Two-dimensional Numerical Wave Flume Research Articles

Transient gap resonance between two closely-spaced boxes triggered by nonlinear focused wave groups

A two-dimensional (2D) viscous numerical wave flume is developed based on OpenFOAM® to investigate the transient gap resonance problem triggered by nonlinear focused wave groups. The narrow gap is formed by two closely-spaced boxes, where the weather-side box is allowed to heave freely under wave actions, but the rear one is firmly fixed. The overset mesh method is introduced in the numerical model to capture the weather-side box's large-amplitude motion accurately. This work mainly focuses on the coupled effects of free-surface nonlinearity and heave-freedom of the weather-side box on the fluid oscillations in the gap and heave motions of the weather-side box. The heave-freedom of the weather-side box is demonstrated to play an important effect on the period in which the maximum value of non-dimensional amplitude of fluid oscillation in the gap occurs. It is revealed that the free-surface nonlinearity significantly affects the nonlinear fluid oscillations in the gap but has a limited effect on the heave motions of the weather-side box. The four-phase combination method is further employed to conduct the higher harmonic component analysis to clarify the effects of higher harmonic components on the nonlinear response of fluid and box.

SPH Simulation of the Interaction between Freak Waves and Bottom-Fixed Structures

In this paper, the Smoothed Particle Hydrodynamics (SPH) method is used in a C# environment to simulate the interaction between freak waves and bottom-fixed structures by establishing a fluid dynamics model. Paraview software 5.10.1 was used to analyze and visualize the simulation results. In order to simulate wave propagation accurately, the reliability of the model was verified by comparing experimental and simulated data. A two-dimensional numerical wave flume was established based on the SPH method, a conservative Riemann solver was introduced, a repulsive boundary condition was adopted, and a slope was used to eliminate wave reflection. Bottom-fixed structures of different heights and lengths, as well as different wave conditions, were selected to numerically simulate the interaction between freak waves and bottom-fixed structures. The results show that the height of bottom-fixed structures and wave conditions have a significant effect on hindering the propagation of rogue waves, while the length has little effect on the propagation of deformed waves. When the amplitude of the wave remains constant, both the period andthe duration of the deformed wave are longer. This research is of certain significance for the prediction of freak waves in marine engineering and the application and promotion of SPH methods.

Analysis of Sharp Eagle Oscillating Surge Wave Energy Converter Based on a Two-Dimensional Numerical Wave Flume Model

To investigate the overtopping and slamming phenomena that occur in the interactions between waves and oscillating surge wave energy converters (OSWECs), a two-dimensional numerical wave flume was established using computational fluid dynamics (CFD) software Fluent by adding the momentum source terms into the original Navier–Stokes equation. Numerical convergence studies of the mesh sizes and time steps were firstly performed to ensure the sufficient accuracy of the numerical model. The variations in the wave heights along the wave propagation direction in the wave-generating area, working area, and wave-absorbing area were analyzed. The dynamics of the flap-type OSWEC were simulated using the overset mesh function embedded in Fluent. In addition, the numerical results were compared with the experimental data, and good agreements were achieved. External torque was applied to the hinge joint of the OSWEC to simulate the forces due to the power take-off (PTO) system, and the identified optimal PTO damping was compared with the numerical results based on the potential flow theory, which verified the correctness of the numerical PTO system. On this basis, nonlinear wave slamming by the sharp-eagle OSWEC was analyzed. The results show that under certain incident wave conditions, the sharp-eagle OSWEC can effectively reduce the maximum rotation angle and angular velocity compared with those of the flap-type OSWEC, and there is no overtopping that occurring for the sharp-eagle OSWEC. Furthermore, the sharp-eagle OSWEC performs better than the flap-type OSWEC.

Study on the propagation of regular water waves in a numerical wave flume with the [formula omitted]-SPH[formula omitted] model

Waves, a phenomenon of variable scale fluctuations common to the surface of the ocean, are the major loads acting on marine floats and play a pivotal role in the study of the hydrodynamics of offshore and deep-water structures. In this work, a two-dimensional (2D) numerical wave flume (NWF) is formed to simulate the propagation of regular water waves by the weakly compressible smoothed particle hydrodynamics-based (WCSPH) model. Artificial density and viscosity diffusion terms are used to stabilize the pressure field and numerical simulation, respectively. Based on the δ-SPH model, the δ-SPHC one is constructed by introducing the correction matrix into the calculation of the pressure gradient operator in the momentum equation. The δ-SPHC model can guarantee second-order calculation accuracy even if the kernel function support domain is truncated. Besides, the destruction of momentum conservation can be greatly suppressed with its high symmetric, which facilitates the reduction of energy dissipation in the wave propagation process. In order to confirm the accuracy and stability of the developed 2D δ-SPHC-based NWF, five classical benchmark tests are examined and discussed. The simulation results indicate that the adopted numerical wave flume performs well in predicting the dynamic evolution of regular water waves, which shows its potential for further investigation of more challenging hydrodynamic issues in real-world applications.

Interaction between medium-long period waves and smoothed mound breakwater: Physical model tests and SPH simulations

Medium-long period waves have attracted increasing attention. Laboratory and numerical investigations on the interaction between medium-long period waves and a smoothed mound breakwater were conducted. A two-dimensional numerical wave flume based on smoothed particle hydrodynamics was established. A good agreement between experimental and numerical results was observed.Wave force on the slope is positively correlated with the wave period. It is found that Neelamani's method is slightly overestimated wave force on the slope. By comparing with other overtopping methods, a new formula considering the wave period was proposed to predict the overtopping of the smoothed mound breakwater. The energy transmission coefficient was used to evaluate the protective effect of the breakwater. The results show that the smooth mound breakwater provides significant protection against longer-period waves. As the wave period increases, the number of peaks (Np) in the wave spectrum behind the breakwater increases. A formula was presented to describe the relationship between Np and wave period.

Accumulation and Dispersion of Microplastics near A Submerged Structure: Basic Study Using A Numerical Wave Tank

The presence of microplastics has been reported in most marine environments. Their accumulation can affect the marine ecosystem, and their consumption by small organisms of various sizes can indirectly affect human beings who consume them. Recent observations have reported the pathways and fates of microplastics surrounding man-made coastal structures, such as artificial reefs. However, basic research elucidating the physical behavior near the structure is scarce. We implemented a two-dimensional numerical wave flume simulating intermediate waves with a weak current in a coastal area to investigate the behaviors of microplastics corresponding to parameters such as particle size (0.2, 1, and 5 mm), particle density (900, 1000, and 1100 kg/m3), and submerged artificial structure. The results showed that smaller particles had a stronger horizontal dispersion but a weaker horizontal advection. Installing a submerged structure increased the flow rate above the structure. It also increased particle accumulation upstream and downstream near the edge and corner of the structure. The accumulation was significantly affected by the installation of the structure when the resuspension of microplastics occurred intermittently. This work elucidates the mechanisms underlying the distribution, accumulation, and dispersion of microplastics that are important in predicting the fate of microplastics in the vicinity of artificial structures.

Investigations on the second-order transient gap resonance induced by focused wave groups

Two or more marine structures deployed side by side may encounter strong water-body resonances within narrow gaps between them. It may cause significant wave loads on structures and the green water phenomenon on the deck. In this article, the transient fluid motion within a narrow gap formed by two fixed boxes suffered from incident focused wave groups is investigated using a two-dimensional viscous flow numerical wave flume. The focused wave groups adopted have the spectral peak frequency equal to half the fluid resonant frequency inside the gap. The wave fields both inside the gap and around the two-box system, the response/damping time of the transient wave surfaces inside the gap, the maximum wave forces and the ratios of the 2nd-order to the corresponding 1st-order wave surfaces/forces are investigated. It is revealed that the most dangerous place to green water is always the front edge of the two-box system. The damping time of the 2nd-order wave surface is significantly larger than that of the 1st-order one. As the incident wave amplitude rises, the ratios of the 2nd-order to the first-order wave surfaces/forces becomes increases gradually and can even exceed 100% for the wave surface, the horizontal wave force and the moment.

Effects of narrow gap wave resonance on a dual-floater WEC-breakwater hybrid system

The effects of gap wave resonance on the performance of a dual-floater hybrid system consisting of an oscillating-buoy type wave energy converter (WEC) and a floating breakwater are important for the design of such a hybrid system. This paper investigates the gap wave resonance by employing a two-dimensional numerical wave flume developed using the Star-CCM + software. The maximum wave elevation in the WEC-breakwater gap and the effects of the gap wave resonance on the performance of the dual-floater hybrid system were studied. The influence of the WEC motion and the geometrical parameters of the hybrid system on the maximum wave elevation were analyzed. The maximum gap wave elevation is essentially controlled by the vertical velocity of the free surface in the WEC-breakwater gap. The gap wave resonance was found to significantly improve the wave energy extraction performance of the hybrid system. This allowed the maximum conversion efficiency to exceed the well-known limit of 0.50 for a symmetric body in single degree-of-freedom motion. The wave resonance frequencies in the WEC-breakwater gap decreased with the increase of the gap width and the WEC draft. Due to the energy extraction of the WEC, the horizontal and vertical forces on the breakwater were reduced by up to 0.79 and 0.59, respectively.

Numerical Study of the Influence of U-shaped Walls on Energy Capture Property of OWC Wave Energy Devices

Cui, L.; Zheng, X.B.; Ji, M.Z., and He, X., 2020. Numerical study of the influence of u-shaped walls on energy capture property of OWC wave energy devices. In: Guido Aldana, P.A. and Kantamaneni, K. (eds.), Advances in Water Resources, Coastal Management, and Marine Science Technology. Journal of Coastal Research, Special Issue No. 104, pp. 192–197. Coconut Creek (Florida), ISSN 0749-0208.In this paper, a two-dimensional numerical wave flume has been established based on the incompressible viscous fluid theory and by using STAR-CCM + software, verifying the convergence and accuracy of the numerical flume. By building a numerical model for the interaction between waves and U-OWC devices, this paper studies the influence of each major control parameter on the wave energy capture efficiency of U-OWC wave energy devices. The research results show that the height of U-shaped walls has a great impact on the wave energy capture efficiency of the devices and that proper U-shaped wall height can enhance the wave energy capture efficiency; the distance between the U-shaped wall and the anterior wall of air chamber as well as the inclination of U-shaped walls also have a large effect on the hydrodynamic property of the devices, and appropriate distance between the U-shaped wall and the anterior wall of air chamber and correct inclination of U-shaped walls can increase the wave energy capture efficiency of U-OWC devices to a certain extent.

Wave-Structure Interaction for a Stationary Surface-Piercing Body Based on a Novel Meshless Scheme with the Generalized Finite Difference Method

The wave-structure interaction for surface-piercing bodies is a challenging problem in both coastal and ocean engineering. In the present study, a two-dimensional numerical wave flume that is based on a newly-developed meshless scheme with the generalized finite difference method (GFDM) is constructed in order to investigate the characteristics of the hydrodynamic loads acting on a surface-piercing body caused by the second-order Stokes waves. Within the framework of the potential flow theory, the second-order Runge-Kutta method (RKM2) in conjunction with the semi-Lagrangian approach is carried out to discretize the temporal variable of governing equations. At each time step, the GFDM is employed to solve the spatial variable of the Laplace’s equation for the deformable computational domain. The results show that the developed numerical method has good performance in the simulation of wave-structure interaction, which suggests that the proposed “RKM2-GFDM” meshless scheme can be a feasible tool for such and more complicated hydrodynamic problems in practical engineering.

Numerical investigations of wave loads on fixed box in front of vertical wall with a narrow gap under wave actions

Violent fluid oscillations may appear inside the narrow gap between multiple structures in close proximity and cause severe damage to such structures and safe operations. Here, based on the OpenFOAM® package, this paper presents a numerical investigation of wave loads during gap resonance between a fixed box and a vertical wall by utilizing a two-dimensional (2D) numerical wave flume. The box-wall system is subjected to incident regular wavesco with various wave heights and frequencies. The topographies of plane slopes with various inclinations are arranged in front of the vertical wall. This paper focuses on the influences of the topographical variation on the wave loads, including the horizontal wave force, the vertical wave force and the moment on the box. It is found that all the frequencies, at which the maximum horizontal wave force, the maximum vertical wave force and the maximum moment appear, decrease with the increase of topographical slope, S, overall. Moreover, these frequencies are also shown to deviate from the fluid resonant frequency to different degrees. For all the incident wave heights considered, both the maximum horizontal wave force and the maximum moment present a pattern of fluctuation with the topographical slope.

Numerical simulation of wave resonance in the narrow gap between two non-identical boxes

Wave resonance in the narrow gap between two side-by-side non-identical boxes is investigated by employing a two-dimensional numerical wave flume based on the OpenFOAM® package. The focus of this study is to examine the influence of the energy transformation and the energy dissipation on the hydrodynamic behavior of wave response around resonant conditions. Numerical simulations show that the unrealistic wave resonant responses in the narrow gap by the linear potential flow model are due to not only the energy dissipation induced by the fluid rotational motion, but also the energy transformation associated with the free surface. With the increase of incident wave amplitude, relatively more energy is reflected, leading to the decrease of wave resonant response and energy dissipation in the narrow gap at the resonant frequency. When slightly away from the resonant frequency, the energy dissipation becomes the dominant factor for the decrease of wave response in the narrow gap with increasing the incident wave amplitude. As for the influence of gap configuration, on one hand, energy dissipation has the dominant effect for the typical case of small upstream and large downstream box drafts. On the other hand, the reflected energy is more important for the typical large upstream and small downstream box drafts. More resonant fluid exists in the gap with the increase of gap breadth, leading to the decrease of reflection coefficient and the increase of transmission coefficient.

Numerical simulation of fluid resonance in a moonpool by twin rectangular hulls with various configurations and heaving amplitudes

Fluid resonance in a moonpool formed by two identical rectangular hulls during in-phase heaving motion is investigated by employing a two-dimensional numerical wave flume based on OpenFOAM package with Re-Normalization Group (RNG) turbulent model. The focus of the study is to examine the influence of heaving frequency and amplitude with various moonpool configurations on fluid resonant behavior. It is found that the resonant frequency of wave response in moonpool tends to decrease with the increase of moonpool breadth and hulls draft. The decrease of resonant amplitude can be observed for large moonpool breadth. The influence of hulls draft on resonant amplitude is not remarkable, especially for large heaving amplitude. The increase in heaving amplitude results in the decrease of relative resonant amplitude in an approximate power function, implying a complicated dependence of the resonant amplitude on heaving amplitude. Flow patterns in the vicinity of the moonpool are also analyzed, mainly regarding the dependence on the heaving frequency. The negligible influence of vortices on the wave response in moonpool is expected for low-frequency excitation because it is hard to observe the vortex structures. Intensive vortical flow and vortex structure can be identified under resonant condition, which gives rise to significant dissipation and accounts for the smaller relative resonant amplitude in moonpool. As for high-frequency excitation, the vortex motion is rather weak and dissipates rapidly, leading to insignificant effect on wave response amplitude.

Numerical investigation of solitary wave action on two rectangular boxes with a narrow gap

Based on the time-domain higher-order boundary element method (HOBEM), a two-dimensional numerical wave flume is developed to investigate solitary wave interaction with two rectangular boxes with a narrow gap. In the numerical model, the fully nonlinear boundary conditions are satisfied on the free surface, the mixed Eulerian-Lagrangian method is adopted to track the transient water surface and the fourth-order Runga-Kutta method is used to predict the velocity potential and wave elevation on the free surface. The acceleration potential technique is used to compute the transient wave forces along the wetted object surface. A piston-type wavemaker is used to generate solitary waves. The proposed model is validated by comparing the simulated wave run-up and the wave loads with the published experimental and numerical results of the reflection of a solitary wave from a vertical wall. Then, numerical experiments are performed to study the effects of the narrow gap and the size of each box on the wave run-ups at the two sides of the two-box system and in the narrow gap between two boxes, and the wave loads on the two boxes. The interaction between double solitary waves with a time interval between them with a two-box system is also investigated.

Numerical calculation of total horizontal wave force on a perforated caisson with a top cover based on smoothed particle hydrodynamics method

The revised smoothed particle hydrodynamics method based on Riemann solution has been used to calculate the total horizontal wave force acting on a perforated caisson with a top cover. The interaction process between the wave and perforated caisson is simulated in a two-dimensional numerical wave flume which is verified by linear regular wave theory, water particles flowing in or out of the dissipation chamber are also described in this article, including the distribution of velocity vector. The effect of main non-linear influence factor on total horizontal force is examined here; wave pressure distribution along the height of the perforated caisson in front, inner side or the rear wall of the dissipation chamber is also presented in order to exhibit the more practical performance of perforated caisson with a top cover. The relationship between the total horizontal force and top cover height is anglicized, and the influence of top cover height on components of the total horizontal force is discussed here. A comparison between the numerical total horizontal force results and values tested from the test data is finished; it can be seen that the numerical results agree well with the test data. It is concluded that the smoothed particle hydrodynamics method described in this article can be utilized to calculate the total horizontal force on a perforated caisson with a top cover.

Wave energy extraction by horizontal floating cylinders perpendicular to wave propagation

A two-dimensional numerical wave flume is established based on finite element and Volume of Fluid (VOF) methods for incompressible viscous flow. The numerical model is used to simulate waves interacting with single and double horizontal floating cylinders perpendicular to the direction of wave propagation. In the simulations, motion of the floating cylinders, wave forces and wave surface elevations in front of and behind the cylinders are calculated. By applying a damping force on the cylinders to simulate the electrical load, the primary conversion efficiency of wave power is derived. The effect of the cylinders’ cross-sectional size, the normalized damping coefficient for the cylinders’ heave motion, the primary conversion efficiency and the wave transmission coefficient are discussed. This investigation reveals that: larger cylinders are capable of extracting more wave power than smaller ones and also lowering wave transmission; an optimum normalized damping coefficient exists for wave power conversion; when this coefficient increases, heave motions of the cylinders decrease whilst the relative vertical wave force on the cylinders increases; total primary conversion efficiency for double cylinders is higher than that of two separately deployed cylinders due to cylinder-wise interaction.

Effect of inlet configuration on wave resonance in the narrow gap of two fixed bodies in close proximity

Wave resonance in the narrow gap between two side-by-side fixed bodies is investigated numerically in a two-dimensional (2D) numerical wave flume. The focus of the study is to examine the influence of incident wave frequency and inlet configuration of the gap on wave resonance behavior. It is found that the gap inlet configuration has significant effects on the resonant wave amplitude and frequency. The maximum resonant wave height in the gap is found to be as high as about 11 time of the incident wave height while the resonance frequency shifts to higher values at larger corner curvatures of the gap inlet. The physical mechanisms that are responsible for the influence of the inlet configuration on wave resonance are explained in light of the results of some controlled numerical tests. In addition, the geometrical properties of the fixed bodies, such as the body breadth, gap width and draft, are also found to have significant influence on gap resonance characteristics. Finally, an empirical model is proposed to predict wave resonance frequency for different curvatures of the gap inlet.

Numerical Examination of Wave-induced Coupling Roll Motion and Fluid Resonance between twin Floating Barges in Proximity

Coupling effects of roll motion and fluid resonance between twin rectangular barges subjected to incident waves normal to the spanwise of the narrow gap are investigated employing a two-dimensional numerical wave flume based on a CFD package OpenFOAM. The governing equations for the fluid flow are the Navier-Stokes equations of incompressible Newtonian fluid. The interface between water and air phases is captured by a VOF (volume of fluid) method. The fluid-structure interaction (FSI) is treated with moving meshes in the Arbitrary Lagrangian-Eulerian frame. The present numerical model is validated against wave generation and propagation over a flat bed and the decay of a free rolling rectangular barge in still water. The comparisons with available numerical results show that the present numerical wave flume works well. It is then used to investigate the roll response of the twin floating barges in proximity. The numerical results of this work show that the resonant frequency of the fluid oscillation in the narrow gap between twin rolling barges is smaller than that between twin fixed barges. However, the resonant wave height in the gap between twin rolling barges is observed to be in the same magnitude as that between twin fixed barges. Moreover, the present numerical results indicate that the maximum rolling amplitudes of the twin barges are close to each other, and they appear at the same resonant frequency of the fluid oscillation in the narrow gap. At the low frequency band, the amplitude of the rear barge is larger than that of the leading one. Otherwise, in the frequency band higher than the resonant conditions, the leading barge has a larger response. The present numerical solutions also suggest that the twin barges roll in anti-phase.

Numerical Simulation of Interaction Between Waves and Net Panel Using Porous Media Model

Based on the finite volume method, adopting the movement border as a wave generator, a two-dimensional numerical wave flume is established. The volume of fluid (VOF) method is used to track the wave surface. After comparison of the numerical results with the theoretical results, the accuracy of the numerical wave flume is verified. In the numerical simulation, the net panel is simplified as porous media entirely. The coefficients of the porous media are determined by the least squares method. In this way, the porous media model will have the same pressure drop as the net panel. In order to validate the numerical model, the numerical results were compared with the data obtained from corresponding physical model tests, and the numerical results and the corresponding experimental data show reasonably good agreement. Using the proposed numerical approach, this paper presents wave propagation through a net panel with different net solidities, different attack angles as well as two nets with different spacing distances. The impacts of the wave height and wavelength on the wave propagation through the net panel are also discussed.

Numerical Study of Wave Overtopping Based on Local Method of Approximate Particular Solution Method

In order to study the wave overtopping process, this paper establishes a two-dimensional numerical wave flume based on a meshless algorithm, local method of approximate particular solution (the LMAPS method), and the technology of momentum source wave. It calculates the climbing and overtopping process under regular waves on a typical slope, results of which are more consistent with the physical model test results. Finally, wave action simulation is carried out on six different structural forms of wave walls (vertical wave wall, 1/4 arc wave wall, reversed-arc wave wall, smooth surface wave wall with 1: 3 slope ratio, smooth surface wave wall with 1: 1.5 slope ratio and stepped surface wave wall with 1: 1.5 slope ratio). Numerical results of the simulation accurately describe the wave morphological changes in the interaction of waves and different structural forms of wave walls, in which, average error of wave overtopping is roughly 6.2% compared with the experimental values.