Numerical Wave Tank Research Articles

Energy Transfer and Reverse Flow Characteristics in the Interaction Process between Non-Breaking Solitary Wave and a Steep Seawall: A Case Study

This study utilized a two-dimensional numerical viscous wave tank to simulate the run-up and run-down processes of non-breaking solitary waves on a steep seawall. The research aimed to investigate the transformation between wave potential energy and kinetic energy, the evolution mechanisms of the wave and flow fields, and the correlation between the dynamic pressure gradient and the reverse flow near the sloping bed. The numerical model results were consistent with laboratory measurements of free surface elevations and flow velocity profiles, demonstrating the accuracy of the numerical model. This study focused on a solitary wave with a wave-height-to-water-depth ratio of 0.15, propagating on a representative seawall with a steep slope of 1:3 along the western coast of Taiwan. The simulation results indicate that the maximum run-up height occurs when the potential energy is at its highest. Undertow is caused by the adverse pressure gradient within the flow field, and the dynamic pressure on the sloping bed is directly proportional to the free surface elevation. Therefore, by observing the spatial changes in the free surface elevation, we can indirectly determine the occurrence time of undertow.

High-fidelity modelling of lift-based wave energy converters in a numerical wave tank

This work presents the development of a numerical model for the investigation of lift-based wave energy converter (lift-WEC) hydrodynamics. The developed model, based on the RANS equation, is validated regarding its ability to replicate foil-flow interaction in various conditions based on experimental references from literature. Limitations of the numerical model are discussed, such as the overprediction of stall angles at low Reynolds numbers and the possibility of artificial rotor ventilation near the free surface. Within the range of relevant operating conditions for a lift-WEC, the model is found to replicate experimental results with good accuracy. Subsequently, a particularity of the cyclorotor WEC concept is investigated: Load measurements in calm water showed positive tangential forces, apparently indicating the generation of thrust in the absence of external energy sources. Numerical simulations reveal that this is the result of a significant azimuthal shift of the hydrodynamic load centre for non-zero pitch and that the consideration of foil pitch moments is required in order to obtain accurate shaft torque predictions. The hydrodynamic coefficients of the cyclorotor foils are compared with coefficients obtained for symmetrical foils in straight flight. It is shown that the assumption of similarity, which is often applied when modelling these devices in semi-analytical tools, is only valid for small angles of attack.

Physical and numerical modelling of extreme wave conditions

This paper presents the results of an experimental and numerical investigation into the generation of realistic model scale extreme waves for survivability testing of offshore structures. The objective of this investigation was to develop a numerical method to accurately model the maximum wave height (Hmax) and wave spectrum of a realistic focused wave group that was embedded into an irregular sea state. The sea state selected for this investigation was based on extreme conditions recorded during a Tropical Cyclone. The sea state was experimentally modelled using NewWave theory and was subsequently replicated in a computational fluid dynamics (CFD) numerical wave tank. The wave component amplitudes and phase angles were derived from the experimental data, which were then used to generate a polychromatic wave in CFD. The NewWave formula was then modified by applying an exponential function which intended to explicitly amplify the largest waves in the wavefield while applying minimal amplification to the remainder of the waves. This technique reduced the difference between the experimental and numerical Hmax while maintaining a level of spectral similarity. The methodologies presented in this paper are appropriate for modelling realistic extreme sea states for model scale survivability testing of offshore structures.

Evolution of porous boundary condition in numerical wave tank

A vertical porous or perforated structure can be considered an effective breakwater due to its efficient use in deep water when compared to conventional breakwaters. The hydrodynamic performance of this breakwater can be evaluated by studying the wave reflection and transmission through it. Various experimental studies in the past have shown the performance characteristics of this structure, but their application is limited due to the required effort, time, and manpower (Rajendra et al., 2017). As an alternative, a numerical model can be advantageous in representing exact situations and providing additional benefits. Therefore, as a preliminary study, the wave reflection and transmission of the vertical perforated breakwater are simulated in a numerical wave tank using a unique approach to defining porous boundary conditions. The numerical wave tank is developed using a finite volume-based FLUNET tool with a viscous-laminar model configuration. However, the porous boundary condition is defined in terms of the inertial resistance coefficient, which was derived from pressure drop measurements taken across the perforated structure during lab experiments. The wave reflection and transmission obtained from the numerical wave tank show good agreement with the experimental data. Interestingly, a closer examination of the flow field in the vicinity of the breakwater indicates partial standing wave formation, which contributes to an increase in wave reflection for a limited case.

The nonlinear wave interaction with a two-dimensional large-scale floating elastic plate

A two-dimensional fully nonlinear numerical wave tank is developed based on the higher order boundary element method and modal expansion to simulate the nonlinear interaction between waves and a finite horizontal floating elastic plate with draft. The large second harmonic displacement of a large-scale elastic plate near a second-order particular frequency is successfully calculated by this model. By the comparison with the results in a frequency model that involve perturbation expansion method, it is found that the large values of the second-order waves in a finite elastic plate near the particular frequency are not introduced by perturbation expansion. It is different from the case in infinite plate. The effect of the third-order particular triple frequency on the hydroelastic problem is small compared to the effect of the second-order particular frequency.

Numerical Study on the Green-Water Loads and Structural Responses of Ship Bow Structures Caused by Freak Waves

In recent decades, freak waves, characterized by their unusual high amplitude, sharp crest, and concentrated energy, have attracted researchers’ attention due to their potential threat to marine structures. Green-water loads caused by freak waves can be significant and may lead to local damage to the ship structures. Therefore, this paper focuses on the study of green-water loads and examines the structural responses of ship bow structures under the influence of the green-water loads caused by freak waves. Firstly, a three-dimensional numerical wave tank is established in which the superposition model is used to generate freak waves. Validations on the freak-wave generation, ship motion response and the wave loading are carried out to verify the present solvers. The simulation on the interaction between the freak wave and the ship are conducted to obtain the interaction process and green-water loads. Secondly, a finite element (FEM) model of the ship bow is built, on which the green-water loads are applied to calculate the structural responses. Finally, the displacement and stress of the deck and breakwater structures are analyzed. It is found that green water events caused by freak waves can generate enormous impact forces on the bow deck and breakwater, resulting in severe structural responses and even possible damage to the structures. The local strength of structures under freak waves needs to be considered in practical engineering applications.

Derivation of an improved smoothed particle hydrodynamics model for establishing a three-dimensional numerical wave tank overcoming excessive numerical dissipation

This paper presents an improved smoothed particle hydrodynamics (SPH) model through a rigorous mathematical derivation based on the principle of virtual work, aiming at establishing a three-dimensional numerical wave tank overcoming excessive numerical dissipation that has been usually encountered in traditional SPH models in practical applications. In order to demonstrate the accuracy and convergence of the new scheme, the viscous damping of a standing wave is first investigated as a quantitative validation, with particular attention on emphasizing (1) its physical rationality with respect to energy conservation and (2) its ability to alleviate wave over-attenuation even using fewer neighbors compared with the traditional δ-SPH model. Subsequently, several fully three-dimensional engineering problems, with respect to water wave propagation and the interaction with structures, are investigated to demonstrate the effectiveness of the new scheme in alleviating wave over-attenuation. It is demonstrated that the present model can be performed with relatively few neighbors (i.e., higher computational efficiency) to obtain accurate and convergent numerical results for those SPH simulations involving long-term and long-distance water wave propagation.

Numerical Study on Modeling and Local Characteristics of a Predetermined Freak Wave

Abstract A numerical study on the modeling and local characteristics of a predetermined freak wave has been conducted with Computational Fluid Dynamics method. Following the available experimental investigations, a numerical wave tank was accordingly set up based on openfoam source packets. The experimental flap-type wave-maker motion was employed directly to reproduce a specific freak wave. The effects of mesh scheme on freak wave modeling were investigated in depth. Reasonable agreements were achieved between the numerical and experimental results. The wavelet transform method was applied to demonstrate the energy structures of freak wave trains. Special attentions were paid to the particle velocities as well as the dynamic pressure. The results showed that insufficient mesh resolutions could probably result in energy dissipations and phase errors of high-frequency wave components during wave propagations which in turn lead to the shifts of focal positions of freak waves. The particle velocities near the wave crest are extremely large, indicating possible severe wave breaking and impact loads. The theoretical values of similar-shape regular waves could considerably underestimate the particle velocities of freak waves.

Dynamic response of floating offshore wind turbines under freak waves with large crest and deep trough

Floating offshore wind turbines (FOWTs) are at high risk being attacked by freak waves with profiles of large crest or deep trough, which could damage the structures or weaken the efficiency of power generation. This study developed a numerical model to address the dynamic response of an in-place FOWT under the action of freak waves with large crest and deep trough. Based on the modulation method of freak wave profiles, various random wave trains embedded freak waves were firstly generated in the numerical wave tank. Noted that these waves generated match Gaussian seas. Then, the effect of freak waves was investigated extensively through the FOWT motions, axial acceleration on nacelle, tether forces as well as wave loads and wave fields in time domain and time-frequency domain. The results show that the occurrence of freak waves significantly amplified the dynamic response of FOWT and the impact lasted for approximately 20 spectral peak periods. Under freak waves, the effect of quadratic phase coupling on nacelle acceleration was first observed. The large crest led to a larger horizontal excursion. While the deep trough caused a larger pitch inducing a larger axial acceleration on nacelle. In addition, the nonlinear interaction (between FOWT and freak waves) caused by the large crest was stronger than that caused by deep trough.

A Comparative Study on Generation and Propagation of Nonlinear Waves in Shallow Waters

This study is concerned with the generation and propagation of strongly nonlinear waves in shallow water. A numerical wave flume is developed where nonlinear waves of solitary and cnoidal types are generated by use of the Level I Green-Naghdi (GN) equations by a piston-type wavemaker. Waves generated by the GN theory enter the domain where the fluid motion is governed by the Navier–Stokes equations to achieve the highest accuracy for wave propagation. The computations are performed in two dimensions, and by an open source computational fluid dynamics package, namely OpenFoam. Comparisons are made between the characteristics of the waves generated in this wave tank and by use of the GN equations and the waves generated by Boussinesq equations, Laitone’s 1st and 2nd order equations, and KdV equations. We also consider a numerical wave tank where waves generated by the GN equations enter a domain in which the fluid motion is governed by the GN equations. Discussion is provided on the limitations and applicability of the GN equations in generating accurate, nonlinear, shallow-water waves. The results, including surface elevation, velocity field, and wave celerity, are compared with laboratory experiments and other theories. It is found that the nonlinear waves generated by the GN equations are highly stable and in close agreement with laboratory measurements.

Numerical simulation on the energy capture spectrum of heaving buoy wave energy converter

Based on the Wave Energy Capture Spectrum (ECS) theory, the characteristics of the ECS of a cylindrical heaving buoy WEC with consideration of linear PTO damping are studied in this paper. A 3D numerical wave tank (NWT) based on the RANS equations and the two-phase VOF model was established using the CFD software Flow-3D and validated by the corresponding experimental data. The ECSs of the heaving buoy WEC with different settings were calculated by the energy capture fluctuation signal, which was based on the incident wave elevation and the power output of the heaving buoy. The procedures of ECS solution using numerical method were proposed, and the effects of irregular wave, linear PTO damping, and relative draught on the ECS of the heaving buoy were studied, respectively. The results showed that the average period of incident wave is the key control factor of the peak frequency of the ECS. Compared to linear PTO damping, the relatively draught has little influence on the peak frequency of ECS. With the evaluation of the ECS method, the cylindrical heaving buoy WEC shows good adaptability to variable wave conditions and could be further improved by adjusting its ECS.

Numerical study of energy capture equipment using tanker rolling motion for different wave heights and encounter angles

ABSTRACT An energy capture equipment is proposed, which can harvest the mechanical energy generated by the rolling motion of a tanker, and the structure of the equipment is designed. The mass-spring-damping mathematical model of the slider is established. Then, a numerical wave tank is created by Fluent to simulate the rolling motion of a typical ship equipped with equipment. According to the data of ship rolling motion and the mathematical model solved by the Newmark-β method in MATLAB, the equipment's power is obtained. Specifically, when the encounter angle is beam wave condition (90 degree), the rolling motion is violent and the equipment power reached the maximum value (187.16 W). Besides, the power generation with the quartering wave is better by comparing the equipment's power under the conditions of the bow and quartering wave. Finally, the wave height becomes bigger, the ship's rolling angular displacement and the equipment's power become larger.

The application of laminar numerical wave tank for a heaving buoy hydrodynamics study in low-turbulence nonlinear waves

Numerical Wave Tanks (NWTs) allow for in-depth investigations into the hydrodynamics and wave responses of floating objects. Thus, they are widely used during the design phase of many offshore platforms and devices. Such problems often feature low turbulence, with wave propagation and wave-object interaction being the key features. In this paper, the merits of using a laminar flow model for a NWT with a free-to-heave buoy, subject to second order Stokes waves in a low sea state is investigated. The simulations are implemented using the interFoam solver, which is embedded in OpenFOAM. The time series of waves measured upstream and downstream of the buoy, and the buoy hydrodynamics are compared to analytical and experimental results for accuracy evaluations. It is shown that, due to the low turbulence level of the problem, the laminar approach can deliver more accurate results than turbulent models, such as Reynolds-averaged Navier-Stokes Simulation (RANS) or partially-averaged Navier-Stokes Simulation (PANS). Moreover, the simulation time of the laminar simulations is significantly shorter than to those of RANS and PANS.

Modeling of a hinged-raft wave energy converter via deep operator learning and wave tank experiments

Model identification for a hinged-raft wave energy converter (WEC) is investigated in this paper, based on wave tank experiments and deep operator learning. Different from previous works which all formulated this issue as a function approximation task, this work, for the first time, formulates it as an operator approximation task (which learns the mapping from a function space to another function space). As such, a continuous-time WEC model is identified from data, greatly expanding the horizon of data-based WEC modeling because previous works were limited to discrete-time model identification. The error accumulation for multi-step predictions in the discrete-time formulation is thus also addressed. The model is developed by first carrying out a set of wave tank experiments to generate the training data, and then the deep operator learning model, i.e. the DeepONet, is constructed and trained based on the experimental data. The validation study shows that the model captures the WEC dynamics accurately. A new set of experimental runs are further carried out and the results show that after training, the model can be used as a digital wave tank, an alternative to the expensive numerical and physical wave tanks, for accurate and real-time simulations of the WEC dynamics.

3D CFD Study of Scour in Combined Wave–Current Flows around Rectangular Piles with Varying Aspect Ratios

This study utilizes three-dimensional simulations to investigate scour in combined wave–current flows around rectangular piles with various aspect ratios. The simulation model solves the Reynolds-averaged Navier–Stokes (RANS) equations using the k–ω turbulence model, and couples the Exner equation to compute bed elevation changes. The model also employs the level-set approach to realistically capture the free surface, and couples a hydrodynamic module with a morphological module to simulate the scour process. The morphological module employs a modified critical bed shear stress formula on a sloping bed and a sand-slide algorithm for erosion and deposition calculations in the sediment bed. To validate the numerical model, simulations are conducted in a truncated numerical wave tank with the Dirichlet boundary condition and active wave absorption method. After validation, the numerical model is used to investigate the effect of aspect ratio and the Keulegan–Carpenter (KC) number on scour depth in a combined wave–current environment. The study finds that the normalized scour depth is highest for a rectangular pile with an aspect ratio of 2:1 and lowest for an aspect ratio of 1:2. The maximum normalized scour depth (S/D) for aspect ratios of 2:1 are 0.151, 0.218, and 0.323 for KC numbers 3.9, 5.75, and 10, respectively, whereas the minimum normalized scour depth (S/D) for aspect ratios of 1:2 are 0.132, 0.172, and 0.279. Additionally, the research demonstrates that the normalized scour depth increases with an increase in the KC number for a fixed wave–current parameter (Ucw).

Computational and experimental studies of wave–structure interaction: Wave attenuation by a floating breakwater

Interactions between surface gravity waves and a floating rigid body are complex, as waves may reflect from, break on, and be transmitted behind the body. Studies of these phenomena are critically important in improving the safety and functional efficiency of offshore structures. Here, the wave attenuation performance and motions of a type of floating breakwater (FB) are studied through numerical and experimental approaches. A numerical wave tank (NWT) is developed based on the software OpenFOAM and properties of wave channel from a laboratory. In the NWT, the air–water interface is captured by the volume of fluid method. The motions of FB are tracked by the six degrees of freedom model. A mooring system model is developed to simulate the constraints of the FB. Large eddy simulation turbulence modeling is implemented for the wave breaking processes. A model FB with a scale of 1:20 is tested in both the experimental and numerical wave channel. Wave heights at the back/front of the FB and the constraint forces of the mooring wires are measured. The numerical models are validated by comparing the results with experimental measurements. The variations of transmission/reflection coefficients, energy dissipation rate, and maximum mooring force are calculated. Changes of the response amplitude operators with the ratio of FB width to wavelength ( B / L w) and wave steepness are analyzed. The wave transmission coefficient will drop below 0.8 if the value of B / L w is larger than 0.3, but will go over 0.95 if B / L w is less than 0.1. Wave steepness has a large influence on FB motions and the mooring system. The effect of Stokes drift is observed by the shift of position of the FB.

Multi-directional irregular wave forces acting on a tandem pile group

In this study, the interactions between multi-directional irregular waves and a tandem pile group are experimentally investigated. A systematic statistical analysis of the force coefficients of the pile group and the wave force on a tandem pile group under multi-directional waves is first carried out. The results show that the wave force of the pile group is significantly affected by the wave directionality. Further, Reynolds-averaged Navier–Stokes equations are used to establish a 3D numerical wave tank by considering the interactions between the waves and the pile groups, and this is verified by using experimental data. The characteristics of the wave force on the first and the last pile in the tandem pile group were numerically examined. The flow field around the front first pile was affected by its rear pile such that the pressure at its rear increased. However, without the rear pile, the pressure difference between the upward and rearward zone of the last pile significantly increased compared with that of the first pile, and this caused the wave force of the last pile to be larger than that of the first pile.

An energetic signature for breaking inception in surface gravity waves

A dynamical understanding of the physical process of surface gravity wave breaking remains an unresolved problem in fluid dynamics. Conceptually, breaking can be described by inception and onset, where breaking inception is the initiation of unknown irreversible processes within a wave crest that precede the visible manifestation of breaking onset. In the search for an energetic indicator of breaking inception, we use an ensemble of non-breaking and breaking crests evolving within unsteady wave packets simulated in a numerical wave tank to investigate the evolution of each term in the kinetic energy balance equation. We observe that breaking onset is preceded by around one quarter of a wave period by a rapid increase in the rate of convergence of kinetic energy that triggers an irreversible acceleration of the kinetic energy growth rate. This energetic signature, which is present only for crests that subsequently break, arises when the kinetic energy growth rate exceeds a critical threshold. At this point the additional kinetic energy convergence cannot be offset by converting excess kinetic energy to potential energy or by dissipation through friction. Our results suggest that the ratio of the leading terms of the kinetic energy balance equation at the time of this energetic signature is proportional to the strength of the breaking crest. Hence this energetic inception point both predicts the occurrence of breaking onset and indicates the strength of the breaking event.

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