energies
Article
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
2
*
Graduate School, Department of Mechanical Engineering, Mokpo National University, Mokpo,
Jeollanam-do 58555, Korea; [email protected] (Z.C.); [email protected] (P.M.S.)
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 Lee
Received: 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 basis
of the port area and loss analysis. The meridional shape of the runner was designed focusing mainly
on 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, while the port area of blade was modified by
keeping constant angles of the blade at inlet and outlet. The results show that the effect of the port
area of runner blade on the flow exit angle from runner passage is significant. A correct flow exit
angle reduces the energy loss at the draft tube, thereby improving the efficiency of the turbine. The
best efficiency of 92.6% is achieved by this method, which is also similar to the design conditions by
the 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 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.
Energies 2016, 9, 164; doi:10.3390/en9030164
www.mdpi.com/journal/energies
Energies 2016, 9, 164
2 of 12
Energies 2016, 9, 164 2 of 12 2. Turbine Runner Design and Numerical Method
2. Turbine Runner Design and Numerical Method Figure 1 shows the flow chart of the Francis turbine runner blade design. For one dimension
hydraulicFigure 1 shows the flow chart of the Francis turbine runner blade design. For one dimension design, calculation is required for the blade angle at leading and trailing edges. For the
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
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
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
vane height is determined according to the guide vane loss analysis, and the other parameters, such as theas the runner inlet and outlet diameters, are determined by experience. The outflow angle from the runner inlet and outlet diameters, are determined by experience. The outflow angle from the
runner
passage
is controlled
by the
portport areaarea andand blade
outlet
angle.
Moreover,
thethe blade
outlet
runner passage is controlled by runner
the runner blade outlet angle. Moreover, blade angle outlet angle can be calculated by the Euler head equation. Therefore, the port area can be determined can be calculated by the Euler head equation. Therefore, the port area can be determined by the
by the outflow angle from the runner passage. outflow
angle from the runner passage.
Figure 1. Flow chart of Francis turbine runner blade design. CFD: computational fluid dynamics. Figure 1. Flow chart of Francis turbine runner blade design. CFD: computational fluid dynamics.
2.1. One Dimension Loss Analysis 2.1. One Dimension Loss Analysis
In this study, the runner is designed for the Miryang power station in Korea. The turbine design 3/s for flow rate and the rotational speed is In
this study,
the runner is designed for the Miryang power
station in Korea. The turbine design
point is at H
e = 64.2 m for the effective head, the Q = 1.21 m
3 /s for flow rate and the rotational speed is
−1. The specific speed at the design point is N
point N = 914 min
is at He = 64.2
m for the effective head, the Q = 1.21 ms = 130 m‐kW, which is within the range of Francis turbines with N
N = 914
min´1 . The specifics = 60–450 m‐kW and H = 20–700 m [3]. speed at the design point is Ns = 130 m-kW, which is within the range of
To obtain vane pressure for the meridional shape design, the Francis turbines
withthe Nsguide = 60–450
m-kW
andloss H = coefficient 20–700 m [3].
numerical analysis was performed with different guide vane openings (a
0) and heights (Bg). The To obtain the guide vane pressure loss coefficient for the meridional
shape
design, the numerical
boundary condition at inlet was set as mass flow rate and the flow angle was set same as the guide analysis was performed with different guide vane openings (a0 ) and heights (Bg ). The boundary
vane inlet angle. Inlet turbulence condition was specified as 5% turbulence intensity. The boundary condition at inlet was set as mass flow rate and the flow angle was set same as the guide vane inlet
condition of average static pressure was set at outlet of the guide vane passage. According to the angle.previous study [4,5], the SST k‐ω turbulence model is adopted as turbulence model, which has been 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
well known to estimate both separation and vortex occurrence on the wall of a complicated blade studyshape. [4,5], the
SST k-ωthe turbulence
is adopted
turbulence model,
whichfrom has been
Moreover, value of model
y+, which means as
non‐dimensional distance wall well
[6,7], known
is to estimate
both separation and vortex occurrence on the wall of a complicated blade shape. Moreover,
determined to be around 9 for the guide vane blade surface. The pressure difference measurement locations shown in Figure 2. The location P2 is between the [6,7],
guide isvane and stay to
vane, and 9
the value
of y+are , which
means
non-dimensional
distance
from wall
determined
be around
location P3 is between the guide and runner vane. for the guide vane blade surface. The pressure difference measurement locations are shown in Figure 2.
For P2
evaluating the the
guide vane pressure loss vane,
coefficient (ζ), the equation is determined by and
The location
is between
guide
vane
and stay
and location
P3 is between
the guide
Equation (1): runner vane.
For evaluating the guide vane pressure lossζ coefficient (ζ),2 the
equation is determined by Equation
(1) (1):
ρ
pp2 ´ p3 q ˆ 2
ζ“
ρVth 2
(1)
Energies 2016, 9, 164
Energies 2016, 9, 164 Energies 2016, 9, 164 3 of 12
3 of 12 3 of 12 where p
where
p222 and p
and p333 are the averaged total pressure at locations P2 and P3, respectively. V
are the averaged total pressure at locations P2 and P3, respectively. V ththth is the velocity is the velocity
at the throat of guide vane passage and ρ is the density of the water. 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. Figure 2. Pressure difference location for guide vane loss analysis. 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 (a00/Dr1r1) is 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 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 flow angle is the outflow angle of guide vane passage. The relationship between the outflow angle and
and guide vane opening ratio is obtained as shown in Figure 3. guide vane opening ratio is obtained as shown in Figure 3.
40
y = 1335.7x22 + 65.5x + 5.0
Flow angle (α
Flow angle (α )) [°]
[°]
35
30
25
20
15
10
5
0
0.03
0.05
0.07
0.09
0.11
0.13
Guide vane opening ratio a00/Dr1r1
0.15
Figure
3. Relation of flow angle and guide vane opening ratio.
Figure 3. Relation of flow angle and guide vane opening ratio. Figure 3. Relation of flow angle and guide vane opening ratio. Figure 44 shows
shows the
the relation pressure coefficient guide hydraulic Figure
relation
ofof thethe pressure
lossloss coefficient
and and guide
vanevane hydraulic
radiusradius ratio
ratio (m/D
r1
). It can be seen that there is lower pressure loss coefficient at the larger guide vane r1
(m/Dr1 ). It can
be seen that there is lower pressure loss coefficient at the larger guide vane hydraulic
hydraulic radius. the
Moreover, the between
relationship between pressure loss coefficient and guide vane radius.
Moreover,
relationship
pressure
loss coefficient
and guide
vane hydraulic
radius
hydraulic radius ratio can be obtained as shown in Figure 4. The definition of the hydraulic radius ratio
can be obtained as shown in Figure 4. The definition of the hydraulic radius (m) is shown in
(m) is shown in Equation (2): Equation
(2):
a Bg
`0
˘
m“
(2)
2 ˆ a0 ` Bg (2)
2
Energies 2016, 9, 164 Energies 2016, 9, 164
Energies 2016, 9, 164 44 of 12 of 12
4 of 12 Pressure loss coefficient (ζ)
Pressure loss coefficient (ζ)
0.1
0.1
y = 119.6x2 ‐ 9.5x + 0.2
y = 119.6x2 ‐ 9.5x + 0.2
0.08
0.08
0.06
0.06
0.04
0.04
0.02
0.02
0
00.015
0.015
0.02
0.025
0.03
0.035
0.02
0.025
0.03
0.035
Guide vane hydraulic radius ratio m/Dr1
Guide vane hydraulic radius ratio m/Dr1
0.04
0.04
0.045
0.045
Figure 4. Relation of the pressure loss coefficient and guide vane hydraulic radius ratio. Figure 4. Relation of the pressure loss coefficient and guide vane hydraulic radius ratio.
Figure 4. Relation of the pressure loss coefficient and guide vane hydraulic radius ratio. 350
350
300
300
250
250
200
200
150
150
100
100
50
50
0
0 0
0
η = 93.57% η = 93.57% η = 93.58%
η = 93.58%
GV height
GV height
Efficiency
Efficiency
Bg = 103 Bg = 103 Bg = 95
Bg = 95
0.05
0.1
0.15
0.05
0.1
0.15
Guide vane opening ratio a0/Dr1
Guide vane opening ratio a0/Dr1
Figure 5. One dimension loss analysis result.
Figure 5. One dimension loss analysis result. Figure 5. One dimension loss analysis result. 0.2
0.2
1
1
0.95
0.95
0.9
0.9
0.85
0.85
0.8
0.8
0.75
0.75
0.7
0.7
0.65
0.65
Efficiency (η
Efficiency (η
) [%]
) [%]
Guide vane height (Bg) [mm]
Guide vane height (Bg) [mm]
For the design and best efficiency point, it can be assumed that there is no swirl flow remaining For the design and best efficiency point, it can be assumed that there is no swirl flow remaining at
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 the
draft
tube.
Therefore,
according
to theto Euler
turbineturbine head equation
[2,8–11],[2,8–11], the relation
at the draft tube. Therefore, according the Euler head equation the between
relation between Euler head, guide vane height (Bg) and the outflow angle from guide vane passage (α) is Euler
head,
guide
vane
height
(B
)
and
the
outflow
angle
from
guide
vane
passage
(α)
is
shown
in
g
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 Equation
(3).
Additionally,
according
to
the
pressure
loss
coefficient,
the
relation
between
guide
vane
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 head loss,
guide
(a0 ) and
guide(avane
height
asg) shown
in Equation
(4):in g ) is derived
guide vane head vane
loss, opening
guide vane opening 0) and guide (Bvane height (B
is derived as shown Equation (4): ˆ
˙
Equation (4): U V
1
NQ
Hth “ 1 u1 “ 1
(3)
(3)
g
g1 60
60Bg tanα
tan α (3)
60 tan α
ˆ
˙2
11
Q
Vth 2
(4)
“ ζζ 1
Hgv “ ζ ζ
(4)
(4)
ζ2g2
ζ2g2 Zg a0 Bg 2
2
According to the outflow angle from guide vane passage, guide vane pressure loss coefficient
According to the outflow angle from guide vane passage, guide vane pressure loss coefficient and According to the outflow angle from guide vane passage, guide vane pressure loss coefficient the Euler head, the one dimension loss analysis results are plotted in Figure 5. These results are
and the Euler head, the one dimension loss analysis results are plotted in Figure 5. These results are and the Euler head, the one dimension loss analysis results are plotted in Figure 5. These results are obtained only
flow
rate
andand head.
As the
turbine
head for
thefor design
is point constant
obtained only at
at design
design flow rate head. As Euler
the Euler turbine head the point
design is obtained only at design flow rate and head. As the Euler turbine head for the design point is and
the
turbine
head
is
controlled
by
the
guide
vane
passage
opening,
the
guide
vane
opening
ratio
constant and the turbine head is controlled by the guide vane passage opening, the guide vane constant and turbine head by the guide vane opening, the 5.guide vane (a0 /Dr1 ) has
tothe be
foris a controlled specified guide
vane
height
(Bgpassage ), as shown
in Figure
opening ratio (a
0/Ddetermined
r1) has to be determined for a specified guide vane height (B
g), as shown in Figure 5. opening ratio (a0/Dr1) has to be determined for a specified guide vane height (Bg), as shown in Figure 5. Energies 2016, 9, 164
5 of 12
Energies 2016, 9, 164 5 of 12 The efficiency curve shown in the graph is the design point efficiency with different designs of
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 5 of 12 that there
Energies 2016, 9, 164 guide vane heights (Bg) and guide vane opening ratios (a0/Dr1). As a result, it can be seen that there is is a best
efficiency
guidevane vaneopening opening
ratio
). Additionally,
The efficiency curve shown in the graph is the design point efficiency with different designs of a best efficiency point
point by
by the
the different
different guide ratio (a0(a
/D0r1/D
). r1
Additionally, there there
is a is a
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/Dr1). As a result, it can be seen that there is relatively
wide
guide
vane
opening
ratio
(guide
vane
height)
with
high
efficiency,
meaning
that
relatively wide guide vane opening ratio (guide vane height) with high efficiency, meaning that there
guide vane heights (B
g) 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/Dvane
r1). Additionally, there study,
is a in
is a wide
range
for the
design
of guide
vane
opening
ratio and
guide
height. In this
there is a wide range for the design of guide vane opening ratio and guide vane height. In this study, a relatively best efficiency point by the opening different guide vane vane opening ratio (a0/D
r1). Additionally, there is a wide guide vane ratio (guide height) with high efficiency, meaning that orderin order to fit the runner to the existing Francis turbine plant for performance test, the guide vane to fit the runner to the existing Francis turbine plant for performance test, the guide vane height
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, height (B
g) of 103 mm is selected, which belongs to the high efficiency range according to the one (Bg ) of
103 mm
is selected, which belongs to the high efficiency range according to the one dimension
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 dimension loss analysis. Finally, the meridional plane shape with basic dimensions is determined as loss analysis.
Finally, the meridional plane shape with basic dimensions is determined as shown in
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 shown in Figure 6. Figure
6.
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 dimension loss analysis. Finally, the meridional plane shape with basic dimensions is determined as shown in Figure 6. shown in Figure 6. Figure 6. Meridional plane shape and basic dimensions. Figure 6. Meridional plane shape and basic dimensions.
Figure 6. Meridional plane shape and basic dimensions. 2.2. Turbine Runner Blade Model 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 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. 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 Therefore, the dimension of the port area plays a very important role in controlling the exit relative located
atFigure 7 reveals the definition of the runner blade port area. The port area of the runner blade is the exit of the runner flow passage, which is the minimum area at the runner flow passage.
located at the exit of the runner flow passage, which is the minimum area at the runner flow passage. velocity from runner passage as shown in Figure The relative (W2) reduces with Therefore,
the
dimension
of the port
area plays
a very8. important
rolevelocity in controlling
the exit
relative
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 increasing port area, which causes the outflow angle (α
2) to drop. The outflow angle from runner velocity
from
runner
passage
as
shown
in
Figure
8.
The
relative
velocity
(W
)
reduces
with
increasing
2
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 passage is perpendicular (90°) only with correct relative velocity. Therefore, it is possible to achieve port velocity area,
which
causes
the
outflow
angle
(α
)
to
drop.
The
outflow
angle
from
is
from runner passage as shown in Figure 8. The relative velocity (W2) runner
reduces passage
with 2
increasing port area, which causes the outflow angle (α
2) to drop. The outflow angle from runner correct outflow angle by modifying the port area and relative outflow velocity. ˝ ) only with correct relative velocity.2) to drop. The outflow angle from runner increasing port area, which causes the outflow angle (α
perpendicular
(90
Therefore,
it
is
possible
to
achieve
correct
passage is perpendicular (90°) only with correct relative velocity. Therefore, it is possible to achieve passage is perpendicular (90°) only with correct relative velocity. Therefore, it is possible to achieve outflow
angle by modifying the port area and relative outflow velocity.
correct outflow angle by modifying the port area and relative outflow velocity. correct outflow angle by modifying the port area and relative outflow velocity. Figure 7. Definition of the runner blade port area. Figure 7. Definition of the runner blade port area. Figure
7. Definition of the runner blade port area.
Figure 7. Definition of the runner blade port area. Figure 8. Velocity triangle at runner outlet. Figure 8. Velocity triangle at runner outlet. Figure 8. Velocity triangle at runner outlet. Figure 8. Velocity triangle at runner outlet.
Energies 2016, 9, 164
6 of 12
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
Figure 9 shows the port area distribution from crown to shroud in the runner flow passage 1. port area
has
to be modified until the outflow angle is satisfactory.
The port area has to be modified until the outflow angle is satisfactory. Energies 2016, 9, 164 6 of 12 34
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. Port area (ar) [mm]
Port area (ar) [mm]
32
30 34
28 32
Case 1
Case 2
Case 3
24 28
Case 4
Case 5
Case 1
22 26
Case 2
0
0.25
0.5
0.75
Case 31
24 Crown to Shroud [Crown=0; Shroud=1]
Case 4
Case 5
22Figure 9. Port area distribution of the five cases. Figure
9. Port area distribution of the five cases.
0
0.25
0.5
0.75
Crown to Shroud [Crown=0; Shroud=1]
2.3. Numerical Method 26 30
1
2.3. Numerical Method
Figure 9. Port area distribution of the five cases.
for predicting hydro Computational fluid dynamics (CFD) analysis is a very useful tool 96104
92100
88 96
η/ηselected
η/ηselected
Computational
fluid dynamics (CFD) analysis is a very useful tool for predicting hydro machinery
machinery performance at various operating conditions [12–15]. Commercial code of ANSYS CFX [16] 2.3. Numerical Method performance
at
various
operating conditions [12–15]. Commercial code of ANSYS CFX [16] was
was employed to predict the characteristics of the Francis turbine. The general connection was set as employed
to
predict
the
characteristics
of the(CFD) Francis
turbine.
general
connection
was set ashydro “stage”
“stage” condition between the rotational area and the fixed area. The SST k‐ω model was selected for Computational fluid dynamics analysis is The
a very useful tool for predicting the turbulence model. Inlet turbulence condition is specified as 5% turbulence intensity and the flow condition
between the rotational area and the fixed area. The SST k-ω model was selected for the
machinery performance at various operating conditions [12–15]. Commercial code of ANSYS CFX [16] direction is normal to the inlet boundary. turbulence
model. Inlet turbulence condition is specified as 5% turbulence intensity and the flow
was employed to predict the characteristics of the Francis turbine. The general connection was set as There are two kinds of numerical domain for the CFD analysis. Considering the computation “stage” condition between the rotational area and the fixed area. The SST k‐ω model was selected for direction is normal to the inlet boundary.
time consumption, the cases for different port area calculation (Cases 1–5) was conducted by 1 pitch the turbulence model. Inlet turbulence condition is specified as 5% turbulence intensity and the flow There
are two kinds of numerical domain for the CFD analysis. Considering the computation time
domain. Moreover, for the Francis turbine performance analysis, the full domain analysis was direction is normal to the inlet boundary. consumption, the cases for different port area calculation (Cases 1–5) was conducted by 1 pitch domain.
conducted. For 1 pitch flow passage (1 stay vane, 1 guide vane and 1 runner blade flow passage), the There are two kinds of numerical domain for the CFD analysis. Considering the computation Moreover,
for the
Franciswas turbine
performance
the full
domain
analysis
wasoutlet conducted.
mass flow condition applied at the inlet analysis,
and the static pressure was set at the of the For
time consumption, the cases for different port area calculation (Cases 1–5) was conducted by 1 pitch 1 pitch
flow
passage
(1
stay
vane,
1
guide
vane
and
1
runner
blade
flow
passage),
the
mass
flow
calculation domain. However, for the full domain calculation, the total pressure boundary condition domain. Moreover, for the Francis turbine performance analysis, the full domain analysis was condition
was
applied
at
the
inlet
and
the
static
pressure
was
set
at
the
outlet
of
the
calculation
domain.
was applied at the inlet, and the static pressure was set at the outlet of the domain. This is done to conducted. For 1 pitch flow passage (1 stay vane, 1 guide vane and 1 runner blade flow passage), the However,
forflow the full
domain
calculation,
the inlet totaland pressure
boundary
condition
was
the
maintain the design head and check the flow rate is matched with design point. mass condition was applied at the the static pressure was set at the applied
outlet of atthe 6, for which the y+ around the For 1 pitch flow passage, the total number of elements is 5.5 × 10
inlet, and
the
static
pressure
was
set
at
the
outlet
of
the
domain.
This
is
done
to
maintain
the
design
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 head blade surface is 9. Therefore, the total number of elements for 1 pitch flow passage is sufficient for and
check the flow rate is matched with design point.
reliable results. order to the effect of mesh on the ˆprediction accuracy, mesh the
+ around
maintain the design head and check the flow rate is matched with design point. For
1 pitch
flowIn passage,
theexclude total number
of elements
is 5.5
106 , for which
the ythe 6
+
dependence was conducted for full domain CFD analysis as shown in Figure 10. The efficiency was , for which the y
around the blade surfaceFor 1 pitch flow passage, the total number of elements is 5.5 × 10
is 9. Therefore, the total number of elements for 1 pitch flow
passage is sufficient
for
normalized by the selected efficiency. It can be concluded that the turbine efficiency is insensitive 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 6mesh on the prediction accuracy, the mesh dependence
6 after the number of elements exceed 7.5 × 10
reliable results. In order to exclude the . Therefore, the number of elements around 7.5 × 10
effect of mesh on the prediction accuracy, the mesh was conducted
for full domain CFD analysis as shown in Figure 10. The efficiency was normalized by
was selected for full domain calculation. dependence was conducted for full domain CFD analysis as shown in Figure 10. The efficiency was the selected efficiency. It can be concluded that the turbine efficiency is insensitive after the number of
normalized by the selected efficiency. It can be concluded that the turbine efficiency is insensitive elementsafter the number of elements exceed 7.5 × 10
exceed 7.5 ˆ104
106 . Therefore, the number6. Therefore, the number of elements around 7.5 × 10
of elements around 7.5 ˆ 106 was selected for full
6 domain was selected for full domain calculation. calculation. 100
84 92
0 1
88
2
3
4 5 6 7 8 9 10 11 12 13 14 15
Number of elements (×106)
84
Figure 10. Mesh dependence for the full domain calculation. 0
1
2
3
4 5 6 7 8 9 10 11 12 13 14 15
Number of elements (×106)
Figure 10. Mesh dependence for the full domain calculation. Figure
10. Mesh dependence for the full domain calculation.
Energies 2016, 9, 164
Energies 2016, 9, 164 Energies 2016, 9, 164 7 of 12
7 of 12 7 of 12 3. Results and Discussion 3. Results and Discussion 3.
Results and Discussion
3.1. Outflow Pattern 3.1.
Outflow Pattern
3.1. Outflow Pattern The criterion for the runner blade port area design is the outflow angle. The effect of draft tube The
criterion for the runner blade port area design is the outflow angle. The effect of draft tube on
The criterion for the runner blade port area design is the outflow angle. The effect of draft tube on recycling the kinetic kinetic energy is limited. limited. Especially, the kinetic kinetic energy from the circumferential circumferential recycling
the the kinetic
energy
is limited.
Especially,
the kinetic
energyenergy from the
circumferential
velocity
on recycling energy is Especially, the from the velocity is very hard to collect. Therefore, a correct outflow angle plays a role of reducing the loss at is
very hard to collect. Therefore, a correct outflow angle plays a role of reducing the loss at draft
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 tube
and improving the efficiency of the turbine. The modification of port area is satisfactory until the
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 outflow
angle is as close to 90˝ . Figure 11 shows the outflow angle distribution from runner crown to
until the outflow angle is as close to 90°. Figure 11 shows the outflow angle distribution from runner crown to to shroud. The outflow angle of Case Case is to
located close to 90° with with only small small deviation. deviation. shroud.
The
outflow
angle
of Case
5 is located
close
90˝ with
only
small
deviation.
Moreover,
as the
crown shroud. The outflow angle of 5 5 is located close to 90° only Moreover, as the effect of boundary wall, the deviation increases near the crown and shroud walls. effect of boundary wall, the deviation increases near the crown and shroud walls. Overall, the port
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. area
and the outflow angle of Case 5 are satisfactory for the runner design.
Overall, the port area and the outflow angle of Case 5 are satisfactory for the runner design. 130
130
Outflow angle (α
Outflow angle (α22) [°]
) [°]
110
110
90
90
70
70
Case 1
Case 1
Case 2
Case 2
Case 3
Case 3
Case 4
Case 4
Case 5
Case 5
50
50
30
30
10
10
0.0
0.0
0.2
0.2
0.4
0.4
0.6
0.6
0.8
0.8
1.0
1.0
Crown to Shroud [Crown=0; Shroud=1]
Crown to Shroud [Crown=0; Shroud=1]
Figure
11. Outflow angle distribution.
Figure 11. Outflow angle distribution. Figure 11. Outflow angle distribution. Figure 12 12 shows shows the the streamline streamline distribution distribution in in the the draft
draft tube.
tube. It It is is clearly clearly indicated indicated that that the the Figure draft tube. Figure
12
shows
the
streamline
distribution
in
the
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 streamline of Case 1 in the draft tube shows large swirl flow, which increases the loss at the draft 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 tube. However, by modifying the port area to a correct extent (Case 5), there are vertically straight 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 streamlines in the draft tube, and exit flow angle is close to 90°. The effect of modifying the port area 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. on correcting the exit flow angle is significant in reducing the swirl flow. on
correcting the exit flow angle is significant in reducing the swirl flow.
Figure 12. Streamline distribution in draft tube. Figure 12. Streamline distribution in draft tube. Figure
12. Streamline distribution in draft tube.
3.2. Loss Analysis 3.2. Loss Analysis For the loss analysis, the equation is defined as following: For the loss analysis, the equation is defined as following: Energies 2016, 9, 164
8 of 12
3.2. Loss Analysis
Energies
2016, 9, x
Energies 2016, 9, 164 88 of 12 of 12
For the loss analysis, the equation is defined as following:
∆p∆
HLoss “ = total ρgρg
(5)
(5)
ω
Tω
−
∆p∆
total ´
(6)
=
Q HLoss runner “
(6)
ρg
ρg
where
the
HLoss
the
pressure
loss
for
the
stay
vane,
guide
vane
and
draft
tube,
HLoss runner is
where the Loss is
is the pressure loss for the stay vane, guide vane and draft tube, is the
the where the HLoss is the pressure loss for the stay vane, guide
vane
and
draft
tube,
HLossLoss runner
runner is the
pressure
loss for the runner passage.
pressure loss for the runner passage. pressure loss for the runner passage.
Figure
13 shows the loss distribution on each component. As the result is obtained from 1 pitch
Figure 13 shows the loss distribution on each component. As the result is obtained from 1 pitch 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
analysis without casing, there is no casing component loss analysis. The loss exists to a large extent analysis without casing, there is no casing component loss analysis. The loss exists to a large extent at
at
draft tube at Cases 1 and 2, for which swirl flow exists with large deviation outflow angle from 90°
at draft tube at Cases 1 and 2, for which swirl flow exists with large deviation outflow angle from 90° 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
(as shown in Figure 11). However, the loss at draft tube reduces with correct outflow angle. The total (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
loss distribution by each case is obtained in Figure 14. There is minimum total loss at Case 5, which 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.
satisfies outflow angle from runner exit and has the lowest loss at draft tube. satisfies
outflow angle from runner exit and has the lowest loss at draft tube.
3.5
3.5
3.0
3.0
HLoss
H
Loss / H [%]
2.5
2.5
Case
Case 11
Case
Case 22
Case
Case 33
Case
Case 44
Case
Case 55
2.0
2.0
1.5
1.5
1.0
1.0
0.5
0.5
0.0
0.0
Stay vane
Guide vane
Runner
Draft tube
Figure
13.Loss
Lossdistribution
distributionon
oneach
eachcomponent.
component.
Figure 13. Loss distribution on each component. Figure
13.
HLoss/HLoss Max [%]
HLoss/HLoss Max [%] 100
99.6
99.2
98.8
98.4
Case
1
Case 1
Case
2
Case 2
Case
3
Case 3
Case
4
Case 4
Case
5
Case 5
Figure
14.Total
Totalloss
lossdistribution
distributionby
byeach
eachcase.
case.
Figure
14.
Figure 14. Total loss distribution by each case. 3.3.
Performance Analysis
3.3. Performance Analysis The
The performance
performance analysis
analysis of
of the
the Francis
Francis turbine
turbine was
was conducted
conducted by
by full
full domain
domain as
as shown
shown in
in Figure
15. There is best efficiency point of 92.6% with leakage loss at the Q11
of 0.525, at which the
Figure 15. There is best efficiency point of 92.6% with leakage loss at the Q
11 of 0.525, at which the flow
flow rate
rate is
is the
the design
design flow
flow rate
rate for
for this
this Francis
Francis turbine.
turbine. In
In comparison
comparison to
to the
the efficiency
efficiency without
without Energies 2016, 9, 164
9 of 12
3.3. Performance Analysis
The performance analysis of the Francis turbine was conducted by full domain as shown in
9 of 12 of 92.6% with leakage loss at the Q11 of 0.525, at which the
flow
9 of 12 rate is the design flow rate for this Francis turbine. In comparison to the efficiency without leakage,
leakage, is 1.4% at the rate.
design rate. The ofleakage loss of of
1.4% of disk leakage, is 1.4% difference at the design flow rate. The loss
leakage loss of 1.4% consists of disk there
isthere 1.4%there difference
atdifference the design
flow
Theflow leakage
1.4%
consists
diskconsists friction
loss
friction loss and volume loss. friction loss and volume loss. and volume loss.
94
93
93
92
91
94.0%94.0%
(Without leakage)
(Without leakage)
90
80
80
92
70
70
91
60
60
90
90
50
50
89
89
Efficiency
Efficiency
40
40
88
88
Output Power
Output Power
30
30
87
87
20
20
86
10
0.36 0.360.4 0.40.44 0.440.48 0.480.52 0.520.56 0.560.6 0.60.64 0.64
Q11 Q11
10
86
92.6%92.6%
Output power [kW]
90
Figure
15. Performance of the Francis turbine by the flow rate.
Figure 15. Performance of the Francis turbine by the flow rate. Figure 15. Performance of the Francis turbine by the flow rate. Output power [kW]
94
Efficiency [%]
Efficiency [%]
Energies 2016, 9, 164 Figure
15. There is best efficiency point
Energies 2016, 9, 164 Figure
16 shows the component loss at different flow rates. It can be seen that the loss at the
Figure 16 shows the component loss at different flow rates. It can be seen that the loss at the 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
casing and stay vane passage is relatively small and the loss increases slightly at high flow rate. 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
loss at the guide vane passage and runner passage exists relatively to a large extent. The loss at 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
guide vane passage reduces with increasing the flow rate. However, the loss at the runner passage is 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
insensitive to the flow rate. Minimum amount of loss exists at the design flow rate. However, the insensitive to the flow rate. Minimum amount of loss exists at the design flow rate. However, the increases
rapidly
at the off design flow rates. Especially at the partial flow rate, the loss at draft tube
loss increases rapidly at the off design flow rates. Especially at the partial flow rate, the loss at draft loss increases rapidly at the off design flow rates. Especially at the partial flow rate, the loss at draft exists
in
a
significant
amount.
tube exists in a significant amount. tube exists in a significant amount. Casing loss
Casing loss
GV loss
GV loss
Efficiency [%]
Efficiency [%]
100 100
98 98
96
94
RV loss
94 RV loss
92
92
90
90
88
88
96
86
SV loss
SV loss
DT loss
DT loss
86
0.36 0.360.4 0.40.44 0.44
0.48 0.48
0.52 0.52
0.56 0.560.6 0.60.64 0.64
Q
Q11 11
Figure 16. Component loss by the flow rate. Figure
16. Component loss by the flow rate.
Figure 16. Component loss by the flow rate. 3.4. Fluid‐Structure Interaction Analysis 3.4.3.4. Fluid‐Structure Interaction Analysis Fluid-Structure Interaction Analysis
In order to verify the runner blade structure integrity, fluid‐structure interaction (FSI) is an In In
order to toverify the blade structure integrity, fluid‐structure interaction (FSI) is is
an an
order
verify
therunner runner
blade
structure
integrity,
fluid-structure
interaction
(FSI)
effective method to calculate the stresses in the Francis turbine runner. Saeed et al. [17] found stress effective method to calculate the stresses in the Francis turbine runner. Saeed et al. [17] found stress effective
method to calculate the stresses in the Francis turbine runner. Saeed et al. [17] found stress
maxima in different of runner the runner by method. FSI method. Xiao et al. investigated the dynamic maxima in different parts parts of the by FSI Xiao et al. [18] [18] investigated the dynamic stresses in a Francis turbine runner successfully based on FSI analysis. In this study, the FSI analysis 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. 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 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 540 MPa and yield stress is 415 MPa. The pressure load applied on the runner surface is imported 3 m3/s and from the full domain CFD analysis at the design flow rate, where the flow rate is 1.21 Energies 2016, 9, 164
10 of 12
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
Energies 2016, 9, 164 10 of 12 Energies 2016, 9, 164 10 of 12 Energies 2016, 9, 164 10 of 12 from
the full domain CFD analysis at the design flow rate, where the flow rate is 1.21 m3 /s and turbine
´
1
rotational speed is 914 min .
The surfaces of hub, shroud, pressure and suction sides of the runner blades are selected for The surfaces of hub, shroud, pressure and suction sides of the runner blades are selected for The surfaces of hub, shroud, pressure and suction sides of the runner blades are selected for 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 pressure loading as shown in Figure 17. The pressure imported to the runner surfaces for the FSI pressure loading as shown in Figure 17. The pressure imported to the runner surfaces for the FSI 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 analysis is shown in Figure 18. The highest imported pressure of around 0.39 MPa exists on the hub analysis is shown in Figure 18. The highest imported pressure of around 0.39 MPa exists on the hub 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. and shroud surface near the runner inlet. and shroud surface near the runner inlet. and shroud surface near the runner inlet.
Figure 17. Runner hub and shroud surfaces for pressure loading. Figure 17. Runner hub and shroud surfaces for pressure loading. Figure 17. Runner hub and shroud surfaces for pressure loading. Figure
17. Runner hub and shroud surfaces for pressure loading.
Figure 18. Pressure imported to the runner surfaces. Figure
18. Pressure imported to the runner surfaces.
Figure 18. Pressure imported to the runner surfaces. 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 The structural feasibility is based on the stress on the runner, which is shown in Figure 19. The The structural feasibility is based on the stress on the runner, which is shown in Figure 19. The 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 maximum stress point of 23 MPa can be found at the corner between runner blade leading edge and maximum stress point of 23 MPa can be found at the corner between runner blade leading edge and 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 shroud, which is much lower than the material yield stress. The safety factor is 18, which is more shroud, which is much lower than the material yield stress. The safety factor is 18, which is more shroud,
which is much lower than the material yield stress. The safety factor is 18, which is more than
than sufficient for a safe structure. than sufficient for a safe structure. than sufficient for a safe structure. sufficient
for a safe structure.
Figure 19. Stress distribution on the runner. Figure 19. Stress distribution on the runner. Figure
19. Stress distribution on the runner.
Figure 19. Stress distribution on the runner. 4. Conclusions 4. Conclusions 4. Conclusions The Francis turbine runner design and numerical analysis are presented for the Miryang power The Francis turbine runner design and numerical analysis are presented for the Miryang power 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 station of Korea. A successful design of the Francis turbine runner based on the one‐dimension loss 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 analysis and port area of the runner flow passage has been presented. The port area of runner blade 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 plays a role of correcting the outflow angle from runner passage to reduce the swirl flow and the loss plays a role of correcting the outflow angle from runner passage to reduce the swirl flow and the loss Energies 2016, 9, 164
11 of 12
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.
Acknowledgments: This work was supported by the New and Renewable Energy of the Korea Institute of Energy
Technology Evaluation and Planning (KETEP) grant funded by the Korea Government Ministry of Trade, Industry
and Energy (No. 2013T100200079). Moreover, the authors are very grateful to Kazuyoshi Miyagawa of Waseda
University, 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 analysis
tools; 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
a0
ar
Bg
Dr1
g
He
Hgv
Hloss
Hloss runner
Hth
m
N
Ns
p
Q
Q11
T
U
V th
Vu
W
Zg
α
β
βb
ζ
ρ
ω
Total pressure difference
Guide vane opening
Port area
Guide vane height
Runner inlet diameter
Gravitational acceleration
Effective head
Guide vane head loss
Pressure loss
Runner pressure loss
Euler head
Hydraulic radius
Rotational speed
Specific speed
Pressure
Flow rate
Unit flow rate
Torque
Peripheral velocity
Velocity
Rotational component of absolute velocity
Relative velocity
Guide vane number
Flow angle
Relative flow angle
Blade angle
Pressure loss coefficient
Water density
Angular speed
Energies 2016, 9, 164
12 of 12
Abbreviations
DT
GV
RV
SV
Draft tube
Guide vane
Runner vane
Stay vane
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