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Francis Turbine Blade Design on the Basis of PortArea 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; [email protected] (Z.C.); [email protected] (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: [email protected]; Tel.: +82-61-450-2419

Academic Editor: Jang-Ho LeeReceived: 17 December 2015; Accepted: 1 March 2016; Published: 4 March 2016

Abstract: In this study, a Francis turbine with specific speed of 130 m-kW was designed on the basisof the port area and loss analysis. The meridional shape of the runner was designed focusing mainlyon the combination of the guide vane loss analysis and experience. The runner blade inlet and outletangles were designed by calculation of Euler’s head, while the port area of blade was modified bykeeping constant angles of the blade at inlet and outlet. The results show that the effect of the portarea of runner blade on the flow exit angle from runner passage is significant. A correct flow exitangle reduces the energy loss at the draft tube, thereby improving the efficiency of the turbine. Thebest efficiency of 92.6% is achieved by this method, which is also similar to the design conditions bythe one dimension loss analysis.

Keywords: Francis turbine; runner design; port area; performance; loss analysis

1. Introduction

There is an increasing demand for renewable energy for sustainable development to solve thecoming energy crisis. The necessity of the use of renewable energy as one of the clean and sustainablenatural energy resources has become high. Francis turbines are applicable to a wide range of head andspecific speed values. Their wide range of applicability and easier structural design makes Francisturbines more advantageous than other hydraulic turbines. As a key component of a Francis turbinefacility, the runner performance plays a vital role in the performance of the turbine. A Francis turbinerunner blade with good performance by the one dimensional hydraulic design method can be designedeffectively and successfully. Korea relies on foreign products, and the technology for local manufacturewas 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 turbinerunner was developed for the Miryang power station in Korea. In this study, the port area is definedas the minimum blade passage area at the exit of the blade passage, which will be defined in moredetail in Section 2.2. The meridional shape of the runner was designed on the basis of the combinationof the guide vane loss analysis and experience. The runner blade inlet and outlet angles were designedby calculation of Euler’s head, and the port area of blade was modified by keeping the inlet and outletangles of the blade constant. Unlike conventional direct design methods, where much attention is paidto draw the meridional plane streamlines to obtain the meridional velocity [2], the new method tries toadjust the port area of the runner blade passage to correct the outflow angle at the runner exit.

Energies 2016, 9, 164; doi:10.3390/en9030164 www.mdpi.com/journal/energies

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Energies 2016, 9, 164 2 of 12

2. Turbine Runner Design and Numerical Method

Figure 1 shows the flow chart of the Francis turbine runner blade design. For one dimensionhydraulic design, calculation is required for the blade angle at leading and trailing edges. For themeridional plane shape design part, because the guide vane is movable, a minimum guide vane lossexists according to different guide vane height (Bg) at the design condition. In this study, the guidevane height is determined according to the guide vane loss analysis, and the other parameters, suchas the runner inlet and outlet diameters, are determined by experience. The outflow angle from therunner passage is controlled by the runner port area and blade outlet angle. Moreover, the blade outletangle can be calculated by the Euler head equation. Therefore, the port area can be determined by theoutflow angle from the runner passage.

Energies 2016, 9, 164 2 of 12

2. 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.

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

2.1. One Dimension Loss Analysis

In this study, the runner is designed for the Miryang power station in Korea. The turbine design

point is at He = 64.2 m for the effective head, the Q = 1.21 m3/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):

ζ2

ρ (1)

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

2.1. One Dimension Loss Analysis

In this study, the runner is designed for the Miryang power station in Korea. The turbine designpoint is at He = 64.2 m for the effective head, the Q = 1.21 m3/s for flow rate and the rotational speed isN = 914 min´1. The specific speed at the design point is Ns = 130 m-kW, which is within the range ofFrancis 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 numericalanalysis was performed with different guide vane openings (a0) and heights (Bg). The boundarycondition at inlet was set as mass flow rate and the flow angle was set same as the guide vane inletangle. Inlet turbulence condition was specified as 5% turbulence intensity. The boundary conditionof average static pressure was set at outlet of the guide vane passage. According to the previousstudy [4,5], the SST k-ω turbulence model is adopted as turbulence model, which has been well knownto 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 9for 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 andrunner vane.

For evaluating the guide vane pressure loss coefficient (ζ), the equation is determined by Equation (1):

ζ “pp2 ´ p3q ˆ 2

ρVth2 (1)

Energies 2016, 9, 164 3 of 12

where p2 and p3 are the averaged total pressure at locations P2 and P3, respectively. Vth is the velocityat the throat of guide vane passage and ρ is the density of the water.

Energies 2016, 9, 164 3 of 12

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.

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

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

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. The definition of the hydraulic radius

(m) is shown in Equation (2):

2 (2)

y = 1335.7x2 + 65.5x + 5.0

0

5

10

15

20

25

30

35

40

0.03 0.05 0.07 0.09 0.11 0.13 0.15

Flow angle (α)[°]

Guide vane opening ratio a0/Dr1


The result of the guide vane flow angle according to the guide vane opening ratio (a0/Dr1) isshown in Figure 3. The flow angle is the measurement at the outlet of guide vane, which means theflow angle is the outflow angle of guide vane passage. The relationship between the outflow angle andguide vane opening ratio is obtained as shown in Figure 3.

Energies 2016, 9, 164 3 of 12

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. The definition of the hydraulic radius

(m) is shown in Equation (2):

2 (2)

y = 1335.7x2 + 65.5x + 5.0

0

5

10

15

20

25

30

35

40

0.03 0.05 0.07 0.09 0.11 0.13 0.15

Flow angle (α)[°]



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 hydraulicradius. Moreover, the relationship between pressure loss coefficient and guide vane hydraulic radiusratio can be obtained as shown in Figure 4. The definition of the hydraulic radius (m) is shown inEquation (2):

m “a0Bg

2ˆ`

a0 ` Bg˘ (2)

Energies 2016, 9, 164 4 of 12Energies 2016, 9, 164 4 of 12

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

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 [2,8–11], 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):

160 tanα

(3)

ζ2

ζ12

(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.

Figure 5. One dimension loss analysis result.

y = 119.6x2 ‐ 9.5x + 0.2

0

0.02

0.04

0.06

0.08

0.1

0.015 0.02 0.025 0.03 0.035 0.04 0.045

Pressure loss coefficient (ζ)

Guide vane hydraulic radius ratio m/Dr1

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

0

50

100

150

200

250

300

350

0 0.05 0.1 0.15 0.2

Efficiency (η) [%

]

Guide van

e height (Bg) [mm]


GV height

Efficiency

η = 93.57% η = 93.58%

Bg = 103

Bg = 95


For the design and best efficiency point, it can be assumed that there is no swirl flow remaining atthe draft tube. Therefore, according to the Euler turbine head equation [2,8–11], the relation betweenEuler head, guide vane height (Bg) and the outflow angle from guide vane passage (α) is shown inEquation (3). Additionally, according to the pressure loss coefficient, the relation between guide vanehead loss, guide vane opening (a0) and guide vane height (Bg) is derived as shown in Equation (4):

Hth “U1Vu1

g“

1g

ˆ

NQ60Bgtanα

˙

(3)

Hgv “ ζVth

2

2g“ ζ

12g

ˆ

QZga0Bg

˙2(4)

According to the outflow angle from guide vane passage, guide vane pressure loss coefficientand the Euler head, the one dimension loss analysis results are plotted in Figure 5. These results areobtained only at design flow rate and head. As the Euler turbine head for the design point is constantand 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.

Energies 2016, 9, 164 4 of 12


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 [2,8–11], 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):

160 tanα

(3)

ζ2

ζ12

(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.


y = 119.6x2 ‐ 9.5x + 0.2

0

0.02

0.04

0.06

0.08

0.1

0.015 0.02 0.025 0.03 0.035 0.04 0.045

Pressure loss coefficient (ζ)

Guide vane hydraulic radius ratio m/Dr1

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

0

50

100

150

200

250

300

350

0 0.05 0.1 0.15 0.2

Efficiency (η) [%

]

Guide van

e height (Bg) [mm]


GV height

Efficiency

η = 93.57% η = 93.58%

Bg = 103

Bg = 95


Energies 2016, 9, 164 5 of 12

The efficiency curve shown in the graph is the design point efficiency with different designs ofguide vane heights (Bg) and guide vane opening ratios (a0/Dr1). As a result, it can be seen that thereis a best efficiency point by the different guide vane opening ratio (a0/Dr1). Additionally, there is arelatively wide guide vane opening ratio (guide vane height) with high efficiency, meaning that thereis a wide range for the design of guide vane opening ratio and guide vane height. In this study, inorder 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 dimensionloss analysis. Finally, the meridional plane shape with basic dimensions is determined as shown inFigure 6.

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.

Figure 6. Meridional plane shape and basic dimensions.

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

Figure 8. Velocity triangle at runner outlet.



Figure 7 reveals the definition of the runner blade port area. The port area of the runner blade islocated 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 relativevelocity from runner passage as shown in Figure 8. The relative velocity (W2) reduces with increasingport area, which causes the outflow angle (α2) to drop. The outflow angle from runner passage isperpendicular (90˝) only with correct relative velocity. Therefore, it is possible to achieve correctoutflow angle by modifying the port area and relative outflow velocity.

Energies 2016, 9, 164 5 of 12









shown in Figure 6.











Figure 8. Velocity triangle at runner outlet.


Energies 2016, 9, 164 5 of 12









shown in Figure 6.











Figure 8. Velocity triangle at runner outlet. Figure 8. Velocity triangle at runner outlet.

Energies 2016, 9, 164 6 of 12

Figure 9 shows the port area distribution from crown to shroud in the runner flow passage 1. Theport 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.

Figure 9. Port area distribution of the five cases.

2.3. Numerical Method

Computational fluid dynamics (CFD) analysis is a very useful tool for predicting hydro

machinery performance at various operating conditions [12–15]. 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 × 106, 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 × 106. Therefore, the number of elements around 7.5 × 106

was selected for full domain calculation.

Figure 10. Mesh dependence for the full domain calculation.

22

24

26

28

30

32

34

0 0.25 0.5 0.75 1

Port area (ar) [mm]

Crown to Shroud [Crown=0; Shroud=1]

Case 1Case 2Case 3Case 4Case 5

84

88

92

96

100

104

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

η/ηselected

Number of elements (×106)



Computational fluid dynamics (CFD) analysis is a very useful tool for predicting hydro machineryperformance at various operating conditions [12–15]. Commercial code of ANSYS CFX [16] wasemployed 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 theturbulence model. Inlet turbulence condition is specified as 5% turbulence intensity and the flowdirection is normal to the inlet boundary.

There are two kinds of numerical domain for the CFD analysis. Considering the computation timeconsumption, 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. For1 pitch flow passage (1 stay vane, 1 guide vane and 1 runner blade flow passage), the mass flowcondition 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 theinlet, and the static pressure was set at the outlet of the domain. This is done to maintain the designhead and check the flow rate is matched with design point.

For 1 pitch flow passage, the total number of elements is 5.5 ˆ 106, for which the y+ around theblade surface is 9. Therefore, the total number of elements for 1 pitch flow passage is sufficient forreliable results. In order to exclude the effect of mesh on the prediction accuracy, the mesh dependencewas conducted for full domain CFD analysis as shown in Figure 10. The efficiency was normalized bythe selected efficiency. It can be concluded that the turbine efficiency is insensitive after the number ofelements exceed 7.5 ˆ 106. Therefore, the number of elements around 7.5 ˆ 106 was selected for fulldomain 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.



Computational fluid dynamics (CFD) analysis is a very useful tool for predicting hydro

machinery performance at various operating conditions [12–15]. 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 × 106, 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 × 106. Therefore, the number of elements around 7.5 × 106

was selected for full domain calculation.


22

24

26

28

30

32

34

0 0.25 0.5 0.75 1

Port area (ar) [mm]


Case 1Case 2Case 3Case 4Case 5

84

88

92

96

100

104

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

η/ηselected

Number of elements (×106)


Energies 2016, 9, 164 7 of 12

3. Results and Discussion

3.1. Outflow Pattern

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

Energies 2016, 9, 164 7 of 12



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 11. Outflow angle distribution.

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.

Figure 12. Streamline distribution in draft tube.

3.2. Loss Analysis

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

10

30

50

70

90

110

130

0.0 0.2 0.4 0.6 0.8 1.0

Outflow angle (α2) [°]


Case 1

Case 2

Case 3

Case 4

Case 5


Figure 12 shows the streamline distribution in the draft tube. It is clearly indicated that thestreamline of Case 1 in the draft tube shows large swirl flow, which increases the loss at the drafttube. However, by modifying the port area to a correct extent (Case 5), there are vertically straightstreamlines in the draft tube, and exit flow angle is close to 90˝. The effect of modifying the port areaon correcting the exit flow angle is significant in reducing the swirl flow.

Energies 2016, 9, 164 7 of 12



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.


3.2. Loss Analysis


10

30

50

70

90

110

130

0.0 0.2 0.4 0.6 0.8 1.0

Outflow angle (α2) [°]


Case 1

Case 2

Case 3

Case 4

Case 5


Energies 2016, 9, 164 8 of 12

3.2. Loss Analysis


HLoss “∆ptotalρg

(5)

HLoss runner “

∆ptotal ´TωQ

ρg(6)

where the HLoss is the pressure loss for the stay vane, guide vane and draft tube, HLoss runner is thepressure loss for the runner passage.

Figure 13 shows the loss distribution on each component. As the result is obtained from 1 pitchanalysis without casing, there is no casing component loss analysis. The loss exists to a large extent atdraft 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 totalloss distribution by each case is obtained in Figure 14. There is minimum total loss at Case 5, whichsatisfies outflow angle from runner exit and has the lowest loss at draft tube.

Energies 2016, 9, 164 8 of 12

∆ρg

(5)

∆ω

ρg (6)

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 tube0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

HL

oss

/ H

[%

]

Case 1 Case 2 Case 3 Case 4 Case 5

Figure 13. Loss distribution on each component.

Figure 14. Total loss distribution by each case.

3.3. 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

98.4

98.8

99.2

99.6

100


HLoss/HLoss Max [%]


Energies 2016, 9, x 8 of 12

= ∆ ρg (5)

= ∆ − ωρg (6)

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 tube0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

H Loss

/ H

[%]





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

98.4

98.8

99.2

99.6

100


HLo

ss/H

Loss

Max

[%]


Energies 2016, 9, 164 9 of 12


The performance analysis of the Francis turbine was conducted by full domain as shown inFigure 15. There is best efficiency point of 92.6% with leakage loss at the Q11 of 0.525, at which the flowrate 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 lossand volume loss.

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

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.

Figure 16. Component loss by the flow rate.

3.4. 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 m3/s and

turbine rotational speed is 914 min−1.

10

20

30

40

50

60

70

80

90

86

87

88

89

90

91

92

93

94

0.36 0.4 0.44 0.48 0.52 0.56 0.6 0.64

Output power [kW]

Efficiency [%]

Q11

Efficiency

Output Power

94.0%

(Without leakage)

92.6%

86

88

90

92

94

96

98

100

0.36 0.4 0.44 0.48 0.52 0.56 0.6 0.64

Efficiency [%]

Q11

RV loss

GV loss

DT loss

SV loss

Casing loss


Figure 16 shows the component loss at different flow rates. It can be seen that the loss at thecasing and stay vane passage is relatively small and the loss increases slightly at high flow rate. Theloss at the guide vane passage and runner passage exists relatively to a large extent. The loss at theguide vane passage reduces with increasing the flow rate. However, the loss at the runner passage isinsensitive to the flow rate. Minimum amount of loss exists at the design flow rate. However, the lossincreases rapidly at the off design flow rates. Especially at the partial flow rate, the loss at draft tubeexists 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.


3.4. 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 m3/s and

turbine rotational speed is 914 min−1.

10

20

30

40

50

60

70

80

90

86

87

88

89

90

91

92

93

94

0.36 0.4 0.44 0.48 0.52 0.56 0.6 0.64

Output power [kW]

Efficiency [%]

Q11

Efficiency

Output Power

94.0%

(Without leakage)

92.6%

86

88

90

92

94

96

98

100

0.36 0.4 0.44 0.48 0.52 0.56 0.6 0.64

Efficiency [%]

Q11

RV loss

GV loss

DT loss

SV loss

Casing loss


3.4. Fluid-Structure Interaction Analysis

In order to verify the runner blade structure integrity, fluid-structure interaction (FSI) is aneffective method to calculate the stresses in the Francis turbine runner. Saeed et al. [17] found stress

Energies 2016, 9, 164 10 of 12

maxima in different parts of the runner by FSI method. Xiao et al. [18] investigated the dynamic stressesin a Francis turbine runner successfully based on FSI analysis. In this study, the FSI analysis has beenconducted 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 is540 MPa and yield stress is 415 MPa. The pressure load applied on the runner surface is importedfrom the full domain CFD analysis at the design flow rate, where the flow rate is 1.21 m3/s and turbinerotational speed is 914 min´1.

The surfaces of hub, shroud, pressure and suction sides of the runner blades are selected forpressure loading as shown in Figure 17. The pressure imported to the runner surfaces for the FSIanalysis is shown in Figure 18. The highest imported pressure of around 0.39 MPa exists on the huband shroud surface near the runner inlet.

Energies 2016, 9, 164 10 of 12

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.

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

Figure 18. Pressure imported to the runner surfaces.

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.

Figure 19. Stress distribution on the runner.

4. 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.


Energies 2016, 9, 164 10 of 12












4. Conclusions









The structural feasibility is based on the stress on the runner, which is shown in Figure 19. Themaximum stress point of 23 MPa can be found at the corner between runner blade leading edge andshroud, which is much lower than the material yield stress. The safety factor is 18, which is more thansufficient for a safe structure.

Energies 2016, 9, 164 10 of 12












4. Conclusions









Energies 2016, 9, 164 11 of 12

4. Conclusions

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

Acknowledgments: This work was supported by the New and Renewable Energy of the Korea Institute of EnergyTechnology Evaluation and Planning (KETEP) grant funded by the Korea Government Ministry of Trade, Industryand Energy (No. 2013T100200079). Moreover, the authors are very grateful to Kazuyoshi Miyagawa of WasedaUniversity, Japan, for his valuable advices.

Author Contributions: Zhenmu Chen conceived, designed and analyzed the hydro Francis turbine; Patrick M.Singh analyzed the data; Young-Do Choi planed the study project, as well as contributed the design and analysistools; Zhenmu Chen and Patrick M. Singh wrote the paper and Young-Do Choi revised the paper.

Conflicts of Interest: The authors declare no conflict of interest.

Nomenclature

4ptotal Total pressure differencea0 Guide vane openingar Port areaBg Guide vane heightDr1 Runner inlet diameterg Gravitational accelerationHe Effective headHgv Guide vane head lossHloss Pressure lossHloss runner Runner pressure lossHth Euler headm Hydraulic radiusN Rotational speedNs Specific speedp PressureQ Flow rateQ11 Unit flow rateT TorqueU Peripheral velocityVth VelocityVu Rotational component of absolute velocityW Relative velocityZg Guide vane numberα Flow angleβ Relative flow angleβb Blade angleζ Pressure loss coefficientρ Water densityω Angular speed

Energies 2016, 9, 164 12 of 12

Abbreviations

DT Draft tubeGV Guide vaneRV Runner vaneSV Stay vane

References

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© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open accessarticle distributed under the terms and conditions of the Creative Commons by Attribution(CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

http://dx.doi.org/10.5916/jkosme.2012.36.5.618

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http://dx.doi.org/10.1115/1.2409363

http://dx.doi.org/10.1016/j.advengsoft.2010.09.001

http://dx.doi.org/10.1016/S1007-0214(08)70096-8

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