# Performance of a Closed Cycle Power Takeoff for a Shore-Based Wave Energy Device
## 1 Introduction  
Ocean waves as a renewable energy source offer a relatively high energy density and limited impact on competing land uses (e.g., agriculture, tourism). Wave power has long been recognized as an attractive potential renewable energy source due to its high density and availability worldwide, with early attempts documented in the late 19 th century [1]. The ready availability of petroleum suppressed interest in harvested energy sources such as wave power [2]. However, the oil shocks of the 1970s and the growing interest in low-carbon electricity production have resulted in a large variety of concepts at various stages of development. For example, in 2010, it was estimated that there were over 100 active wave energy projects [3], and it has been reported that there have been over 1000 different prototypes tested [4]. While [PERSON] et al. [5] have attempted to identify the \"optimal\" design concept, the indices used are open to debate. The difficulty in development is caused in part by the variability in the wave energy resource at a wide range of timescales due to individual waves (seconds), weather (days), seasonal variations (months) or even climatic events (years). Nonetheless, the resource has good predictability and is decorrelated with wind and solar power [6]. Furthermore, the potential resource is significant. For example, it has been estimated that the Northeastern Atlantic potential could be as much as 290 GW [7], while the global potential power of ocean waves impinging on coasts is estimated at 1 TW [3]. The first commercial wave energy converter (WEC) was designed by [PERSON] in Japan in 1965 and consisted of a floating oscillating water column (OWC) device [8]. In an OWC, the wave action drives the water in a chamber open to the sea, which in turn drives air through a turbine. While work continues on floating OWC devices for both the small scale (e.g., [9]) and large scale [10], there have been several examples of fixed OWCs, either shore-based (e.g., Pico, LIMPET) or bottom standing in shallow water near shore (e.g., OSPREY, Oceanlinx). The Pico plant was a 400 kW OWC with a Wells turbine commissioned in 1999 in the Azores, Portugal [11]. A similar 500 kW device, called the LIMPET, was installed in Islay, Scotland [12]. The OSPREY in Scotland and the Oceanlinx in Australia were both large scale near shore, bottom standing OWC devices, but both were destroyed shortly after deployment. However, a comparable device was successfully deployed near Jeju Island, Korea [8], and interest in near shore installations of OWC devices is continuing (e.g., [13]). Wave energy conversion based on OWC devices whether floating or fixed offers several advantages: the mechanism is not submerged; the sea chamber can provide an effective gearing of the flow and perhaps the most useful is that the energy presented to the turbine (i.e., in the air) can be dramatically reduced by venting in highly energetic sea states [9]. The main disadvantage is that the flow of air across the turbine is bidirectional; i.e., the airflow reverses twice per wave cycle. This has been overcome to some extent with self-rectifying turbines (e.g., Wells, axial impulse or biradial turbines) [14], but these can have poor performance as the rotational speed of the turbine is nearly always mismatched to the instantaneous airflow velocity. A closed cycle power takeoff (CCPTO) system consisting of two large air reservoirs connected by a unidirectional turbine has been proposed [15], and this arrangement was examined for a floating installation [16]. In those studies, the turbine performance was not considered directly. In the CCPTO arrangement, shown conceptually in Figure 1, the power takeoff consists of three air chambers: the sea chamber, which is exposed to the OWC, the high pressure (HP) reservoir and the low pressure (LP) reservoir. The sea chamber is connected to the HP and LP reservoirs by non-return valves, while the HP and LP reservoirs are connected by the air turbine.