll stabilization mechanism is studied experimentally and numerically. A numerical wave tank based on computational fluid dynamics (CFD) method is established, verified and validated against the experiments. Both experimental and numerical results show that the thruster group biasing strategy can increase roll damping and reduce the roll motion of the platform by approximately 16% under the given sea condition.

Hydrodynamic performance analysis of a new hybrid wave energy converter system using OpenFOAM

In this research study, a newly proposed hybrid device of Wave Energy Converters (WEC) is investigated by considering computational fluid dynamic (CFD)-based numerical wave tanks (NWTs). The open-source CFD code solver, OpenFOAM (Open Field Operation and Manipulation) is implemented, which is numerically solved the Reynolds-averaged Navier–Stokes (RANS) equations to simulate the two-phase flow. The hybrid system consists of an Oscillating Water Column (OWC) and a point absorber (Wavestar) device installed in a shared platform. The main goal is to recognize how wave diffractions caused by the adjacent floating body could affect the rate of power absorption by the Fixed-OWC. This aim is followed by a 2D numerical analysis of three different installation configurations, variable intervals between the Wavestars' buoy and the Fixed-OWCs' front wall, in four different wavelengths with and without Power Take-Off (PTO). Finally, the efficiency characteristics of the integrated system such as free surface velocity and air pressure within the chamber, besides floating body motions are investigated and compared for the hybrid system. Although the overall assessment for 28 different case studies reveals an efficiency reduction in some cases, the superiority of this hybrid plan is recording several incremental efficiency rates.

CFD studies of the nonlinearity of NewWave group propagation and wave-structure interaction

NewWave groups are simulated using a numerical wave tank based on the CFD method. Multiple sets of NewWave groups with varying input wave amplitudes are numerically generated, and the numerical results are compared with theoretical results. The theoretical focusing time and location are backward drifting as the input wave amplitudes increase. As a result, nonlinearity should not be ignored when simulating NewWave groups for large extreme wave heights. The horizontal and vertical forces on the pile-cap foundation of a sea-crossing bridge caused by the NewWave group are investigated. Taking input amplitude A=0.06m as an example, the maximum horizontal force for a high elevated cap that is above the still water level 0.9 m is roughly twice that of a cap immersing in water 0.6 m. However, the vertical forces show less deviation. This research is primarily concerned with determining the realistic focusing location of the numerical NewWave model. Furthermore, the impact of NewWave on pile-cap foundations is studied preliminarily. It lays a solid foundation for the subsequent study of NewWave's impact on offshore structures.

Representative linearised models for a wave energy converter using various levels of force excitation

In guiding the progression, development, and operation of wave energy converters (WECs) in a more efficient way, mathematical analysis and understanding of the dynamic process is essential. Mathematical WEC models, obtained either by numerical analysis or physical modelling, form the basis of most (model-based) energy maximising control strategies available in the literature, where experimental design and system identification methodology directly impact the resulting model. This study, using an experimental-based WEC model (which can be used for linear control design), investigates the dynamic behaviour of a WEC by analysing the dominant poles of the system, generated using fully nonlinear computational fluid dynamics (CFD)-based numerical wave tank (NWT) experiments. The aim is to effectively track the dominant dynamics of the WEC, using different force-input amplitude levels in the NWT setup, and perform a comparison with the classical linear boundary-element-methods (BEM) equivalent methodology. Thus, the presented case studies are shown to agree with previously proposed model assessment of linear WEC models, based on a free-decay NWT setup. In addition, the representative WEC models determined as part of this study can be used for WEC controller design, either singly, or using a form of model/controller gain scheduling.

An efficient methodology for the simulation of nonlinear irregular waves in computational fluid dynamics solvers based on the high order spectral method with an application with OpenFOAM

An efficient methodology for simulating nonlinear irregular waves in a Computational Fluid Dynamics (CFD) solver is proposed. The High Order Spectral (HOS) method is used to generate nonlinear irregular waves in an open ocean and a numerical wave tank. The inverse Fast Fourier Transforms (FFTs) and multi-dimensional interpolation from the HOS simulation results are used for the efficient reconstruction of nonlinear waves in the CFD solver. The proposed procedure is published as an open-source project called Grid2Grid, which is developed to interface with a generic CFD solver. It provides the function Application Programming Interface (API), which can communicate with different programming languages. Extreme wave events were used to validate the proposed procedure. The predicted wave breaking events are reported both in OpenFOAM CFD and HOS simulations, and the wave elevations of CFD during simulations show good agreement with experiments and with HOS simulation.

An effective approach for VARANS-VOF modelling interactions of wave and perforated breakwater using gradient boosting decision tree algorithm

In this paper, we propose a systematic and time-efficient approach to calibrate 2D VARANS-VOF models for simulation of wave interaction with porous plate in numerical wave tank. To reach this goal, we develop a data-driven approach in combination with numerical and experimental data to figure out the optimal empirical coefficient associated with linear and non-linear drag force coefficients (α, β). Advanced gradient boosting decision trees algorithms (GBDT) are adopted to capture the accuracy of the prediction model. Although only limited samples, for instance 72 samples are generated and chosen to train and test the prediction model, the GBDT model is able to identify the trend in non-linear influence of model parameters. The advantage of GBDT algorithm can obviously be seen through the regression analysis with very high regression coefficient (R2 > 0.99). The developed model is subsequently employed for a large range of considered parameters as input features of the models to predict the possible hydrodynamics characteristics. The smallest mean squared error between predicted and experimental results, which is 0.00204, is found and used to determine the best performing combination of these model parameters. The numerical model together with selected values of empirical coefficients is then validated using available experimental data in literature. The free surface elevations in front of and behind the structure from the numerical model are nearly identical with the experimental data.

A study of wave-driven flow characteristics across a reef under the effect of tidal current

Recent field observations have improved our understanding of the role of tidal currents in modulating the wave dynamics over coral reefs. In this study, detailed flow measurements are conducted across an idealized reef profile in a wave-current flume. A typical plunging breaker propagating over both the flooding (shoreward) and the ebbing (seaward) tides are tested, respectively, and compared to the scenario without tidal current (wave only). Laboratory results are reported for the cross-shore distributions of wave height and mean water level as well as the vertical variation of cross-shore mean current below wave trough across a reef. Subsequently, to reproduce the laboratory measurements, the Reynolds-Averaged Navier-Stokes (RANS) equations with a stabilized k-ω SST turbulence model are solved to establish a numerical wave tank. The Volume of Fluid (VOF) method is used to track the free surface and an existing wave generation module is modified to consider the tidal current effect on waves. The numerical model is first validated by the experimental measurements based on the aforementioned three wave-current scenarios. Subsequently, the mean flow field around the reef surf zone and the cross-shore distribution of turbulent kinetic energy (TKE) and Reynolds shear stress along the reef profile are examined via numerical simulations.

A Navier–Stokes numerical wave tank with a pressure-based relaxation zone method

In the relaxation zone method for numerical wave tank modelling, the numerical fields are usually relaxed in the generation zone to the solution given by the potential theory. In the adopted procedure, the two-phase viscous flow is blended with the potential solution and this underlying inconsistency in the generation region can lead to instability in the flow. In this work, we present a new method for the wave generation in the context of the relaxation zone method which overcome the issue on the velocity forcing by introducing a body force equal to the potential pressure gradient. Results show that the method gives accurate results when compared with classical test case for wave propagation.

Numerical investigation of a dual cylindrical OWC hybrid system incorporated into a fixed caisson breakwater

In this paper, a hybrid Oscillating Water Column (OWC)system combining with a heaving floater Wave Energy Converters (WEC) was investigated. The traditional cylindrical-type breakwater consists of dual cylinders with an opening inlet located at the outer wavefront wall, allowing a ring-type wave chamber formed between two cylinders. The oscillating buoy OB is hinged at the front of the OWC device. The WAVE Chamber formed between the two breakwater cylinders is to be used as OWC. Based on the Computational Fluid Dynamics (CFD) software Star CCM+, A three-dimensional numerical wave tank is developed to investigate the hydrodynamic performance of the hybrid system, and the numerical model is validated with published experimental results. The power take-off (PTO) damping performance and the hydrodynamic efficiency affected by water conditions and geometrical dimensions of the device are discussed. Results show that the after combining the floater to the breakwater-type WEC, a great improvement on frequency bandwidth was achieved and the efficiency increase to 83.28% compared to the case of a single device, which was of 57%. Furthermore, the effects of the opening inlet height and the volume ratio of the OWC chamber were studied to optimize the certain geometrical parameters. Lower height ratio of the opening inlet of the OWC chamber should be avoid for larger water depth condition while designing such a hybrid system.

Analysis of the peaks of ship motions in linear and nonlinear focused waves

Three focused waves, which have almost identical temporal profiles, are successfully generated in a numerical wave tank with both linear and nonlinear methods, and they are utilized to act upon an LNG carrier to study the induced differences of the ship peak responses for the first time. The influences of focal location and incident wave direction are taken into account and the fundamental reason for the response difference is revealed from the perspective of energy variation. It can be concluded that when the LNG carrier encounters the same temporal focused waves, the peak motion responses can be different due to the different hydrodynamic characteristics under the focused crests, which can be further attributed to the distinct physical mechanisms involved in the energy concentration of these focused waves. The focal location and incident wave angle can further enlarge the corresponding discrepancy under some circumstances. From a spectral point of view, the motion discrepancy is mainly caused by the actions of the distinct fundamental wave components. Specifically speaking, the relatively high-frequency components of the nonlinear focused waves tend to induce a smaller heave response and the quasi-monochromatic wave component cannot trigger a larger pitch motion than the linear focused waves.

Numerical Simulation of Wave Overtopping of an Ecologically Honeycomb-Type Revetment with Rigid Vegetation

Traditional concrete revetments can destroy the ecological environment and the water landscape. An increasing number of ecological revetment structures have been applied in coastal, lake, and river regulation projects. It has been found that honeycomb-type revetments display a better performance in the attenuation of wave overtopping when compared to experimental data collected using the Eurotop and Muttray’s formula; recording a 40% decrease in the wave run-up in comparison to the latter. To further investigate the wave run-up and overtopping of the ecologically vegetated honeycomb-type revetment, based on OpenFOAM, an open source computational fluid dynamics software, a three-dimensional numerical wave tank was established. The Discrete Particle Method (DPM) was used to simulate gravel movement, and the flexible plant move boundary model was developed to simulate vegetation. The results of wave run-up calculated by the numerical model and those obtained by the experiments were in good agreement, with errors less than 20%. The modeled results of wave overtopping were within the same order of magnitude as those from the experiments; however, critical limitations were noticed due to effects of plant generalization and grid restrictions imposed by DPM methods. The results showed that wave overtopping increased with increasing wave period and wave height. However, with an increase in the wave overtopping, the influence of the wave period on wave overtopping decreased. The increase in vegetation density effectively reduced wave overtopping. Furthermore, an empirical formula for wave overtopping, considering the effects of vegetation density, was proposed.

Higher-order gap resonance and heave response of two side-by-side barges under Stokes and cnoidal waves

Coupled piston-mode fluid response and the heave motion of two identical barges in side-by-side configuration is studied under finite-depth and shallow-water waves using a two-dimensional fully nonlinear numerical wave tank. To understand possible critical responses of the gap flow and the floating barge, regular-wave conditions which are able to excite up to 5th-order nonlinear gap resonance and also the resonant heave motion of the barge are considered. In shallow-water waves, high-frequency oscillations, featured by secondary peaks in the time histories, are observed for both wave elevation in the gap and the heave motion of the barge. The shallow-water wave-induced 4th- or 5th-order gap resonance can be equally crucial as the 1st- and 2nd-order resonances due to finite-depth waves. At higher-order gap resonance, the higher-harmonic heave motion of the barge is negligibly small, in contrast to the gap-flow response. Compared with fixed barges, the free-heave motion of an upstream barge tends to increase the wave elevation in the gap in most of the resonant conditions, except at 1st-order gap resonance where the gap response is greatly reduced. When the resonant heave motion of a floating barge, either located upstream or downstream, is excited, significant barge motion is observed. However, the relative motion between the gap flow and the floating barge is seen to be very small, ascribed by small phase difference between the two. The present study suggests that the effects of heave motion and water-depth should be carefully considered in the design of side-by-side marine operations, and hiding the small bunkering ships behind the large receiving ships is regarded as a preferred arrangement during the bunkering operations in offshore and coastal environments.

Diffraction and Refraction of Nonlinear Waves by the Green–Naghdi Equations

Abstract Diffraction and refraction of nonlinear shallow water waves due to uneven bathymetry are studied by use of the Green–Naghdi (GN) equations in three dimensions. A numerical wave tank consisting of deep, transitional, and shallow regions is created. Various forms of three-dimensional bathymetry, consisting of ramps with nonuniform profiles and large slopes, are used to connect the deep-water side of the tank to the shallow water shelf. A wavemaker is placed at the upwave side of the domain, capable of generating solitary and cnoidal waves of the GN equations. A numerical wave absorber is located downwave of the domain to minimize the wave reflection back into the domain. The system of equations is solved numerically in time domain by use of a second-order finite-difference approach for spatial discretization, and in a boundary-fitted coordinate system, and by use of the modified Euler method for time marching. Results include solitary and cnoidal wave surface elevation and particle velocities and are compared with the existing solutions where possible. Overall, very good agreement is observed. Discussion is provided on the nonlinearity and dispersion effects on the wave diffraction and refraction by the various forms of the ramps, as well as on the performance of the GN equations in solving these problems.

Efficient Calculation of Hydrodynamic Loads on Offshore Wind Substructures Including Slamming Forces

Abstract Estimation of the hydrodynamic loads based on strip theory using the Morrison equation provides an inexpensive method for load estimation for the offshore industry. The advantage of this approach is that it requires only the undisturbed wave kinematics along with inertia and viscous force coefficients. Over the recent years, the development in numerical wave tank simulations makes it possible to simulate nonlinear 3-h sea states, with computational times in the order of real time. This presents the possibility to calculate loads using wave spectrum input in numerical simulations with reasonable computational time and effort. In the current paper, the open-source fully nonlinear potential flow model REEF3D::FNPF is employed for calculating the nonlinear wave kinematics. Here, the Laplace equation for the velocity potential is solved on a σ-coordinate mesh with the nonlinear free surface boundary conditions to close the system. A technique to calculate the total acceleration on the σ-coordinate grid is introduced which makes it possible to apply strip theory in a moving grid framework. With the combination of strip theory and 3-h wave simulations, a unique possibility to estimate the hydrodynamic loads in real time for all discrete positions in space within the domain of the numerical wave tank is presented in this paper. The numerical results for inline forces on an offshore wind mono-pile substructure are compared with measurements, and the new approach shows good agreement.

Numerical Analysis of a Horizontal Pressure Differential Wave Energy Converter

CFD modeling of an innovative wave energy device has been carried out in this study. OpenFoam wave modeling solver interFoam has been employed in order to investigate the energy extraction capability of the wave energy device. The innovative concept is based on utilizing the pressure differential under the crest and trough of a wave to drive flow through a pipe. The simulated surface elevation of a wave has been validated against the reported wave tank experimental data in order to provide confidence in the modeling outcome. Further, simulations have been carried out with the device placed near to the bottom of the numerical wave tank in order establish the energy extraction potential. The simulation results confirm that effective power can be generated from the wave energy device. The efficiency of the device decreases with the increase in wave height, although it increases with the wave period. Higher power-take off (PTO) damping is also beneficial in extracting increased energy from waves.

Numerical investigation of wave run-up and impact forces on large offshore jacket platforms

This paper focuses on wave interactions with large deep-sea jacket platforms. A numerical wave tank is designed and developed to simulate the wave-structure interactions, and the accuracy and precision of this numerical wave tank are verified by the theoretical values and LWI experimental tests. Then the processes of wave run-up along with the legs and impact the lower deck of a large deep-sea jacket platform located at the South China Sea are simulated, analyzed, and discussed. The results show that the greater the wave steepness, the stronger the wave run-up ability. The wave run-up processes are mainly concentrated within a radius R around the legs, and the maximum wave run-up ratio reaches 1.56 on the front side of leg 1 when the wave steepness is 0.03. Due to the interference, reflection, and superposition effects, all the legs show different wave run-up characteristics, and additional high-frequency side wave peaks are observed around the legs, which are mainly focused on 0–0.6 Hz in the frequency domain. With the increase of wave steepness λ, the wave drag forces increase significantly during the wave run-up processes. Especially, when the waves impact the lower deck under case 3, it will cause huge vertical wave impact loads, and the maximum value reaches 46.59 MPa, which will cause further attenuation to the vertical and lateral resistance of the jacket platform.