Francis Turbine Blade Design on the Basis of Port Area and Loss Analysis

Zhenmu Chen 1, Patrick M. Singh 1 and Young-Do Choi 2,* 1 Graduate School, Department of Mechanical Engineering, Mokpo National University, Mokpo, Jeollanam-do 58555, Korea; chenzhenmu@163.com (Z.C.); pms72006@yahoo.com (P.M.S.) 2 Department of Mechanical Engineering, Institute of New and Renewable Energy Technology Research, Mokpo National University, Mokpo, Jeollanam-do 58555, Korea * Correspondence: ydchoi@mokpo.ac.kr; Tel.: +82-61-450-2419


Introduction
There is an increasing demand for renewable energy for sustainable development to solve the coming energy crisis.The necessity of the use of renewable energy as one of the clean and sustainable natural energy resources has become high.Francis turbines are applicable to a wide range of head and specific speed values.Their wide range of applicability and easier structural design makes Francis turbines more advantageous than other hydraulic turbines.As a key component of a Francis turbine facility, the runner performance plays a vital role in the performance of the turbine.A Francis turbine runner blade with good performance by the one dimensional hydraulic design method can be designed effectively and successfully.Korea relies on foreign products, and the technology for local manufacture was limited until 2010 [1].Currently, Korea is in the process of developing its hydropower technology.
In this study, a new method on basis of the port area and loss analysis to design a Francis turbine runner was developed for the Miryang power station in Korea.In this study, the port area is defined as the minimum blade passage area at the exit of the blade passage, which will be defined in more detail in Section 2.2.The meridional shape of the runner was designed on the basis of the combination of the guide vane loss analysis and experience.The runner blade inlet and outlet angles were designed by calculation of Euler's head, and the port area of blade was modified by keeping the inlet and outlet angles of the blade constant.Unlike conventional direct design methods, where much attention is paid to draw the meridional plane streamlines to obtain the meridional velocity [2], the new method tries to adjust the port area of the runner blade passage to correct the outflow angle at the runner exit.

Turbine Runner Design and Numerical Method
Figure 1 shows the flow chart of the Francis turbine runner blade design.For one dimension hydraulic design, calculation is required for the blade angle at leading and trailing edges.For the meridional plane shape design part, because the guide vane is movable, a minimum guide vane loss exists according to different guide vane height (B g ) at the design condition.In this study, the guide vane height is determined according to the guide vane loss analysis, and the other parameters, such as the runner inlet and outlet diameters, are determined by experience.The outflow angle from the runner passage is controlled by the runner port area and blade outlet angle.Moreover, the blade outlet angle can be calculated by the Euler head equation.Therefore, the port area can be determined by the outflow angle from the runner passage.

Turbine Runner Design and Numerical Method
Figure 1 shows the flow chart of the Francis turbine runner blade design.For one dimension hydraulic design, calculation is required for the blade angle at leading and trailing edges.For the meridional plane shape design part, because the guide vane is movable, a minimum guide vane loss exists according to different guide vane height (Bg) at the design condition.In this study, the guide vane height is determined according to the guide vane loss analysis, and the other parameters, such as the runner inlet and outlet diameters, are determined by experience.The outflow angle from the runner passage is controlled by the runner port area and blade outlet angle.Moreover, the blade outlet angle can be calculated by the Euler head equation.Therefore, the port area can be determined by the outflow angle from the runner passage.

One Dimension Loss Analysis
In this study, the runner is designed for the Miryang power station in Korea.The turbine design point is at He = 64.2m for the effective head, the Q = 1.21 m 3 /s for flow rate and the rotational speed is N = 914 min −1 .The specific speed at the design point is Ns = 130 m-kW, which is within the range of Francis turbines with Ns = 60-450 m-kW and H = 20-700 m [3].
To obtain the guide vane pressure loss coefficient for the meridional shape design, the numerical analysis was performed with different guide vane openings (a0) and heights (Bg).The boundary condition at inlet was set as mass flow rate and the flow angle was set same as the guide vane inlet angle.Inlet turbulence condition was specified as 5% turbulence intensity.The boundary condition of average static pressure was set at outlet of the guide vane passage.According to the previous study [4,5], the SST k-ω turbulence model is adopted as turbulence model, which has been well known to estimate both separation and vortex occurrence on the wall of a complicated blade shape.Moreover, the value of y + , which means non-dimensional distance from wall [6,7], is determined to be around 9 for the guide vane blade surface.The pressure difference measurement locations are shown in Figure 2. The location P2 is between the guide vane and stay vane, and location P3 is between the guide and runner vane.
For evaluating the guide vane pressure loss coefficient (ζ), the equation is determined by Equation (1):

One Dimension Loss Analysis
In this study, the runner is designed for the Miryang power station in Korea.The turbine design point is at H e = 64.2m for the effective head, the Q = 1.21 m 3 /s for flow rate and the rotational speed is N = 914 min ´1.The specific speed at the design point is N s = 130 m-kW, which is within the range of Francis turbines with N s = 60-450 m-kW and H = 20-700 m [3].
To obtain the guide vane pressure loss coefficient for the meridional shape design, the numerical analysis was performed with different guide vane openings (a 0 ) and heights (B g ).The boundary condition at inlet was set as mass flow rate and the flow angle was set same as the guide vane inlet angle.Inlet turbulence condition was specified as 5% turbulence intensity.The boundary condition of average static pressure was set at outlet of the guide vane passage.According to the previous study [4,5], the SST k-ω turbulence model is adopted as turbulence model, which has been well known to estimate both separation and vortex occurrence on the wall of a complicated blade shape.Moreover, the value of y + , which means non-dimensional distance from wall [6,7], is determined to be around 9 for the guide vane blade surface.The pressure difference measurement locations are shown in Figure 2. The location P2 is between the guide vane and stay vane, and location P3 is between the guide and runner vane.
For evaluating the guide vane pressure loss coefficient (ζ), the equation is determined by Equation (1): where p 2 and p 3 are the averaged total pressure at locations P2 and P3, respectively.V th is the velocity at the throat of guide vane passage and ρ is the density of the water.
where p2 and p3 are the averaged total pressure at locations P2 and P3, respectively.Vth is the velocity at the throat of guide vane passage and ρ is the density of the water.The result of the guide vane flow angle according to the guide vane opening ratio (a0/Dr1) is shown in Figure 3.The flow angle is the measurement at the outlet of guide vane, which means the flow angle is the outflow angle of guide vane passage.The relationship between the outflow angle and guide vane opening ratio is obtained as shown in Figure 3. Figure 4 shows the relation of the pressure loss coefficient and guide vane hydraulic radius ratio (m/Dr1).It can be seen that there is lower pressure loss coefficient at the larger guide vane hydraulic radius.Moreover, the relationship between pressure loss coefficient and guide vane hydraulic radius ratio can be obtained as shown in The result of the guide vane flow angle according to the guide vane opening ratio (a 0 /D r1 ) is shown in Figure 3.The flow angle is the measurement at the outlet of guide vane, which means the flow angle is the outflow angle of guide vane passage.The relationship between the outflow angle and guide vane opening ratio is obtained as shown in Figure 3. where p2 and p3 are the averaged total pressure at locations P2 and P3, respectively.Vth is the velocity at the throat of guide vane passage and ρ is the density of the water.The result of the guide vane flow angle according to the guide vane opening ratio (a0/Dr1) is shown in Figure 3.The flow angle is the measurement at the outlet of guide vane, which means the flow angle is the outflow angle of guide vane passage.The relationship between the outflow angle and guide vane opening ratio is obtained as shown in Figure 3. Figure 4 shows the relation of the pressure loss coefficient and guide vane hydraulic radius ratio (m/Dr1).It can be seen that there is lower pressure loss coefficient at the larger guide vane hydraulic radius.Moreover, the relationship between pressure loss coefficient and guide vane hydraulic radius ratio can be obtained as shown in Figure 4 shows the relation of the pressure loss coefficient and guide vane hydraulic radius ratio (m/D r1 ).It can be seen that there is lower pressure loss coefficient at the larger guide vane hydraulic radius.Moreover, the relationship between pressure loss coefficient and guide vane hydraulic radius ratio can be obtained as shown in Figure 4.The definition of the hydraulic radius (m) is shown in Equation (2): For the design and best efficiency point, it can be assumed that there is no swirl flow remaining at the draft tube.Therefore, according to the Euler turbine head equation [2,[8][9][10][11], the relation between Euler head, guide vane height (Bg) and the outflow angle from guide vane passage (α) is shown in Equation (3).Additionally, according to the pressure loss coefficient, the relation between guide vane head loss, guide vane opening (a0) and guide vane height (Bg) is derived as shown in Equation ( 4): According to the outflow angle from guide vane passage, guide vane pressure loss coefficient and the Euler head, the one dimension loss analysis results are plotted in Figure 5.These results are obtained only at design flow rate and head.As the Euler turbine head for the design point is constant and the turbine head is controlled by the guide vane passage opening, the guide vane opening ratio (a0/Dr1) has to be determined for a specified guide vane height (Bg), as shown in Figure 5.For the design and best efficiency point, it can be assumed that there is no swirl flow remaining at the draft tube.Therefore, according to the Euler turbine head equation [2,[8][9][10][11], the relation between Euler head, guide vane height (B g ) and the outflow angle from guide vane passage (α) is shown in Equation ( 3).Additionally, according to the pressure loss coefficient, the relation between guide vane head loss, guide vane opening (a 0 ) and guide vane height (B g ) is derived as shown in Equation ( 4): According to the outflow angle from guide vane passage, guide vane pressure loss coefficient and the Euler head, the one dimension loss analysis results are plotted in Figure 5.These results are obtained only at design flow rate and head.As the Euler turbine head for the design point is constant and the turbine head is controlled by the guide vane passage opening, the guide vane opening ratio (a 0 /D r1 ) has to be determined for a specified guide vane height (B g ), as shown in Figure 5.For the design and best efficiency point, it can be assumed that there is no swirl flow remaining at the draft tube.Therefore, according to the Euler turbine head equation [2,[8][9][10][11], the relation between Euler head, guide vane height (Bg) and the outflow angle from guide vane passage (α) is shown in Equation ( 3).Additionally, according to the pressure loss coefficient, the relation between guide vane head loss, guide vane opening (a0) and guide vane height (Bg) is derived as shown in Equation ( 4): According to the outflow angle from guide vane passage, guide vane pressure loss coefficient and the Euler head, the one dimension loss analysis results are plotted in Figure 5.These results are obtained only at design flow rate and head.As the Euler turbine head for the design point is constant and the turbine head is controlled by the guide vane passage opening, the guide vane opening ratio (a0/Dr1) has to be determined for a specified guide vane height (Bg), as shown in Figure 5.The efficiency curve shown in the graph is the design point efficiency with different designs of guide vane heights (B g ) and guide vane opening ratios (a 0 /D r1 ).As a result, it can be seen that there is a best efficiency point by the different guide vane opening ratio (a 0 /D r1 ).Additionally, there is a relatively wide guide vane opening ratio (guide vane height) with high efficiency, meaning that there is a wide range for the design of guide vane opening ratio and guide vane height.In this study, in order to fit the runner to the existing Francis turbine plant for performance test, the guide vane height (B g ) of 103 mm is selected, which belongs to the high efficiency range according to the one dimension loss analysis.Finally, the meridional plane shape with basic dimensions is determined as shown in Figure 6.
The efficiency curve shown in the graph is the design point efficiency with different designs of guide vane heights (Bg) and guide vane opening ratios (a0/Dr1).As a result, it can be seen that there is a best efficiency point by the different guide vane opening ratio (a0/Dr1).Additionally, there is a relatively wide guide vane opening ratio (guide vane height) with high efficiency, meaning that there is a wide range for the design of guide vane opening ratio and guide vane height.In this study, in order to fit the runner to the existing Francis turbine plant for performance test, the guide vane height (Bg) of 103 mm is selected, which belongs to the high efficiency range according to the one dimension loss analysis.Finally, the meridional plane shape with basic dimensions is determined as shown in Figure 6.

Turbine Runner Blade Model
Figure 7 reveals the definition of the runner blade port area.The port area of the runner blade is located at the exit of the runner flow passage, which is the minimum area at the runner flow passage.Therefore, the dimension of the port area plays a very important role in controlling the exit relative velocity from runner passage as shown in Figure 8.The relative velocity (W2) reduces with increasing port area, which causes the outflow angle (α2) to drop.The outflow angle from runner passage is perpendicular (90°) only with correct relative velocity.Therefore, it is possible to achieve correct outflow angle by modifying the port area and relative outflow velocity.

Turbine Runner Blade Model
Figure 7 reveals the definition of the runner blade port area.The port area of the runner blade is located at the exit of the runner flow passage, which is the minimum area at the runner flow passage.Therefore, the dimension of the port area plays a very important role in controlling the exit relative velocity from runner passage as shown in Figure 8.The relative velocity (W 2 ) reduces with increasing port area, which causes the outflow angle (α 2 ) to drop.The outflow angle from runner passage is perpendicular (90 ˝) only with correct relative velocity.Therefore, it is possible to achieve correct outflow angle by modifying the port area and relative outflow velocity.
Energies 2016, 9, 164 5 of 12 The efficiency curve shown in the graph is the design point efficiency with different designs of guide vane heights (Bg) and guide vane opening ratios (a0/Dr1).As a result, it can be seen that there is a best efficiency point by the different guide vane opening ratio (a0/Dr1).Additionally, there is a relatively wide guide vane opening ratio (guide vane height) with high efficiency, meaning that there is a wide range for the design of guide vane opening ratio and guide vane height.In this study, in order to fit the runner to the existing Francis turbine plant for performance test, the guide vane height (Bg) of 103 mm is selected, which belongs to the high efficiency range according to the one dimension loss analysis.Finally, the meridional plane shape with basic dimensions is determined as shown in Figure 6.

Turbine Runner Blade Model
Figure 7 reveals the definition of the runner blade port area.The port area of the runner blade is located at the exit of the runner flow passage, which is the minimum area at the runner flow passage.Therefore, the dimension of the port area plays a very important role in controlling the exit relative velocity from runner passage as shown in Figure 8.The relative velocity (W2) reduces with increasing port area, which causes the outflow angle (α2) to drop.The outflow angle from runner passage is perpendicular (90°) only with correct relative velocity.Therefore, it is possible to achieve correct outflow angle by modifying the port area and relative outflow velocity.The efficiency curve shown in the graph is the design point efficiency with different designs of guide vane heights (Bg) and guide vane opening ratios (a0/Dr1).As a result, it can be seen that there is a best efficiency point by the different guide vane opening ratio (a0/Dr1).Additionally, there is a relatively wide guide vane opening ratio (guide vane height) with high efficiency, meaning that there is a wide range for the design of guide vane opening ratio and guide vane height.In this study, in order to fit the runner to the existing Francis turbine plant for performance test, the guide vane height (Bg) of 103 mm is selected, which belongs to the high efficiency range according to the one dimension loss analysis.Finally, the meridional plane shape with basic dimensions is determined as shown in Figure 6.

Turbine Runner Blade Model
Figure 7 reveals the definition of the runner blade port area.The port area of the runner blade is located at the exit of the runner flow passage, which is the minimum area at the runner flow passage.Therefore, the dimension of the port area plays a very important role in controlling the exit relative velocity from runner passage as shown in Figure 8.The relative velocity (W2) reduces with increasing port area, which causes the outflow angle (α2) to drop.The outflow angle from runner passage is perpendicular (90°) only with correct relative velocity.Therefore, it is possible to achieve correct outflow angle by modifying the port area and relative outflow velocity.Figure 9 shows the port area distribution from crown to shroud in the runner flow passage 1.The port area has to be modified until the outflow angle is satisfactory.
Energies 2016, 9, 164 6 of 12 Figure 9 shows the port area distribution from crown to shroud in the runner flow passage 1.The port area has to be modified until the outflow angle is satisfactory.

Numerical Method
Computational fluid dynamics (CFD) analysis is a very useful tool for predicting hydro machinery performance at various operating conditions [12][13][14][15].Commercial code of ANSYS CFX [16] was employed to predict the characteristics of the Francis turbine.The general connection was set as "stage" condition between the rotational area and the fixed area.The SST k-ω model was selected for the turbulence model.Inlet turbulence condition is specified as 5% turbulence intensity and the flow direction is normal to the inlet boundary.
There are two kinds of numerical domain for the CFD analysis.Considering the computation time consumption, the cases for different port area calculation (Cases 1-5) was conducted by 1 pitch domain.Moreover, for the Francis turbine performance analysis, the full domain analysis was conducted.For 1 pitch flow passage (1 stay vane, 1 guide vane and 1 runner blade flow passage), the mass flow condition was applied at the inlet and the static pressure was set at the outlet of the calculation domain.However, for the full domain calculation, the total pressure boundary condition was applied at the inlet, and the static pressure was set at the outlet of the domain.This is done to maintain the design head and check the flow rate is matched with design point.
For 1 pitch flow passage, the total number of elements is 5.5 × 10 6 , for which the y + around the blade surface is 9. Therefore, the total number of elements for 1 pitch flow passage is sufficient for reliable results.In order to exclude the effect of mesh on the prediction accuracy, the mesh dependence was conducted for full domain CFD analysis as shown in Figure 10.The efficiency was normalized by the selected efficiency.It can be concluded that the turbine efficiency is insensitive after the number of elements exceed 7.5 × 10 6 .Therefore, the number of elements around 7.5 × 10 6 was selected for full domain calculation.

Numerical Method
Computational fluid dynamics (CFD) analysis is a very useful tool for predicting hydro machinery performance at various operating conditions [12][13][14][15].Commercial code of ANSYS CFX [16] was employed to predict the characteristics of the Francis turbine.The general connection was set as "stage" condition between the rotational area and the fixed area.The SST k-ω model was selected for the turbulence model.Inlet turbulence condition is specified as 5% turbulence intensity and the flow direction is normal to the inlet boundary.
There are two kinds of numerical domain for the CFD analysis.Considering the computation time consumption, the cases for different port area calculation (Cases 1-5) was conducted by 1 pitch domain.Moreover, for the Francis turbine performance analysis, the full domain analysis was conducted.For 1 pitch flow passage (1 stay vane, 1 guide vane and 1 runner blade flow passage), the mass flow condition was applied at the inlet and the static pressure was set at the outlet of the calculation domain.However, for the full domain calculation, the total pressure boundary condition was applied at the inlet, and the static pressure was set at the outlet of the domain.This is done to maintain the design head and check the flow rate is matched with design point.
For 1 pitch flow passage, the total number of elements is 5.5 ˆ10 6 , for which the y + around the blade surface is 9. Therefore, the total number of elements for 1 pitch flow passage is sufficient for reliable results.In order to exclude the effect of mesh on the prediction accuracy, the mesh dependence was conducted for full domain CFD analysis as shown in Figure 10.The efficiency was normalized by the selected efficiency.It can be concluded that the turbine efficiency is insensitive after the number of elements exceed 7.5 ˆ10 6 .Therefore, the number of elements around 7.5 ˆ10 6 was selected for full domain calculation.
Energies 2016, 9, 164 6 of 12 Figure 9 shows the port area distribution from crown to shroud in the runner flow passage 1.The port area has to be modified until the outflow angle is satisfactory.

Numerical Method
Computational fluid dynamics (CFD) analysis is a very useful tool for predicting hydro machinery performance at various operating conditions [12][13][14][15].Commercial code of ANSYS CFX [16] was employed to predict the characteristics of the Francis turbine.The general connection was set as "stage" condition between the rotational area and the fixed area.The SST k-ω model was selected for the turbulence model.Inlet turbulence condition is specified as 5% turbulence intensity and the flow direction is normal to the inlet boundary.
There are two kinds of numerical domain for the CFD analysis.Considering the computation time consumption, the cases for different port area calculation (Cases 1-5) was conducted by 1 pitch domain.Moreover, for the Francis turbine performance analysis, the full domain analysis was conducted.For 1 pitch flow passage (1 stay vane, 1 guide vane and 1 runner blade flow passage), the mass flow condition was applied at the inlet and the static pressure was set at the outlet of the calculation domain.However, for the full domain calculation, the total pressure boundary condition was applied at the inlet, and the static pressure was set at the outlet of the domain.This is done to maintain the design head and check the flow rate is matched with design point.
For 1 pitch flow passage, the total number of elements is 5.5 × 10 6 , for which the y + around the blade surface is 9. Therefore, the total number of elements for 1 pitch flow passage is sufficient for reliable results.In order to exclude the effect of mesh on the prediction accuracy, the mesh dependence was conducted for full domain CFD analysis as shown in Figure 10.The efficiency was normalized by the selected efficiency.It can be concluded that the turbine efficiency is insensitive after the number of elements exceed 7.5 × 10 6 .Therefore, the number of elements around 7.5 × 10 6 was selected for full domain calculation.

Outflow Pattern
The criterion for the runner blade port area design is the outflow angle.The effect of draft tube on recycling the kinetic energy is limited.Especially, the kinetic energy from the circumferential velocity is very hard to collect.Therefore, a correct outflow angle plays a role of reducing the loss at draft tube and improving the efficiency of the turbine.The modification of port area is satisfactory until the outflow angle is as close to 90 ˝. Figure 11 shows the outflow angle distribution from runner crown to shroud.The outflow angle of Case 5 is located close to 90 ˝with only small deviation.Moreover, as the effect of boundary wall, the deviation increases near the crown and shroud walls.Overall, the port area and the outflow angle of Case 5 are satisfactory for the runner design.

Outflow Pattern
The criterion for the runner blade port area design is the outflow angle.The effect of draft tube on recycling the kinetic energy is limited.Especially, the kinetic energy from the circumferential velocity is very hard to collect.Therefore, a correct outflow angle plays a role of reducing the loss at draft tube and improving the efficiency of the turbine.The modification of port area is satisfactory until the outflow angle is as close to 90°. Figure 11 shows the outflow angle distribution from runner crown to shroud.The outflow angle of Case 5 is located close to 90° with only small deviation.Moreover, as the effect of boundary wall, the deviation increases near the crown and shroud walls.Overall, the port area and the outflow angle of Case 5 are satisfactory for the runner design.Figure 12 shows the streamline distribution in the draft tube.It is clearly indicated that the streamline of Case 1 in the draft tube shows large swirl flow, which increases the loss at the draft tube.However, by modifying port area to a correct extent (Case 5), there are vertically straight streamlines in the draft tube, and exit flow angle is close to 90°.The effect of modifying the port area on correcting the exit flow angle is significant in reducing the swirl flow.

Loss Analysis
For the loss analysis, the equation is defined as following: Figure 12 shows the streamline distribution in the draft tube.It is clearly indicated that the streamline of Case 1 in the draft tube shows large swirl flow, which increases the loss at the draft tube.However, by modifying the port area to a correct extent (Case 5), there are vertically straight streamlines in the draft tube, and exit flow angle is close to 90 ˝.The effect of modifying the port area on correcting the exit flow angle is significant in reducing the swirl flow.

Outflow Pattern
The criterion for the runner blade port area design is the outflow angle.The effect of draft tube on recycling the kinetic energy is limited.Especially, the kinetic energy from the circumferential velocity is very hard to collect.Therefore, a correct outflow angle plays a role of reducing the loss at draft tube and improving the efficiency of the turbine.The modification of port area is satisfactory until the outflow angle is as close to 90°. Figure 11 shows the outflow angle distribution from runner crown to shroud.The outflow angle of Case 5 is located close to 90° with only small deviation.Moreover, as the effect of boundary wall, the deviation increases near the crown and shroud walls.Overall, the port area and the outflow angle of Case 5 are satisfactory for the runner design.Figure 12 shows the streamline distribution in the draft tube.It is clearly indicated that the streamline of Case 1 in the draft tube shows large swirl flow, which increases the loss at the draft tube.However, by modifying the port area to a correct extent (Case 5), there are vertically straight streamlines in the draft tube, and exit flow angle is close to 90°.The effect of modifying the port area on correcting the exit flow angle is significant in reducing the swirl flow.

Loss Analysis
For the loss analysis, the equation is defined as following:

Loss Analysis
For the loss analysis, the equation is defined as following: H Loss runner " where the H Loss is the pressure loss for the stay vane, guide vane and draft tube, H Loss runner is the pressure loss for the runner passage.
Figure 13 shows the loss distribution on each component.As the result is obtained from 1 pitch analysis without casing, there is no casing component loss analysis.The loss exists to a large extent at draft tube at Cases 1 and 2, for which swirl flow exists with large deviation outflow angle from 90 (as shown in Figure 11).However, the loss at draft tube reduces with correct outflow angle.The total loss distribution by each case is obtained in Figure 14.There is minimum total loss at Case 5, which satisfies outflow angle from runner exit and has the lowest loss at draft tube.
Energies 2016, 9, 164 8 of 12 ∆ ω ρg where the HLoss is the pressure loss for the stay vane, guide vane and draft tube, HLoss runner is the pressure loss for the runner passage.
Figure 13 shows the loss distribution on each component.As the result is obtained from 1 pitch analysis without casing, there is no casing component loss analysis.The loss exists to a large extent at draft tube at Cases 1 and 2, for which swirl flow exists with large deviation outflow angle from 90° (as shown in Figure 11).However, the loss at draft tube reduces with correct outflow angle.The total loss distribution by each case is obtained in Figure 14.There is minimum total loss at Case 5, which satisfies outflow angle from runner exit and has the lowest loss at draft tube.

Stay vane
Guide vane Runner Draft tube 0.0 0.5

Performance Analysis
The performance analysis of the Francis turbine was conducted by full domain as shown in Figure 15.There is best efficiency point of 92.6% with leakage loss at the Q11 of 0.525, at which the flow rate is the design flow rate for this Francis turbine.In comparison to the efficiency without where the HLoss is the pressure loss for the stay vane, guide vane and draft tube, HLoss runner is the pressure loss for the runner passage.
Figure 13 shows the loss distribution on each component.As the result is obtained from 1 pitch analysis without casing, there is no casing component loss analysis.The loss exists to a large extent at draft tube at Cases 1 and 2, for which swirl flow exists with large deviation outflow angle from 90° (as shown in Figure 11).However, the loss at draft tube reduces with correct outflow angle.The total loss distribution by each case is obtained in Figure 14.There is minimum total loss at Case 5, which satisfies outflow angle from runner exit and has the lowest loss at draft tube.

Performance Analysis
The performance analysis of the Francis turbine was conducted by full domain as shown in Figure 15.There is best efficiency point of 92.6% with leakage loss at the Q11 of 0.525, at which the flow rate is the design flow rate for this Francis turbine.In comparison to the efficiency without

Performance Analysis
The performance analysis of the Francis turbine was conducted by full domain as shown in Figure 15.There is best efficiency point of 92.6% with leakage loss at the Q 11 of 0.525, at which the flow rate is the design flow rate for this Francis turbine.In comparison to the efficiency without leakage, there is 1.4% difference at the design flow rate.The leakage loss of 1.4% consists of disk friction loss and volume loss.Figure 16 shows the component loss at different flow rates.It can be seen that the loss at the casing and stay vane passage is relatively small and the loss increases slightly at high flow rate.The loss at the guide vane passage and runner passage exists relatively to a large extent.The loss at the guide vane passage reduces with increasing the flow rate.However, the loss at the runner passage is insensitive to the flow rate.Minimum amount of loss exists at the design flow rate.However, the loss increases rapidly at the off design flow rates.Especially at the partial flow rate, the loss at draft tube exists in a significant amount.

Fluid-Structure Interaction Analysis
In order to verify the runner blade structure integrity, fluid-structure interaction (FSI) is an effective method to calculate the stresses in the Francis turbine runner.Saeed et al. [17] found stress maxima in different parts of the runner by FSI method.Xiao et al. [18] investigated the dynamic stresses in a Francis turbine runner successfully based on FSI analysis.In this study, the FSI analysis has been conducted for verifying the runner structure by the hydraulic force.
The material of SCS5 steel was applied for the runner, for which the tensile ultimate strength is 540 MPa and yield stress is 415 MPa.The pressure load applied on the runner surface is imported from the full domain CFD analysis at the design flow rate, where the flow rate is 1.21 m 3 /s and   Figure 16 shows the component loss at different flow rates.It can be seen that the loss at the casing and stay vane passage is relatively small and the loss increases slightly at high flow rate.The loss at the guide vane passage and runner passage exists relatively to a large extent.The loss at the guide vane passage reduces with increasing the flow rate.However, the loss at the runner passage is insensitive to the flow rate.Minimum amount of loss exists at the design flow rate.However, the loss increases rapidly at the off design flow rates.Especially at the partial flow rate, the loss at draft tube exists in a significant amount.
Energies 2016, 9, 164 9 of 12 leakage, there is 1.4% difference at the design flow rate.The leakage loss of 1.4% consists of disk friction loss and volume loss.Figure 16 shows the component loss at different flow rates.It can be seen that the loss at the casing and stay vane passage is relatively small and the loss increases slightly at high flow rate.The loss at the guide vane passage and runner passage exists relatively to a large extent.The loss at the guide vane passage reduces with increasing the flow rate.However, the loss at the runner passage is insensitive to the flow rate.Minimum amount of loss exists at the design flow rate.However, the loss increases rapidly at the off design flow rates.Especially at the partial flow rate, the loss at draft tube exists in a significant amount.

Fluid-Structure Interaction Analysis
In order to verify the runner blade structure integrity, fluid-structure interaction (FSI) is an effective method to calculate the stresses in the Francis turbine runner.Saeed et al. [17] found stress maxima in different parts of the runner by FSI method.Xiao et al. [18] investigated the dynamic stresses in a Francis turbine runner successfully based on FSI analysis.In this study, the FSI analysis has been conducted for verifying the runner structure by the hydraulic force.
The material of SCS5 steel was applied for the runner, for which the tensile ultimate strength is 540 MPa and yield stress is 415 MPa.The pressure load applied on the runner surface is imported

Fluid-Structure Interaction Analysis
In order to verify the runner blade structure integrity, fluid-structure interaction (FSI) is an effective method to calculate the stresses in the Francis turbine runner.Saeed et al. [17] found stress maxima in different parts of the runner by FSI method.Xiao et al. [18] investigated the dynamic stresses in a Francis turbine runner successfully based on FSI analysis.In this study, the FSI analysis has been conducted for verifying the runner structure by the hydraulic force.
The material of SCS5 steel was applied for the runner, for which the tensile ultimate strength is 540 MPa and yield stress is 415 MPa.The pressure load applied on the runner surface is imported from the full domain CFD analysis at the design flow rate, where the flow rate is 1.21 m 3 /s and turbine rotational speed is 914 min ´1.
The surfaces of hub, shroud, pressure and suction sides of the runner blades are selected for pressure loading as shown in Figure 17.The pressure imported to the runner surfaces for the FSI analysis is shown in Figure 18.The highest imported pressure of around 0.39 MPa exists on the hub and shroud surface near the runner inlet.The surfaces of hub, shroud, pressure and suction sides of the runner blades are selected for pressure loading as shown in Figure 17.The pressure imported to the runner surfaces for the FSI analysis is shown in Figure 18.The highest imported pressure of around 0.39 MPa exists on the hub and shroud surface near the runner inlet.The structural feasibility is based on the stress on the runner, which is shown in Figure 19.The maximum stress point of 23 MPa can be found at the corner between runner blade leading edge and shroud, which is much lower than the material yield stress.The safety factor is 18, which is more than sufficient for a safe structure.

Conclusions
The Francis turbine runner design and numerical analysis are presented for the Miryang power station of Korea.A successful design of the Francis turbine runner based on the one-dimension loss analysis and port area of the runner flow passage has been presented.The port area of runner blade plays a role of correcting the outflow angle from runner passage to reduce the swirl flow and the loss  The surfaces of hub, shroud, pressure and suction sides of the runner blades are selected for pressure loading as shown in Figure 17.The pressure imported to the runner surfaces for the FSI analysis is shown in Figure 18.The highest imported pressure of around 0.39 MPa exists on the hub and shroud surface near the runner inlet.The structural feasibility is based on the stress on the runner, which is shown in Figure 19.The maximum stress point of 23 MPa can be found at the corner between runner blade leading edge and shroud, which is much lower than the material yield stress.The safety factor is 18, which is more than sufficient for a safe structure.

Conclusions
The Francis turbine runner design and numerical analysis are presented for the Miryang power station of Korea.A successful design of the Francis turbine runner based on the one-dimension loss analysis and port area of the runner flow passage has been presented.The port area of runner blade plays a role of correcting the outflow angle from runner passage to reduce the swirl flow and the loss The structural feasibility is based on the stress on the runner, which is shown in Figure 19.The maximum stress point of 23 MPa can be found at the corner between runner blade leading edge and shroud, which is much lower than the material yield stress.The safety factor is 18, which is more than sufficient for a safe structure.The surfaces of hub, shroud, pressure and suction sides of the runner blades are selected for pressure loading as shown in Figure 17.The pressure imported to the runner surfaces for the FSI analysis is shown in Figure 18.The highest imported pressure of around 0.39 MPa exists on the hub and shroud surface near the runner inlet.The structural feasibility is based on the stress on the runner, which is shown in Figure 19.The maximum stress point of 23 MPa can be found at the corner between runner blade leading edge and shroud, which is much lower than the material yield stress.The safety factor is 18, which is more than sufficient for a safe structure.

Conclusions
The Francis turbine runner design and numerical analysis are presented for the Miryang power station of Korea.A successful design of the Francis turbine runner based on the one-dimension loss analysis and port area of the runner flow passage has been presented.The port area of runner blade plays a role of correcting the outflow angle from runner passage to reduce the swirl flow and the loss

Conclusions
The Francis turbine runner design and numerical analysis are presented for the Miryang power station of Korea.A successful design of the Francis turbine runner based on the one-dimension loss analysis and port area of the runner flow passage has been presented.The port area of runner blade plays a role of correcting the outflow angle from runner passage to reduce the swirl flow and the loss in the draft tube.Finally, the best efficiency of 92.6% is achieved by full domain calculation with leakage loss at the design point.From the FSI results it is evident that the maximum stress on the runner is much less than the ultimate stress the runner can withstand before failure.

Figure 1 .
Figure 1.Flow chart of Francis turbine runner blade design.CFD: computational fluid dynamics.

Figure 1 .
Figure 1.Flow chart of Francis turbine runner blade design.CFD: computational fluid dynamics.

Figure 2 .
Figure 2. Pressure difference location for guide vane loss analysis.

Figure 3 .
Figure 3. Relation of flow angle and guide vane opening ratio.

Figure 4 .Figure 2 .
Figure4shows the relation of the pressure loss coefficient and guide vane hydraulic radius ratio (m/Dr1).It can be seen that there is lower pressure loss coefficient at the larger guide vane hydraulic radius.Moreover, the relationship between pressure loss coefficient and guide vane hydraulic radius ratio can be obtained as shown in Figure4.The definition of the hydraulic radius (m) is shown in Equation (2):

Figure 2 .
Figure 2. Pressure difference location for guide vane loss analysis.

Figure 3 .
Figure 3. Relation of flow angle and guide vane opening ratio.

Figure 4 .Figure 3 .
Figure4shows the relation of the pressure loss coefficient and guide vane hydraulic radius ratio (m/Dr1).It can be seen that there is lower pressure loss coefficient at the larger guide vane hydraulic radius.Moreover, the relationship between pressure loss coefficient and guide vane hydraulic radius ratio can be obtained as shown in Figure4.The definition of the hydraulic radius (m) is shown in Equation (2):

Figure 4 .
Figure 4. Relation of the pressure loss coefficient and guide vane hydraulic radius ratio.

Figure 5 .
Figure 5.One dimension loss analysis result.

Figure 4 .
Figure 4. Relation of the pressure loss coefficient and guide vane hydraulic radius ratio.

Figure 4 .
Figure 4. Relation of the pressure loss coefficient and guide vane hydraulic radius ratio.

Figure 6 .
Figure 6.Meridional plane shape and basic dimensions.

Figure 7 .
Figure 7. Definition of the runner blade port area.

Figure 6 .
Figure 6.Meridional plane shape and basic dimensions.

Figure 6 .
Figure 6.Meridional plane shape and basic dimensions.

Figure 7 .
Figure 7. Definition of the runner blade port area.

Figure 7 .
Figure 7. Definition of the runner blade port area.

Figure 6 .
Figure 6.Meridional plane shape and basic dimensions.

Figure 7 .
Figure 7. Definition of the runner blade port area.

Figure 9 .
Figure 9. Port area distribution of the five cases.

Figure 10 .Figure 9 .
Figure 10.Mesh dependence for the full domain calculation.

Figure 9 .
Figure 9. Port area distribution of the five cases.

Figure 10 .Figure 10 .
Figure 10.Mesh dependence for the full domain calculation.

Figure 13 .
Figure 13.Loss distribution on each component.

Figure 14 .
Figure 14.Total loss distribution by each case.

Figure 13 .
Figure 13.Loss distribution on each component.

Figure 13 .
Figure 13.Loss distribution on each component.

Figure 14 .
Figure 14.Total loss distribution by each case.

Figure 14 .
Figure 14.Total loss distribution by each case.
is 1.4% difference at the design flow rate.The leakage loss of 1.4% consists of disk friction loss and volume loss.

Figure 15 .
Figure 15.Performance of the Francis turbine by the flow rate.

Figure 16 .
Figure 16.Component loss by the flow rate.

Figure 15 .
Figure 15.Performance of the Francis turbine by the flow rate.

Figure 15 .
Figure 15.Performance of the Francis turbine by the flow rate.

Figure 16 .
Figure 16.Component loss by the flow rate.

Figure 16 .
Figure 16.Component loss by the flow rate.

Figure 17 .
Figure 17.Runner hub and shroud surfaces for pressure loading.

Figure 18 .
Figure 18.Pressure imported to the runner surfaces.

Figure 19 .
Figure 19.Stress distribution on the runner.

Figure 17 .
Figure 17.Runner hub and shroud surfaces for pressure loading.

Figure 17 .
Figure 17.Runner hub and shroud surfaces for pressure loading.

Figure 18 .
Figure 18.Pressure imported to the runner surfaces.

Figure 19 .
Figure 19.Stress distribution on the runner.

Figure 18 .
Figure 18.Pressure imported to the runner surfaces.

Figure 17 .
Figure 17.Runner hub and shroud surfaces for pressure loading.

Figure 18 .
Figure 18.Pressure imported to the runner surfaces.

Figure 19 .
Figure 19.Stress distribution on the runner.

Figure 19 .
Figure 19.Stress distribution on the runner.