Nonlinear hydrodynamic modeling of an offshore stationary multi-oscillating water column platform

Highlights

• Numerical and experimental studies on a multi-OWC platform were carried out.

• A second-order time-domain HOBEM model for an arrayed OWC devices was developed.

• Multi-interactions among the OWC devices can lead to a higher power generation.

• Strategic design of the spacing can produce an optimal capture efficiency.

Abstract

The hydrodynamics of an offshore stationary platform consisting of four cylindrical Oscillating Water Column (OWC) Wave Energy Converters (WECs) are considered in this paper. Based on the potential flow theory, a second-order Higher-Order Boundary Element Method (HOBEM) model is developed to simulate the wave interaction with the multi-OWC platform in time domain. Laboratory tests of a carefully instrumented scale model are also conducted, and the results from the two methods are compared for the validation. It is found that the linear model overestimates the relative capture width of the OWC device by approximately 10% around the resonant frequency. Subsequently, the hydrodynamic properties of the multi-OWC platform are investigated systematically in terms of the air pressure and free surface oscillations in the chamber, as well as the relative capture width. The isolated cylindrical OWC device is also considered for the comparison. The effects of the incident wave direction, the column and row spacing between the OWC devices are explored. The surface elevation distribution inside and around the OWC device is discussed. The occurrence of the maximum free surface elevation inside the chambers is found to lag behind the crest of the incident wave. The optimum angle of wave incidence in terms of energy capture is β = 0, i.e. multi-OWC platform aligned with the incoming waves. A strategic design of the column and row spacing can lead to a significant improvement for capturing wave energy.

Introduction

Wave energy is one of the most promising sources of renewable energy under development (López et al., 2013); however, wave energy capturing technology is still relatively immature, with only very few systems having reached commercial stage – which highlights the need for further research (Ahamed et al., 2020). Among a variety of Wave Energy Converters (WECs), the oscillating water column (OWC) WEC has been studied and applied widely due to its mechanical and structural simplicity (Zabala et al., 2019). The OWC device consists of a partially submerged chamber (either fixed or freely floating) and an air turbine (Falcão and Henriques, 2016). The air flow generated by the free surface rising and falling within the OWC chamber (i.e. the oscillating water column) drives a bi-directional air turbine coupled to a generator. OWC WECs have attained the full-scale prototyping stage worldwide, e.g. the OE Buoy tested by MaREI in Ireland (which at the time of writing is about to be deployed off Hawai), the Mighty Whale in Japan, the Oceanlinx Mk3 in Australia and the Spar-buoy OWC in UK (Falcão and Henriques, 2016). Moreover, an OWC plant has been in commercial operation in Mutriku, Spain, since 2011 (Ibarra-Berastegi et al., 2018). However, the real challenge for wave energy capturing technology is to develop WEC(s) with lower costs and higher conversion efficiency (Gaebele et al., 2020). To achieve this, WECs will typically be deployed in arrays, i.e. in the form of a wave farm, so as to reduce the Levelised Cost of Energy (LCOE) (Astariz and Iglesias, 2016). Indeed, for a wave farm the LCOE can be reduced by realizing economies of scale and sharing a number of elements, such as the export cable or the mooring system (Astariz and Iglesias, 2015; De Chowdhury et al., 2015). In addition, for certain arrangement the multi-interactions among the WECs in a wave farm can lead to a higher power generation (Vicente et al., 2009). Nevertheless, the commercial-scale deployment of a WEC farm is still uncompetitive when compared with other fuel-based sources (Doyle and Aggidis, 2019).

A multi-functional marine platform equipped with WECs is a promising alternative, which reduces the construction costs and utilizes the ocean space efficiently when compared to an individual floating platform and WEC (Wan et al., 2015; Zhao et al., 2020a). And a number of novel concepts for multi-purpose integrated platforms have been proposed (Naty et al., 2016; Zhao et al., 2020b). Zhang et al. (2017) proposed an elastic platform integrated with an array of floating buoyant columns, which provides novel design guidelines for such facility. It is found that the anti-phase motions between the platform and buoyant columns can enhance the performance in terms of energy absorption. Zheng et al. (2019a) presented an analytical model to evaluate the performance of an array of OWC WECs integrated into coastal structures. The hydrodynamic interactions between the WECs and the coastline increase the power extraction significantly. Based on linear potential flow theory, Zheng et al. (Doyle and Aggidis, 2019) further developed a semi-analytical model to simulate a rectangular breakwater incorporating multi-OWC WECs. The effects on the wave attenuation and power extraction of the Power Take-Off (PTO) control strategies, the number of chambers and the geometrical parameters were assessed systematically. He et al. (2017) carried out an experimental investigation to examine the wave power extraction of a dual-chamber OWC WEC integrated into a floating breakwater. It was concluded that the WEC with a shallower chamber draft achieves a higher peak power extraction.

The functional integration between a wind turbine and an OWC device is another successful concept for extracting multiple marine resources by means of one hybrid system (Perez-Collazo et al., 2018). The characterization of a hybrid wind-wave system which integrates an OWC WEC with an offshore wind turbine on a monopile foundation has been investigated experimentally and numerically by Perez-Collazo et al. (2019). Based on the Boundary Element Method (BEM), Zhou et al. (2020) further discussed the hydrodynamic wave force on the monopile of this hybrid system. Based on linear potential flow theory, Michele et al. (2019) developed an analytical model to analyze the effects of a skirt on an OWC device integrated into an offshore wind turbine monopile. Sarmiento et al. (2019) performed scaled model testing on a multi-use floating platform embedded with three cylindrical OWC devices. The experimental result suggested that the turbine damping has limited influence on the hydrodynamic response of the whole floating platform. Mazarakos et al. (2019) carried out a hydro-aero-elastic analysis of a floating wind turbine integrated with OWC devices. It was found that the PTO damping has little influence on the horizontal motion of the platform.

In this work, the hydrodynamics of an offshore stationary multi-OWC platform consisting of four cylindrical OWC devices are simulated. This platform could be integrated with an offshore wind turbine; the optimized design/arrangement of which could be informed by the hydrodynamic analysis carried out in this work.

Extensive research on the wave interaction with OWC devices (either be a stand-alone device or as a component of arrays) has been carried out (Zheng et al., 2019b), using experimental, theoretical and numerical analyses (Ulazia et al., 2020). Based on linear potential flow theory and the eigenfunction matching method, Martins-Rivas (Martins-Rivas and Mei, 2009) derived an analytical model for a thin-walled OWC device along a straight coast. Zheng et al. (2019b) further extended Martins-Rivas's (Martins-Rivas and Mei, 2009) model to investigate the influence of the wall thickness, radius and draft of the OWC chamber on the wave power absorption. The limitations associated with e.g. the wall thickness in Martins-Rivas (Sarmiento et al., 2019) were removed. It is found that due to the wave reflection of the coast/breakwater, the capture efficiency can be twice as large as in the offshore case. Konispoliatis and Mavrakos (2016) presented an analytical model to evaluate the hydrodynamics of an array of freely floating OWC devices; the first- and second order mean wave forces, the air pressure and the capturing efficiency were considered. Konispoliatis et al. (2016) further used this analytical method to solve the diffraction and radiation problems around a three-unit array of OWC platform. Nader et al. (2014) applied a linear Finite Element Method (FEM) model to investigate the performance of an array of OWC devices; three different types of array arrangement were considered. It is shown that the overall power extraction and the effective frequency bandwidth increase with the array arrangement considered.

The linear theory mentioned above is incapable in capturing all the detailed physics involved in the problem, including strong nonlinearities, complex viscous effects and vortex shedding (Rezanejad et al., 2013; Yang and Zhang, 2018). Nonlinear numerical models have thus been developed and the experimental tests been conducted to investigate the strong nonlinear wave interaction with OWC devices (Elhanafi et al., 2017; Ning et al., 2019). A triangular arrayed spar-buoy OWC experiment was carried out to model the wave dynamics, the energy extraction and the mooring system dynamics in both regular and irregular waves (Da Fonseca et al., 2016). It was observed that the spar-buoy device with a heavier ballast can improve the energy conversion performance. Xu and Huang (2018) performed a series of wave flume tests to evaluate the performance of a dual-functional wave power plant. Such dual-functional integration can not only significantly increase the capture width ratio of the OWC devices, but also reduce both the reflection and transmission coefficients when acting as a breakwater.

Based on the Navier-Stokes (N-S) equations, Shalby et al. (2019) constructed an incompressible 3D Computational Fluid Dynamics model for the cases of a fixed multi-chamber OWC device. The CFD predictions agree well with the experimental measurements collected in all chambers. Dai et al. (2019) used the Reynolds Average Navier-Stokes (RANS) method to investigate the scale effects on a fixed OWC device. Compared with the large-scale model, the small-scale CFD simulation underestimates the peak capture factor by about 22.9%. Based on the RANS-based CFD model and experimental campaign, Lopez et al. (López et al., 2020) quantified the error in the assessment of the capture width ratio of OWCs when the air compressibility is neglected. It was concluded that the errors could be significant on resonant period and capture width ratio. Simonetti et al. (2018) evaluated the error induced by neglecting the air compressibility using a compressible CFD model. An overestimation up to 15% occurs for both the air volume flux and the air pressure inside the OWC chamber, but less than 10% for the capture width ratio.

It has been demonstrated that the CFD-type model can be an effective tool for investigating OWC devices. However, the computational efficiency of these CFD models is low, especially for the simulation of the 3D array OWC devices (Ning et al., 2015; Huang et al., 2019). Recently, the time-domain Boundary Element Method (BEM) has been applied to simulate the nonlinear wave interaction with the OWC devices (Wang et al., 2018; Koo and Kim, 2010). Wang et al. (2020) applied a 2D time-domain higher-order boundary element method (HOBEM) to investigate the wave loads on a land-fixed dual-chamber OWC device. A shorter curtain wall draft is suggested for the smaller wave load and larger power capture efficiency (Ning et al., 2019). A 3D time-domain HOBEM model is used to evaluate the wave loads on the monopile of a wind turbine integrated with a cylindrical OWC device (Zhou et al., 2020).

This paper focuses on the study of the hydrodynamics of an offshore stationary multi-OWC platform. The primary objective is to evaluate the wave energy capturing of the system using a nonlinear HOBEM numerical model. The effects of the incident wave direction, the column and row spacing on the hydrodynamic performance are considered. The rest of the paper is organized as follows. Section 2 presents mathematics associated with a 3D nonlinear time-domain HOBEM model. A nonlinear PTO damping effect is introduced on the surface boundary conditions inside the OWC chamber to simulate the effects of the air turbine. The numerical model is validated by comparison with the experimental results in Section 3. Section 4 discusses the effects of the wave direction and the array layout (column and row spacing). Finally, conclusions are summarized in Section 5.