# Performance of a Closed Cycle Power Takeoff for a Shore-Based Wave Energy Device
## 1 Introduction
Whether the sea level in the sea chamber of the OWC is rising or falling, the pressure in the HP reservoir is always above that in the LP reservoir, and thus the flow across the turbine is unidirectional. This is the principal benefit of this arrangement. An additional benefit is that, during excessive sea states, the turbine and generator set can easily be protected simply by venting the pressure chambers. To understand the operation of the closed cycle PTO, consider the wave cycle as two half cycles: a compression process and an expansion process. During the compression process, the rising water surface in the sea chamber compresses air, raising the pressure, \(P_{S}\), in this chamber. For a short time, both valves are closed. This is not achieved by active control of the valves but by the temporal variation in the pressure in the three chambers. When the sea chamber pressure rises above the pressure in the HP reservoir, \(P_{H}\), the HP valve opens while the LP valve remains closed. For the remainder of the compression process, the OWC compresses all the system's air through the HP reservoir, turbine and LP reservoir. Due to the pressure drop across the valves and turbine, the LP pressure, \(P_{L}\), is always lower than the HP pressure, \(P_{H}\). Hence, the LP valve remains closed during the OWC compression process. During expansion, the opposite happens. The sea level drops in the sea chamber, reducing the pressure, until \(P_{S}\) is below the HP pressure, \(P_{H}\), which causes the HP valve to shut off. As the pressure \(P_{S}\) continues to drop, it will fall below the LP pressure, \(P_{L}\), causing the LP valve to open. From this point on, the expansion process is expanding the air in the HP and LP reservoirs into the sea chamber. The compressibility of the air means that the pneumatic spring effect is asymmetric around the equilibrium, with the compression cycle experiencing a harder spring than the expansion. Thus, the system is nonlinear, and it is necessary to model the CCPTO in the time domain. A reduced order model for the CCPTO is introduced in Section 2.1. A key component of the system is the turbine: it is essential to ensure that an efficient turbine can be designed that is suitable for this application. To design the turbine, the specific conditions encountered in the CCPTO are needed. This includes characteristics such as the nominal pressure drop and mass flow rate, as well as their variation. To obtain realistic estimates of the turbine working conditions, the reduced order model of a CCPTO was applied to a notional shore-based installation that would be compatible with Mutriku breakwater. Mutriku is a fixed OWC structure installed into the breakwater at the entrance to the port of Mutriku, Spain. It is the world's first multi-turbine wave energy facility and was first connected to the grid in 2011. The breakwater consists of 16 air chambers. In each chamber, an open cycle OWC system has been fitted with an 18.5 kW Wells fixed-pitch turbine, providing a total capacity to the plant of 296 kW, although in practice the actual achieved power is much lower (the capacity factor reported is 11% or an average power output of 28 kW [17]). Section 2.2 presents the results of the reduced order model for the breakwater at Mutriku. The turbine design process is then shown. It is divided into two parts: the preliminary 1D design in Section 2.3, followed by a CFD analysis and refinement in Section 2.4, yielding detailed performance characteristics. Finally, the resulting performances expected for the designed turbine in Mutriku's breakwater are presented in Section 3.