Hydrodynamic responses and efficiency analyses of a heaving-buoy wave energy converter with PTO damping in regular and irregular waves
Introduction
The global power potential carried by waves in the open sea has been estimated to be on the order of 1013 W, which is almost comparable to the world's current power consumption [1]. The utilization of ocean waves by human can trace back to more than two centuries ago, and hundreds of wave energy converters (WECs) have been developed till now [2]. Generally, the utilization of the wave energy is composed of two conversion steps: in the primary conversion step, the wave energy is captured from the sea with a WEC, which generally can be classified into oscillating water column (OWC), overtopping device and heaving body types, etc., depending on the operational principle [3], [4], [5], [6], [7], [8]; in the second conversion step, the mechanical energy or potential energy captured by the WEC is utilized to generate electricity by a variety of power take-off (PTO) systems, such as air turbines, water turbines, hydraulic motors and direct-drive linear generators, etc. [9]. There have been a number of literature reviews on PTO system, power performance and construction technology of WECs [1], [2], [9], [10], [11].
Recently, a concept design for a bottom-standing wave power generator, which is suitable for near-shore conditions, was proposed, as shown in Fig. 1. In the primary conversion step, the wave energy is captured with a heaving buoy. In the second conversion step, a liquid metal magnetohydrodynamic (LMMHD) generator, which is similar to the one studied by Liu et al. [12], is driven by the heaving buoy to generate electricity. This type of wave power generator is easy to construct in the near-shore condition because it can be installed as a whole system on the sea bottom after assembling each part of the system onshore. Furthermore, the LMMHD generator has higher energy conversion efficiency than most of conventional PTO systems because it does not require a mechanical interface and thus avoids the non-negligible friction losses in the mechanical machine. Additionally, as one type of direct-drive linear generators, the LMMHD generator can utilize the power performed by the wave excitation force to a maximum extent whenever the buoy goes up or down [9].
Theoretical analyses and numerical simulations are usually conducted at the early stage of design of a WEC. A number of investigations have been performed on the optimization of the geometry size and efficiency of a heaving buoy for wave energy capture based on mathematic methods [13], [14], [15], [16], [17], [18]. The early theoretical studies on a heaving body or OWC converter revealed that to make the device an efficient absorber, its frequency of oscillation should match the frequency of the incident waves, i.e., it should operate under near-resonance conditions, i.e., the body velocity in phase with the excitation force [9]. A variety of advanced control methods, such as phase control and latching control, were proposed to minimize the phase difference. In the phase control method [14], [15], [16], a spring is introduced to adjust the natural frequency of the oscillating body to match the dominant wave frequency. In the latching control method [17], [18], [19], the motion of the body is locked at the moment when its velocity vanishes at the end of one oscillation, and the body is released under the most favourable conditions to achieve the approximate optimal phase. The amplitude of the motion and the year-average power production of a heaving buoy can be effectively magnified when a control method is applied [14], [15], [16]. However, to optimally determine the latched time interval in real irregular waves is a complicated theoretical control problem, which, in addition to requiring relatively heavy computation, also requires the prediction of the incident irregular waves sometime in the future. There are still many practical challenges to be solved before the advanced control is feasible [2]. Thus, in the present study, only passive control (without the advanced control) is considered at the early stage of design.
In many cases, the large-amplitude motion of a heaving device introduces significant nonlinearities to the dynamic systems of a WEC and creates difficulties in the understanding and analysis of the system. Although mathematical methods can manipulate the advanced control, the main limitations are the inability to account for losses in water due to real (viscous) fluid effects (large eddy turbulence) and the inability to accurately model large-amplitude water oscillations (nonlinear waves) [20]. These effects are important. It has been reported that the maximal difference between the experimental and theoretical results can be up to 37% [19]. Thus, small-scale models are often tested under laboratory conditions in a manner that some of the dynamic effects can be isolated. The analysis and understanding of the dynamic process can be simplified and specified. Sheng et al. (2014) presented a theoretical analysis of the requirements and explanation to the feasibility of physical modelling and some important scaling issues in the physical modelling of WECs [11]. For a heaving-buoy WEC, Su et al. [8] experimentally studied the wave capture efficiency of a heaving buoy installed onshore, where the wave energy was much lower than that of near-shore conditions due to the wave dissipation when approaching the shore. Kang et al. [21] conducted flume tests on an oscillating buoy with constant damping and showed that the heaving response of an oscillating buoy reaches resonance when the period of incident waves is delayed slightly compared with the natural heaving period of the buoy due to the damping system. Hager et al. [22] showed that a circular cylinder buoy with convex face performed better than a cuboid buoy with flat faces. The above experimental studies were mainly conducted under regular waves, and the ranges of the wave parameters were limited.
When a WEC is working in real sea conditions, it encounters irregular waves. There were a few studies on the power performance of a heaving-buoy in irregular waves using mathematical methods [17], [23], [24], [25], while the published experimental studies were rare. How to apply the experimental results under regular waves to the real wave condition has not been quantitatively investigated. Furthermore, there was still few effort on the effect of PTO damping on the behaviour and power performance of a heaving-buoy WEC.
In this study, a series of model tests are conducted in a wave flume to investigate the power performance of a heaving-buoy WEC in regular and irregular waves. Various air dampers are employed to simulate the LMMHD PTO damping of different power rates. The effects of the incident wave amplitude, frequency and PTO damping on the dynamic response and power capture efficiency of the WEC are studied. The wave energy absorption in irregular waves is also determined and compared with that in regular waves. Finally, the flows around the heaving buoy are visualized, and the formation of vortex structures around the buoy is analysed.
Section snippets
Experimental methodology
In developing a WEC, the important issues are the assessment of the hydrodynamic response and its wave power capture capacity. The responses of a heaving buoy involve complex interactions between waves and the structure with damping. It is noted that only the heave motion of the buoy is considered in this study, based on the operation principle of the LMMHD generator. The governing equation of the buoy motion in heave can be expressed as below:in which is the
Heave motion of the buoy
As mentioned in the introduction, the resonance is indicated by a zero phase difference between the buoy velocity and wave excitation force. For the present study, this corresponds to a zero phase difference between the buoy velocity and wave elevation, i.e., a π/2 phase difference between the buoy motion and the wave elevation, assuming that the wave excitation force is in phase with the wave elevation for a long wave period [26]. Fig. 3(a) ∼ (e) show the time histories of the wave elevation a(
Conclusions
In this study, a series of experiments were conducted in a wave flume to study the power performance of a heaving-buoy WEC with an LMMHD generator under regular and irregular waves. In the model tests, the PTO was simulated using a series of air dampers. The effects of some influential factors, including the incident wave height, frequency and PTO damping, on the maximum heave displacement, phase angle between the buoy velocity and wave elevations, and the capture width ratio were
Acknowledgement
This research was supported by the General Programs (Grant no 51579232) and the Science Fund for Creative Research Groups (Grant no 51321065) of National Natural Science Foundation of China and the Open Funding of State Key Laboratory of Hydraulics and Mountain River Engineering. The authors also would like to appreciate Institute of Mechanics, Chinese Academy of Sciences for providing the test facility.
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