Incident Wave Elevation Research Articles

Numerical simulation on the energy capture spectrum of heaving buoy wave energy converter

Based on the Wave Energy Capture Spectrum (ECS) theory, the characteristics of the ECS of a cylindrical heaving buoy WEC with consideration of linear PTO damping are studied in this paper. A 3D numerical wave tank (NWT) based on the RANS equations and the two-phase VOF model was established using the CFD software Flow-3D and validated by the corresponding experimental data. The ECSs of the heaving buoy WEC with different settings were calculated by the energy capture fluctuation signal, which was based on the incident wave elevation and the power output of the heaving buoy. The procedures of ECS solution using numerical method were proposed, and the effects of irregular wave, linear PTO damping, and relative draught on the ECS of the heaving buoy were studied, respectively. The results showed that the average period of incident wave is the key control factor of the peak frequency of the ECS. Compared to linear PTO damping, the relatively draught has little influence on the peak frequency of ECS. With the evaluation of the ECS method, the cylindrical heaving buoy WEC shows good adaptability to variable wave conditions and could be further improved by adjusting its ECS.

Wave Front Steepness and Influence on Horizontal Deck Impact Loads

In design storm sea states, wave-in-deck forces need to be analysed for fixed and floating offshore platforms. Due to the complex physics of wave impact phenomena, numerical analyses should be complemented by model test data. With a large statistical variability, such experiments usually involve running many 3-h storm realisations. Efforts are being done to establish efficient procedures and still obtain improved statistical accuracy, by means of an initial simplified screening based on parameters derived from the incident wave record only. Here, we investigate the vertical rise velocity of the incident wave elevation at a fixed point in space, which indirectly measures both the local slope and the near-surface orbital velocity. A derived simple deck slamming model is also suggested, to support the check of the physical basis of the approach. Correlation against data from a GBS wave-in-deck model test is used for checking this model. The results show that, although there is a significant random scatter in the measured impact forces, especially in the local slamming forces but also in the global forces, there is a correlation to the rise velocity. Comparisons to the simple load model also show promising results when seen on background of the complex physics and random scatter of the impact problem.

Weakly nonlinear modeling of submerged wave energy converters

Wave-to-Wire numerical models being developed for the study of wave energy converters usually make use of linear potential flow theory [1–5] to describe wave-structure interaction. This theory is highly efficient from a computational perspective. However, it relies on assumptions of small wave steepness and small amplitude of motion around mean positions. Often, maximization of wave energy converters’ energy performance implies large amplitude motion [6–8], thus contradicting the assumption of small amplitude motion.An alternative approach is to linearize the free surface conditions on the instantaneous incident wave elevation (Weak-Scatterer approach [9]) while the body conditions are evaluated at the exact body position. Studies of wave energy converters’ dynamic response using this method are expected to be more accurate, while maintaining a reasonable computational time. With this aim, a Weak-Scatterer code (CN_WSC) was developed and used to study two submerged wave energy converters. The first is a heaving submerged sphere and the second is a bottom-hinged fully submerged oscillating flap. They are inspired respectively by the Ceto [10] and WaveRoller [11] devices.Initial calculations were performed in linear conditions first to verify the CN_WSC against linear theory. Subsequently, calculations in nonlinear conditions were performed, using large wave steepness and amplitude of body motion. In linear conditions, results of CN_WSC showed good agreement with linear theory, whereas significant deviations from linear theory were observed in nonlinear conditions. As amplitude of body motion increases, linear theory tends to overestimate energy performance in comparison with Weak-Scatterer theory. In contrast, with smaller amplitude of motion but larger wave steepness, the opposite result is obtained: energy performance is underestimated by linear theory compared to Weak-Scatterer theory.

Analysis of measurements and simulations from the Hywind Demo floating wind turbine

A comparative dynamic analysis between full-scale measurements from the floating wind turbine Hywind Demo and corresponding numerical simulations is presented. A description of the main characteristics of the Hywind Demo structure, control system and important measurements are given. A method for estimation of the incident wave elevation on Hywind Demo is outlined. Comparative dynamic simulations are carried out with the estimated wave elevation time series as input, together measured and further refined statistical parameters of the wind field. Roll, pitch and yaw motions, tower bending moments, mooring line tensions, power production, rotor speed and blade pitch angle are compared for one case below and one case above the rated wind speed. Overall, good agreement is seen between the measured and simulated responses, and it is believed that the considered analysis tool is well suited for confirming the design of a future optimized floating wind turbine based on the Hywind concept. Copyright © 2014 John Wiley & Sons, Ltd.

Influence of the nonlinearity on statistical characteristics of long wave runup

Abstract. Runup of long irregular waves on a plane beach is studied experimentally in the water flume at the University of Warwick. Statistics of wave runup (displacement and velocity of the moving shoreline and their extreme values) is analyzed for the incident wave field with the narrow band spectrum for different amplitudes of incident waves (different values of the breaking parameter Brσ). It is shown experimentally that the distribution of the shoreline velocity does not depend on Brσ and coincides with the distribution of the vertical velocity in the incident wave field as it is predicted in the statistical theory of nonlinear long wave runup. Statistics of runup amplitudes shows the same behavior as that of the incident wave amplitudes. However, the distribution of the wave runup on a beach differs from the statistics of the incident wave elevation. The mean sea level at the coast rises with an increase in Brσ causing wave set-up on a beach, which agrees with the theoretical predictions. At the same time values of skewness and kurtosis for wave runup are similar to those for the incident wave field and they might be used for the forecast of sea floods at the coast.

A study on Prediction Requirements in time-domain Control of Wave Energy Converters

Abstract Wave energy converters (WECs) based on oscillating bodies or oscillating water columns would earn huge benefits from a time-domain control on a wave by wave basis. Such a control would allow efficient energy extraction over a wider range of frequencies than what could possibly be achieved when no real-time control is adopted, thus increasing the economical attractiveness of the WECs. Almost every control strategy that showed some potential, however, suffers from the problem that future knowledge of the incident wave elevation, or wave excitation force, is required. In this paper a general control framework for oscillating WECs is presented and a methodology to understand and quantify the wave excitation force prediction requirements, along with the achievable prediction accuracy, is discussed. The two features are compared against each other and linked to the dynamic characteristics of a device. Along with the qualitative discussion, the methodology is applied to some heaving cylinders when reactive control and linear passive control are applied, under different sea conditions.

Short-Term Wave Forecasting for Real-Time Control of Wave Energy Converters

Real-time control of wave energy converters requires knowledge of future incident wave elevation in order to approach optimal efficiency of wave energy extraction. We present an approach where the wave elevation is treated as a time series and it is predicted only from its past history. A comparison of a range of forecasting methodologies on real wave observations from two different locations shows how the relatively simple linear autoregressive model, which implicitly models the cyclical behavior of waves, can offer very accurate predictions of swell waves for up to two wave periods into the future.

A Study on the Combination Resonance Response of a Classic Spar Platform

The sum type combination resonance response of a classic spar platform is studied under a long periodic regular wave in this paper. The nonlinear differential equations for heave and pitch are established considering the time-varying incident wave elevation which is regarded as a parametric excitation. The first order steady-state response is solved by the method of multiple scales when the incident wave frequency approaches the sum of heave natural frequency and pitch natural frequency. The heave and pitch responses of a practical spar platform are obtained by solving the bifurcation equation using a numerical method. It is observed that the large amplitude sub-harmonic motion of heave and pitch mode are tripped when the wave height exceeds a certain value. The result shows that the spar platform may exhibit complicated dynamic behaviors when the sum type combination resonance occurs and indicates that the available damping plays a very important role in suppressing the instable motion responses.

A time domain simulation method for nonlinear motion and wave loads of fast ships

A nonlinear time domain method is presented to calculate the vertical responses of fast ships. The extended 2.5D theory is used to evaluate nonlinear fluid radiation and diffraction forces which can take into account both the effects of the change of the underwater wet surface and the forward speed of a fast ship at free surface. A matched boundary integration equations algorithm is applied to solve the 2.5D theory in order to avoid numerical divergence observed when ships have large flare. The hydrostatic and Froude–Krylov forces are calculated below the incident wave elevation. The comparison of numerical results with model test data shows that the numerical method can capture the main nonlinear effects and is valid for the calculation of vertical motions and wave loads of high speed ships.

A meshless numerical wave tank for simulation of nonlinear irregular waves in shallow water

AbstractTime domain simulation of the interaction between offshore structures and irregular waves in shallow water becomes a focus due to significant increase of liquefied natural gas (LNG) terminals. To obtain the time series of irregular waves in shallow water, a numerical wave tank is developed by using the meshless method for simulation of 2D nonlinear irregular waves propagating from deep water to shallow water. Using the fundamental solution of Laplace equation as the radial basis function (RBF) and locating the source points outside the computational domain, the problem of water wave propagation is solved by collocation of boundary points. In order to improve the computation stability, both the incident wave elevation and velocity potential are applied to the wave generation. A sponge damping layer combined with the Sommerfeld radiation condition is used on the radiation boundary. The present model is applied to simulate the propagation of regular and irregular waves. The numerical results are validated by analytical solutions and experimental data and good agreements are observed. Copyright © 2008 John Wiley & Sons, Ltd.

On non-causal impulse response functions related to propagating water waves

Particular attention is drawn to the non-causality of two impulse response functions, one of which relates the excitation force on an immersed body to the incident wave elevation at the body's reference position, while the other relates the incident wave elevations at two different positions along the line of wave propagation. An explanation is proposed for the non-causality of the impulse response functions, in spite of the fact wave propagation is a causal process. An indication is given of how far ‘upstream’ the incident wave elevation should be measured in order to be able to know, with reasonable accuracy, the current heave excitation force on a floating truncated cylinder with vertical axis, given current and past wave-elevation measurements. This provides a method for wave prediction, which is required for optimum control of the oscillation of the immersed body.

State-space modelling of a vertical cylinder in heave

The (first-order) wave forces on structures interacting with ocean waves may be represented by complex transfer functions in the frequency domain or by convolution integrals in the time domain. The integration kernels are causal for radiation forces, but not necessarily so for excitation (scattering) forces. As a convenient approximation, these integrals may be replaced by a finite-order system of differential equations with constant coefficients. This method is applied to a heaving cylinder with a vertical axis, and good approximations are obtained when the order of the differential equation system is three for the radiation force and five for the excitation force. The corresponding state-space model for the heave motion response due to the incident wave elevation has an order of 10, but it is demonstrated that it is possible to reduce the order to five without increasing the inaccuracy in the heave motion too much.