Numerical Wave Tank Research Articles

A Numerical Study of the Performance of Point Absorber Wave Energy Converters

Free-floating and submerged wave energy converters (SWECs) are regarded as promising technologies for renewable energy production. These converters rely on a heave-motion buoy to capture the kinetic energy of ocean waves and convert it into electrical energy through power conversion systems. To better understand the impact of various factors on power generation and efficiency, the effects of different buoy shapes (rectangular, circular cylinder, and trapezoidal fin), submergence depths (0, 0.1, and 0.2 m), wave heights (0.04, 0.06, and 0.1 m), and spring stiffness (50 and 100 N/m) were investigated. A 2D numerical wave tank with a buoy was simulated, and the results were validated against experimental data. Information on vorticity, vertical displacement, power absorption, and efficiency are provided. The findings indicate that the buoy shape and wave height significantly affect power absorption and efficiency. Additionally, this study reveals that increasing submergence leads to higher power absorption and lower conversion efficiency.

Research On Numerical Wave Tank Based on SPH Method

Numerical wave-current flume is one of the effective methods to study waves and their effects on structures. In this paper, the Smoothed Particle Hydrodynamics (SPH) method is used to simulate and analyze the numerical wave flume. Based on the SPH method, an efficient and flexible numerical wave tank model is constructed to simulate complex water wave dynamics. Firstly, the basic principle of SPH method is summarized, and then the establishment process of numerical wave tank model is described in detail, including particle initialization, boundary condition setting and so on. Through the flume simulation under different wave conditions, the accuracy and stability of the model are verified. Finally, the interaction between wave and structure is studied. It provides a new and effective tool for the numerical simulation of wave flume, and also provides a useful reference for the related research in the fields of marine engineering and coastal protection.

Numerical Simulation of Ship-added Resistance Based on a Numerical Wave Tank

The wave resistance increase of a ship during its actual voyage can affect its speed and safety. To design ships with excellent sailing performance, it is necessary to accurately predict the wave resistance increase of a ship in waves, as well as the motion response and wave resistance prediction of ships in waves, which involves complex hydrodynamic problems. This paper first establishes a physical model of the KCS vessel, then utilizes the numerical wave tank platform independently developed by our university. Based on viscous flow theory, it calculates the resistance of the KCS under calm water conditions. Using three-dimensional potential flow methods and spectral analysis, it computes the wave-induced resistance values for the KCS under six-degree sea states, analyzes the wave-induced resistance performance of the KCS, and ultimately, based on the calculation results of calm water resistance and wave-induced resistance combined with propeller efficiency parameters, calculates the effective power of the engine.

Numerical investigation on the hydrodynamic and conversion performance of a dual cylindrical OWC integrated into a caisson-type breakwater

The hydrodynamic performance of an integrated oscillating water column (OWC) combined with a cylindrical caisson type breakwater was investigated. A three-dimensional numerical wave tank was established to simulate the overall energy conversion performance and hydrodynamics of the integrated system with the software Star-CCM+. The developed Computational Fluid Dynamics (CFD) model was initially verified with the published physical results and numerical results derived from an analytical solution. The effects of the structural geometry and the pneumatic damping of the PTO system on the wave absorption and power conversion efficiency of the proposed device were investigated using this developed model. Based on this proposed numerical model, the velocity of the air flow, the corresponding air pressure characteristics in the air turbine nozzle and chamber zone were discussed. The results indicate that this proposed half-open land based OWC is adapted to absorb shorter nearshore waves, characterized by dimensionless wave number kd approaching 1.49. Furthermore, a larger opening inlet zone for this proposed OWC would shift the resonant corresponding kd to higher wave frequencies, while lowering the opening inlet could help to increase the power extraction efficiency for long waves. The peak hydrodynamic efficiency is observed at a ratio of OWC inlet width to diameter B/D of 0.97, which is approximately six times larger than that at B/D = 0.5. The inclusion of an impulse turbine yields a more uniform pressure distribution within the central chamber and effectively mitigates wave reflection for smaller incident waves, with maximum efficiency achieved using 37 blades. The property of the efficiency mitigation with insufficient certain intake depth of the wave chamber should be avoided for system design.

The hydrodynamic study of the interaction between waves and objects in permeable reef environment

This study employed a self-developed viscous numerical wave tank based on the piston type wave maker and user-defined functions of Fluent software to explore the wave shadowing effect of the transmission of waves near the underwater object and the reef. In the study, various factors such as the permeability of the reef, changes in topography, and objects motion were considered, and detailed simulation analyses were conducted for five scenarios: a solitary reef, a fixed underwater object, a forced moving underwater object, and a free moving underwater object. The results showed that this method can effectively simulate the complex flow field changes around the underwater object and the reef under different conditions, while also fully considering the strong nonlinearity and fluid viscosity effects between the wave surface and the object. Furthermore, it was found that between the free-moving object and the reef, there would be significant swirls and streamline distortion. This indicates that a portion of the incident wave energy is transformed into kinetic energy of swirls, resulting in a smoother and more uniform flow field and reducing wave forces.

Spatial energy evolution of focused waves generated in numerical wave tank

This paper numerically investigates the energy evolution of the focused wave and its correlation with input parameters for the wave generation. The focused wave is numerically generated based on the fully nonlinear potential wave theory which is solved by the Quasi Arbitrary Lagrangian Eulerian-Finite Element Method. The investigation is performed by dividing the generated wave energy into three categories according to their frequency intervals, i.e., the initially assigned frequency interval [f1fN], the frequencies lower (f < f1) and higher (f > fN) than the initial interval. The amount of the generated energy falling into three energy categories and the energy distribution in the initial frequency interval are analysed against amplitude parameters and frequency bands under three amplitude spectra. Four indicators are proposed to indicate the actual energy variations comparing to the initial design. It is found that for all the three frequency intervals the energies increase when the amplitude parameters increases or the given frequency shifts towards the lower frequency domain. The choice of wave amplitude spectrum plays a significant role to maintain the distribution of the energy in the design frequency range and to minimise the energies out of the design frequency range. The results from the second-order wave group theory are used to assist analyses of the mechanism of the energy evolution alongside the focused wave generation. It is found that the lower-frequency energy in the vicinity of the focusing point is dominated by the second-order difference waves, whereas the higher-frequency energy is mainly produced by the wave flap. The waves which are higher than the second-order and the complex interactions not considered by the second-order wave theory are found significantly disturbing the energy distribution in the originally assigned wave-frequency interval.

Environmental-Sensing and adaptive optimization of wave energy converter based on deep reinforcement learning and computational fluid dynamics

This paper introduces a novel coupled model for real-time control of the point absorber wave energy converter (WEC) using parallelized deep reinforcement learning (DRL), where the WEC is situated within a numerical wave tank (NWT) built with the method of computational fluid dynamics (CFD). An in-house solver is developed to couple with the DRL and CFD to solve the interaction between WEC and the fluid environment. Validations on wave generation, wave-floater interaction, and power take-off (PTO) unit are carried out. Then, neglecting the detailed model for the PTO technologies, the DRL-based strategy dynamically adjusts the PTO force as a function of the wave features and floater motion. Based on the interaction data, the model-free DRL is outstanding in adaptability and robustness. Simulation results reveal that DRL control improves the wave energy absorption in irregular wave environments, resulting in improvement of 107.5 % compared to the resistive control, with better device protection performance than the model predictive control (MPC). An additional analysis of model-free characteristics of DRL demonstrates the optimization ability independent of floater modeling. This work is the first in-depth study of DRL control of WECs in CFD simulation, providing a more accurate simulation and an optimization process closer to the reality.

Development of a numerical wave tank of deep ocean engineering basin via high order spectral method

ABSTRACT In this study, we developed a numerical model for simulating wave environments of the deep ocean engineering basin (DOEB) by utilising the high order spectral (HOS) method. The approach employed the pseudospectral basis of the cosine function to automatically account for the tank wall boundary conditions. Additionally, the fast Fourier transform (FFT) algorithm was implemented to maximise the numerical efficiency. For selecting an appropriate wave generation technique for the DOEB, which distinguishes itself as a large-scale facility with controllable depth, in contrast to conventional wave basins, two-dimensional wave generation simulations were executed. These simulations entailed the application and subsequent evaluation of the embedded wave generation technique and the additional potential technique. Of these, the embedded wave generation technique, characterised by its suitability for numerical efficiency and adaptability to variable water depths, was chosen for implementation in the DOEB numerical tanks. The Stroke–source converting procedure was established to transform the stroke time history of the wave maker into the input wave source time history for the embedded wave generation technique, with due consideration to phase correction. In order to validate the developed numerical model, a wave generation experiment was conducted, and its results were compared with the numerical simulations. This comparative analysis revealed a high degree of correspondence between the nonlinear simulations and the experimental wave time history, demonstrating the model’s ability to accurately replicate higher-order wave components, including wave–wave interactions. The resulting numerical model serves as a valuable computer-aided tool, enhancing the efficiency of experiments within the DOEB.

Effects of nonlinearities on the gap resonances between two free-heaving barges

The hydrodynamic characteristics of the gap resonances between two identical side-by-side barges are investigated in a constrained interpolation profile method-based numerical wave tank. Each barge can heave freely under the excitation of the incident waves. This paper mainly concentrates on the influences of the nonlinearities during the gap resonances on their hydrodynamic performance, via the parameter study of the incident-wave height. Numerical results demonstrated that the nonlinear gap resonances' magnitudes may reach close to or exceed that of the linear gap resonance and naturally contain strong nonlinearities when considering the heave responses of the side-by-side barges. Meanwhile, the effects of the heave responses on the key hydrodynamic parameters cannot be ignored as well. Therefore, the wave run-ups of the barges are of significant importance for the investigation. On the one hand, the wave run-ups directly reflect the coupling effects between the gap resonances and the twin barges' heave responses. On the other hand, the nonlinearities of the wave run-ups perform stronger than the wave elevation at the gap. Moreover, the linear wave run-ups are proposed via the linear formulas to qualitatively and quantitively investigate the effects of the nonlinearities on the inner process of the wave run-ups by comparison. Based on the harmonic analysis, the features of the distributions of the first four order harmonics of the wave elevation at the gap, the wave run-ups, and the wave loads are illustrated.

Investigations into Motion Responses of Suspended Submersible in Internal Solitary Wave Field

When the underwater submersible encounters an internal solitary wave (ISW), its loadings and motions are significantly disturbed. To investigate the interaction mechanism between the suspended submersible and the ISW, a three-dimensional ISW–submersible-interaction numerical model was established, based on the computational fluid dynamics (CFD) method. The generation and propagation of the ISW was simulated in a two-layer fluid numerical wave tank, according to the eKdV theory. The standard operation equation of the submersible was introduced to simulate the six degree of freedom (6DoF) motions of the submersible combined with the overset dynamic mesh method. The motion simulation method was effectively validated by comparing it with published experimental results on the motion responses of a slender body under the ISW. Based on the constructed numerical model, the dynamic mechanisms between the suspended submersible and the ISW were studied, and the effects of the initial submerged depths and the ISW amplitudes on the dynamic responses of the submersible were revealed. According to the numerical results, the motions of the submersible have been significantly determined by its initial submerged depths. The submersible located above the ISW interface has a significant motion along the propagation direction of the ISW and its motion trajectory resembles a counterclockwise semi ellipse. The motion of the submersible located below the ISW interface follows the trace of the lower layer of fluid, which presents as an unclosed clockwise ellipse. The corresponding motions of the submersible would be increased with the increase in the ISW amplitudes.

General formulation for floating body with elastic mooring in irregular waves: A hybrid linear and nonlinear framework and validation

In the present study, an advanced computational platform has been developed for offshore renewable energy converter systems, considering nonlinear wave input, body dynamics, mooring line dynamics, and kinematic and mechanical constraints. In particular, a hybrid linear and nonlinear hydrodynamic model is formulated through coupling with a numerical wave tank generated by OceanWave3D. A novel nodal position finite element model considering geometrical and material nonlinearities is developed to simulate the nonlinear behaviour of the mooring dynamics. Then, an implicit solver with an iteration process solves the dynamics of the rigid body, the dynamics of the mooring lines, and kinematic and mechanical constraints simultaneously. Therefore, the developed platform is capable of studying the wave body interaction with mooring lines in extreme wave conditions. Wave basin model tests of a single float on a nonlinear mooring line are carried out under a series of irregular waves for comparison. The developed model was also validated against commercial software under identical conditions for idealised cases. In steep wave conditions, the hybrid nonlinear/linear hydrodynamics give improved predictions over the linear hydrodynamic method.

CFD analysis of wave loading on a 10 MW TLP-type offshore floating wind turbine in regular waves

This paper aims to study the higher-harmonics wave-induced surge force on the CENTEC-TLP platform in regular head waves with non-breaking assumptions, using a CFD-based numerical wave tank model, which is a useful tool for the analysis of the nonlinear interaction of waves and structures. Moreover, the influence of change in the wave diffraction and the incident wave angle on the surge force subject to operational and extreme wave conditions is investigated. The numerical analysis is conducted using the CFD toolbox OpenFOAM. The link between Secondary Load Cycle and the wave scattering Type2 is apparent and it is concluded that they are all inertia-driven and that 2nd harmonics play an important role.

Hydrodynamic performance optimization of a cost-effective WEC-type floating breakwater with half-airfoil bottom

Aiming to design and develop an affordable integrated floating breakwater and wave energy converter (WEC) system that has high performance in power absorption and wave attenuation, a novel integrated floater with a half-airfoil bottom is proposed. The genetic algorithm combined with the boundary element method is employed to optimize the half-airfoil bottom surface represented by the class-shape function transformation parameterization method, for maximizing the power density over the operating bandwidth. Then the operating performance of the optimal half-airfoil bottom floater is further studied in a validated two-dimensional viscous numerical wave tank. The result shows that the optimal half-airfoil bottom floater is a more effective and affordable solution than square and triangular bottom ones. The effective ratio of the floater breadth to the wavelength can be reduced to about a tenth, far below that of the conventional floating breakwater, denoting its excellent wave attenuation capability. The increase in floater breadth induces more intense vortex dynamic behaviors and thus higher dissipation coefficient. A shallow front-wall draft design can improve the maximum conversion efficiency to more than 74%, slightly broaden the resonance bandwidth, and reduce energy dissipation while minimizing costs. The nonlinear PTO damping force contributes to a more stable response. The research results denote the feasibility of bio-inspired WEC-type floating breakwaters and show their superiority in energy extraction, wave attenuation, as well as cost reduction.

Numerical study on wave run-up and forces on a fixed cylinder under linear and nonlinear focused waves

To study the difference between wave run-up and wave forces on a fixed column under the action of focused waves formed with different physical mechanisms, a 3D two-phase numerical wave tank is developed based on the Navier-Stokes equation and the Finite Volume Method. The influences of wave nonlinearity, column radius and water depth on the run-up and force discrepancies are systematically investigated in four sets of numerical experiments. For focused waves with identical crest height and trough-to-trough period, the run-up height and dynamic pressure around the circumference of a cylinder are mostly larger in linear focused waves than in nonlinear focused waves, due to their different hydrodynamic characteristics. With the increased wave nonlinearity either by changing the period or crest height of the focused waves, the discrepancies become greater for run-up height while smaller for dynamic pressure. Moreover, both of them, less affected by water depth, are more sensitive to the variation of column radius in linear focused waves, showing a steeper gradient in space. Therefore, in practical engineering, the physical generation mechanism must be considered in evaluating the safety of columns of wind turbines hit by freak waves.

Effects of Wave Parameters on Load Reduction Performance for Amphibious Aircraft with V-Hydrofoil

An investigation of the influence of the hydrofoil on load reduction performance during an amphibious aircraft landing on still and wavy water is conducted by solving the unsteady Reynolds-averaged Navier–Stokes equations coupled with the standard k−ω turbulence model in this paper. During the simulations, the numerical wave tank is realized by using the velocity-inlet boundary wave maker coupled with damping wave elimination techniques on the outlet, while the volume of fluid model is employed to track the water–air interface. Subsequently, the effects of geometric parameters of hydrofoil have been first discussed on still water, which indicates the primary factor influencing the load reduction is the static load coefficient of hydrofoil. Furthermore, the effects of descent velocity, wave length, and wave height on load reduction are comprehensively investigated. The results show that the vertical load reduces by more than 55% at the early stage of landing on the still water by assembling the hydrofoil for different descent velocity cases. Meanwhile, for amphibious aircraft with high forward velocity, the bottom of the fuselage will come into close contact with the first wave when landing in crest position, and then the forebody will impact the next wave surface with extreme force. In this circumstance, the load reduction rate decreases to around 30%, which will entail a further decline with the increase in wave length or wave height.

Numerical analysis of 3D hydrodynamics and performance of an array of oscillating water column wave energy converters integrated into a vertical breakwater

Performance and hydrodynamics of an array of Oscillating Water Column (OWC) Wave Energy Converter (WEC) integrated into a vertical breakwater is studied. The FLUENT® software, in which the numerical model is based on the Reynolds-Averaged Navier-Stokes equations and the Volume of Fluid method for free surface flow modeling, is used in a 3D numerical wave tank. Three vertical breakwater configurations subject to the action of incident regular waves with periods from 6 to 12 s are studied: normal breakwater, with vertical walls parallel to the direction along the breakwater length; and two novel breakwater geometries, partially and fully convergent breakwaters, whose converging vertical walls are inclined θ in relation to this direction. Different spacing S from 0 to 20 m between the array of OWC devices and two converging wall angles θ, 30 and 45°, are investigated. Firstly, analysis of the influence of S for the normal breakwater shows that the vertical wall concentrates naturally a higher quantity of the incident wave energy inside OWC chamber devices and, consequently, increases their efficiencies. This effect is intensified as the spacing S increases. Secondly, analyses of the partially and fully convergent breakwaters allow concluding that these novel geometries, which direct an amount of incident wave energy into the OWC chamber, increase significantly the efficiency of the array of the OWC devices at the range of the wave periods. The highest performance of OWC device is obtained by the fully convergent breakwater with S = 20 m and θ = 45°, once 10 OWC devices inserted in a breakwater 300 m long have the same efficiency of 20 OWC devices inserted into the normal breakwater.

Numerical simulation of water wave propagation using DualSPHysics

In this study, the study of water waves was carried out using one of major the mesh-free CFD i.e. Smoothed Particle Hydrodynamics (SPH). DualSPHysics ver 5.0 which is an open-source SPH solver based on Weakly Compressible Smoothed Particle Hydrodynamics (WCSPH) was used to reproduce three dimension of water waves in large and medium numerical wave tanks (NWT). This study analyses water wave profiles and the accuracy of DualSPHysics for regular waves with period 1.15 second and two NWT were used, i.e., 35 and 15 m. In addition, advanced post-processing using VisualSPHysics was used to mimic water waves in real conditions. Single water depth was used, i.e. 0.4 meters for large and medium NWT. The results showed SPH has limitations for reproducing large NWT. However medium NWT successfully reproduce water wave with advanced post-processing using VisualSPHysics.

Effect of Interparticle Distance on Smoothed Particle Hydrodynamics on Wave Transformation Through Submerged Breakwater

Beach abrasion and erosion are problems that many beaches in Indonesia experience. Waves are the most influential processes in this phenomenon. When the waves move towards the coast, they will transform, generating currents near the coast. Currents moving along the coast displace sediment on the beach, causing changes in the shoreline. So it is necessary to carry out coastal protection efforts so that abrasion does not occur, which results in the erosion of coastal areas so that the island’s area is reduced and the coastline retreats. To overcome this problem, one of the supporting facilities is a submerged breakwater. In this paper, researchers will numerically study the effect of particle size on smoothed particle hydrodynamics (SPH) when waves pass through a submerged breakwater structure. The simulation is carried out on a Numerical Wave Tank (NWT), the piston is at the end of the tank, and the structure of the submerged breakwater is set according to the experimental scenario. The distance between the particles varied from 0.03, 0.025, 0.02, 0.015, and 0.01. The results show that the smaller the distance between the particles used, the wave elevation results are closer to the experimental model.

Simulation of a Wave Hydrodynamic Numerical Model on a Single Vertical Porous Breakwater

One of the problems in the coastal area is a change in the coastline in the form of a coastline retreat which results in the loss or damage of infrastructure and settlement facilities caused by extreme sea wave activity. One way to anticipate this problem is to build a breakwater. This research is focused on the effect of porosity and freeboard on the transmission and reflection of waves in a single vertical porous breakwater. Numerical modeling was done using a 3D Numerical Wave Tank (NWT) based on Smoothed Particle Hydrodynamic (SPH). The numerical model results show that the average transmission and reflection coefficients are 0.58 and 0.42. In addition, it can be seen that the freeboard and porosity influence the value of the transmission and reflection coefficients. Generally, the smaller the freeboard, the greater the transmission coefficient and the smaller the reflection coefficient. Meanwhile, the greater the porosity, the greater the transmission coefficient, and vice versa, the smaller the reflection.

Scour around twin-piles under combined wave–current flows

The paper presents three dimensional simulations of scour around a pair of piles arranged side-by-side configurations under combined wave–current flow conditions using a computational fluid dynamics model. The Reynolds-averaged Navier–Stokes (RANS) equation is solved using the k-ω turbulence model in the present work. The Exner equation is used to measure the variations in bed elevation. The level-Set approach is used to capture the free surface realistically. The numerical model couples the hydrodynamic module with the morphological module to simulate the scour process. For accurate erosion and deposition calculations in the sediment bed, the morphological model employs a modified bed shear stress formula on a sloping bed in combination with a sand slide algorithm. In the present study, the simulations have been done in a truncated numerical wave tank with the Dirichlet boundary condition and active wave absorption method. The numerical model is validated with the experimental results of combined wave–current hydrodynamics and scour around a pair of piles. The validated numerical model is utilized to study the effect of the gap ratio and the effect of KC number in the various combined wave–current environment. In low KC conditions, normalized scour depth increments owing to waves alone, weak currents, and moderate currents are less, whereas the scour depth increases dramatically for waves with high currents. It is also found that the gap flow between the piles increases the depth of scour in a significant manner. For a given pile gap ratio, the scour depth is dependent on the KC number, which implies the larger the KC number, the larger scour depth. For a given KC number, the scour hole stretch in the flow direction reduces as the gap ratio increases, whereas the perpendicular stretch increases. It is also observed that the normalized scour depth decreases as the gap ratio increases for a fixed KC number and fixed Ucw. It is evident from the present research that the normalized scour depth increases with increase in KC number for a fixed wave–current parameter (Ucw).