Application of the time-dependent mild-slope equations for the simulation of wake effects in the lee of a farm of Wave Dragon wave energy converters

Time-dependent mild-slope equations have been extensively used to compute wave transformations near coastal and offshore structures for more than 20 years. Recently the wave absorption characteristics of a Wave Energy Converter (abbreviated as WEC) of the overtopping type have been implemented in a time-dependent mild-slope equation model by using numerical sponge layers. In this paper the developed WEC implementation is applied to a single Wave Dragon WEC and multiple Wave Dragon WECs. The Wave Dragon WEC is a floating offshore converter of the overtopping type. Two wave reflectors focus the incident wave power towards a ramp. The focussed waves run up the ramp and overtop in a water reservoir above mean sea level. The obtained potential energy is converted into electricity when the stored water drains back to the sea through hydro turbines. The wave reflectors and the main body (ramp and reservoir) are simulated as porous structures, exhibiting the same reflection, respectively absorption characteristics as obtained for the prototype Wave Dragon WEC. The wake effects behind a single Wave Dragon WEC are studied in detail for uni- and multidirectional waves. The shadow zone indicating the wake effect is decreasing with increasing directional spreading. The wake in the lee of a farm of five Wave Dragon WECs, installed in a staggered grid (3 WECs in the first row and 2 WECs in the second row), is calculated for three in-between distances of respectively D, 2D and 3D, with D the distance between the tips of the wave reflectors of a single WEC. As a result, a farm of five Wave Dragon WECs installed in a staggered grid with an in-between distance of 2D is preferred, when taking cost and spatial considerations into account.     

Experimental and numerical comparisons of hydrodynamic responses for a combined wind and wave energy converter concept under operational conditions

The spar torus combination (STC) concept is a combined wind and wave energy converter concept that is composed of a spar floating wind turbine and a torus-shaped, heaving-body wave energy converter (WEC). The WEC is installed on the spar floater. Wave power can be absorbed by a power-take off (PTO) system through the relative heave motions between spar and torus. Numerical model was established to predict dynamic responses of the STC concept ​under different sea states. To validate the numerical model, a model test of the STC concept under operational conditions was performed. A two-body physical model at a 1:50 scaling ratio was built. A series of tests were performed to assess the performance of the concept. During the tests, different PTO damping levels were applied. When large power output was achieved, air compressibility of the PTO damper in the model matters, making relevant a suitable nonlinear PTO modeling in the numerical simulations. Wind conditions were considered to model the effect of the thrust force on the rotor using a wind drag disc. Numerical and experimental results are presented and compared. Good agreements are achieved.     

Free Vibration Analysis of an Eccentric Thermoelastic Hollow Cylinder

The three-dimensional free vibrations in a simply supported homogeneous isotropic, thermally conducting, circular cylinder of finite length with an eccentrically located inner circular cavity have been studied. The surfaces of the cylinder are subjected to stress free and thermally insulated or isothermal boundary conditions. The three-dimensional linear theory of coupled thermoelasticity has been employed to model the problem. The displacement potential functions have been introduced to decouple purely shear and longitudinal motions. The purely transverse wave has been found to remain unaffected due to thermal field. The translation addition theorem for cylindrical wave functions along with orthogonal series expansions has been used to develop the exact solution. To illustrate the analytical results, the numerical solution of some relations and equations have been obtained to compute lowest frequency and dissipation factor versus eccentricities, for selected length to radius ratio and radius ratio of hollow cylinder. The computer simulated results have been carried out with the help of MATLAB software and are presented graphically.     

Adaptability of a generic wave energy converter to different climate conditions

This study evaluates the influence of wave climate tunability on the performance of a generic Wave Energy Converter (WEC) for different climate scenarios. The generic WEC is assumed to be composed of an array of heaving, floating cylinders. In this study, two natural periods for the cylinders of 4 s and 8 s (typical of enclosed seas and the mean Atlantic swell, respectively) and a location-tunable cylinder are considered to evaluate the influence of tuning on the power performance of the cylinder. The WEC power matrix is computed using a frequency domain model, and the performance of the WEC is evaluated along the global coasts; the met-ocean data originated from the global reanalysis database (GOW) from Reguero et al. (2012). The performance of the WEC is evaluated using two parameters: the capture width ratio (CWR), which evaluates the efficiency of the converter at each location, and the kW/Ton (KWT) parameter, which evaluates the efficiency of the converter using “economic” terms. Tuning a converter for each location displayed a positive CWR; however, the KWT was low after WEC tuning because of the weight of the structures required to tune the converter that experiences high peak periods.     

Effect of stochastic thermal input on elastic and thermal properties of an infinitely long annular cylinder

Random elastic and thermal properties for an infinitely long solid conducting circular cylinder are investigated under the effect of random thermal input. The problem is considered in the context of a generalized thermoelasticity theory with one relaxation time. The lateral surface of the solid is traction free and subjected to known stochastic temperature, driven by an additive Gaussian white noise. Laplace transform technique is used to obtain the solution in the transformed domain. Statistically, we derive and analyze the mean and variance for temperature, displacement and stress. Numerical inversion of the transformed solution is carried out, represented graphically and discussed.     

An investigation of the impacts of climate change on wave energy generation: The Wave Hub,Cornwall, UK

In this paper a generic methodology is presented that allows the impacts of climate change on wave energy generation from a wave energy converter (WEC) to be quantified. The methodology is illustrated by application to the Wave Hub site off the coast of Cornwall, UK. Control and future wave climates were derived using wind fields output from a set of climate change experiments. Control wave conditions were generated from wind data between 1961 and 2000. Future wave conditions were generated using two IPCC wind scenarios from 2061 to 2100, corresponding to intermediate and low greenhouse gas emissions (IPCC scenarios A1B and B1 respectively). The quantitative comparison between future scenarios and the control condition shows that the available wave power will increase by 2–3% in the A1B scenario. In contrast, the available wave power in the B1 scenario will decrease by 1–3%, suggesting, somewhat paradoxically, that efforts to reduce greenhouse gas emissions may reduce the wave energy resource. Meanwhile, the WEC energy will yield decrease by 2–3% in both A1B and B1 scenarios, which is mainly due to the relatively low efficiency of energy extraction from steeper waves by the specific WEC considered. Although those changes are relatively small compared to the natural variability, they may have significance when considered over the lifetime of a wave energy farm. Analysis of downtime under low and high thresholds suggests that the distribution of wave heights at the Wave Hub will have a wider spread due to the impacts of climate change, resulting in longer periods of generation loss. Conversely, the estimation of future changes in joint wave height-period distribution provides indications on how the response and power matrices of WECs could be modified in order to maintain or improve energy extraction in the future.     

Numerical solution of the phase change problem around a horizontal cylinder in the presence of natural convection in the melt region

This paper deals with the numerical study of melting of phase change material around a horizontal circular cylinder in the presence of the natural convection in the melt phase. A two dimensional unsteady mathematical model has been formulated in terms of primitive variables and a coordinate transformation technique has been used to fix the moving front. The finite volume approach was used to discretize the system of governing equations, boundary and initial conditions and obtain a system of linear algebraic equations. In the numerical solution an implicit scheme was used for the momentum and energy equations and an explicit scheme for the energy balance at the interface. The numerical predictions were compared with available results to establish the validity of the model and the numerical approach.     

Reflection and refraction of plane wave at the interface between elastic and thermoelastic media with three-phase-lag model

The problem of reflection and refraction phenomenon due to longitudinal and transverse waves incident obliquely at a plane interface between uniform elastic solid half-space and thermoelastic solid with three-phase-lag model half-space has been studied. In thermoelastic solid medium, potential functions are introduced to represent two longitudinal waves and one transverse wave. The amplitude ratios of various reflected and refracted waves to that of incident wave are derived. These amplitude ratios are further used to find the expressions of energy ratios of various reflected and refracted waves to that of incident wave. The graphical representation is given for these energy ratios for different directions of propagation. The law of conservation of energy at the interface is verified.     

A novel analytical solution of the non-uniform convective boundary conditions problem for heat conduction in cylinders

The problem of heat conduction in a still cylinder exposed to non‐uniform convective conditions on both inner and outer surfaces has been addressed by a method based on the series solution and a novel analytic solution is derived to predict the temperature field in the cylinder. Compared to previous available results this method allows a simpler implementation and its almost straightforward extension to multilayered cylinders represents one of the main advantages over more complex numerical solutions. As an example of application the effect of the non-uniform distribution of heat transfer coefficients on the solid temperature field and the heat transferred is analysed, as function of the fluid flow regime, the Biot number and the cylinder thickness.     

Uncertainty in wave energy resource assessment. Part 1: Historic data

The uncertainty in estimates of the energy yield from a wave energy converter (WEC) is considered. The study is presented in two articles. This first article deals with the accuracy of the historic data and the second article considers the uncertainty which arises from variability in the wave climate. Estimates of the historic resource for a specific site are usually calculated from wave model data calibrated against in-situ measurements. Both the calibration of model data and estimation of confidence bounds are made difficult by the complex structure of errors in model data. Errors in parameters from wave models exhibit non-linear dependence on multiple factors, seasonal and interannual changes in bias and short-term temporal correlation. An example is given using two hindcasts for the European Marine Energy Centre in Orkney. Before calibration, estimates of the long-term mean WEC power from the two hindcasts differ by around 20%. The difference is reduced to 5% after calibration. The short-term temporal evolution of errors in WEC power is represented using ARMA models. It is shown that this is sufficient to model the long-term uncertainty in estimated WEC yield from one hindcast. However, seasonal and interannual changes in model biases in the other hindcast cause the uncertainty in estimated long-term WEC yield to exceed that predicted by the ARMA model.     

Development of a novel point absorber in heave for wave energy conversion

This paper presents an advanced design methodology for electric power generation from the vast ocean wave energy. A novel single-buoy heaving device called wave energy converter (WEC) based on hydrostatic transmission (HST), or can be shortened as HSTWEC, is proposed to convert mechanical energy generated by ocean waves into electric energy. Modeling and simulations with both regular and irregular waves were then carried out to investigate working performances of the designed HSTWEC. The results showed that more than 78% of wave energy can be absorbed. In addition, an adaptive controller was designed to improve the performance of the suggested device. Effectiveness of the overall HSTWEC control system was finally proved by simulations.     

Model predictive control of sea wave energy converters – Part II: The case of an array of devices

This paper addresses model predictive control (MPC) of highly-coupled clusters of sea wave energy converters (WECs). Since each WEC is not only a wave absorber but also a wave generator, the motion of each WEC can be affected by the waves generated by its adjacent WECs when they are close to each other. A distributed MPC strategy is developed to maximize the energy output of the whole array and guarantee the safe operation of all the WECs with a reasonable computational load. The system for an array is partitioned into subsystems and each subsystem is controlled by a local MPC controller. The local MPC controllers run cooperatively by transmitting information to each other. Within one sampling period, each MPC controller performs optimizations iteratively so that a global optimization for the whole array can be approximated. The computational burden for the whole array is also distributed to the local controllers. A numerical simulation demonstrates the efficacy of the proposed control strategy. For the WECs operating under constraints explored, it is found that the optimized power output is an increasing function of degree of WEC–WEC coupling. Increases in power of up to 20% were achieved using realistic ranges of parameters with respect to the uncoupled case.     

Numerical modeling of the effects of wave energy converter characteristics on nearshore wave conditions

Modeled nearshore wave propagation was investigated downstream of simulated wave energy converters (WECs) to evaluate overall near- and far-field effects of WEC arrays. Model sensitivity to WEC characteristics and WEC array deployment scenarios was evaluated using a modified version of an industry standard wave model, Simulating WAves Nearshore (SWAN), which allows the incorporation of device-specific WEC characteristics to specify obstacle transmission. The sensitivity study illustrated that WEC device type and subsequently its size directly resulted in wave height variations in the lee of the WEC array. Wave heights decreased up to 30% between modeled scenarios with and without WECs for large arrays (100 devices) of relatively sizable devices (26 m in diameter) with peak power generation near to the modeled incident wave height. Other WEC types resulted in less than 15% differences in modeled wave height with and without WECs, with lesser influence for WECs less than 10 m in diameter. Wave directions and periods were largely insensitive to changes in parameters. However, additional model parameterization and analysis are required to fully explore the model sensitivity of peak wave period and mean wave direction to the varying of the parameters.     

Reflection of plane waves in a thermoelastic diffusive medium under the effect of microtemperatures

Abstract

The present analysis is aimed to model and study the characteristics of various reflected waves in a homogeneous and isotropic thermoelastic diffusive half-space with microtemperatures. It is shown that there exist four kinds of coupled longitudinal waves in addition to transverse and microtemperature waves in such type of medium. The reflection coefficients and energy ratios of these reflected waves have been computed numerically with the help of MATLAB programing when (i) a set of coupled longitudinal waves is made incident and (ii) a transverse wave is made incident. The numerical values of modulus of reflection coefficients are presented graphically to depict the effect of thermodiffusive parameter. It has been verified that there is no dissipation of energy at the free plane boundary during reflection phenomena.     

Melting of PCM around a horizontal cylinder with constant surface temperature

A numerical study of melting of phase change material (PCM) around a horizontal circular cylinder of constant wall temperature and in the presence of the natural convection in the melt region is presented. A two dimensional mathematical model is formulated in terms of primitive variables and a coordinate transformation technique is used to fix the moving front. The finite volume approach is used to discretize the system of governing equations to obtain a system of linear algebraic equations. An implicit scheme is used for the momentum and energy equations and an explicit scheme for the energy balance at the interface. The numerical predictions were compared with available results to establish the validity of the model and additional results are obtained to demonstrate the effects of Rayleigh and Stefan numbers as well as the wall temperature on the time for complete fusion and total melt volume.     

Blowing models for cooling surfaces

To study the cooling of surfaces exposed to high temperature stress and heat flux, the blowing, or transpiration, technique is numerically investigated in the case of a porous circular cylinder. Two models are developed to simulate the blowing impact on the outer flow and an experimental set-up available allows for direct comparison and validation of the numerical simulations. The heat exchange occuring within the porous wall itself between the coolant and the solid part of the wall is accounted. The results show an excellent effectiveness of the blowing in terms of surface temperature reduction, even for low blowing ratii. The incident heat flux exhibits a maximum for medium blowing rates due to a decreasing heat transfer coefficient and a growing temperature difference between the surface and the main flow with the injection rate. Finally, the blowing is demonstrated to be very effective in cooling heavily thermally stressed parts in terms of homogeneity and coolant rate required.     

Bluff body with built-in piezoelectric cantilever for flow-induced energy harvesting

This paper investigates a flow-induced vibration energy harvester comprising a piezoelectric beam (piezo-beam) installed within a hollow circular cylinder. Under the flow excitation, the energy-harvesting system including the cylinder and the piezo-beam vibrates and generates electricity. A lumped parametric model incorporating the fluid-structure interaction (FSI) is developed to evaluate the performance of the proposed energy harvester. Based on the theoretical analysis, several guidelines on the design and optimization of the proposed energy harvester are provided. Subsequently, a numerical model is used to simulate the FSI between the proposed system and the external flow field. Finally, a physical prototype is fabricated and an experiment is conducted to test the actual performance for validation. The theoretical analysis results are verified by the numerical and experimental results.     

Three-dimensional vibration analysis in transversely isotropic cylinder with matrix Frobenius method

Abstract

This article deals with the study of three-dimensional vibrations in stress free as well as rigidly fixed, thermally insulated (or isothermal), homogeneous transversely isotropic solid cylinder under the purview of three-phase lag model of generalized thermoelasticity. The displacement potential functions have been introduced in the equations of motion and heat conduction in order to decouple the purely shear and longitudinal motions. The matrix Frobenius method of extended power series is employed to obtain the solution of coupled ordinary differential equations along the radial coordinate. Circumferential wave propagation in cylindrical curved plate is discussed. To illustrate the analytic results, the numerical solution of various relations and equations have been carried out to compute the lowest frequency, inverse quality factor, and dissipation factor of vibrations and the computer-simulated results are presented graphically for different thermoelastic models.     

同轴双浮体波能装置最优获能研究

该文以同轴双浮体波能装置为研究对象,通过理论分析建立运动方程,求解线性能量摄取(PTO)作用下的最优阻尼系数及最大输出功率。同时探究了装置能量捕获的影响因素及控制策略,提出一种具有普遍意义的最优获能估算公式。研究结果表明:双浮体波能装置可通过调节PTO阻尼力使得获能最大化,且较单浮体装置具有更宽的能量俘获频率范围;不同PTO控制策略及水体粘性阻尼均对该类装置获能影响显著。     

人工鱼礁-波浪能模块化浮体耦合动力响应分析

为综合利用海洋空间资源、生物资源以及可再生能源,该文提出一种基于张力腿平台的新型六边形浮体、浮式人工鱼礁以及波浪能装置（WEC）的集成结构系统。基于势流理论,并考虑六边形浮体与浮式人工鱼礁之间的多体水动力耦合效应和机械耦合效应,建立该集成结构系统的耦合时域分析模型。对浮式人工鱼礁和波浪能装置的主要设计参数进行初步优化,重点研究该新型集成结构系统在典型海况下的动力响应和波浪能发电特征,揭示了外侧浮式人工鱼礁可有效减弱作用于内侧六边形浮体结构的波浪载荷,并产生可观的波浪能能源供给。此外,还进一步验证了该集成结构系统在极端海况下的安全性能。