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shown in Figure 10b. It is obvious that a higher GV angle causes a lower input coefficient. As the input parameter is related to the pressure, this can be justified regarding the influence of the GV angle on the pressure drop and losses in the turbine domain. This fact was also reported in a study by Setoguchi et al. [35], in which for a fixed LE angle, there is a reverse relationship between the angle of the upstream guide vanes and the CA parameter. The LE angle affects the input coefficient by Energies 2019, 12, 2791 11 of 22 shaping the blade flow passage and affecting the VR term in the definition of CA in Equation (2). As illustrated in Figure 10c, the LE angle has the highest contribution among the variations in torque coefficient. Increasing the LE angle causes more inclination of the rotor blade and reduces the area The sensitivity of output parameters regarding the rate of changes applied to each input parameter and flow velocity at the mean radius of the rotor (known as AR and VR respectively). These terms was evaluated and shown in Figure 10. The local sensitivity statistics were generated regarding the contribute to the CT as defined in Equation (1). The sensitivity of the turbine total to static efficiency trend of the efficiency at the optimum design point and determined the rate of impact of each parameter to the studied input parameters is shown in Figure 10d. It is observed that the efficiency is mostly on the efficiency variations. The local sensitivity is an exploration tool included in the response surface, affected by the LE angle followed by the GV angle and TE angle. The LE angle being an effective which analyses the weight of each input parameter on the output parameters independently [43]. If the parameter on both CT and CA, has a positive effect on the efficiency due to its higher impact on the increase of a parameter fulfils the objective function in the optimisation journey, that parameter is shown torque coefficient than the input coefficient. The negative effect of the GV angle can also be explained with a positive sign. In other words, the positive and negative bars in Figure 10 show the increase and by its effect on the input power and flow coefficient terms. decrease of the parameter, respectively, with respect to its initial values in the reference geometry. 70 50 30 10 -10 -30 nergies -50 (a) 2019, 12, x FOR PEER REVIEW GV Angle Chord length LE Angle TE Angle LE Radius PS Radius Stagger Angle Flow Coefficient 70 50 30 10 -10 -30 -50 (c) GV Angle Chord length LE Angle TE Angle LE Radius PS Radius Stagger Angle Torque Coefficient 70 50 30 10 -10 -30 -50 GV Angle Chord length LE Angle TE Angle LE Radius PS Radius Stagger Angle Input Coefficient (b) o3 E7 70 50 30 10 -10 -30 -50 (d) GV Angle Chord length LE Angle TE Angle LE Radius PS Radius Stagger Angle Efficiency Figure 10. Local sensitivity of input parameters at the optimum design point. Local sensitivity of the Figure 10. Local sensitivity of input parameters at the optimum design point. Local sensitivity of the input parameters on the: (a): Flow coefficient; (b) Input coefficient; (c) Torque coefficient; (d) Efficiency. input parameters on the: (a): Flow coefficient; (b) Input coefficient; (c) Torque coefficient; (d) Efficiency. Considering the local sensitivity data illustrated in Figure 10a, the angle of the guide vane (GV angle) affects the flow coefficient significantly. It is obvious that an increase of the GV angle It should be noted that changes to the combination of input parameters lead to the optimum leads to a wider area between the upstream guide vanes and reduces the flow incidence and losses design point, however, the 3D response of efficiency based on the two most sensitive parameters (LE at the rotor upstream to a high extent. The LE angle has a reverse effect, which can be explained by angle and GV angle) is illustrated in Figure 11. This figure shows that the optimum efficiency was the role of this parameter in shaping the flow passage between the rotor blades. Increasing the LE identified clearly within the specified variation bounds of these two parameters. angle in the rotor geometry of this study leads to a narrower blade to blade area and increases the resistance to the flow at the rotor inlet. The input coefficient is mainly sensitive to GV angle and the LE angle as shown in Figure 10b. It is obvious that a higher GV angle causes a lower input coefficient. As the input parameter is related to the pressure, this can be justified regarding the influence of the GV angle on the pressure drop and losses in the turbine domain. This fact was also reported in a study by Setoguchi et al. [35], in which for a fixed LE angle, there is a reverse relationship between the angle of the upstream guide vanes and the CA parameter. The LE angle affects the input coefficient by shaping the blade flow passage and affecting the VR term in the definition of CA in Equation (2). As illustrated in Figure 10c, the LE angle has the highest contribution among the variations in torque coefficient. Increasing the LE angle causes more inclination of the rotor blade and reduces the area and flow velocity at the mean radius of the rotor (known as AR and VR respectively). These terms contribute to the CT as defined in Equation (1). The sensitivity of the turbine total to static efficiency to Figure 11. Turbine efficiency response versus the most sensitive input parameters. Local Sensitivity (%) Local Sensitivity (%) Local Sensitivity (%) Local Sensitivity (%)PDF Image | Unidirectional Radial-Air-Turbine OWC Wave Energy Converters
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