Elsevier

Ocean Engineering

Volume 111, 1 January 2016, Pages 483-492
Ocean Engineering

Numerical and experimental analysis of the power output of a point absorber wave energy converter in irregular waves

https://doi.org/10.1016/j.oceaneng.2015.11.011Get rights and content

Highlights

  • The optimum power output of a wave energy converter (WEC) was examined.

  • The linear numerical method provides an upper estimate for wave energy absorption.

  • The experimental results show lower energy absorption due to the non-linear effects.

  • This WEC, however, has an excellent power output in comparison with other WECs.

Abstract

This paper examines the optimum power output of a pitching-surge point absorber wave energy converter in irregular wave climates. A mathematical model based on frequency domain is used as the first step to estimate the hydrodynamic parameters of the device and its potential power output in realistic sea waves. The numerical results predict that the point absorber energy converter has the potential to absorb more energy than what is contained in its own geometrical width. The optimum power of the device is then obtained from wave tank experiments in irregular wave climates. The comparison of numerical and experimental results demonstrates that the frequency domain method based on linear theory will lead to an overestimation of the energy absorption for this device. The frequency domain method provides an upper estimate for wave energy absorption due to the non-linear, viscous effects and constrained amplitude of device oscillation. However, comparison of the performance of the device with other point absorber wave energy converters shows that this wave energy converter is one of the most efficient in terms of absorbing wave energy.

Introduction

The oil crisis of 1973 led to a period of high energy prices which intensified interest in renewable energies such as large-scale energy production from the sea waves. One of the earliest works in the UK was a paper published in Nature by Salter (1974) which brought the feasibility of wave energy conversion to the attention of the international scientific community. Research into wave energy started at Lancaster University in the mid-1970s, mainly concentrating on the invention and development of wave energy converters (WECs) at model scale, along with generic work on the theory and systematic design of WECs. This has led to the great understanding of the theory and systematic prototype design of WECs (French and Bracewell, 1985, Chaplin and Folley, 1998). One of the earliest WECs was Lancaster flexible bag invented by Michael French at Lancaster University which was subsequently developed by Wave power limited in the UK (Platts, 1981). By the early 1980s, the period of high energy prices was ended and consequently the economic and political climate in which WECs were being developed had changed drastically from that in the mid to late 1970s. Nevertheless, research devoted to wave energy converters for the production of electricity continued but a greater emphasis was placed upon the economic analysis of wave energy extraction and efficiency of WECs. As a result, hundreds of WECs with various technologies to efficiently harvest this energy have been proposed during the last decades, see for example Antonio and Falcao (2010) and Lopez et al., (2013). A few of those technologies has reached the sea trial test status. Lindroth and Leijon (2011) have provided a review of various WECs that have made ocean trials, together with the details of the data measurement during the trials. It was demonstrated that, very few of those devices have reported detailed measurements of the performance of the devices which could be due to the great difficulties in working with experiments in a harsh environment.

Babarit (2015) has provided a database for the hydrodynamic performance of various WECs based on the collection and analysis of data available in the literature. The study focused on the capture width ratio of the different technologies. The terms ‘capture width’ and ‘capture width ratio’ instead of efficiency is normally used for evaluating WECs in wave tanks. Capture width is a parameter defined as the width of the wave front (assuming uni-directional waves) that contains the same amount of power as that absorbed by the WEC, see Price et al. (2009). Capture width (Cw) is defined by:Cw=PdPwwhere Pd is the device power and Pw is the wave power per meter.

The capture width ratio, cw, is a better parameter as it is a non-dimensional parameter which best reflects the hydrodynamic performance of various WECs. Capture width ratio reflects the fraction of wave power flowing through the device that is absorbed by the device and defined by:cw=CwWwhere W is a characteristic parameter usually considered as the width of a WEC.

WEC technologies can be broadly classified based on their operational principle to three groups: oscillating water columns (OWCs), overtopping devices and oscillating bodies. Oscillating bodies WECs are usually referred to as Oscillating Wave Surge Converters (OWSCs). Since OWSCs covers a broad range of devices, this category can be divided further into floating (heaving device) and bottom fixed devices (Babarit, 2015). Power can be absorbed from heave, surge, pitch, or some combination of these modes. The majority of existing point absorber devices operates in heave mode alone. However, the potential power capture in OWSC which operate in surge and pitch is twice that of the device working in heave mode, as shown by Falnes (2002). A typical OWSC is the Frog, of which several offshore point-absorber versions have been developed at Lancaster University, UK. The Frog consists of a large buoyant paddle with an integral ballasted handle hanging below it (McCabe et al., 2003, McCabe et al., 2006). The waves act on the blade of the paddle and the ballast beneath provides the necessary reaction. When the wave energy converter is pitching, power is extracted by partially resisting the sliding of a power-take-off mass, which moves in guides above sea level. It is interesting to note that the first two categories (i.e. OWCs and overtopping devices) have been studied for more than 30 years, whereas most fixed OWSCs have only started developing over the last decade. However, as demonstrated by Babarit (2015), the most efficient categories of WECs, in terms of absorbing wave energy, are fixed OWSCs.

OWSCs can be further classified according to their horizontal size. If the extension is comparable to or larger than the typical wavelength, the WEC is called a line absorber. On the contrary, if the size is very small compared to the typical wavelength, the WEC is called a point absorber (Budal and Falnes, 1975, Evans, 1980). Whilst some designs are quite large, there is much interest in ‘point absorber’ devices which are relatively small compared to the most common sea wavelengths, and have the potential for more efficient power conversion, in terms of output per unit volume. This is because during the initial research into the hydrodynamics of wave energy converters it was discovered that bodies with dimensions small relative to the incident wavelengths could act in a similar way to an aerial and capture energy from a width greater than their own width. This became known as the point-absorber theory (Evans, 1980; Falnes and Budal, 1978). At an early stage the theory proposed by Budal and Falnes (1975) that the most promising and economic form of WEC is a point absorber tuned to the frequency of the waves was followed at Lancaster. This theory, however, predicts that such a performance can only be achieved if the device undergoes oscillations whose magnitude may be many times that of the incident wave amplitude. This behavior is not permissible in practice and has led to the development of theories to predict the maximum capture width when the amplitude of the device oscillation is constrained in magnitude but permitted to maintain the frequency of oscillation (Falnes, 2002)

Oyster is a typical example of point absorber OWEC. The concept for this device originated from research at Queen׳s University, Belfast, and is consisted of a buoyant flap which is hinged at the seabed and moves back and forth with movement of the waves. This back and forth oscillations operate hydraulic pistons that feed high-pressured water to a hydro-electric turbine, which generate electric power. The first full-scale prototype of the device was installed at the European Marine Energy Center (EMEC) in Orkney when it began producing power to the grid in 2009. Recently Renzi et. al. (2014) has presented a mathematical model, called ‘flap-type absorber’ which describes the dynamics of Oyster. Another point absorber OWEC that has reached the stage of offshore device testing is a heaving point absorber WEC which was developed at Uppsala University. In the device the collector body which is a floating buoy at the sea surface directly drives a linear generator for power production. The buoy at the sea surface is connected through a wire to a linear generator placed in a capsule on the seabed. The translator inside the linear generator follows the heaving motion of floating buoys, thus inducing a varying magnetic flux in the stationary stator windings, Leijon et al. (2005). Recently Bozzi et. al. (2013) used the boundary element package, ANSYS AQWA, to investigate the feasibility of this heaving point absorber WEC for wave energy exploitation under Mediterranean Sea conditions. Their numerical results show that the estimated power captures are in good agreement with those obtained by Babarit et. al. (2012) for the same device. ANSYS AQWA (2010) was also used by Bhinder et al. (2009, 2015b) for modeling the motion response of a pitching WEC,WRASPA. The capabilities of the method are validated against both corresponding experimental data and a time-domain CFD method. It is shown that the time domain methods offer incorporation of viscous and vortex phenomenon and capturing flow details such as turbulence. These methods however require significant computer resources and long runtimes. The BEM method on the other hand relies on the linear frequency domain hydrodynamic calculation which provides an efficient numerical approach capable of capturing the major features of interest while reducing the solution time to an acceptable level for use in routine design.

One of the widely used boundary-element method package has been WAMIT. An assessment of this package for modeling a free-floating sloped wave energy device, developed at Edinburgh University, was reported by Payne et al., 2008a, Payne et al., 2008b. Although there are significant discrepancies between numerical computations and experimental measurements of the capture width, the agreement is generally good enough, to provide a first assessment of the performance of the WEC. They suggested that the validity of linear boundary-element method for this kind of wave energy converter is case specific. Recently Zurkinden et al (2014) provided an assessment of WAMIT for the prototype of a point absorber OWEC. The laboratory device developed at Aalborg University is similar to the Wavestar float which is located in the Danish North Sea. It was shown that the linear assumption is a good approximation of the physical model of the device. In particular, the capture width predicted using the linear numerical methods agrees well with the experimental capture width.

This paper brings together the latest developments in analyzing numerical and experimental capture width of WRSPA (Rahmati et al., 2008a,b) which is a fixed OWEC operating in surge and pitch mode. A 1:100 scale model of the device was developed. A brief description of the model and its dimension is given in the next section; this is followed by the numerical power estimation and the results of wave tank tests on the scaled model in irregular waves. The experimental results are provided to serve two purposes: the first is to evaluate the actual optimum power of the device in irregular waves; the second is to verify the capability of the numerical method in predicting the optimum power of the device.

Section snippets

The WRASPA device

WRASPA (Wave-driven, Resonant, Arcuate action, Surging Point-Absorber) was developed at Lancaster University for moderate deep water with water depths of 20–50 m. The dynamics of this wave energy converter (Fig. 1) is similar to other bottom-hinged WECs e.g. Oyster (Whittaker and Folley, 2012) and WaveRoller (Lucas et al., 2012). In this device, wave forces act on the face of a collector body carried on an arm that rotates about a fixed horizontal axis below sea level. Accordingly, the body

3. Numerical dynamic performance

Frequency domain analyses are conventionally used as the first step in validation and analysis of the performance of wave energy converters. For the evaluation of motions and forces the program system WAMIT (Wave Analysis, developed at Massachusetts Institute of Technology) for wave/structure interaction at zero-speed is applied (WAMIT, 2002). In the program a three-dimensional panel method using potential theory is implemented (Lee and Newman, 2005). WAMIT solves the equation of motion in

Numerical power estimation in irregular waves

Pizer (1993) showed that the mean power absorbed, P¯IN,opt, by an optimally tuned unconstrained point absorber in a regular wave of amplitude, α, and frequency, f, is given byP¯IN,opt=(qp)2|F1|2α28b55

Irregular waves are often defined by their energy period, Te, and significant wave height (here using the spectral moment definition), Hm0. The equivalent regular wave, in terms of energy capacity, has frequency, fe (=1/Te), and amplitude α=Hm0/22. If the incident wave comprises the superposition

Experiment in irregular waves

The experimental studies of controlled motion of the device, in irregular waves were performed at University of Manchester wave tank. The tank length, width and depth are 18 m, 5 m and 0.6 m respectively, see Fig. 15. Waves were generated by eight Edinburgh Designs piston-type wave paddles which are capable of generating Bretschneider, Pierson Moskowitz, and Jonswap spectra with spectra frequency in range of 0.5–2 Hz. The Bretschneider spectrum wave was generated in the tank for this experiment and

Actual power output and comparisons with other WECs

In Table 2, capture width and wave power of the model at the peak frequency of 1 Hz is shown. It can be seen that a maximum of 935 kW power from a full scale device in real sea climate can be captured which is very significant considering the small size of the device. The range of the capture width ratio of the device is from 33% to 60%. This is significantly less than the range 140–210% predicted by the frequency domain method.

The main reason for these discrepancies is that the commercial code

Conclusion

The optimum power of a point absorber wave energy converter in irregular wave was estimated using a linear potential theory, a method commonly used for evaluating the performance of WECs. Numerical results show that the choice of tuning period has a major effect on the power output of the device. The frequency model predicts that when the device is tuned with the spectrum peak period, it could absorb more than twice energy than was contained in its own geometrical width. The wave tank

Acknowledgments

The authors are indebted to late Dr. Andy McCabe for his help in performing the numerical studies in this study. We would also like to thank the Joule Center (Grant no. JIRP306/02) for providing financial support for this work. We thank two anonymous reviewers for their constructive comments and highly valuable suggestions, which helped us to improve the manuscript. We are also extremely grateful to Bob Chaplin and Tim Stallard for their useful advice, help and guidance given during the

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