Numerical Wave Tank Research Articles

A large-eddy-simulation-based numerical wave tank for three-dimensional wave-structure interaction

A three-dimensional numerical wave tank (NWT) based on the open-source large eddy simulation (LES) code Hydro3D is introduced. The code employs the level set and immersed boundary methods to enable accurate computations of the deformation of the water surface and to account for solid structures in the fluid domain, respectively. The spatially-filtered Navier–Stokes (N–S) equations are solved on a staggered Cartesian grid using the finite difference method while time advancement is achieved using the fractional-step method based with a three-step Runge–Kutta scheme. Velocities and pressure are coupled with the Poisson equation and its solution is obtained via a multi-grid technique. The code is then applied to predict the progression and damping of monochromatic waves and the interaction of non-linear waves with various submerged obstacles. The accuracy of Hydro3D is confirmed by comparing numerical results with data of previously reported laboratory experiments. Comparisons of numerically predicted and measured water-levels, local velocity and pressure fields and forces acting on structures under the influence of incoming waves with laboratory data are convincing and confirm that the code is able to predict accurately three-dimensional wave-structure interaction.

Numerical Analysis of Nonlinear Wave Characteristics Under Porous Sloped-Seabed Conditions

Min, E.-H. and Koo, W., 2021. Numerical analysis of nonlinear wave characteristics under porous sloped-seabed conditions. In: Lee, J.L.; Suh, K.-S.; Lee, B.; Shin, S., and Lee, J. (eds.), Crisis and Integrated Management for Coastal and Marine Safety. Journal of Coastal Research, Special Issue No. 114, pp. 116–120. Coconut Creek (Florida), ISSN 0749-0208. The characteristics of nonlinear wave attenuation were analyzed under porous sloped-seabed conditions. Nonlinear wave propagation was simulated in the time domain using a two-dimensional fully nonlinear numerical wave tank (NWT). The NWT technique was based on the boundary element method and consisted of two computational domains: A fluid domain and a porous seabed domain. To account for the wave-porous subsea interaction, the boundary value problem was solved in each domain, and the calculated values were exchanged at the interface boundary between the fluid domain and the porous domain at each time step. The shoaling coefficients for wave propagation on a sloped-seabed were calculated, and the attenuation of the waves due to interaction with the porous bottom was investigated. Waves traveling to the coast were decomposed into each frequency component, and the magnitude of the wave attenuation ratio for each component was compared. The characteristics of wave propagation according to the permeability coefficients on the seabed, wave steepness, and wave periods were also investigated.

A Computational Fluid Dynamics Approach for Modeling the Fluid–Structure Interaction of Offshore Aquaculture Cages and Waves

Abstract Open ocean aquaculture cages became a promising alternative to traditional fish cage designs recently. The offshore environment implies larger loads on the structure and thus higher risk for fish loss. Floating rigid aquaculture cages with stiff nets are considered as a possible solution to cope with these new challenges. Their design process requires more advanced tools to account for the non-linear fluid–structure interaction. This paper presents a suitable numerical approach for analyzing the interaction of offshore aquaculture cages and waves using computational fluid dynamics. Here, a numerical wave tank accounts for the accurate propagation of the waves, and dynamic solutions are utilized for the cage system. Two-way coupling is enabled by accounting for the influence of the net on the fluid. The numerical model is validated against measurements for the loads on and the responses of a mobile floating fish farm in waves and current.

A fully nonlinear potential flow wave modelling procedure for simulations of offshore sea states with various wave breaking scenarios

An accurate representation of a given sea state is crucial for the study of hydrodynamic loads on offshore structures. It is straightforward to check the quality of the reproduced regular waves in a numerical wave tank (NWT). However, many more parameters need to be considered to ensure the quality of irregular waves. In this paper, a fully non-linear potential flow (FNPF) wave model is used to reproduce irregular sea states with different severity of wave breaking. The numerical model solves the velocity potential from the Laplace equation and the free surface boundary conditions using a finite difference method on a σ-coordinate grid. A comprehensive procedure is introduced to ensure the quality of the reproduced full-scale sea states. The effect of wave spectrum discretisation techniques and breaking wave algorithms are compared for an optimal performance. The evaluation of the simulation results takes into account the kurtosis and the wave crest distribution in addition to the wave spectra. The vertical arrangement of the σ-coordinate grid plays an important role in representing the dispersion relation and a grid optimisation method is explained. The current study provides a working procedure that reproduces high-fidelity irregular sea states with breaking waves in an efficient FNPF NWT.

Hydrodynamic investigations on the performance of an underwater remote operated vehicle under the wave using OpenFOAM

ABSTRACT Underwater remotely operated vehicle (ROV) is used to monitor the subsea-surface mooring and piping lines. In this study, the hydrodynamic characteristics of a remote-operated vehicle are analysed using an open-source computational fluid dynamics (CFD) software. In the first CFD simulation set, the ROV is tested at surge velocity in the water current flow and the pressure coefficient is validated against the experimental measurements. In the second CFD simulation set, a numerical wave tank is proposed to study two cases with ROV and pipe under the action of surface waves after verification with the literature. Coefficients of lift and drag of ROV are compared and the streamlines are visualised. Substantial reduction of velocity ratio with normalised pressure difference and higher frequency of vortex shedding are observed in the case of ROV with pipe against ROV alone. From this study, the time history of velocity near ROV is found to be essential during the operation.

Numerical study on wave attenuation of extreme waves by emergent rigid vegetation patch

Attributed to the processes of wave focusing, extreme waves often occur unexpectedly with huge wave height in both deep and shallow water regions, which can cause serious damages to the coastal infrastructures, and threaten the intactness of coastal communities. Field observations after extreme weather events have revealed that as a type of natural barrier, coastal vegetations can effectively attenuate the intensity of extreme surges and waves and thus play a good role in naturally protecting the coast. Usually, focused wave is used as a typical extreme wave model to study the great impact of extreme waves on the coast. To numerically evaluate the wave attenuation of extreme waves by the emergent rigid vegetation patch, a high-resolution numerical wave tank has been established by applying the nonhydrostatic numerical wave model (NHWAVE), where both 2nd-order crest and trough focused waves can be generated by considering wave-wave interactions. The efficiencies of the rigid emergent vegetation patch in mitigating the maximum wave amplitude and total wave energy of both crest and trough focused waves as function significant wave height, peak wave period, water depth, vegetation density and width have been well analyzed and discussed. The results indicate that the emergent rigid vegetation patch can effectively reduce the maximum wave amplitude of focused wave by averagely 31% and the total wave energy by averagely 45%, thus, showing that coastal vegetation can effectively protect the coast from extreme waves. It is hoped that the research findings drawn from this study can further broaden our understanding on the wave attenuation of extreme waves by coastal vegetations.

CFD study of wave interaction with single and two tandem circular cylinders

Wave-structure interaction is a key consideration for the safe design of offshore structures. This work investigates the non-linear wave interactions with a single cylinder and two tandem cylinders using a numerical wave tank. The numerical simulations are carried out by the in-house CFD solver naoe-FOAM-SJTU, which is developed on the open-source platform OpenFOAM. The numerical simulation is first validated by comparing numerical results and experimental data for regular wave interaction with a single cylinder. Wave interaction with tandem cylinders is then investigated for different center-to-center distances between the cylinders. The surface elevation around the cylinder is probed by a series of wave probes and analyzed using the Fast Fourier analysis. The response amplitude operates of surface elevation for single cylinder case agrees well with experimental data. The wave scattering around the cylinder is qualitatively compared with experimental observation and discussed in detail. The wave scattering fields and wave forces are systematically analyzed. Then the interaction between wave and two tandem cylinders is investigated. The distance between the cylinders highly influences the free surface elevation and wave forces experienced by the tandem cylinders. The local surface elevation and the scattered wave field around the cylinders are also discussed.

Three-dimensional Computational Fluid Dynamics modelling of scour around a single pile due to combined action of the waves and current using Level-Set method

This paper presents three dimensional (3D) numerical modeling of local scour around a single pile under the combined action of waves and currents. A semi-coupled hydrodynamic and morphological model (REEF3D) is used in this study which solves the Reynolds-averaged Navier–Stokes (RANS) equation with k-ω turbulence model closure. The Exner equation is used to calculate the changes in bed elevation. The use of the Level-Set method is done to capture the changes in the free surface. Realistic scour and deposition calculations are aided with the use of modified critical bed shear stress reduction formulation on a sloping bed supplemented with the use of Sand Slide algorithm in the morphological model. The scouring process is modeled in this study using a reduced-length numerical wave tank with wave generation and wave absorption implemented using active wave absorption method. The model is validated for the numerical modeling of local scour around a single pile in steady current, waves alone, and combined wave–current environment. The validated model is used to analyze the effect of Keulegan–Carpenter (KC) number and combined wave–current parameter (Ucw) on normalized equilibrium scour depth. It is found that the normalized equilibrium scour depth for scour under waves alone, waves combined with weak currents, and waves combined with mild current do not significantly differ for flow developed in a low KC number environment. However for waves combined with strong currents the normalized equilibrium scour depth increases significantly. For large KC numbers, the normalized equilibrium scour depth is found to have increased with an increase in KC number as well as combined wave–current parameter (Ucw).

Design optimization of a novel vertical augmentation channel housing a cross-flow turbine and performance evaluation as a wave energy converter

A novel vertical augmentation channel housing a direct-drive cross-flow turbine, with nozzles on both the sides of the turbine, was designed and an optimized configuration was obtained. The geometries of the guide nozzle and the front nozzle were optimized under steady flow conditions. The performance of the cross-flow turbine was analyzed using commercial computational fluid dynamics (CFD) code ANSYS-CFX. The optimized design was then evaluated as a wave energy converter both experimentally and computationally. The waves in the numerical wave tank (NWT) were generated using a piston type wave-maker. The optimized design gave a maximum output power of 13.2 W and an efficiency of 48.31% at a wave height of 0.2 m and wave period of 2.75 s for a rotational speed of 35 rpm. The difference between numerical and experimental efficiencies was within 3.5%. In addition to this, particle image velocimetry was used to study the flow characteristics in the augmentation channel and the turbine. The results show that the CFD code captures the flow in the augmentation channel and around the turbine accurately. The optimized design, which occupies less space than other wave energy converters, can be used to efficiently harness energy from the waves.

Reduction of the wave propagation error of a sigma grid based numerical tank using a vertical spacing based on the constant truncation error

Numerical wave models that solve the Laplace equation for the velocity potential with a σ-grid in the vertical direction have been proven to be flexible and efficient. However, it is observed that the dispersion relation is sensitive to the variation of the vertical σ-grid arrangements. So far, there is no recommended practice to optimise the vertical σ-grid for a correct representation of the dispersion relation. In order to reduce the uncertainty of the dispersion relation and optimise the choice of the vertical grid distribution, a new method based on the constant truncation error of the finite difference scheme is presented in this article. The optimised vertical grids estimated by the novel method are applied in the fully nonlinear potential flow model REEF3D::FNPF to provide simulated wave surface elevations, which are compared with the measured time series in the long wave flume at SINTEF Ocean, Trondheim. Several different wave scenarios are considered, including regular waves, bichromatic waves, trichromatic waves as well as irregular waves. The wavemaker motions in the physical flume are used to generate waves in the numerical wave tank of REEF3D::FNPF. The proposed truncation error method is seen to effectively mitigate the dispersion (phase) error in all scenarios and the simulations show high accuracy in comparison with the experimental data.

Assessment of uncertainty in the CFD simulation of the wave-induced loads on a vertical cylinder

The paper addresses different uncertainty analysis methods commonly used for uncertainty quantification in Computational Fluid Dynamics (CFD) studies and compares a constant Courant–Friedrichs–Lewy (CFL) number based approach for uncertainty estimation to the ITTC recommended grid and time-independent procedures. Four different uncertainty estimation procedures are presented and discussed. To compare their performance and better understand CFD related uncertainty quantification in wave load simulations on offshore structures, the methods are applied to a case study of the wave loads on a fixed vertical cylinder. The numerical or CFD wave tank is generated using the open-source CFD toolkit OpenFOAM. Uncertainty is assessed for the case study using four different uncertainty estimation procedures for verification and later, validation is attempted by comparing the CFD results with experiments. The study concludes that a constant CFL number based uncertainty study provides more stable results and is better suited for uncertainty estimation in CFD than the ITTC recommended individual grid and time step uncertainty study.

Numerical Analysis of Wave Energy Extraction Performance According to the Body Shape and Scale of the Breakwater-integrated Sloped OWC

Research on the development of marine renewable energy is actively in progress. Various studies are being conducted on the development of wave energy converters. In this study, a numerical analysis of wave-energy extraction performance was performed according to the body shape and scale of the sloped oscillating water column (OWC) wave energy converter (WEC), which can be connected with the breakwater. The sloped OWC WEC was modeled in the time domain using a two-dimensional fully nonlinear numerical wave tank. The nonlinear free surface condition in the chamber was derived to represent the pneumatic pressure owing to the wave column motion and viscous energy loss at the chamber entrance. The free surface elevations in the sloped chamber were calculated at various incident wave periods. For verification, the results were compared with the 1:20 scaled model test. The maximum wave energy extraction was estimated with a pneumatic damping coefficient. To calculate the energy extraction of the actual size WEC, OWC models approximately 20 times larger than the scale model were calculated, and the viscous damping coefficient according to each size was predicted and applied. It was verified that the energy, owing to the airflow in the chamber, increased as the incident wave period increased, and the maximum efficiency of energy extraction was approximately 40% of the incident wave energy. Under the given incident wave conditions, the maximum extractable wave power at a chamber length of 5 m and a skirt draft of 2 m was approximately 4.59 kW/m.

Development and validation of a numerical wave tank based on the Harmonic Polynomial Cell and Immersed Boundary methods to model nonlinear wave-structure interaction

A fully nonlinear potential Numerical Wave Tank (NWT) is developed in two dimensions, using a combination of the Harmonic Polynomial Cell (HPC) method for solving the Laplace problem on the wave potential and the Immersed Boundary Method (IBM) for capturing the free surface motion. This NWT can consider fixed, submerged or wall-sided surface piercing, bodies. To compute the flow around the body and associated pressure field, a novel multi overlapping grid method is implemented. Each grid having its own free surface, a two-way communication is ensured between the problem in the body vicinity and the larger scale wave propagation problem. Pressure field and nonlinear loads on the structure are computed by solving a boundary value problem on the time derivative of the potential. The stability and convergence properties of the solver are studied basing on extensive tests with standing waves of large to extreme wave steepness, up to H/λ=0.2 (H is the crest-to-trough wave height and λ the wavelength). Ranges of optimal time and spatial discretizations are determined and high-order convergence properties are verified, first without using any filter. For cases with either high level of nonlinearity or long simulation duration, the use of mild Savitzky-Golay filters is shown to extend the range of applicability of the model. Then, the NWT is tested against two wave flume experiments, analyzing forces on bodies in various wave conditions. First, nonlinear components of the vertical force acting on a small horizontal circular cylinder with low submergence below the mean water level are shown to be accurately simulated up to the third order in wave steepness. The second case is a dedicated experiment with a floating barge of rectangular cross-section. This very challenging case (body with sharp corners in large waves) allows to examine the behavior of the model in situations at and beyond the limits of its formal application domain. Though effects associated with viscosity and flow separation manifest experimentally, the NWT proves able to capture the main features of the wave-structure interaction and associated loads.

Simulation of Water Wave Interaction with Large Submerged Square Obstacles

Water waves propagation over submerged obstacles is considered. The problem serves as an efficient model for modeling breakwaters. A numerical wave tank is developed to simulate the induced flow field. The model is based on multiphase viscous flow assumptions. Computations are performed adopting clustered grids and suitable initial and boundary conditions. The results are verified using the flow field particle image velocimetry (PIV) measurements. Spatial and temporal resolutions are validated. Complex flow phenomena occurring due to the presence of the relatively large sized obstacle are visualized. The effect of wave parameters on the flow structure is investigated. A brief parametric study is presented and the resultant wave forces and turning moments are provided.

Numerical analysis on wave load reduction effect of a solid wall with porous plate by macroscopic CFD approach

The porous structures are widely designed in coastal and ocean engineering to reduce the wave load. A macroscopic CFD approach is established to study the wave interaction with a porous plate placed in front of a solid wall. The established numerical wave tank was firstly validated by the analytical results of a vertical wall, and the macroscopic CFD model was validated by the experimental results of a single vertical porous plate. Then the wave load reduction effect of a solid wall with a vertical porous plate in front is investigated, the influences of porosity and relative gap width are compared, and the effects of wave height are also analyzed. The results demonstrate that the porosity and relative gap width are the main effect factors to the wave force reduction effect, and the wave forces on structure increase almost linearly with the increase of relative wave height, while the wave load reduction coefficient and refection coefficient are not linearly. A porosity of 0.2 and relative gap width of 0.2–0.3 are deemed to be optimal geometry parameters at which the wave load reduction effect is optimal. The total horizontal wave force increases nonlinearly with the increase of wave heights, and the quadratic pressure drop condition is essential when studying the wave force on thin porous structures.

CFD Modeling of Regular and Irregular Waves Generated by Flap Type Wave Maker

The improvement of wave generation in numerical tanks represents the key factor in ocean engineering development to save time and effort in research concerned with wave energy conversion. For this purpose, this paper introduces a numerical simulation method to generate both regular and irregular waves using Flap-Type wave maker. A 2D numerical wave tank model is constructed with a numerical beach technique, the independence of the numerical beach slope is tested to reduce the wave reflections. The different governing parameters of the Flap type wave maker were studied such as periodic time dependency and length of the flap stroke. The linear wave generated was validated against the wave maker theory WMT, the numerical results agreed with WMT. The Pierson-Moskowitz model is used to generate irregular waves with different frequencies and amplitudes. The numerical model succeeded to generate irregular waves which was validated against published experimental data and with Pierson-Moskowitz spectrum model using Fourier expansion theory in the frequency domain. Useful results are presented in this paper based on the numerical simulation to understand the characteristics of the waves. This paper produces a full guide to generate both regular and irregular waves numerically using ANSYS-CFX approach to solve the 2D Unsteady Reynolds Averaged Navier-Stokes Equation (URANS).

Non-linear dynamic simulations of two-body wave energy converters via identification of viscous drag coefficients of different shapes of the submerged body based on numerical wave tank CFD simulation

Two-body point absorbers are useful for wave energy conversion in high energetic and high wave period sea locations. Analysis and simulation show that the two-body point absorbers have high efficiencies which makes them a potential candidate to promote wave energy harvesting technology towards commercialization and implementation. The submerged body of the two-body point absorbers has a large effect on their performance, hence the question arises: which geometric shape of the submerged body will lead to the best performance of the two-body wave energy harvesters? This paper presents a comprehensive study that analyses the different shapes of the submerged bodies based on the numerical wave tank simulated viscous drag coefficient and hydrodynamic property parameters of the oscillating device. A set of transient and three-dimensional computational fluid dynamic simulations of a numerical wave tank were carried out in Ansys Fluent to determine the viscous drag coefficients of the different submerged body shapes. And then the boundary element hydrodynamic simulation and linear dynamic frequency-domain modeling have been applied to identify the optimized PTO damping. Finally, non-linear time-domain modeling has been applied with the identified viscous damping drag coefficient and PTO damping coefficients to predict and compare the power output performance of different large-scale devices with different shapes of submerged bodies. It is found that each submerged body shape is suitable for a different range of wave frequencies, as one must establish a balance between the hydrodynamic properties and the viscous drag of the submerged body based on the sea location. It is also found that the typical viscous drag coefficient values used in the past studies underestimate the drag coefficient, and the linearized model widely adopted in frequency domain models is non-accurate for the devices with large viscous drag forces.

Simulation of fully nonlinear water wave propagation over the flat bottom and uneven bottom by meshless numerical wave tank

Simulation of fully nonlinear water wave propagation over the flat bottom and uneven bottom by meshless numerical wave tank

Numerical Stability Investigations of the Method of Fundamental Solutions Applied to Wave-Current Interactions Using Generating-Absorbing Boundary Conditions

In this paper, the goal is to revolve around discussing the stability of the Method of Fundamental Solutions (MFS) for the use case of wave-current interactions. Further, the reliability of Generating-Absorbing Boundary Conditions (GABCs) applied to the wave-current interactions is investigated using the Method of Fundamental Solutions (MFS), in a Numerical Wave Tank (NWT) within the potential theory where the main regular manifestations are the periodicity, and symmetry of traveling waves. Besides, the investigations cover different aspects of currents (coplanar current, without current, and opposing current), and also different water depths. Furthermore, the accuracy and stability of the numerical method (MFS) used in this work is evaluated for different locations and numbers of source points.

Hydrodynamic Performance of an Asymmetry OWC Device Mounted on a Box-Type Breakwater

To share the construction and maintenance cost, an asymmetric oscillating water column (OWC) device integrated with a pile-fixed box-typed offshore breakwater is considered experimentally and numerically. A fully nonlinear numerical wave tank is established and validated with the open source solver OpenFOAM. The effects of the width and draft of rear box, and the incident wave height on the wave energy conversion efficiency, reflection and transmission coefficients, and energy dissipation coefficient are examined. In addition, the superiority of the present coupling system, compared to the traditional box-type breakwater, is discussed. With well comparisons, the results show that the existence of the rear breakwater is beneficial for the formation of partial standing waves and further wave energy conversion. In the range of wave heights tested, the higher the incident wave height, the larger the energy absorption efficiency except for the short-wave regimes. Moreover, the OWC-breakwater coupling system can obtain a similar wave blocking ability to the traditional one, and simultaneously extract wave energy and decrease wave reflection.