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Energies 2019, 12, 2791 3 of 22 an 11.3% increase of the power output compared to the initial design of the blade. Design optimisation methods were also used by Mohamed and Shaaban [31] to predict the performance of a Wells turbine with self-pitch controlled blades. They used parameters in a non-symmetric airfoil shape to identify the optimum design. Optimised sweep angle of the rotor blade of a wells turbine was studied using the surrogate modelling [32]. The optimum blade was reported to have a backward sweep angle at the mid-section and a forward angle at the tip and improved the torque by 28%. Apart from the blade profile, the number of blades and guide vanes were also investigated using the optimisation methods. A multi-fidelity analysis coupled with the CFD was performed to maximize the efficiency of impulse turbine used with an OWC [33]. The authors of this work have completed several studies on design improvement of a unidirectional radial turbine. An analysis of the losses at different sections of a radial inflow turbine was performed, and significant energy losses were reported due to the radial-axial transition of flow at the elbow section. To overcome this problem, the authors suggested an increase of the casing height from the inlet to the outlet of the turbine and elbow sections, which achieved 10% total efficiency improvement [24]. In addition, the downstream section was design optimised for proper coupling with the inflow radial turbine, and it was concluded that a diffuser-shaped duct with a diffusion angle of seven degrees leads to a significant recovery of the kinetic energy [34]. This study focuses on the design optimisation of a unidirectional radial turbine for maximum efficiency in the outward flow direction. The investigation was conducted using CFD, and design optimisation techniques were used to maximise the efficiency of the rotor and upstream guide vanes in a radially-outward-flow configuration over a range of steady-state flowrates. A list of design variables was considered in the creation of the parametric CAD geometry of the rotor blades and the upstream guide vanes. The impact of design variables on the turbine efficiency, output power, input power and flow resistance were analysed, and the most sensitive parameters were identified. In this article, the parametric geometry and input parameters are defined in Section 2. The numerical setup and validation of the numerical model are outlined in Sections 3 and 4, respectively. In Section 5, the setup of the optimisation study and the output parameters are explained, followed by the discussion of the results. In Section 6, the significance of the optimisation study is discussed by comparing the performance of the initial and optimum outflow turbines. In addition, the outflow turbine has been evaluated regarding the rotor energy exchange in a centrifugal radial configuration. Finally, in conclusion, the main findings of this work are provided. 2. Turbine Geometries A bidirectional configuration of a radial turbine extracted from a study by Setoguchi et al. [35] was used for validation of the numerical method and creation of a reference for an initial centrifugal (outflow) radial turbine. The bidirectional turbine geometry has main characteristics presented in Table 1. The initial outflow turbine geometry was designed according to the main geometrical characteristics of the bidirectional turbine. The geometries of the duct and upstream guide vanes (UGVs) were chosen to be similar to that of the bidirectional turbine. In addition, the inner diameter, number of upstream guide vanes and the rotor blades (RBs) were equal in both turbines (more details can be found in [35]). The main differences were, first, using asymmetric rotor blades appropriate for an outward flow direction. Secondly, removing the downstream guide vanes (DGVs) since only outward flow direction was considered as operational. Schematics of the bidirectional geometry and the initial outflow turbine are shown in Figure 1. Table 1. Bidirectional turbine specifications. DGV RB UGV Blade Number 52 51 73 Chord Length 50 mm 54 mm 50 mm Setting Angle 25◦ 19.8◦/35.8◦ 25◦PDF Image | Unidirectional Radial-Air-Turbine OWC Wave Energy Converters
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