پیاده سازی عددی و تجزیه و تحلیل حساسیت از یک مبدل انرژی امواج در یک مدل معادلات خفیف شیب وابسته به زمان
|کد مقاله||سال انتشار||مقاله انگلیسی||ترجمه فارسی||تعداد کلمات|
|26338||2010||22 صفحه PDF||سفارش دهید||محاسبه نشده|
Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت)
Journal : Coastal Engineering, Volume 57, Issue 5, May 2010, Pages 471–492
Several Wave Energy Converters (abbreviated as WECs) have intensively been studied and developed during the last decade and currently small farms of WECs are getting installed. WECs in a farm are partly absorbing, partly redistributing the incident wave power. Consequently, the power absorption of each individual WEC in a farm is affected by its neighbouring WECs. The knowledge of the wave climate around the WEC is needed to predict its performance in the farm. In this paper a technique is developed to implement a single and multiple WECs based on the overtopping principle in a time-dependent mild-slope equation model. So far, the mild-slope equations have been widely used to study wave transformations around coastal and offshore structures, such as breakwaters, piles of windmills and offshore platforms. First the limitations of the WEC implementation are discussed through a sensitivity analysis. Next the developed approach is applied to study the wave height reduction behind a single WEC and a farm. The wake behind an isolated WEC is investigated for uni- and multidirectional waves; it is observed that an increase of the directional spread leads to a faster wave redistribution behind the WEC. Further the wake in the lee of multiple WECs is calculated for two different farm lay-outs, i.e. an aligned grid and a staggered grid, by adapting the performance of each WEC to its incident wave power. The evolved technique is a fast tool to find the optimal lay-out of WECs in a farm and to study the possible influence on surrounding activities in the sea.
The need for renewable energy is rising at light-speed. The increasing energy demand, the greenhouse effect, the shrinking reserves of fossil fuels and consequently the increasing cost of electricity generation, have resulted in an accelerated development of renewable energy supplies, a.o. wave energy. Many concepts for wave power conversion, with an installed capacity from a few kilowatts up to more than 1 MW, have been invented. To extract a substantial amount of wave power, Wave Energy Converters (abbreviated as WECs) are arranged in several rows or in a ‘farm’. WECs in a farm are interacting and the overall power absorption is affected. The incident waves are partly reflected, transmitted and absorbed by a WEC. Consequently the incident wave power is partly absorbed and partly redistributed around the WEC which has a positive or negative effect on the power absorption of the neighbouring WECs in the farm. Finally the wave height behind a large farm of WECs is reduced and this reduction may possibly influence other users in the sea. WECs can be divided into two major categories: (i) devices based on the oscillation principle, where a body or water column is oscillating and (ii) devices based on the overtopping principle, where waves are overtopping in a basin at a higher level than the surrounding sea. The first category comprises different types of floating or submerged bodies and oscillating water columns, while the second category consists of fixed or slack moored overtopping devices. Oscillating systems absorb power by simultaneously generating a wave (Falnes and Budal, 1978). The incident wave is partly diffracted (also called scattered) and partly absorbed due to the destructive interference with the generated (also called radiated) wave. Furthermore the performance of neighbouring devices in a farm is influenced by the scattered incident wave and radiated wave from the oscillating device and vice versa. On the other hand WECs based on the overtopping principle absorb power by capturing the water volume of overtopped waves in a basin and creating a hydraulic head. Consequently a wake is created behind the WEC which affects the performance of WECs installed in that wake. The redistribution of wave power in the farm is different for both categories, as each category has its own specific way of absorbing power. This study comprises WECs based on the overtopping principle. A lot of research has been carried out on the hydrodynamic behaviour of WECs based on the oscillation principle in an array. The hydrodynamic problem of power absorption is usually studied as a combination of two simpler problems: the diffraction problem (scattered incident wave field due to the presence of the WEC) and the radiation problem (wave field generated by the body or water column oscillations). An overview of theoretical methods used to calculate the hydrodynamic interactions of oscillating bodies in arrays is given in Mavrakos and McIver (1997): (i) the plane wave approximation where all scattered and radiated waves are approximated as plane waves under the assumption that the device spacing is many wave lengths (Simon, 1982, McIver, 1984 and McIver, 1994), (ii) the point-absorber method where the scattered waves are neglected under the assumption that the device dimension is much smaller than the wave length (Budal, 1977, Evans, 1980 and Falnes, 1980) and (iii) the multiple scattering method which accounts accurately for all hydrodynamic interactions (Mavrakos, 1991, Mavrakos and Koumoutsakos, 1987 and Mavrakos and Kalofonos, 1997). A theoretical study concerning an infinite periodic array of identical oscillating water columns can be found in Falcão (2002). Recently, with the improvement of computer technology, Boundary Element Methods based on potential flow (e.g. WAMIT) have intensively been used to study the hydrodynamic interaction of multiple oscillating bodies in an array (a.o. Justino and Clément, 2003, Ricci et al., 2007 and De Backer et al., 2009). Still the required simulation time is increasing rapidly with the number of bodies considered in the arrays and the dimensions of the domain. The before mentioned studies all concentrate on maximising the absorbed power of an array of oscillating bodies or oscillating water columns while the knowledge of the wake of a single WEC and the wave height reduction in the lee of a farm is as important in the design of a farm of WECs as a change in wave height behind a large farm can affect other activities in the oceans. The study of the latter aspects requires a large computational domain which makes the discussed Boundary Element Methods less convenient. Recently the coastal impact of a farm of WECs has been studied in numerical wave propagation models. Millar et al. (2006) have used the spectral wave propagation model, SWAN (Booij et al., 2004), to study the change of the wave climate caused by the installation of a farm of WECs 20 km off the north coast of Cornwall, UK. In Venugopal and Smith (2007) an array of five bottom mounted, fixed WECs have been modelled in a nonlinear Boussinesq wave model (MIKE 21). In the latter models the WEC is simplified as a porous structure which is able to extract a predefined amount of wave power. This way the incoming waves are partly reflected, transmitted and absorbed by the WEC. This simplification is only applicable to the second category of WECs, i.e. WECs based on the overtopping principle, as absorption of power is not caused by generation of waves. In this paper a new technique to implement the combined effects of reflection, transmission and consequently absorption of a WEC is developed in a linear mild-slope model, MILDwave, based on the equations of Radder and Dingemans (1985). According to the authors knowledge it is the first time that a mild-slope equation model is used to study the wake effect of a single WEC and a farm of WECs. In a subsequent paper (Beels et al., in press) the evolved technique is applied to the wave energy converter Wave Dragon. In the next section the use of various wave propagation models for farm modelling is discussed. A short description of the mild-slope wave propagation model MILDwave is given in Section 3. The mild-slope equations of Radder and Dingemans (1985), the generation of uni- and multidirectional waves and the finite difference scheme to solve these mild-slope equations are briefly described. Section 4 gives a detailed overview of the implementation of wave power absorption in MILDwave. Through a sensitivity analysis the limitations of the modelling approach are studied. Section 5 deals with the reduction of the wave height in the lee of a single hypothetical WEC of the overtopping type. The shadow zone behind this WEC is discussed in detail for sea states with increasing directional spread. The model's ability to simulate a farm of WECs based on the overtopping principle is discussed in Section 6.
نتیجه گیری انگلیسی
In this paper the implementation of a single WEC and a farm of WECs based on the overtopping principle in the time-dependent mild-slope equation model MILDwave has been presented. A WEC is composed of an array of absorbing cells, with the same spatial dimensions of the WEC, that have been assigned a specific absorption coefficient to obtain the amounts of reflection and absorption as specified by the developer of the WEC. The possibilities and constraints of the latter approach have been discussed. When the WEC has a constant absorption coefficient equal to 0, the WEC is fully reflective. Cells with an absorption coefficient of 1 correspond to water cells. All values of the absorption coefficient between 0 and 1 result in a combination of reflection, absorption and transmission, depending on the dimensions of the WEC. The reflection and transmission coefficient are respectively decreasing and increasing with increasing value of the absorption coefficient. Further the amount of transmission is decreasing with increasing length of the WEC, while the amount of reflection is approximately constant. By changing the shape of the absorption function through the WEC, the amounts of reflection and absorption are uncoupled. As the amount of power absorption depends on the incident wave period, the WEC needs to be tuned for each sea state. For a WEC with sufficiently large dimensions (≥ 18 m for T = 5.2 s or View the MathML sourcelengthofWECL≥0.4), which is generally the case for WECs based on the overtopping principle, and a small amount of reflection (minimal loss of energy), each combination of reflection and absorption can be modelled, except small levels of absorption which are in contradiction with the concept of a WEC (absorbing as much wave power as possible). Finally the developed model has been utilized to study the wave height reduction behind a single hypothetical WEC and two lay-outs of multiple hypothetical WECs of the overtopping type. The dimensions and the magnitude of the wake depend on the WEC specifications and on the incident wave climate. The higher the peak period the wider the shadow zone behind the WEC. An increasing directional spread results in a faster redistribution and a shorter shadow zone behind the WEC. In a farm the efficiency of a WEC in the lee of neighbouring WECs has been adapted according to the remaining wave height in front of the WEC by using the technique of uncoupling the amounts of reflection and absorption. The overall power absorption of a farm has been compared for two lay-outs. A staggered grid results in a higher overall absorption compared to an aligned grid. The evolved methodology to implement a farm of WECs can be used to study on the one hand the power absorption and on the other hand the coastal impact of a farm of WECs.