1. A methodology for designing Francis runner blade to find minimum
sediment erosion using CFD
Krishna Khanal a, *
, Hari P. Neopane b
, Shikhar Rai a
, Manoj Thapa a
, Subendu Bhatt a
,
Rajendra Shrestha a
a
Tribhuvan University, Nepal
b
Kathmandu University, Nepal
a r t i c l e i n f o
Article history:
Received 23 June 2015
Received in revised form
15 October 2015
Accepted 15 October 2015
Available online xxx
Keywords:
Francis turbine
Erosion
Efficiency
b-distribution
a b s t r a c t
Sediment particles, especially quartz which has very high hardness factor, flowing along with water
erodes turbo machinery parts such as guide vanes, runner, draft tube etc. Among them runner is very
crucial part, so its design should be optimum for minimum erosion by maintaining the highest possible
efficiency.
This paper reports on methodology for designing Francis runner blade. This involves finding best
outlet angle (b2) and blade angle distribution (b-distribution) causing minimum possible erosion for
given volume flow rate (Q ¼ 14.34 m3
/s), head (H ¼ 40 m), rpm (N ¼ 333.33 rpm) and eroding particle
flow rate (0.08 kg/s). At first, the outlet angle b2 (designing parameter) was varied from 14
to 32
using
linear blade angle distribution for all models. Then these models were simulated to find b2. In second,
with that b2, blade angle distribution was varied and simulated to find the best blade angle distribution
having minimum erosion rate with considerable efficiency. By using hydrodynamic theory for given Q
and H, main dimensions were found out and 3D model was generated using b-distribution. Relation of
designing parameters with erosion and efficiency was made. Optimum blade was obtained from pro-
posed methodology and was compared with the reference blade in terms of erosion and efficiency.
© 2015 Elsevier Ltd. All rights reserved.
1. Introduction
The hydroelectric projects in the Himalayan range of Nepal is
facing severe silt erosion problem in turbines, which over a
period of time significantly reduce the overall efficiency of hy-
dropower. Erosion is complex process which depends upon the
number of factors such as particle hardness, size, shape, con-
centration, velocity of water, base material of turbine, etc. [1].
Erosion in run-of-river is more challenging than that of reservoir
type. Rivers contain very high sediment concentration, especially
quartz, during the monsoon season. Quartz is one of the
extremely hard particle which causes mechanical wear on the
turbo components due to dynamic action of particles flowing
along water [2].
Studying the dynamics of a Francis turbine has been a chal-
lenging and costly job. As Francis turbine is a reaction turbine, its
runner is completely dipped in water and covered by various
mechanical parts like wicket gates, guide vanes and spiral casing.
This makes the visualization of the flow very difficult in the
runner and very special arrangements and experimental setup is
required to study the flow inside the Francis turbine. However,
with the advent of CFD techniques the studies of the flow inside
such complex structure have been made easy. CFD has been
widely used in the field of turbo-machineries and hydraulic
turbines. CFD tools specially for solving turbo-machineries'
problems have been developed and lots of researches related to
hydraulic turbines and turbo-machineries have been done with
CFD.
Francis turbine is widely used in many hydropower of Nepal
and some researchers have studied the erosion problem in un-
derwater turbo machines and suggested the recommendation on
reducing erosion. Thapa et al. summarizes the standard pro-
cedures used for design of high head turbines and explained the
effect of design parameters on sediment erosion in Francis run-
ner [3]. Shrestha et al. presents the alternative new way in
Francis turbine design with less erosion impact by incorporating* Corresponding author.
E-mail address: krishnakhanal2048@gmail.com (K. Khanal).
Contents lists available at ScienceDirect
Renewable Energy
journal homepage: www.elsevier.com/locate/renene
http://dx.doi.org/10.1016/j.renene.2015.10.023
0960-1481/© 2015 Elsevier Ltd. All rights reserved.
Renewable Energy 87 (2016) 307e316

2. the application of CFD, FEM and FSI at different stages [4]. Neo-
pane et al. presents the laboratory study of particle velocity
measurement in highly swirl conditions similar to turbine flow in
curved path [5]. Thapa et al. studied the relation between blade
angle distribution of runner blade and the erosion rate [6].
Gaungjie et al. investigated the relation between the wear rates
on the surface of runner blade and guide vane and the sediment
concentration, and analyzed the distribution of wear rates for
normal turbine operating condition [7].
The main objective of the research is to propose a method-
ology which minimizes the erosion in Francis runner blade by
considering efficiency. This research also aims to obtain the
relation of designing parameters with erosion and efficiency so
that it can help in prediction of designing parameters for any
analogous case. Based on the methodology, this paper intends to
propose an optimum blade and compare result with reference
blade. For this, Devighat Hydropower Plant (DHP) with head
(H) ¼ 40 m, volume flow rate (Q) ¼ 14.34 m3
/s, speed
(N) ¼ 333.33 rpm situated at Nuwakot district of Nepal was taken
as the reference site. This study focuses on the erosion of the
Francis runner blade for design condition (not for partial and full
load condition) without considering the effect of guide vanes and
draft tubes. Coalesced effect of erosion and cavitation was also
not included in this study.
2. Blade design and sediment theory
2.1. Francis turbine design
Francis turbine is operated by utilizing the potential energy of
the storage water partially into the kinetic energy and partially into
pressure energy. The water enters the turbine radially, imparts
energy to the runner blades and leaves axially. It works above at-
mospheric pressure and will be fully immersed in water. If there are
sediment particles in the water flow during energy transfer process,
then it will strike turbine and erode the surface to the turbine.
The turbine design calculations are based on hydraulic param-
eters head (H) and discharge (Q). Velocity triangle at inlet and
outlet of the runner are used in design process. Fig. 1 shows the
axial view of runner and Fig. 2 shows the velocity triangle at inlet
and outlet of the Francis runner blade.
The dimensioning of the outlet starts with assuming no
rotational speed at best efficiency point (BEP) i.e. Cu2 ¼ 0. Outlet
angle (b2) is selected from 14 to 32 and calculations were made
as:
Known parameters are Q, N, H and b2. Unknown parameters like
D2, U2, U1, D1, B and b1 are calculated from following relations [3].
D2 ¼
ffiffiffiffiffiffiffiffiffiffi
4:Q
P:Cm2
q
N ¼ 60.U2/(P.D2)
Cm2 ¼ U2.tan (b2)
h ¼ (U1Cu1 À U2Cu2)/(gH)
Rearranging we have
D2 ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
240:Q
p2:N:tanðb2Þ
3
q
U2 ¼ (P.D2.N)/60
Cm1 ¼ Cm2/1.1 (10% meridional acceleration)
C1 ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ð1 À reaction degreeÞ:2gH
p
(reaction degree 0.5 chosen)
Cu1 ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
C2
1 À C2
m1
q
U1 ¼ hgH/Cu1 (whirl component at outlet is zero and h assumed
to be 0.96)
D1 ¼ (60.U1)/(PN)
B ¼ Q/(PDCm1)
b1 ¼ tanÀ1
(Cm1/(U1 À Cu1))
Nomenclature
b1 Inlet blade angle
b2 Outlet blade angle
B Runner height, [m]
C Absolute velocity, [m/s]
D Runner diameter, [m]
U Peripheral velocity, [m/s]
W Relative velocity, [m/s]
N Synchronous speed, [rpm]
Cm Meridian component of C, [m/s]
Cu Tangential component of C, [m/s]
h Efficiency, [-]
1 Inlet section
2 Outlet section
Fig. 1. Axial view of runner.
Fig. 2. Velocity triangle.
K. Khanal et al. / Renewable Energy 87 (2016) 307e316308

3. 2.2. Wear mechanism and erosion model
Damages in hydro power turbines are mainly caused by cavi-
tation problems, sand erosion, material defects and fatigue. In
general, wear mechanisms can be classified in three categories;
mechanical, chemical and thermal actions. In hydraulic turbine
mechanical wear of main concern.
There are three types of mechanical wear; abrasive, erosive and
cavitation wear. Abrasive and erosive are due to particles on the
fluid flow, while cavitation is caused by the collapse of bubbles on
the surface. Abrasive wear is defined as the loss of material by the
passage of hard particles over a surface. Erosive wear is caused by
the impact of particles against a solid surface. Fig. 3 shows the
schematic images of four representative wear modes.
CFX solver has two inbuilt erosion model in it, namely: Finnie
and Tabakoff model. Tabakoff and Grant Erosion Model [9] was
preferred. Erosion rate E is determined from the following relation:
E ¼ k1$f ðgÞ$V2
p $Cos2
ðgÞ
h
1 À R2
T
i
þ f ðVPNÞ
where
f ðgÞ ¼ 1 þ k1k12 sin
g
p
2
go
!2
RT ¼ 1 À k4Vp sin g
f ðVPNÞ ¼ k3
À
Vp sin g
Á4
k2 ¼
1:0 if g 2go
0:0 if g 2go
Here, E is the dimensionless mass (mass of eroded wall material
divided by the mass of particle), Vp is the particle impact velocity, g
is the impact angle in radians between the approaching particle
track and the wall, go being the angle of maximum erosion, k1 to k4,
k12 and go are model constants and depend on the particle/wall
material combination.
3. CFD analysis
Computational Fluid Dynamics (CFD) is one of the branches of
fluid mechanics that uses numerical methods and algorithms to
solve and analyze problems that involve fluid flows. The numerical
solution of NaviereStokes (NS) equations in CFD usually implies a
discretization method: it means that derivatives in partial differ-
ential equations are approximated by algebraic expressions which
can be either obtained by means of the finite-difference or the
finite-element method or finite-volume method. The result is a set
of algebraic equations through which mass, momentum, and en-
ergy transport are predicted at discrete points in the domain. The
governing equations are non-linear and coupled; several iterations
of the solution loop must be performed before a converged solution
is obtained. Millions of calculations are required to simulate the
interaction of fluids and gases with complex surfaces. However,
even with simplified equations and high speed supercomputers,
only approximate solutions can be achieved in many cases [10].
The CFD software includes the package to model the fluid flow
phenomena under the turbulent models. Usually turbulent nu-
merical simulation consists of two main parts, namely: Direct Nu-
merical Simulation (DNS) and Indirect Numerical Simulation (INS).
DNS has a precise calculated result, but the whole range of spatial
and temporal scales of the turbulence must be resolved which re-
quires a very small time step size. So, this is not suitable for CFD
simulation. There are three different types of simulated methods
under the Indirect Numerical Simulation which are large eddy
simulation (LES), Reynolds-averaged NaviereStokes (RANS) and
Fig. 3. Schematic images of four representatives wear mode [8].
K. Khanal et al. / Renewable Energy 87 (2016) 307e316 309

4. detached eddy simulation (DES). RANS is the oldest and most
common approach to turbulence modeling. The equation of
Reynolds-averaged NaviereStokes (RANS) is defined as:
r
DUi
Dt
¼
vP
vXi
þ
v
vXj
m
vUi
vxj
þ
vUj
vxi
!
À ru0
i
u0
j
#
The left hand side of the equation describes the change in mean
momentum of fluid element and the right hand side of the equation
is the assumption of mean body force and divergence stress. ru;
i
u;
j
is
an unknown term and called Reynolds stresses. Due to the aver-
aging procedure information is lost, which is then feed back into
the equations by turbulence model [9].
The shear-stress transport (SST) k-u model [9] was developed by
Menter to effectively blend the robust and accurate formulation of
the k-u model in the near-wall region with the free-stream inde-
pendence of the k-ε model in the far field. To achieve this, Baseline
(BSL) k-w model, which combines advantages of Wilcox k-w and k-
ε model, is provided with the proper transport behavior to limit the
over prediction of eddy viscosity. The equations are:
BSL model:
vðrkÞ
vt
þ
v
vxj
À
rUjk
Á
¼
v
vxj
m þ
mt
sk3
vk
vxj
#
þ Pk À b
0
rku þ Pkb
vðruÞ
vt
þ
v
vxj
À
rUju
Á
¼
v
vxj
m þ
mt
su3
vu
vxj
#
þ ð1 À F1Þ2r
1
su2u
vk
vxj
vu
vxj
þ a3
u
k
Pk
À b3ru2
þ Pub
The proper transport behavior can be obtained by a limiter to
the formulation of eddy-viscosity:
vt ¼
a1k
maxða1u; SF2Þ
where
vt ¼ mt=r
3.1. Mesh independent test
Since the results would be numerical approximation using CFX
solver, the numerical analysis was done to check the numerical
stability and accuracy of the simulation.
Mesh independence test was done for the selection of number
Fig. 4. Head versus mesh elements.
Fig: 5. (a) Test specimen before test. (b) Test specimen after 350 min. (c) Result of CFD analysis d) Runner of JHC [12].
Table 1
Rate of erosion.
SN Test duration (min) Rate of erosion (mg/gm/min)
1 40 0.28
2 80 0.21
3 125 0.27
4 170 0.24
5 215 0.32
6 260 0.30
7 305 0.26
8 350 0.35
Average 0.28
K. Khanal et al. / Renewable Energy 87 (2016) 307e316310

5. of elements in a domain so that the result does not vary signifi-
cantly with increase in the mesh size. This method helps to obtain
minimum number of mesh elements which saves the computation
time without deviating from the accuracy.
Head was chosen as observant parameter. Fig. 4 shows the
relation of head and mesh elements. Since, the change in head is
not so different for more than 600,000 elements. But for the con-
venience and fast computation study was carried out at
300,000 mesh elements with an error of only 0.2 m (with respect to
600,000 elements).
3.2. CFD validation [12]
CFD validation was made by referencing with the experiment
performed at Turbine Testing Lab, Kathmandu University, Nepal. A
test rig called rotating disc apparatus has been developed and
installed in Turbine Testing Laboratory for carrying out sediment
erosion test in Francis runner blades. The main purpose of this test
rig was to compare the wear pattern appearing in test specimens
with the result of the CFD as well as with the wear pattern observed
in turbine operating in real case.
For experiment, hydraulic parameters of Jhimruk Hydropower
Center (JHC) were taken and blade profile of the Francis runner
blade has been modeled. The CFD results, test results and real case
were compared.
The observation for wear pattern was made with painted sur-
face. After running the apparatus for half an hour, it was observed
that paint in some location of blade surface was removed. Fig. 5(a)
and (b) shows the wear pattern in test specimen. The painted
surface has been found to be scratched severely in the outlet region
of blade while some minor scratches have also been observed
throughout the blade surface.
It can be seen that the erosion damage is mostly located in the
far outlet region near to the edge of the blade. The location of paint
removal is identical to the pattern of wear observed in the turbines
operating in real cases. Fig. 5(d) shows the wear observed in the
runner blades of JHC, which is also observed most severe in the
outlet region of the blades. The wear pattern observed during the
experiment is also quite similar to the pattern which has been
predicted from the CFD analysis.
Table 1 shows the rate of erosion in the specimens for each test.
The average rate of erosion was found to be 0.28 mg/gm/min, which
explains that in average, 0.28 mg of material was worn out of 1 g of
test specimen in a minute of operation. It can also be observed that
the overall trend of the erosion rate is increasing with the total
duration of the test run.
CFD results of JHC and DHP will be compared in result and
discussion section so as to confirm the validation of this study.
3.3. Methodology
In general there are two approaches to runner design; the direct
Fig. 6. 3D model obtained in BladeGen.
Fig. 7. Linear b-distribution, Concave downward b-distribution, Concave upward b-distribution.
Fig. 8. Illustrating Curvature position and Curvature percentage.
K. Khanal et al. / Renewable Energy 87 (2016) 307e316 311

6. method and the inverse method. This study uses the direct method,
which begins by setting Q, H and N. Main dimensions such as inlet
diameter, outlet diameter, inlet height, inlet blade angle and outlet
blade angle of runner geometry were obtained by using basic hy-
drodynamic theory [3]. The modeling of the turbine include
creating 2D view in the BladeGen software, which is then converted
into the 3D view by applying the beta distribution. Fig. 6 shows a 3D
model blade obtained in BladeGen.
The 3D Models are created in two ways in two parts:
A) Method on Varying outlet angle:
Design parameter b2 was chosen from 14
to 32
with
difference of 2
i.e. 14, 16, 18, 20, 22, 24, 26, 28, 30, 32. Ten
models were created with linear beta distribution and
simulated to find out best outlet angle.
B) Method on Varying b-distribution:
From the best outlet angle obtained on (A) part, b-dis-
tributions were varied as shown in the Fig. 7.
M-prime is defined as the non-dimensional parameter showing
the position of streamline of blade from leading edge. It ranges from
0 to 1; 0 represents the Leading Edge (LE) and 1 represents the
Trailing Edge (TE). Values from 0 to 1 show the point in streamline
of blade how far from the leading edge.
For the quantification of concave downward and concave upward,
new terms named as curvature percentage and curvature position
(same as M-prime) were defined. Certain percentage of angle is
increased at certain M-prime from the linear b-distribution to form
concave downward distribution (positive curvature percentage) and
certain percentage of angle is decreased at certain M-prime from the
linear b-distribution to form concave upward (negative curvature
percentage). Beizercurvepointsinthe BladeGenwerecreated to form
b-distribution. Fig. 8 describes the various terms such as curvature
percentage, curvature position (M-prime), b1 and b2. At LE, inlet blade
angle is b1 and at TE, outlet blade angle is b2.
Nine curvature position (0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9)
with eleven curvature percentage (À35%, À25%, À15%, À5%, 5%, 0%,
15%, 25%, 35%, 45%, 55%), total 91 models (blade with 0% is same for
all curvature position), were analyzed for the erosion and efficiency
of blade. Positive curvature percentage at all curvature position
produces concave downward b-distribution whereas negative
curvature percentage at all curvature position produces concave
upward b-distribution. Beta-distribution of each blade was created
by BladeGen.
Relation of curvature position (x) and curvature percentage (y):
For each curvature position (x), angle deviation (D) from the
linear blade angle is given by:
D ¼
y
100
*ðb1 À b2Þ
3.3.1. Domain and meshing
Since very large number of mesh elements is needed to simulate
the Francis turbine, the domain with only one passage is created. 3D
model from BladeGen is imported to Ansys Turbogrid for meshing.
Fig. 9 shows the mesh obtained from the Turbogrid.
The mesh resolution is defined by yþ
values, which is a non-
dimensional parameter describing the distance from the wall to
the nearest node.
yþ
¼
rDyut
m
where, ut ¼ tu/r1/2
is the friction velocity, Dy is the distance from
wall to the first mesh node and tu is the wall shear stress.
Theoretically, a mesh resolution of yþ
2 is required for the SST
model to accurately solve the viscous sub-layer. However, such a
low yþ
value is hard to obtain for a Francis turbine runner blade. To
reduce computational cost, wall function is used to approximate
the near-wall flow.
In this study, under Boundary layer refinement control edge
refinement factor of 2.25 was set to adjust the mesh size. Yþ
method with Reynolds number 106
was chosen under near wall
element size specification. Yþ
at hub and shroud was maintained at
150 which is in the range of 20e200 for Francis turbine runner as
recommended by Gjfsæster [11]. Mesh elements number range of
300,000e320,000 (obtained from mesh independence test shown
at Section 3.1) in whole domain was made. The inlet and outlet
radius of the blade was on range 470e675 mm and 600e815 mm
respectively depending upon outlet angle (designing
parameter).
The automatic wall treatment allows a consistent yþ
insen-
sitive mesh refinement from coarse grids, which do not resolve
the viscous sub-layer, to fine grids placing mesh points inside
the viscous sub-layer [9]. CFX solver was used to solve the
domain.
3.4. Result and discussion
At first erosion and efficiency relation with b2 was observed and
best b2 was chosen. From Figs. 10 and 11, erosion as well as
Fig. 9. Mesh obtained from Turbogrid.
Boundary conditions:
Analysis type: Steady State Analysis
Fluid and particle Definition: Water, Quartz
Reference pressure: 1 atm
Erosion model: Tabakoff erosion model
Eroding material: Quartz
Blade material: Steel
Average diameter of quartz: 0.12 mm (Bastakoti et al., 2011)
Shape factor: off
Turbulence model: SST model
Drag force: Schiller Naumann
Volume flow rate: 14.34 m3
/sec
Flow direction: Cylindrical Components for sand also
Number of Position: 5000
Mass flow rate of quartz: 0.08 kg/s
Convergence Criterion: 1e-5 residual
Wall function: automatic
K. Khanal et al. / Renewable Energy 87 (2016) 307e316312

7. efficiency of b2 ¼ 14 and b2 ¼ 16 were nearly same and were best
than others. It can be noticed from the graph that erosion tends to
increase as outlet angle increases and efficiency tends to decrease
with increase in outlet angle with some irregularities. By consid-
ering the manufacturing complexity, b2 ¼ 14 is relatively difficult
to manufacture than b2 ¼ 16. So b2 ¼ 16 was selected as best b2
whose corresponding b1 ¼ 43.
Different blade profile of selected outlet angle (b2 ¼ 16) was
produced and then the result was plotted. Fig. 12 shows meridional
view of Francis runner including the main dimension of the blade
used in the simulation.
The hub and shroud curve were chosen arbitrarily and also the
leading edge and trailing edge of blade were made as shown in
Fig. 12. Each of the stream line has different inlet blade angle b1 and
different outlet blade angle b2. Table 2 and Table 3 summarize the
inlet and outlet blade angle at hub, mean and shroud of the blade.
All the dimension of geometry such as leading edge, trailing
edge, hub, shroud, b1 and b2 were kept same but blade angle dis-
tribution (b-distribution) from leading to trailing edge were varied.
Such variation was done to produce 91 blade models.
91 models were simulated and their erosion and efficiency
pattern was observed. Erosion was not the absolute measurement
but only the relative one. The relation of erosion and efficiency with
blade profiles was obtained from these simulations. Also the opti-
mum blade having minimum erosion relative to other blades
without compromising the efficiency was selected and was then
compared to the reference one.
Fig. 13 shows the relation between erosion and curvature per-
centage for all curvature position. As maximum erosion take place
at single dot point on the blade and contribute more than 60% of
total erosion, so, y-axis is set as total erosion minus maximum
erosion and this compares the blade models effectively. The figure
reveals that erosion is relatively high at À35% curvature and higher
values of curvature position also has higher erosion. For example,
0.9 curvature position has highest erosion at À35%, 55% curvatures.
Although there is no exact regular pattern of erosion according to
curvature percentage, it can be seen that the trend of erosion de-
creases as we shift from negative curvature to zero curvature but
positive curvatures has almost same value of erosion with small
fluctuation for all curvature position. It was observed that the
erosion increased with the increase of curvature towards the
trailing edge; that is at 0.9, 0.85, 0.8 have generally higher erosion
than other curvature positions.
Fig. 14 shows the representative graph for the erosion verses
curvature position. The plot shows that erosion increases as the
curvature is shifted towards trailing edge. It can also be seen that
larger area is eroded when the curvature position is shifted toward
trailing edge as the value of total minus maximum erosion is larger
when the curvature is near trailing edge.
It is necessary to observe the efficiency of the models to deter-
mine the appropriate blade for specific hydro site. Fig. 15 shows the
efficiency verses curvature percentage for all curvature positions.
The graph shows that efficiency at negative curvatures is almost
constant with small deviation but there is significant variation to-
ward positive curvatures. Blade models with curvature position
greater than 0.45 have regular decrease in efficiency as curvature
percentage increases from zero but other curvature position show
some irregularity in efficiency as curvature percentage increases
from zero. The notable point is that the efficiency is higher at
trailing edge (near 0.9 position) for negative curvature percentage
Fig. 10. Erosion vs b2.
Fig. 11. Efficiency Vs b2.
Fig. 12. Meridional view of runner blade showing main dimensions of b2 ¼ 16o
.
Table 2
Detail of runner inlet.
Position Hub Mean Shroud
Circumferential speed (m/sec) 22.2 23.64 26.08
Circumferential component of the
absolute velocity (m/sec)
18.7 18.7 18.7
Blade angle b1 (degree) 63.04 54.4 43.05
Table 3
Detail of runner outlet without swirl.
Position Hub Mean Shroud
Circumferential speed (m/sec) 12.18 17.46 27.06
Blade angle b2 (degree) 31.94 23.52 15.68
K. Khanal et al. / Renewable Energy 87 (2016) 307e316 313

8. but has minimum efficiency for leading edge curvature (near 0.1
position). This trend reverses after zero curvature; that is curvature
at leading edge has higher efficiency compare to those having
curvature at trailing edge.
3.4.1. Optimum blade and comparison
By observing erosion and efficiency plot, an optimum blade was
chosen based on minimum erosion considering performance cri-
terion. The blade model with 25% curvature at 0.25 curvature po-
sition was chosen as optimum blade. Table 4 shows the comparison
of erosion and efficiency.
Although the efficiency of reference blade is slightly higher
(0.25%) than that of optimum one, the erosion rate in optimum
blade is about 31.5 times less than reference blade. So, in almost all
cases, it is beneficial to sacrifice insignificant efficiency loss to
prevent the blade from severe erosion and hence, to increase the
life of blade for considerable period.
The shape of beta-distribution of optimum blade is similar to
shape obtained by Thapa et al. [6]. Figs. 16 and 17 shows the
comparison of erosion between the reference blade and the
Fig. 13. Erosion verses Curvature percentage for all curvature position.
Fig. 14. Erosion (total-maximum) verses Curvature position.
Fig. 15. Efficiency verses Curvature percentage for all Curvature position.
Table 4
Erosion and efficiency of reference and optimum blade.
Blade Erosion Efficiency
Reference 1.7e-6 kg/m2
/s 95.46%
Optimum 5.4E-8 kg/m2
/s 95.21%
K. Khanal et al. / Renewable Energy 87 (2016) 307e316314

9. optimum one respectively. Red color shows the eroded area on the
blade. The figures clearly shows that erosion is significantly less in
optimized blade compare to the reference one. In optimized blade,
pressure side has only some small dots of erosion and has no more
erosion in the suction side.
3.4.2. Blade profile comparison
Fig. 18 shows blade profile comparison of optimum and refer-
ence blade. Red color profile is the optimized blade where as black
color profile is the reference blade.
3.4.3. Comparison of DHP and JHC [3].
CFD results of this study (DHP) were compared to the referenced
JHC results.
Tables 5e7 shows the comparison table of DHP blade (reference
blade) and JHC blade. Although there are some difference in the
input parameters (like shape factors, flow rate), these do not
changes the result pattern significantly. So, it can be said that the
rotating disc apparatus experiment performed for JHC blade can be
taken as a reference material for DHP blade to confirm CFD results.
4. Conclusion and recommendation
This study has showed a methodology for designing Francis
runner blade from starting point by taking flow rate, head and rpm
as designing parameter to optimized blade having minimum
erosion. From the results, it is concluded that blade profile having
25% curvature percentage at 0.25 curvature position is considered as
optimum blade. Although this optimized blade has 0.25% less effi-
ciency than reference one, significant decrease in erosion rate has
been observed; numerically, erosion rate is 31.5 times less than the
reference blade with considerable reduction in erosion area. Thus, it
has been proved that significant improvement can be made to
minimize erosion while maintaining efficiency by changing the
runner blade profile and hence, increase the life of runner blade.
From the charts shown, it can also be deduced that increasing outlet
angle above 200
, in general, increases the erosion and decreases
efficiency. Even if there are some irregularities, erosion is relatively
higher at negative curvature (concave upward) than positive
Fig. 16. Erosion on the pressure and suction side of reference blade respectively.
Fig. 17. Erosion on the pressure and suction side of optimum blade respectively.
Fig. 18. Blade profile comparison of optimum and reference blade.
K. Khanal et al. / Renewable Energy 87 (2016) 307e316 315

10. curvature (concave downward) and curvature towards the trailing
edge causes more erosion than that in the leading edge for both
negative and positive curvatures. Also, it has been revealed that ef-
ficiency would be better if the curvature is made near the leading
edge. Therefore, it can be concluded that it is better to design blade
profile by making positive curvature near leading edges.
This methodology can be used for most of hydro-sites to find out
optimum Francis runner blade by minimizing erosion. However,
even more precise study could be made by producing beta distri-
bution with different shapes for each outlet angle and analysis
could be made on wide range of models to have better under-
standing of erosion and efficiency pattern. Moreover, more so-
phisticated experimental study could be made to validate the
results obtained from simulation so that it will be helpful to predict
and then to reduce erosion effectively in practical application.
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Table 5
General parameters for CFX-Pre.
Parameter DHP JHC
Turbulence SST SST
Flow state Steady Steady
Flow type Inviscid Inviscid
Erosion model Tabakoff Tabakoff
Table 6
Parameters for CFX-pre sediment data.
Data DHP JHC
Material Quartz Quartz
Diameter 0.12 mm 0.1 mm
Shape factor Off 1
Flow rate 0.08 kg/s 0.07 kg/s
Table 7
Result from CFX-post erosion analysis.
Parameter DHP JHC
Sediment erosion 1.7E-6 kg/m2
/s 3.0E-7 kg/m2
/s
Efficiency 95.46% 95.05%
K. Khanal et al. / Renewable Energy 87 (2016) 307e316316