Novel experimental modelling of the hydrodynamic interactions of arrays of wave energy converters

https://doi.org/10.1016/j.ijome.2017.11.003Get rights and content

Highlights

  • A novel approach for experimental modelling of WEC arrays interactions is presented.

  • The q-factor for two heaving and surging generic WECs is derived.

  • Constructive and destructive interactions were found.

  • The Stereo videogrammetry technique was adapted to measure the wave field.

Abstract

Wave energy converters (WECs) range significantly in respect of concepts, technologies and design maturation, with the majority of devices at an early commercial stage. To date, most large scale deployments have been conducted with a single WEC. However, there is a necessity to expand these to ‘arrays’ or ‘farms’ in the future in order to reduce both installation and maintenance cost per unit as well as harnessing maximum energy at a given site. There are complex hydrodynamic and environmental implications which require consideration when moving from a single device installation to an array of devices. Many theoretical and numerical studies exist in this domain, however, limited experimental investigations have been performed due to the cost and size related to testing facilities as well as the complexity of the experiment and related instrumentation.

This paper presents a novel experimental approach, performed as part of a larger project, aiming to address a critical knowledge gap: understanding the performance of WEC arrays, and to develop a methodology to accurately model an array of WECs. The experimental investigation utilised Australia’s most technically advanced wave basin at the Australian Maritime College, specialist institute of the University of Tasmania. For the first time, it applied the phenomenological theory to experimental hydrodynamic investigation of array of generic WECs by separating the problem into its diffraction and radiation problems. Such approach removes the need of power-take-off modelling and control. Using a post-processing analytical model, the q-factor, the parameter representative of the array performance, for several configurations can be derived. Furthermore a bespoke stereo-videogrammetry method was developed to measure the wave field around and in the lee of the array. This paper describes the hydrodynamic approach and experimental methods developed as part of this project and presents preliminary results related to array q-factor and wave field measurements.

Introduction

Ocean gravity waves are one of the most energetic sources of renewable energy, yet remains underutilised in the commercial energy market. In Australia solely, Hemer and Griffin [1] demonstrated that the southern coastline between Western Australia and Tasmania, which are subject to unrestricted westerly swells from the Southern ocean, have a consistent resource of 1329 TW h/yr, roughly five times the nation’s current energy requirement. While there is clearly a high energy resource available, there are significant technological and economic challenges hindering the capture of this energy [2]. As Behrens et al. [3] discuss, the challenge for wave energy is not availability, but rather the economics of extraction and distribution, as well as the environmental impacts of extracting extensive wave energy from the coastal ecosystem, especially when wave energy farms will potentially consist of up to or exceed one hundred devices.

Australian wave energy converter (WEC) concepts and technologies range significantly with each operating under differing hydrodynamic principles, and design maturation with the majority at an early-commercial stage with further validation required before large scale arrays can be deployed. Large scale wave energy projects are currently underway in multiple locations in Australia. These include Tasmania, where Wave Swell Energy is planning on installing a 1 MW commercial demonstrator of its novel vented OWC type WEC off the west coast of King Island in 2018, Victoria, where BioPower Systems’ has installed the 250 kW BioWave device in Port Fairy, Western Australia, where Bombora Wave Energy’s 1:7 scale mWave device is operating in the Swan River and Carnegie Wave Energy’s CETO5 devices at Garden Island. In fact, Carnegie Wave Energy is the first to have demonstrated an array of three devices – the largest of its kind.

While the development process for a single device is relatively well established, the knowledge base for WEC array performance and impact is still limited in large majority by theoretical and numerical studies. Development of knowledge in this area is crucial if in the future significant contributions of energy from large scale WEC arrays is intended [4].

In understanding arrays, the first issue comes from the scattering and radiation effects within farms of WECs. Optimisation of multiple devices has to include positioning as scattering and coupling effects can induce constructive or destructive interactions (see [5], [6]). There is also a need to develop algorithms for the power take-off (PTO) parameters due to the coupling induced by the radiated waves (see [7]). By absorbing wave energy, farms might also impact on the hydrodynamic environment of the site which can lead to changes in current and sediment transport surrounding and in the lee of the WEC array (see [8]).

Most of the experimental investigations have been carried out using heaving buoys. For example, the work reported in Troch et al. [9] describes a study where twenty-five heaving buoys were put in rectilinear arrays with twelve different configurations. They found that the impact of power absorption on local wave climate is significant. Yet, the estimation of the relative performance of the array through the measurement of the q-factor was not reported (the definition of q-factor, as applied to WEC arrays, is described further in Section 3.2). In fact, presently there are not many works available in open literature where one can find such q-factor measured in experiments. The work reported in [10] is one exception. The devices used were a combination of OWC and overtopping type devices. Highest q-factor was achieved for one specific combination of water depth and separation between devices.

A detailed review of analytical and numerical works on WEC arrays have been reported in [11]. A comparison of the performance of few available numerical models in modelling WEC arrays can be found in [12]. Many of array models are based on the well-known potential flow theory solving diffraction and radiation boundary-value problems. Most of the numerical methods based on this theory include finite element method models (see [5], [7]), boundary element method models (see [13], [14]), and the eigenfunction expansion method [15], [16]. The point absorber theory [17], [18], [19] is perhaps the most common theory used for fast calculation of q-factors. However, it is an approximation where the devices are considered small compared to the wavelength and can be erroneous for larger devices. The optimisation of power output from WEC arrays in the presence of PTO is another important emerging topic. Related works can be found in [20].

Most techniques to measure wave elevation use a cluster of resistive wave probes. An alternative method to gain measurements of finer resolution of the water free surface is the use of stereo photographic images; this was used as early as 1960 by Cote [21] where a plane mounted system was successfully used for the measurement of ocean wave spectra. On a smaller scale the photogrammetric method has been well developed for the deformations of many structures and materials capable of being photographed including the flexible membrane of a WEC [22] for example. The use of videogrammetry, being photogrammetry changing in the time domain, for the measurement of a water free surface was examined by Benetazzo [23]: it was found that the principle difficulty was the balance of gained field of view by increasing distance from the surface, and the consequent loss of resolution in the images of the surface. Ultimately it was found that videogrammetry is a highly effective method for water surface measurements where highly accurate results of the three-dimensional space are required.

The experiments presented in this paper represent a novel study into the radiation and diffraction response from an array of generic WEC devices. The experimental approach made use, for the first time, of the superposition principle applied in linear WEC modelling techniques to determine the performance of an array of devices. Furthermore, stereo videogrammetry was adapted and applied to accurately measure the wave climate throughout and downstream of the array. The results from this study is a valuable addition to the current requirement for experimental observations in WEC array hydrodynamics and a benchmark for validating current and future numerical models.

The work undertaken here is part of a larger project funded by the Australian Renewable Energy Agency (ARENA) and supported by the Commonwealth Scientific and Industrial Research Organisation (CSIRO) and two Australian wave-power companies, Carnegie Wave Energy and BioPower Systems. The outcomes of this project include a web-based tool to estimate the true potential of an array using a generic technology that will allow government policy-makers and investors to quickly appreciate the potential of ocean wave power at various locations around the Australian coastline, [24].

Section snippets

WEC and array characterisation

The validity of the present work is restricted to resonant devices, which are the majority of WECs [25]. The underlying assumptions are that the device PTO systems are linear and the wave and device motion amplitudes are small. Including the usual assumptions of inviscid and incompressible flow, the linear water wave theory can be considered. The superposition principles can then be applied where the response of the system to a wave spectra can be divided into the sum of the different

Formulation

For this formulation, we consider an array of n of these WECs, resulting into n degrees of freedom for the whole array system. The devices operate in constant water depth h and have a constant identical volume V and mass m, as seen schematically in Fig. 2. It is noteworthy that a device with both heaving and surging motion can simply be considered as two different buoys of one degree of freedom in this approach. It is also assumed that the PTO system engenders a linear damping coefficient μi

The AMC Model Test Basin

The AMC’s Model Test Basin was used to perform the experiment. The basin is 35 m long, 12 m wide and allowing a water depth up to 1 m (refer Fig. 3). The water depth for this experiment was kept constant at 600 mm. A pit was utilised for this experiment to house the linear motor and frame for the active model, such that this equipment was located in the basin floor. The north side of the basin includes the wave maker while an artificial beach is set up on the opposite side of the basin in order

The excitation force coefficients (diffraction problem)

The results from the diffraction problems allow the derivation of the excitation force coefficients, Γi, for each frequency and configurations. Γi can be written as,Γi=||Γi||eiϕΓi,where ||Γi|| is the complex norm and ϕΓi is the angle of Γi. We could then determine the excitation force and angles as,||Γi||=|Fh,i|η0,ϕΓi=ϕFi-ϕ0,where |Fh,i| and ϕFi are the amplitude and phase of the hydrodynamic force on the device and ϕ0 is the reference phase chosen as the phase wave probe phase.

The radiation impedance coefficients (radiation problem)

The radiation

Results and discussion

A total of 1447 experimental runs were completed in the test session during which many challenges were faced: the common affliction of any novel approaches. The challenges included the new application of stereo videogrammetry and positively-buoyant fluorescing particles to quantify the water surface elevations over a sizable area; deployment of sensitive instrumentation underwater when relatively small forces are to be measured; and automation of the experiments to make maximum use of the

Conclusion

An innovative approach to understanding the performance of ocean wave energy converter arrays has been outlined. The approach combines a novel series of physical experiments with a phenomenological theory, whereby the hydrodynamic forces on each WEC are separated as the sum of coefficients from the various different wave sources. To the authors knowledge this experiment and the methodology is the first of its type and carries significant novelties.

Here the use of one physical model to represent

Acknowledgements

We are grateful to the Australian Renewable Energy Agency (ARENA) who supported this work through their Emerging Renewables Program (grant A00575). The following people provided valuable assistance during the experimental program: Liam Honeychurch, Kirk Meyer, Jeremy Ledoux, Romain Briand, Aidan Bharath and Brian Winship.

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