Incident Irregular Waves Research Articles

Performance of dual‐chamber oscillating water column device under irregular incident waves using Reynolds averaged Navier–Stokes model

AbstractThe purpose of this study is to analyze the hydrodynamic performance and efficiency of a dual‐chamber oscillating water column (OWC) device. For the Joint North Sea Wave Project (JONSWAP) incident waves spectrum, a two dimensional numerical wave tank is employed with nonlinear Reynolds averaged Navier–Stokes equations model along with the standard turbulence model. The free surface elevation is measured using the volume of fluid method. The numerical simulation demonstrates the streamline and velocity vector profiles throughout an entire pressure fluctuation cycle inside the chambers of the given OWC device. Further, investigation is carried out to analyze the impact of pressure drop and air flow rate through the orifice of the dual‐chamber OWC device on the power generation. Moreover, the power spectral density analysis of the free surface elevation is provided to know the variation of the parameters in the frequency domain. These results demonstrate that the effectiveness of the dual‐chamber OWC device is more near the significant wave height m.

Oscillating water column wave energy converter arrays coupled with a parabolic-wall energy concentrator in regular and irregular wave conditions

Based upon previous research on a single, high-efficiency Oscillating Water Column (OWC) wave energy capture system (Mayon et al., 2021), this work further extends the numerical investigation to the layout design and performance of the wave energy convertor (WEC) array coupled with a parabolic, energy concentrating wall in both regular and irregular incident wave conditions. A heuristic method to identify the optimal siting of the component, cylindrical OWC WECs in the array, installed in the concave opening of the wall is presented. The most advantageous location of the chambers is found to lie on a parabolic curvature line which is inset from the wall. Two separate arrays composed of three and five component OWCs are investigated in a range of regular wave conditions. The hydrodynamic power and efficiency of each chamber in each of the arrays is determined, and subsequently the aggregated array performance is established. It is found that the primary OWC chamber in the array configuration can attain approximately the same hydrodynamic power output as a single, isolated OWC chamber located the parabolic wall focus, albeit with a narrower energy capture bandwidth. The secondary and tertiary component chambers in the arrays contribute a lesser, yet still considerable quantity of hydrodynamic power to the consolidated system. The cumulative hydrodynamic efficiency of the collective arrays is less than the hydrodynamic efficiency of a single OWC chamber at the wall focus, but more efficient than an isolated OWC chamber positioned in open-sea conditions. Moreover, the hydrodynamic efficiency of the arrays exhibits better stability across the range of incident wave periods investigated, denoting that the individual component chambers in the array are efficacious at different incident wave conditions. The five chamber array is comprehensively analysed in irregular incident wave conditions. The array system is demonstrated to maintain a high power output and efficient behaviour in irregular incident wave conditions-an effect attributable to the reflecting wall influence. In summary, the five-chamber array configuration yields a higher power output and improved stability in terms of efficiency performance when compared with the three-chamber array configuration in regular waves. The array maintains this exceptional performance in irregular incident wave conditions.

Experimental Study Of The Wave Field Around A Monopile Due To Moderate Steepness Irregular Incident Waves

Most offshore wind turbine foundations are of monopile type and need regular marine operations to be conducted nearby during the lifetime of the turbine. Proper wave estimation around the monopile is needed to assure the safety of the operations. The trend of increasing monopile's diameter also adds the need to investigate the wave field around the increased monopile diameter for the marine operation analysis. Experimental campaigns of wave field around a monopile in irregular incident waves with different steepness are reported in this study to extend the available experiments which focused mostly on the runup of cylindrical structures. The wave field at two radial positions and six angular positions around the monopile is investigated. The results are processed to obtain the Linear Transfer Function of the wave field around the monopile and the Exceedance Probability of the wave height and crest of the waves around the monopile. For the tested conditions, the linear solution accurately captures the frequency domain characteristics and the exceedance probability of wave height but fails to predict the crest exceedance probability.

Optimization of parameters of the OWC wave energy converter device using MLP and XGBoost models

In the present work, we have studied the performance of a breakwater-integrated quarter-circle-shaped front wall OWC device under the influence of irregular incident waves. Firstly, the boundary value problem associated with the hydrodynamics of OWC device is handled for solution using the dual boundary element method (BEM). To examine the complex relationships between all input features and the target variable in a time-efficient manner, supervised machine learning models are developed. Here, two different models: (i) multilayer perceptron (MLP) model based on an artificial neural network, and (ii) a tree ensemble model, namely the XGBoost model are developed. The submergence depth of the front wall of the OWC device, chamber length, rotational speed, and diameter of the turbine blade are considered as input attributes, and the average annual power generated by the OWC device is considered as the output attribute. The MLP model is employed to optimize these input parameters, leveraging the insights provided by the XGBoost model to maximize the annual average power generation. From the dual BEM based numerical results, and using the Latin hypercube sampling technique, 3750 samples were generated to train, validate, and test the machine learning models. Using the XGBoost model with the support of accumulated local effect plots, we find four specific regions of the input space in which the annual average power extraction will be maximum. Hereafter, an extended input database is generated with twenty equally spaced levels for each parameter and the dataset is passed through the developed MLP model to find the optimized values of the parameters of the OWC device which maximizes the power generation. It is obtained that the maximum power generation is attained for y0/h=−0.65, r/h=3, 2.8≤D≤3 and 70≤N≤80∪105≤N≤116.

Effect of tertiary interactions on free-surface motion of a fixed box in realistic irregular sea states

Tertiary interactions between irregular incident waves and their reflections from a rectangular box are investigated experimentally. New experiments feature uni-directional seas with normal and oblique incidence to the side of the box and spread seas, where data is notably lacking in the literature. NewWave conditioning analysis is applied to show that the delays in maximum response associated with tertiary interactions are present in front of the box for both uni-directional and spread sea states. However, only in the uni-directional sea states with normal incidence is there significant amplification of free-surface elevation in front of the box beyond the linear diffraction levels. The nature of the large nonlinear run-up in this case is studied in detail. As an important finding, this work shows that localised tertiary interactions, whilst an interesting physical phenomenon, are unlikely to be important for wave–structure interactions in general, in realistic open ocean wave conditions.

Theoretical and numerical studies on improving absorption power of multi-body wave energy convert device with nonlinear bistable structure

For the energy supplement of deep-sea equipment, we examine a multi-body absolute motion counter-rotating wave energy converter (CR-WEC) in the research. In order to improve the capture efficiency of the absorber, a nonlinear bistable structure is proposed to improve the overall wave-following vibration capability of the CR-WEC. And then, we suggest to employing the harmonic balance method to solve the system dynamics equation in the CR-WEC 2-DOF absolute motion state. Combining the essential assumptions results in an analytical solution that is approximative. The paper also investigates the influence of system-related parameter modifications on absorption efficiency. A multi-degree-of-freedom arrangement with an unaltered overall mass is proposed to further increase the device ability to absorb energy. According to the numerical calculation and simulation results, the combination of 3-DOF state and bistable structure can make the device have the maximum capture width and peak value. In the irregular incident wave under the natural state, the multi-body bistable-linear configuration proposed in this study obtains the highest average absorption power.

An experimental study on the performance of combined membrane breakwaters against incident waves

A series of experimental model tests are conducted to investigate the performance of a combined membrane breakwater consisting of horizontal and vertical flexible membranes against regular and irregular incident waves. A dimensional analysis is carried out to determine the dimensionless parameters used to study the performance of the breakwater. The dependence of the reflection, transmission and dissipation coefficients on non-dimensional breakwater design parameters and wave characteristics such as membrane porosity, submergence depth, membrane length, mooring line stiffness, number of vertical membranes, spacing between horizontal and vertical membranes, spacing between vertical membranes, wave period, and wave height are analysed. Further, the efficiency of the present combined membrane breakwater is analysed by comparing different membranes combinations under different wave conditions. The analysis of the reflection and transmission coefficients as well as the dissipation coefficient of the proposed breakwater will be helpful for better designing of combined membrane protecting infrastructures in coastal and ocean engineering.

Hydrodynamics of an OWC Device in Irregular Incident Waves Using RANS Model

This research examines the hydrodynamic performance of an oscillating water column device placed over a sloping seabed under the influence of irregular incident waves. The numerical model is based on the Reynolds-veraged Navier–Stokes (RANS) equations with a modified k−ω turbulence model and uses the volume-of-fluid (VOF) approach to monitor the air–water interface. To explore the hydrodynamic performance of the OWC device in actual ocean conditions, the Pierson–Moskowitz (P-M) spectrum was used as the incident wave spectrum, together with the four distinct sea states which occur most often along the western coast of Portugal. The numerical simulation offers a comprehensive velocity vector and streamline profiles inside the OWC device’s chamber during an entire cycle of pressure fluctuation. In addition, the impact of the irregular wave conditions on the free-surface elevation at various places, the pressure drop between the chamber and the outside, and the airflow rate via the orifice per unit width of the OWC device are investigated in detail. The results demonstrate that the amplitudes of the inward and outward velocities via the orifice, free-surface elevations, and flow characteristics are greater for more significant wave heights. Further, it is noticed that the power generation and capture efficiency are higher for a seabed having moderate slopes.

Performance of a hybrid wave energy converter device consisting of a piezoelectric plate and oscillating water column device placed over an undulated seabed

The present study investigates the hydrodynamic performance of a hybrid wave energy converter device consisting of a piezoelectric plate and the oscillating water column wave energy converter device placed over an undulated seabed. Primary emphasis is given to analyze the power extraction of the hybrid wave energy converter device, piezoelectric plate, and the OWC devices for various values of incident wave parameters and shape parameters associated with the hybrid wave energy converter device and undulated seabed. Moreover, the time-domain analysis is carried out by considering the Bretschneider spectrum as the incident wave spectrum for irregular incident waves. A multi-parameter optimization based on the Taguchi method is provided. The study reveals that the power extraction by the hybrid wave energy converter device consisting of a piezoelectric plate and the oscillating water column device is significantly higher than the power extraction by the standalone piezoelectric plate and the OWC device for a wider range of frequencies. Further, the present study shows that the power extraction by the hybrid wave energy converter device is higher when the piezoelectric plate is placed in the close proximity of the OWC device. Moreover, the time-domain simulation reveals that the piezoelectric plate is able to capture the incident wave energy for a longer period of time in real sea conditions.

An Improved Hydraulic Energy Storage Wave Power-Generation System Based on QPR Control

According to the inherent characteristics of the hydraulic power take-off (PTO) system, the output power of a generator tends to be intermittent when the wave is random. Therefore, this paper aims to improve the effective utilization of wave energy and reduce power intermittency by constructing a topology with two branches to transmit electrical energy. Firstly, the wave-to-wire (W2W) model of the system is constructed. Secondly, the W2W model is simulated by using synovial and quasi-proportional resonance (QPR) control with regular and irregular incident waves, and the results of PI control are compared. Then, the control strategy in simulation is verified by experiments. The simulation and experimental results show that the control strategy has better performance, and the stability of the system output power is greatly improved.

Probabilistic analysis of irregular wave runup on a fixed and truncated surface-piercing vertical cylinder

This paper presents a numerical and experimental study on irregular wave runup on a fixed and truncated surface-piercing vertical cylinder. The numerical model was set up based on the incompressible two-phase flow solver in the open-source toolbox OpenFOAM. The model was successfully validated against the experimental data on both regular and irregular incident wave and wave runup. We analyse the characteristics of the runup spectrum against different kpHs and kpD, where kp is the wave number at peak frequency, Hs is the significant wave height and D is the diameter of the cylinder. A new method is proposed to predict the distribution of runup height. In this method, the average height of the highest one-third of all wave runup R1/3 is calculated based on the expansion of an empirical formula proposed in Cao et al., (2017). Then the non-dimensional runup height R/R1/3 is fitted into a two-parameter Weibull distribution, where the shape parameter and scale parameter are provided as a function of kpHs and kpD based on the interpolation of the experimental and numerical data. Based on the fitted Weibull distribution, the runup height at any cumulative probability can be determined. This newly proposed method is validated against the numerical and experimental data on the 2% excess wave runup height R2%, and the deviations are found to be within ±15% for most of the cases. Finally, a sensitivity analysis is conducted to demonstrate that the model uncertainty is within 15%.

Power extraction from floating elastic plates

We present a novel mathematical model to investigate the extraction of wave power by flexible elastic floaters. The model is based on the method of dry modes, coupled with a matched eigenfunction expansion. Our model results compare satisfactorily with preliminary data obtained from a demonstrator device, developed at the University of Groningen. We show that the role of elasticity is to increase the number of resonant frequencies with respect to a rigid body, which has a positive effect on wave power output. The mathematical model is then extended to irregular incident waves, described by a JONSWAP spectrum. Our results show that the peak capture factors decrease in irregular waves, as compared to the monochromatic case. However, the system becomes more efficient at non-resonant frequencies. This work highlights the need to scale-up experimental investigations on flexible wave energy converters, which are still a small minority, compared to those on rigid converters.

An empirical model for predicting wave attenuation inside vegetation domain

An empirical model for wave attenuation predictions when periodic waves propagate through vegetation domain is presented based on the dimensional analysis. A new nondimensional parameter KaL which represents the averaged wave attenuation per wavelength in the whole vegetation domain is introduced to denote the wave energy dissipation due to the presence of vegetation stems. The wave attenuation can be predicted by the multiplications of several nondimensional terms containing both wave and vegetation parameters without CD value. The model was firstly calibrated with emergent vegetation cases, and the applicability of Dalrymple et al. (1984)'s model was studied with the same datasets. The comparisons showed the empirical model performed better than Dalrymple et al. (1984)'s one, especially for cases with non-cylindrical stems, incident irregular waves and relatively dense vegetation domain. Then, the empirical model was validated with submerged cases in the literature and also floating cases conducted in the present study. After that, the influence of vegetation domain vertical positions on wave attenuation is discussed based on the validated model, and the non-dimensional vegetation diameter term in the model is changed and analyzed. Moreover, the simplification of the model which substitutes the Ursell number for wave nonlinearity and relative water depth is implemented.

Hydrodynamic Investigation on a Land-Fixed OWC Wave Energy Device under Irregular Waves

The hydrodynamic response of a land-based oscillating water column (OWC) wave energy converter under various irregular wave conditions is investigated numerically. Based on the potential flow theory, a two-dimensional fully nonlinear numerical wave flume (NWF) is developed to model the hydrodynamic characteristics using the time-domain higher-order boundary element method (HOBEM). The inner-domain sources method and JONSWAP energy spectrum is used to generate the irregular incident waves, and a linear pneumatic model is used to determine the pneumatic pressure inside the chamber. The free surface elevations at the chamber centre and the oscillatory pneumatic pressures induced by the vertical motion of the water column are recorded. The influence of irregular waves on the hydrodynamic characteristics of the OWC device is carried out by comparison with the regular waves, and a number of significant wave heights and peak wave periods are considered. The hydrodynamic efficiency of the OWC device in irregular wave conditions is observed to be lower than that in regular waves for most wave frequencies, especially near the resonant frequency.

Wave excitation force forecasting using neural networks

Many wave energy conversion applications require future knowledge or forecasting of the wave excitation force values. Most wave energy converter (WEC) control strategies need to forecast the time-series excitation force for wave energy harvesting maximization. The main aim of this study is to forecast the wave excitation force experiences by a two-body heaving point absorber WEC (as a case study) using three forecasting neural network methods. The wave excitation force is calculated based on the hydrodynamic characteristics of the considered device in the frequency and time-domain simulations. The nonlinear autoregressive neural (NAR) network, group method of data handling (GMDH) network, and Long Short-Term Memory (LSTM) network are fitted to the wave elevation time-series data to forecast the future values of the excitation force. The performance of the examined methods is evaluated for various irregular incident waves that are created using different wave spectrums. Moreover, sensitivity analyses to sampling period and algorithms input parameters are performed to investigate the accuracy and generalizability of the discussed methods at different conditions. Each data set is divided into training and test sets. The results show that the performance of all discussed methods is satisfactory in training data sets and short-term ahead forecasting, but the NAR network method provides a relatively better agreement with test target data compared to other methods.

Experimental study of wave height, crest, and trough distributions of directional irregular waves on a slope

Presently, most studies of wave height distribution on slopes are based on normal incident unidirectional waves. In this study, the wave height, crest, and trough distributions of oblique incident unidirectional and multidirectional irregular waves on a 1:15 slope were experimentally investigated. The Composite Weibull Distribution fitted the experimental data well and could be applied to predict the wave height, crest, and trough distributions for unidirectional and multidirectional waves on the slope. The shape parameter with a constant value k2 = 3.6 in Composite Weibull Distribution proposed by Battjes and Groenendijk (2000) did not describe the actual variation of wave height distribution in the surf zone. The parameters' values in Composite Weibull Distribution were modified and the corresponding fitted formulas were proposed in this paper. The results showed that the fitting parameters' values of Composite Weibull Distribution between normal and oblique incident irregular waves, and between unidirectional and multidirectional irregular waves were slightly different. But the directional spreading had little effect on the fitting parameters’ values for narrow directional spreading waves. These findings for a 1:15 slope can be referenced as a supplement to the conclusions of Battjes and Groenendijk (2000).

Swell-induced flexural vibrations of a thickening ice shelf over a shoaling seabed

A solution method is developed for a linear model of ice shelf flexural vibrations in response to ocean waves, in which the ice shelf thickness and seabed beneath the ice shelf vary over distance, and the ice shelf/sub–ice-shelf cavity are connected to the open ocean. The method combines a decomposition of the ice shelf displacement profile at a prescribed frequency of motion into mode shapes of free vibrations, a finite-element method for the cavity water motion and a non-local operator to connect to the open ocean. An investigation is conducted into the effects of ice shelf thickening, seabed shoaling and the grounding-line conditions on time-harmonic ice shelf vibrations, induced by regular incident waves in the swell regime. Furthermore, results are given for ice shelf vibrations in response to irregular incident waves by superposing time-harmonic responses, and ocean-to-ice-shelf transfer functions are derived. The findings add to evidence that ice shelves experience appreciable flexural vibrations in response to swell, and that ice shelf thickening and seabed shoaling can have a considerable influence on predictions of how ice shelves respond to ocean waves.

Internally-resonant broadband point wave energy absorber

Motivated by the need for broadband point wave energy absorbers (PWAs) whose response is insensitive to the frequency of the incident waves, this work exploits a two-to-one internal resonance energy pump to design a PWA with improved response capabilities. The proposed PWA consists of two elastically-coupled nonlinear oscillators in the form of a partially-submerged buoy and an auxiliary mass suspended inside it by a nonlinear restoring force element. The auxiliary oscillator is designed such that its modal frequency is tuned to the peak frequency in the incoming waves spectrum and to half the modal frequency of the buoy. When the buoy is subjected to low-frequency wave excitations near half its natural frequency, the auxiliary mass resonates with the waves and starts to move. Energy is then channeled to the buoy via a two-to-one nonlinear internal resonance energy pump. This results in reasonably large-amplitude buoy’s displacements over a relatively wide spectrum of incoming waves frequencies. Numerical simulations were presented to evaluate the behavior of the proposed PWA under regular and irregular incident waves. It was shown that the PWA can be designed to have a broad bandwidth, which is insensitive to variations in the incoming waves frequency. It was also shown that, with the proper choice of the PWA’s design parameters, its frequency response can be made almost flat without the clear resonance peak typically shown in the response of the traditional linear PWAs. A proof-of-concept experimental study was also performed on an equivalent prototype using an electrodynamic shaker to simulate the sea waves. Experimental results were shown to corroborate the numerical findings.

Performance analysis of a point-absorber wave energy converter with a single buoy composed of three rigidly coupled structures

A single-body point absorber system is analysed to improve its power absorption at a finite water depth. The proposed wave energy converter consists of a single floating body coupled to a direct-drive power take-off system placed on the seabed. The structure of a cylindrical buoy with large draft is changed by a single body composed of three structures rigidly coupled, reducing its volume and improving its frequency-dependent hydrostatic parameters that are obtained through a numerical analysis tool called NEMOH. The undamped natural frequency of the oscillating system is tuned to a specified wave period and the performance of the WEC system is obtained assuming a linear Power Take-Off system. In time domain, the performance of the WEC device is carried-out under a regular (sinusoidal) and irregular incident wave profile. Comparing the performance of the WEC system using the cylindrical and the proposed buoy outcomes that the system with the proposed buoy is able to absorb more energy from incident waves with a wider frequency range, whereas the oscillating system is kept as simple as possible.

Mathematical modeling of breakwater-integrated oscillating water column wave energy converter devices under irregular incident waves

In the present study, the performance of breakwater-integrated OWC (oscillating water column) wave energy converter devices is analyzed under the action of unidirectional regular and irregular incident waves. Two different types of OWC devices: (i) LIMPET device (sloping-face OWC device) and (ii) quarter-circle-shaped front wall OWC device are considered for the present study. Detailed derivations of the parameters associated with the performance of the OWC devices under the action of irregular waves are provided. To analyze the efficiency of the OWC devices in real sea conditions, the Bretschneider Spectrum is taken as the incident wave spectrum along with nine sea states represent the local wave climate at the OWC plant site Pico, Portugal. The annual-averaged plant efficiencies of the two aforementioned OWC devices are analyzed as a function of chamber length, submergence depth, turbine rotor diameter, and rotational speed of the Wells turbine. It is observed that the annual-averaged plant efficiency can be enhanced significantly with appropriate combinations of chamber length, submergence depth, and turbine characteristics.