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Figure 1. Flow diagram of the proposed conceptual design process [5]. the design space of the runner is defined and the variables, which affect erosion are analyzed. These results allow obtaining the objective functions for the optimization process. The data obtained in the optimization process are: the inlet and outlet velocity, the flow acceleration, degree of reaction, submergence height, outlet diameter and equation of the blade angle distribution. Mathematical adjustment is compared with results available in the open domain literature. Once the hydraulic design parameters are known, the geometry of the blade is built in three dimensions for subsequent numerical assessment.

Figure 1 Flow diagram of the proposed conceptual design process [5]. the design space of the runner is defined and the variables, which affect erosion are analyzed. These results allow obtaining the objective functions for the optimization process. The data obtained in the optimization process are: the inlet and outlet velocity, the flow acceleration, degree of reaction, submergence height, outlet diameter and equation of the blade angle distribution. Mathematical adjustment is compared with results available in the open domain literature. Once the hydraulic design parameters are known, the geometry of the blade is built in three dimensions for subsequent numerical assessment.

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* The reference value is taken from Gjgsezeter [8]. Table 1. Optimization range of hydraulic parameters design.
* The reference value is taken from Gjgsezeter [8]. Table 1. Optimization range of hydraulic parameters design.
The following equations shown the objectives functions used for the optimization process:
The following equations shown the objectives functions used for the optimization process:
Table 2. Results of the optimization process. 3.3. Comparison of the method
Table 2. Results of the optimization process. 3.3. Comparison of the method
Figure 2. Pareto front per intent | (a) and blade angle distribution (b).
Figure 2. Pareto front per intent | (a) and blade angle distribution (b).
To contrast the methodology presented information available in the open domain regarding parametric design of Francis turbines is utilized. Figure 3 shown a comparison between the energy and velocities distribution along the streamline with the energy and the velocities distribution found in work of Thapa [10]. The tendency of distribution of each velocity comes to be like those found by Thapa methodology.
To contrast the methodology presented information available in the open domain regarding parametric design of Francis turbines is utilized. Figure 3 shown a comparison between the energy and velocities distribution along the streamline with the energy and the velocities distribution found in work of Thapa [10]. The tendency of distribution of each velocity comes to be like those found by Thapa methodology.
Figure 4. Geometry obtained from the model. runner, considering the ideal path of the working fluid pat With the design inputs established in Table 2 a graphic user interface program developed in Matlab create 3D runner which can be exported as CAD document for further analysis in ANSYS. The 3D geometrical generation is based on the design of the streamlines of the flow, which goes through the h it is possible to calcu that is to say, from the calculation of the flow ate the points of the geometry that comprise the blade. Figure 4 shows the Ry views obtained from the generation module [13], the design starts by obtaining the main views (axial and is t radial) then join them hickless, so by means o final form of the blade is o flow are the flow rate and t to know the inlet and out calculate its synchronous s forming the figure of the blade in three dimensions. However, this geometry f criteria of form at the inlet (leading edge) and the outlet (trailing edge), the btained. The main inputs required to calculate the parameters of the working he head, in the other hand, to calculate the kinematics variables, is necessary et desired diameter, the number of pole pairs of the turbine generator to peed, and the acceleration of the flow through the blade.
Figure 4. Geometry obtained from the model. runner, considering the ideal path of the working fluid pat With the design inputs established in Table 2 a graphic user interface program developed in Matlab create 3D runner which can be exported as CAD document for further analysis in ANSYS. The 3D geometrical generation is based on the design of the streamlines of the flow, which goes through the h it is possible to calcu that is to say, from the calculation of the flow ate the points of the geometry that comprise the blade. Figure 4 shows the Ry views obtained from the generation module [13], the design starts by obtaining the main views (axial and is t radial) then join them hickless, so by means o final form of the blade is o flow are the flow rate and t to know the inlet and out calculate its synchronous s forming the figure of the blade in three dimensions. However, this geometry f criteria of form at the inlet (leading edge) and the outlet (trailing edge), the btained. The main inputs required to calculate the parameters of the working he head, in the other hand, to calculate the kinematics variables, is necessary et desired diameter, the number of pole pairs of the turbine generator to peed, and the acceleration of the flow through the blade.
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