Three-dimensional Numerical Wave Research Articles

Power absorption and flow-field characteristics analysis for oscillating coaxial twin-buoy wave energy converter by using CFD

The energy conversion capacity of wave energy conversion devices highly depends on the hydrodynamic characteristics of the energy-harvesting structure. To investigate the effect of hydrodynamic performance on the power conversion characteristics, a twin-buoy wave energy converter (WEC) was investigated by using a three-dimensional numerical wave pool based on the Computational Fluid Dynamics (CFD) method. Several factors are examined, including the elasticity coefficient of the anchor chain, the bottom configuration of the floating body, and the power take-off (PTO) damping coefficient. The heave displacement, heave velocity, and heave force of the converter are calculated under specific wave parameters, and the flow field cloud diagram during the heave motion is analyzed. The results indicate that a wave energy converter with a hemispherical floating body exhibits the best kinematic performance. The influence of the mechanical damping coefficient on the energy conversion performance of the device is studied. By appropriately reducing the mechanical damping coefficient, the energy capturing capability of the device can be increased to a certain extent. These findings can serve as a theoretical basis for the application of deep-water wave energy conversion in engineering and the optimization of future WEC designs.

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.

A CFD-FEA coupled model for simulating dynamic response of offshore jacket platform under earthquake considering wind, wave, current and aftershock loads

Offshore platforms as the key equipment in marine oil and gas exploitation are facing challenges from various environmental conditions, such as winds, waves, currents and even earthquakes. Due to the combined action of those concurrent loads, there is potential risk of accidents. The aim of this paper is to systematically study the dynamic response and safety assessment of the large scaled offshore structures against the concurrent loads considering the fluid-structure interaction (FSI) effects. Three-dimensional numerical wave flume including a jacket platform is established by CFD software Fluent, based on which the simulation of wave generation and propagation is carried out. Then the FSI effects between waves and platform are analyzed using the CFD- FEA coupling method. Subsequently, the seismic ground accelerations are inputted into the platform, correspondingly the structural response is analyzed. Moreover, multiple influencing factors including earthquake direction and mainshock-aftershock sequence are discussed. The results show that the structure response under concurrent loads is not a simple linear superposition of different load. The seismic response would be underestimated if wave action is ignored when the earthquake acts on certain angles. The methodology proposed could be regarded as an effective way to analyze the FSI problem under realistic offshore environment.

Research on the hydroelastic response of ice floes and wave scattering field

Abstract The marginal ice zone (MIZ) is the area between sea ice and open water, the structure of which is mainly determined by wave and ice interactions. Thus mastering the characteristics of MIZ is of great significance to the Arctic routes opening and the natural resources development. In this paper, the hydroelastic response of ice floes in waves is studied, a three-dimensional numerical wave tank is established based on the computational fluid dynamics (CFD) technology. The finite volume method (FVM) and finite element method (FEM) are respectively utilized for discrete fluid domain and ice domain. A mapping interface at the junction of the fluid and ice floes domains is created to perform data mapping by the shape function interpolation method and the least square method. This work presents a series of numerical simulations to study the fluid-solid interaction (FSI) of waves and ice floes. Under the given incident wave parameters, the vertical bending deformation of ice floes with different shapes under the excitation of waves, the effect of ice floes' deformation on the wave field are studied, and the effect of wave overwash on the transmitted wave field is emphasized. Results show that the shape of the ice floes significantly affects its elastic deformation and scattered wave field, and the wave overwash phenomenon attenuates the scattering wave.

Numerical investigation of wave-cylinder interaction based on a momentum source wave generation method

A momentum source function is constructed for wave generation based on linear wave theory. Based on Navier-Stokes equation and volume of fluid (VOF) method, a three-dimensional numerical wave tank (NWT) is established. Regular and irregular waves can be simulated by applying the momentum source function to NWT, and the expected wave characteristic parameters and wave spectrum are obtained. Furthermore, the load characteristics of two types of cylinders, fully piercing cylinder (FPC) and truncated cylinder (TC), are studied under regular wave field combined with boundary data immersed method (BDIM). Results show that the transverse force exerted on cylinders is dominated by inertial force. And because of the effects of the cylinder on wave profile and drag force, the maximum transverse force occurs soon after the wave node passes through the centerline of the cylinder. Compared with the FPC, the drag force has a greater influence on TC.

Analysis of the Force Characteristics of Two Tandem Cylinders by Internal Waves over Slope Topography

Large-amplitude internal waves (IWs) with strong lateral shear forces can cause destructive effects on marine engineering structures. In this study, a large eddy simulation (LES) method was employed to simulate the generation and propagation of IWs in a three-dimensional numerical wave tank, and the pressure distribution, flow field characteristics, and force behaviors of two tandem cylinders under the coupling effect of the IWs and slope terrain were studied. The influence mechanism of the normalized value of center-to-center spacing (L) and the diameter of the cylinder (D), i.e., (L/D), on the strength of the vortex disturbance between cylinders was studied by comparing the simulation results of two tandem cylinders with those of a single cylinder (SC) to further explore the mechanical response characteristics of the upstream cylinder (P1) and downstream cylinder (P2). The simulation results showed that the vortex interaction between cylinders is the critical factor that affects the forces acting on the cylinders. The strength of the vortex disturbance could be distinguished by the dimensionless critical center-to-center spacing between cylinders (Lc/D = 3.0). When L/D ≤ Lc/D, the vortex disturbance was severe, causing P1 and P2 to experience significant horizontal positive forces and negative forces, respectively. In the case of L/D > Lc/D, the forces acting on both cylinders gradually returned to those on a single cylinder.

EXPERIMENTAL AND NUMERICAL STUDY ON OBLIQUE WAVE-IN-DECK LOADS

Most studies on wave-in-deck loads focus on head-on wave impingement whereas wave-in-deck loads due to waves incident from oblique directions are rarely reported. Numerical simulations for oblique wave-in-deck loads were presented in Iwanowski et al. (2002), Brodtkorb (2008) and Chen et al. (2018). However, in these studies, only numerical validations were performed against either two-dimensional experiments or empirical formulations due to a lack of experimental results. In light of this, we present the experimental results for wave impacts on a solid deck model due to a transient focused wave group incident from oblique direction in this study. The oblique experimental data is compared with the head-on counterpart by Santo et al, (2020) to investigate the incident wave angle effect on wave-in-deck loads. Numerical simulations are carried out to reproduce both the head-on and oblique wave-in-deck experiments using a three-dimensional (3D) numerical wave tank (NWT), and flow field information is interrogated to derive physical insights into complex wave-deck interactions. The solid deck model is a representative of a typical 2nd generation North Sea topside structures commonly exposed to severe winter weather. The configuration is also applicable to coastal structures such as bridges, piers, jetties or docks.

Study on hydrodynamic characteristics of a hybrid wind-wave energy system combing a composite bucket foundation and wave energy converter

In this paper, a new type of combined wind-wave system is proposed, that is, composite bucket foundation-oscillating buoy (CBF-OB) combined device. A three-dimensional numerical wave flume is established by using the renormalization group k–ε model. The hydrodynamic characteristics around the wave and the combined power generation device are studied. The relationship between wave parameters and wave run-up and wave pressure is analyzed. The absorption efficiency performance of the combined power generation device is evaluated. The results show that in the combined power generation system, the wave run-up and wave pressure at 0°–135° around the CBF are smaller than those in the presence of only CBF, but near 180° the ones are larger than those in the presence of only CBF. In the rear side of the combined power generation system, the smaller the scattering parameters, the more obvious the phenomenon of the second wave peak, and the stronger the nonlinearity of the wave and CBF-OB combined power generation system. The proposed CBF-OB combined power generation device can significantly improve the absorption efficiency of the buoy, which can be increased by about 1.5–4.0 times compared with the absorption efficiency under the action of only the buoy alone. There is an optimal power takeoff parameter, that is, when the damping parameter is 500 N·s/m, to maximize the absorption efficiency of the combined power generation device.

Hydrodynamic performance investigation of the multi-degree of freedom oscillating-buoy wave energy converter

Wave energy is considered to be a kind of promising renewable energy due to its high energy density and enormous reserves. This study aims at examining the hydrodynamic performance of the multi-degree of freedom oscillating-buoy Wave Energy Converter (WEC). A three-dimensional numerical wave tank was developed using Star-CCM + software to investigate the interaction of waves with WEC. A mathematical model is built based on the structure of the multi-degree of freedom oscillating-buoy WEC. This paper investigated the variation in the device's energy conversion efficiency for different wave periods and spectral analyses of the motion of the floater. The effect of different elastic and damping coefficients on the device's performance was compared. The results demonstrate that the surge motion is the leading cause of the periodic variation in amplitude of floater motion. Heave motion is the main contributor to energy capture. Wave height has an influence on the contribution of the elastic and damping coefficients to the energy conversion efficiency.

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.

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.

Analysis of wave added resistance and motion response of fishing boat sailing against waves

In order to accurately predict the on-wave resistance and responses to hull motions of ships in actual sea conditions, the k-ε method of the RNG model is adopted on the basis of the unsteady RANS method. The twoformula turbulence model deals with the viscous flow, the VOF method captures the free surface, the velocity boundary method makes waves, the artificial damping method is used to eliminate waves, and the nested grid technology is used to deal with the motion response of ships on waves. Combined with the 6-DOF motion formula, a three-dimensional numerical wave cell for regular waves is established. For one example, taking a KCS Container ship and fishing boat sailing at a mid-high-speed, the increase of wave resistance and motion response at different wavelengths are analyzed, and the simulation results are compared with the experimental value, the content of strip theory in potential flow theory and the panel method to prove the reliability of CFD method in predicting ship motion.

Viscous Damping Performance Analysis and Prediction of Axisymmetric Cylindrical Oscillating Buoys With Different Geometrical Configurations

Abstract With the intensification of the world's energy demand, clean and efficient marine energy has received more attention, and energy conversion devices are particularly important. As an important part of the oscillating wave energy conversion device, the hydrodynamic characteristics of cylindrical absorbers have a great impacton wave energy conversion efficiency. When cylindrical buoys with different bottom configurations heave under the action of waves, the oscillating motion and flow field become more complex. At present, potential flow theory is usually used to predict the motion response of cylindrical buoys in waves. Although the calculation speed is fast, there will be large errors due to the lack of consideration of the effect of fluid viscosity. To explore this error range, a three-dimensional numerical wave pool is established based on the viscous fluid theory and STARCCM+ software to study the response of buoy and wave coupling action considering the viscous effect. At the same time, based upon the potential flow theory, the analytical solution of the cylindrical buoy oscillating in waves is established. Combined with the computational fluid dynamics numerical simulation results, the oscillation laws of the buoys with different bottom configurations in waves with different periods are compared, and the effects of viscosity on the buoys' motion are also explored. According to the calculation results of floating buoy movement under viscous and nonviscous fluid, the statistical correction algorithmis adopted to obtain the viscous hydrodynamic correction algorithm of floating buoy movement based on the potential flow theory, and the feasibility is verified by viscous numerical simulation under other wave periods.

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

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

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

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

A numerical wave tank with large eddy simulation for wave breaking

A three-dimensional (3D) numerical wave tank (NWT) is developed based on OpenFOAM. The propagation and breaking of waves with a moderate wavelength that could be generated in the laboratory are studied. The wave periods range from 0.5 to 1.79 s and wave steepness goes up to 0.05. The volume of fluid method (VOF) is employed for interface capturing. The relaxation zone method is implemented for wave generation and absorption at the boundaries. Computationally significant factors like grid size, relaxation weight and time step are investigated to find the optimal parameters of the numerical models for various wave regimes. A relationship between grid size and time step, similar to the wave dispersion relation, is found. The accuracy and performance of the NWT are assessed through the reflecting coefficient, wave damping and phase distortion rates. Simulation conditions are monitored to achieve an error rate of less than 3%. To mitigate the effects of numerical errors on the calculation of the reflection coefficient, a modified version of Goda's approach is proposed. The coefficient of wave reflection at the outlet boundary calculated by the conventional Goda's method is as high as 4.3%. This value can be modified to be less than 2% after utilizing the revised Goda's method. Turbulent flows, especially for the breaking wave regime, are investigated by large eddy simulation. A one-equation sub-grid eddy viscosity model, with coefficients being derived from local flow properties, is employed for turbulence closure. A case study of wave breaking on a fixed bar is simulated. The validation of this NWT model is confirmed by comparing the numerical results with experimental data.

URANS Calculation of Ship Heave and Pitch Motions in Marine Simulator Based on Overset Mesh

So as to improve the reliability and accuracy of marine simulators, it is essential to predict ship heave and pitch motions in regular waves. The motions of two ships, the international standard model KVLCC2 and the first training ship, “Yukun”, of Dalian Maritime University, are simulated using a three-dimensional (3D) numerical wave tank based on the Unsteady Reynolds Averaged Navier–Stokes (URANS) equations. The free surface is captured by the volume of fluid (VOF) method, and an SST k-ω turbulence model is used to describe the turbulence flow. The numerical model is first validated for the standard KVLCC2 at three different speeds through a comparison with the published experimental data and the potential flow results. Then, numerical simulation is performed for the motion of the ship Yukun with different speeds under various sea conditions. The heave amplitude of the hull changes with the increase in the wavelength when the maximum value is reached. Upon comparing the RAOs of ship motions under different wave steepness conditions, it is apparent that the heave and pitch motions of ships nonlinearly decrease with an increase in wave steepness. The results were added to the database of the marine simulator to further improve the accuracy and realism of the simulator.

Wave impacts on a solid deck in transient wave groups

Wave impacts on an elevated solid deck due to transient focused wave groups are studied numerically. Previously reported experiments with and without an I-beam grillage beneath the deck by Santo et al. (2020) are reproduced successfully in a three-dimensional numerical wave tank based on a two-phase Navier–Stokes solver. The impact loads on the solid deck are relatively simple. The three-dimensional horizontal force, characterised by a single peak in time, is close to two-dimensional, whereas the vertical force consists of upward force and downward suction force. The downward suction force is related to triangularisation of the wetted area underneath the deck and dominated by the added mass effect, which is a three-dimensional effect and therefore any two-dimensional simulation will overpredict the strongly three-dimensional process and the vertical impact loads. The wave impact loads on the solid deck with a grillage are more complicated, with successive force spikes observed for both the horizontal and vertical loads. The significance of entrapped air pockets in the grillage to global wave impact loads is ascertained through interrogating flow field of numerical experiments. It is found that large upward vertical impulsive forces are caused by high local pressures when entrapped down-wave air-pockets are formed, while large downward suction forces are resulted from both high-frequency up-wave air-pocket effect and the low-frequency added mass effect. Large horizontal impulsive forces are due to the combined effects of the down-wave air-pocket and the upward jetting motion of the wave crests. The entrapped air-pocket effects are found to be more important for vertical than horizontal forces.

Research on the force mechanism of two tandem cylinders in a stratified strong shear environment

A large-eddy simulation of a three-dimensional numerical wave flume is used to study the forces on two tandem cylinders in a stratified strong shear internal wave (IW) environment. By analyzing the pressure distribution and the flow field around two cylinders compared with that of a single cylinder, the mechanism for the influence of the center-to-center (CTC) spacing (L), which is normalized by the cylinder diameter (D), i.e., (L/D), between the two tandem cylinders on the vortex disturbance intensity is explored, further revealing the mechanical response characteristics of the upstream (P1) and downstream (P2) cylinders. The results show that the vortex between two cylinders is the key factor affecting the pressure resistance of the cylinders in the IWs of the depression environment. The vortex disturbance intensity can be distinguished by a normalized critical CTC spacing (Lc/D): when L/D ≤ Lc/D = 2.5, the disturbance is strong, causing P1 and P2 to undergo large forces along and in the opposite direction of the waves, respectively. In addition, the vortex disturbance is more severe in the upper layer than in the lower layer. The correlation between the nondimensional force amplitude (CFn-max) and L/D and that between CFn-max and the nondimensional IW amplitude (ηo/H) is quantified. In the strong disturbance area (L/D ≤ Lc/D), CFn-max has an exponential relationship with (L/D)/(ηo/H) for P1 and is a power function of (L/D)/(ηo/H) for P2.