Effects Of Wave Steepness Research Articles

Effect of relative opening on the moving thin plate under the action of ocean wave in the surging direction: A numerical simulation approach

This paper aims to develop the simulated numerical methodology for sloping beach with nonlinear free-surface waves of sloshing water in a 2D rectangular tank. The current computational tool would be the first step in accurately modeling wave energy converters. The 2D tank model was developed by ANSYS FLUENT software, and Navier–Stokes equations are discretized on a regular structured grid based on the finite volume method (FVM). The model is validated for nonlinear sloshing cases. In addition, tank flexibility is analyzed for its impact on liquid sloshing. The test was conducted in five different wave steepness conditions. There were five conditions of wave steepness used in the test. This study looked at fluid–structure interaction around moving plates. The output power of the plate wave energy converter for different plate heights and streamline motion around the plate are important studies in the flow field. Variations of drag coefficient with the wave steepness are the important study in this paper. It shows that the drag coefficient increases with the increase in wave steepness and plate length. In particular, the new structure can give a new, highly accurate formula for determining the wave power of the ocean structures. Its application is seen in wave energy converter (WEC), where the interaction of solid objects, such as wind turbines with water waves, extracts renewable wave energy from the ocean. A highly efficient CFD approach method is introduced to capture the interaction of solid object with a two-phase flow. The effect of wave steepness using second-order stokes wave theory on a moving thin plate in intermediate water is a new discussion. This research is a highly relevant source of information in the development of many practical systems and has direct employment in the design of WEC in order to extract ocean energy.

Harmonic structure of the nonlinear force on a fixed ship-shaped floating production, storage and offloading vessel under dispersive phase-focused wave groups

This paper presents a numerical investigation on the harmonic structure of hydrodynamic forces on a fixed and simplified representative floating production, storage and offloading (FPSO) vessel hull under dispersive phase-focused wave groups. The high-fidelity numerical model utilizes the two-phase flow solver in the open-source toolbox OpenFOAM. A series of cases were computed using the numerical model, where the effects of wave steepness, bow diameter, and length of the FPSO are investigated. It is found that given an FPSO under different wave steepness, the non-dimensional inline force exhibits remarkable similarity in terms of the temporal development. The harmonic structure of the inline force is only weakly dependent on the steepness of the incident wave group and the bow diameter, but strongly dependent on the FPSO length. When k p L = 2.27, where L is the length of the FPSO and kp is the wave number at peak frequency, the incident wave group is diffracted significantly by the FPSO. The entire wave–structure interaction process is largely linear, where transfer between different harmonics is rarely seen. However, when kpL is further reduced to 0.57, globally the disturbance of the FPSO on the far field incident wave group is reduced, but locally a strongly nonlinear flow occurs at the rear of the FPSO, where severe run-up occurs at the downstream stagnation point. Higher-order harmonics of inline forces are excited, and the interaction process becomes much more nonlinear.

A numerical method to compute flexible vertical responses of containerships in regular waves

In this paper, a series of simulations of hydroelastic problems of containerships are conducted by a nonlinear 3D panel method which is based on the generalized Taylor Expansion Boundary Element Method (TEBEM). In the structure part, the Transfer Matrix Method is selected to perform a modal analysis which provides key parameters of hydroelastic calculation. In the hydrodynamic part, the nonlinearities arising from the variations of instantaneous wetted surface area are considered in the solutions of hydrostatic restoring forces as well as 1st order incident wave forces. Meanwhile, an extended Modified Logvinovich Model (MLM) is presented to predict the slamming forces due to the large-amplitude incident waves. The numerical predictions of the hydroelastic responses of a 6750-TEU containership and S175 in regular waves are presented. The effects of wave steepness and sailing speed as well as the variation characteristics of load components against with wave direction are studied. The numerical and experimental results are in acceptable agreement which proves the accuracy of the proposed method.

Study on the characteristics of Trimaran's surf-riding in stern waves by a hybrid method

In this paper, a hybrid method coupling potential flow method and viscous flow method is applied to simulate the autopilot trimaran in stern waves. The aim is to study the process of being captured by waves and the surf-riding characteristics of the trimaran. The FNPT-based QALE-FEM is used to simulate the wave tank of the external field, and the viscous flow method is used to simulate the autopilot of the trimaran in the wave tank. The sailing and 6DOF motion of the trimaran in waves of different parameters is simulated. The autopilot of a trimaran in stern waves of different lengths and steepness is simulated to study the characteristics of the trimaran's surf-riding in waves. When studying the effect of wave steepness, the wavelength is constant, and various forward speeds of trimaran could change the encounter frequency. However, the trimaran's wave steepness and forward speed are kept constant when the wavelength changes. By the computed results, it is found that the high speed and large wave steepness could significantly increase the vulnerability of trimaran's surf-riding in stern waves, and the wave passing the transom stern and side hulls could accelerate the trimaran to reach the wave celerity.

Intermittency of gravity wave turbulence on the surface of an infinitely deep fluid: Numerical experiment

The intermittency of gravity wave turbulence on the surface of an infinitely deep fluid has been studied numerically. We estimated the scaling exponent of surface elevation structure-functions directly from the equations of motion, e.g., by numerical solution of the underlying equations of motion, without any additional closure assumptions (e.g., phase randomisation) and reduction to the kinetic equations as in the conventional framework of wave turbulence theory. With our high-resolution numerical methods for accurately modelling the nonlinear water surface, we were able to evaluate the scaling exponents of the structure-function up to relatively high orders (p=15), which has not been previously reported. We investigated the effect of wave steepness and forcing on intermittency and compared our results with other analytical and numerical studies, including results on the intermittency of wave turbulence of a different nature (turbulence of bending waves on a plate and magnetohydrodynamic turbulence). Our results support the conjecture of universality for intermittency phenomena in wave turbulence.

Numerical investigation of wave-induced loads on an offshore monopile using a viscous and a potential-flow solver

Wave-induced loads on an offshore monopile were investigated using a viscous-flow solver and a potential-flow solver. Considered were only two steep regular wave trains, with the same height but different periods. The potential-flow approach relied on a weakly nonlinear time-domain solver (i.e., Green function). The viscous-flow solver used three solution schemes, namely, an Euler scheme that neglected the flow viscosity, a Laminar scheme that numerically integrated the full Navier–Stokes equations without a model accounting for the fluctuating portion of the velocity field, and a Reynolds-averaged Navier–Stokes scheme that modeled turbulent flow via a two-equation eddy-viscosity model. Numerical uncertainties of viscous-flow simulations were quantified, and computed results were validated against model test measurements. Overall, the main characteristics of wave-induced forces and bending moments were well predicted by all adopted numerical schemes. In terms of higher harmonic components, predictions only from the viscous-flow solver compared favorably to the experimental measurements, including the local free surface elevations, higher harmonic forces/moments, and the secondary wave load cycles. The effect of strong nonlinear motion of free surface on the wave-induced total loading was secondary, and the contribution from the associated viscous and turbulent effects was also very limited. Nevertheless, they attribute to the generation of higher harmonic forces/moments as well as the secondary load cycle. In addition, the effects of wave steepness on the global, first- and higher harmonic forces were addressed.

Experimental and numerical investigations of hydrodynamic response of biodegradable drifting Fish Aggregating Devices (FADs) in waves

Fish Aggregating Devices (FADs) are artificial floating objects deployed in tropical and subtropical pelagic oceans to attract tuna species for capture. Understanding the wave-induced drifting behavior can optimize the dynamical stability of drifting FADs in oceans and improve catchability. In this study, to investigate the dominant factors for stable performance and the validity of different drifting FADs the model experiments of hydrodynamic responses of 14 types of biodegradable drifting FADs models in heave motion and pitch motion are carried out in regular wave conditions. Numerical simulations of three of the models are implemented, and the experimental results are used to validate the results of the numerical simulations. In the numerical simulation, Reynolds-averaged Navier-Stokes (RANS) solver, a realizable k-ε model with two-layer, all y + wall treatment and wave forcing method based on the Euler Overlay Method (EOM) for wave generating and wave absorbing are performed. The results show that the numerical results agreed well with the experimental values. The effects of wave steepness, relative length, relative width, cover object, hanging object, and weight of sinker on the FADs are analyzed. The results indicate that with the constant wave amplitude, the heave motion response increases significantly as the wave period increase, and opposed to the pitch motion response. Wave steepness, relative length, relative width, and the length of the FADs model have an important influence on the motion response amplitude operators (RAO) of the FADs. The FADs model constructed with netting panel and rope as cover object and hanging object, and weighted by a 2.00 kg sinker behaved the most stable behavior among all the models. This study can be used to find out the interaction between waves and the FADs and provide guidance on the design of high-performance biodegradable FADs with stabilization and a long lifespan in harsh pelagic ocean environments.

Numerical investigation of wave actions on two side by side boxes in close proximity using IMLPG_R method

The capability of the Meshless Local Petrov Galerkin method to understand the gap resonance between two side-by-side fixed boxes in close proximity is reported in this study. The present paper focuses on bilge-shaped boxes, the draft of the downstream box, and various hydrodynamic aspects of the gap resonance problem. Both regular wave and focused wave are used in this study. The piston mode resonance frequencies for different model configurations are determined by conducting regular wave tests within the range of 0.625 Hz to 1.54 Hz. The effect of wave steepness is also discussed. Near the resonance frequency, the model configuration having round bilge shapes showed a 77% increase in wave amplification when compared to square bilge shape. Similarly, horizontal and vertical forces on boxes also showed a significant increase in the case of round bilge configuration. For the different model configurations tested, an increase in the draft of the downstream body is found to amplify free surface elevation in the gap by 19% near gap resonance frequency. The reasons for various distinctive behavior for wave amplification inside the narrow gap and force acting on the boxes are explained with the help of instantaneous velocity and vorticity from the numerical simulation. The paper also discusses the water column in the narrow gap excited with a focused transient wave group. A four-phase combination method is then used to extract the first-order and higher-order harmonics of free surface elevation in the narrow gap and the forces acting on the boxes to analyze the influence.

Nonlinear modelling of a point-absorber wave energy converter based on the weak-scatterer approximation

In this study, a nonlinear time-domain model based on the weak-scatterer approximation is developed to investigate the hydrodynamic performance of a point-absorber wave energy converter (WEC). The simplified WEC consists of a floating cylindrical buoy with a hemispherical bottom, a single tether and a power take-off (PTO) system. The efficiency and survivability of the WEC are analysed by the proposed numerical model in moderately steep regular waves and focused wave groups, respectively. The effects of wave steepness on the power absorption of the WEC and the PTO force are highlighted in the study of regular wave tests by comparison with a linear frequency-domain model, and the influence of the PTO damping coefficient on the performance is discussed. Then the survivability of the WEC in focused wave groups is analysed and validated against the published experimental data. It appears that in terms of the motion responses of the buoy and the mooring force, the present results have a satisfactory agreement with the experimental data. The time–frequency characteristics of the motion responses of the buoy are further analysed based on wavelet transforms.

On the Evolution of Different Types of Green Water Events

Green water events may present different features in the initial stage of interaction with the deck of a structure. It is therefore important to investigate the evolution of different types of green water, since not all the events interact with the deck at the same time. In this paper, the evolution of three types of green water events (dam-break, plunging-dam-break, and hammer-fist) are studied. The water surface elevations and volumes over the deck in consecutive green water events, generated by incident [wave trains in a wave flume, were analyzed using image-based methods. The results show multiple-valued water surface elevations in the early stage of plunging-dam-break and hammer-fist type events. Detailed experimental measurements of this stage are shown for the first time. The effect of wave steepness on the duration of the events, maximum freeboard exceedance, and volumes were also investigated. Although the hammer-fist type showed high freeboard exceedances, the plunging-dam-break type presented the largest volumes over the deck. Some challenges for further assessments of green water propagation are reported.

On the statistical properties of inertia and drag forces in nonlinear multi-directional irregular water waves

Abstract

NUMERICAL INVESTIGATION OF INTERCEPTOR EFFECT ON SEA KEEPING BEHAVIOUR OF PLANING HULL ADVANCING IN REGULAR HEAD WAVES

In this paper an attempt has been made to assess the capability of numerical algorithm based on Reynolds Averaged Navier Stokes (RANS) for predicting the motion characteristics of the planing hull in calm water and regular waves. The focus of the present study is the impact of interceptors on the sea keeping quality of a planing vessel investigated through the application of numerical methods. The wave properties such as wavelength and wave height are taken into consideration to investigate the effect of wave steepness on vessel response. It is found that numerical data can efficiently simulate the motion attitude and the hydrodynamic characteristics of planing craft in regular head waves. The planing hull with and without interceptor fitted at the transom is simulated in numerical wave tank. The results show reduction in heave and pitch motions which gave favorable sea keeping behavior for the hull fitted with interceptor. The numerical solution is useful for the preliminary prediction of navigation safety during sailing.

Experimental studies of a damaged ship section in beam sea waves

This work presents a series of experiments performed with a prismatic hull form in a small wave flume. The model is a midship section with rectangular damage opening on the side. It is slightly smaller than the flume breadth to achieve predominantly two-dimensional behavior in the experiments. Freely-floating tests in regular beam-sea waves have been carried out on the model section in intact and damaged conditions. Free-roll decay tests were performed for intact and damaged sections to understand the effect of floodwater on roll natural period and roll damping of the model. Video recordings and measurements of wave elevation inside the damaged compartment were performed in all experiments. Linear response amplitude operators (RAOs) for water elevation inside the model and model motions are presented and discussed. Effect of wave steepness, wave period, initial loading condition, damage-compartment division about centerplane (symmetric/asymmetric flooding), damage-opening size and air compressibility in the damaged compartment are examined. The presented results demonstrate occurrence of sloshing and piston mode resonances and their influence on damaged ship motions in waves is highlighted. A linearized strip theory method based on viscous flow is implemented to cross-check and complement the experimental results. The latter method can estimate the damaged ship motions with reasonable accuracy. The initial loading condition determines the equilibrium flooding state and, therefore, the sloshing and piston mode resonance frequencies of the flooded water. The damage-opening size mainly affects the roll damping behavior of the section. Air compressibility in the airtight compartment acts as a coupled spring system with the floodwater and restricts the free-surface motion in the damaged compartment. Cases of transient flooding for a damaged section are also presented, where the freely floating model moves in beam-sea waves and subsequent flooding takes place. Effect of wave steepness, incident wave period and initial intact stability of the model is examined for this scenario. The present work is a continuation of a series of experiments conducted on the same damaged section for forced heave motions documented in [1]. Due to the complex and nonlinear behavior of floodwater inside a damaged ship section, as the previous analysis, the current work is aimed to contribute in the physical understanding of ship behavior in damaged conditions, as well as to serve as a database for the research community to be used for numerical validation.

Effect of wave steepness to relative wave run-up on OWEC breakwater

OWEC (Overtopping Wave Energy Converter) breakwater is a coastal structure model concept. The concept is to integrate the breakwater and the overtopping wave energy converter. This coastal protection model concept is equipped with a reservoir at the top of the structure to collect water that overflows from the top of the structure (overtopping). Many factors influence the amount of wave overtopping discharge; one of them is the run-up height. The height of wave run-up that occurs is influenced by many factors, one of which is the steepness of the incoming wave. The effect of the wave steepness to the relative wave run-up on OWEC breakwater is investigated experimentally. The study is carried out in wave flume with regular waves. The OWEC breakwater model is simulated with slope variations and freeboard variations. The results of the study show that small wave steepness value produces a large relative wave run-up value and vice versa. For a review of the structure slope, the results showed that the largest relative run-up value was obtained in the largest slope of the variation of the slope studied, namely 1: 2, at all different freeboard heights.

Numerical Investigation of Heave and Pitch Motion Effects on Green Water Loading for a Floating Body

In this paper, the influence of heave and pitch motions on green water impact on the deck is numerically investigated. The vessel motions are determined using a potential theory based method and provided as input to finite volume based CFD computations of green water phenomenon. A dynamic mesh approach is adopted to determine instantaneous body positioning in the fluid domain. Detailed validation studies with published experimental results for 2D and 3D fixed vessel cases are initially performed to validate the present numerical approach before studying the moving vessel problem. The results show that inclusion of heave and pitch motion changes the disturbed wave field near the bow which influences the free surface as well as the impact loading due to green water. The effect of wave steepness on green water impact is also investigated and it is seen that the present numerical method is capable of capturing green water load. It is observed that the effects of vessel motions on green water load are not negligible and one should consider this effect too. The incorporation of vessel motions in the vertical plane affects the green water loading on the deck.

Assessment of oscillating water column performance: Influence of wave steepness at various chamber lengths and bottom slopes

In this research, the effect of wave steepness on the hydrodynamic efficiency of an oscillating water column is examined at different chamber lengths and bottom slope angles. Results show that the best device efficiency for low wave frequencies is obtained at high chamber length and for high wave frequencies, the best device performance is achieved at low chamber length. Numerical findings reveal that for high wave steepness, the change in the chamber length has a negligible effect on the device efficiency at low wave frequencies and at high wave frequencies, the best device performance is attained at low chamber length. Results indicate that for the shoreline oscillating water column, the change in the bottom slope angle away from the resonance condition has a negligible effect on the device efficiency and at resonance condition, high bottom slope angle is preferred in order to obtain the best device efficiency. It is found that at high wave steepness, the device efficiency decreases and no specific resonance condition could be observed. It is also shown that the sensitivity of the device efficiency around the optimal device performance to the damping produced by power take-off device decreases as the wave steepness increases.

Study on Nonlinear Characteristics of Freak-Wave Forces with Different Wave Steepness

The nonlinear wave forces on vertical cylinders induced by freak wave trains were experimentally investigated. A series of freak wave trains with different wave steepness were modeled in a wave flume. The corresponding wave forces on vertical cylinders of different diameters were measured. The experimental wave forces were also compared with the predicted results based on Morison formula. Particular attentions were paid to the effects of wave steepness on the dimensionless peak forces, asymmetry characteristics of the impact forces and high-frequency force components. Wavelet-based analysis methods were employed in revealing the local energy structures and quadratic phase coupling in the freak wave forces.

Extreme wave crest distribution by direct numerical simulations of long-crested nonlinear wave fields

The wave crest height qualification checks are required during the wave calibration before the model test in wave basin. However, the reliable criteria of nonlinear wave crest probability distribution in 3-h duration (full-scale) has not been well established yet. We investigate wave crest-height statistics of long-crested nonlinear wave fields using high-order spectral (HOS) method, which can take the effects of both second-order bound waves and third-order free waves into account. The energy dissipation effects due to wave breaking were included by employing an eddy viscosity model. Sensitivity analyses to the wave breaking onset criterion have been performed. Validation is provided by comparing the obtained numerical results with the available calibration test data. Based on extensive and direct numerical simulations, semi-empirical single realization distributions for wave calibration have been developed through 3-parameter Weibull fitting and systematic regression analyses. Particular attention has been paid to the tail of upper bound of wave crest distributions. The effects of wave steepness and water depth on the maximum wave crest height in 3-h duration have been examined. It is found that with the increase of wave steepness, the extreme wave crest height increases until it reaches a critical value. In addition, for the scale water depth kph < 1.36, the maximum crest height decreases as the water depth increases, while in the opposite case the maximum crest height increases as the water depth increases. Moreover, it is confirmed that that the fourth-order nonlinearity does not have significant effects on the distribution of the wave crest height.

Experimental Study on the Effect of Ocean Wave Characteristics on Air Pressure in Oscillating Water Column Device

Ocean wave energy conversion process in Oscillating Water Column (OWC) device is affected by several parameters. Wave characteristics are an important parameter that determines the level of water fluctuations in the water column. The later parameter is a main factor which influences air pressure in the air column. One of the important wave characteristics is wave steepness (H/L), which is ratio of wave height to wave length. This experimental study analyzed the effect of wave steepness to wave energy. Furthermore, air pressure in the air column of the OWC device is influenced the effects of changes in wave energy converted by OWC device. Testing was performed with several variations of height and wavelength for three different water depths. Wave height change data was recorded with ultrasonic sensor and stored on the CPU via a data logger. The test showed that the deeper the water, the smaller the wavelength and the greater the wave height. In addition, wavelength increase with the increasing of wave period, vice versa wave height decrease with the increasing of wave period. This condition produced different wave steepness so that the wave energy also changes. Data analysis showed the wave steepness of the test results with the biggest pressure change that corresponds to the actual wave steepness generated by the wind at ocean achieved at water depths h = 240 mm with wave height H = 82.8 mm and L = 1250 mm.

Dissipation of Solitary Wave Due To Mangrove Forest: A Numerical Study by Using Non-Dispersive Wave Model

In this paper, we study a dissipation of solitary wave due to mangrove forest by using numerical simulation. Here, the solitary wave is chosen to represent tsunami wave form. To simulate the wave dynamic, we use the non-dispersive Nonlinear Shallow Water Equations (NSWE). The model is implemented numerically by using finite volume method in a momentum conservative staggered grid. By using the proposed numerical scheme, the numerical code is able to simulate solitary wave breaking phenomenon. Wave dissipation due to mangrove forest is modelled as bottom roughness with an approximate value of manning roughness, which is derived from the classical Morisson’s formula. To test the modelled dissipation by mangrove forest, we reconstruct a physical experiment in hydrodynamic laboratory where a solitary wave propagates above a sloping bottom, which has a parameterized mangrove in the shallower part. Two cases are performed to test the performance of the numerical implementation, i.e. the non-breaking and breaking solitary waves. Results of simulation agree quite well with the measurement data. The results of simulation are also analyzed quantitatively by calculating errors as well as correlation with the measurement data. Moreover, to investigate effects of wave steepness on solitary wave, to the reduction of wave energy, we perform numerical investigation. Various solitary waves with different wave steepness are simulated to see their effects on amplitude and energy reduction due to mangrove forest.