International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 7, July 2012)
Numerical Investigations for Jet Flow Characteristics on Pelton
Turbine Bucket
Vishal Gupta 1, Dr. Vishnu Prasad2
1
2
PhD Scholar, Department of Energy, MANIT, Bhopal, MP
Professor, Department of Civil Engineering, MANIT, Bhopal, MP
Earlier model testing was the only method available for
assessing performance of impulse turbines for different
nozzle and bucket shapes. But this approach is time
consuming, costly and did not provide detailed flow
behavior. With the improvements in the field of computers
and advancement in numerical techniques, detailed flow
analysis in given flow domain can be obtained for its
design optimization in the least time. The geometry can be
altered till the best performance is obtained. The flow of
water jet on Pelton bucket is free surface flow and requires
flow simulation for multiphase flow taking water and air as
fluid medium.
In the present paper, numerical flow simulation of
circular and rectangular shapes of jets for two jet velocities
has been carried out using Ansys CFX for study of jet
shape on flow characteristics on bucket. As Pelton bucket
is symmetrical, geometry of half of the Pelton bucket has
only been considered and thus the shapes of jets: semicircle
and square of same cross section area are considered. The
numerical and theoretical forces have been compared.
Pressure distribution, velocity stream lines, water volume
fraction on stationary half bucket have been shown.
Abstract— In Pelton turbines, the jet of circular cross
section is issued from nozzle and moves in air before striking
the bucket. The bucket is divided into two symmetrical semiellipsoidal cups by sharp edge splitter. The jet strikes the
bucket on the splitter. The splitter divides the jet into two
equal sheets of water having free surface which moves on the
curved path of bucket. The profile of curved path of bucket
affects the force and also pressure and velocity distribution
over bucket. Many investigators have worked for
improvement of bucket profile for circular jet. The jet shape
may also affect force, pressure and velocity distribution on
bucket. Earlier, experimental techniques were used to predict
the forces on bucket but it was difficult to get pressure and
velocity distributions. Secondly, the experimental approach is
time consuming as well as costly and needs special laboratory
facilities. The development of CFD for multi phase free
surface flow made it possible to investigate the fluid flow on
Pelton turbine and also to visualize the flow pattern. The
objective of this paper is compare the flow characteristics on
Pelton bucket with circular and rectangular jet using
numerical multi phase flow simulation. Numerical and
theoretical results have been compared for typical bucket
profile and bears closed comparison.
Keywords— computational fluid dynamics, free surface flow,
Impulse turbine, multi-phase fluid flow.
II. GEOMETRIC MODELING AND BOUNDARY CONDITIONS
Depending on the nature of problem, the numerical flow
simulation needs input of 2D or 3D geometry of flow
domain. The flow domain is divided into small elements
forming mesh. The numerical method is used for
discretisation of governing equations over an element.
I. INTRODUCTION
In hilly areas, high head hydro power plants are
common and the turbines used for such plants are impulse
turbines. Among impulse turbines, Pelton turbine is
commonly used. In an impulse turbine, all the available
energy of water is converted into kinetic energy or velocity
head by passing it through a contracting nozzle provided at
the end of penstock. The water coming out of the nozzle is
circular in cross-section. The water jet moves freely in air
and impinges on a series of buckets of the runner thus
causing it to revolve. The performance of the turbine
depends upon many factors and one of them is the shape of
jet striking the turbine bucket which depends upon the
shape of the nozzle.
A. Geometry
The geometry of two nozzles shapes namely semi-circular
and rectangular with same cross sectional area has been
modeled. The flow domain consists of jet and half of the
bucket. The modeling has been done in ANSYS ICEM
CFD-13.0.
364
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 7, July 2012)
The 3D views of half bucket [5] and complete domain for
semi-circular jet are shown in figure 1 and figure 2
respectively.
Fig 3: Mesh for semi-circular jet
Fig 1: 3D View of half Bucket
Fig 2: 3D View of complete domain for semi-circular jet
Fig 4: Mesh for square jet
B. Mesh Generation
The tetrahedral elements have been used for 3D flow
domain and triangular elements for 2D surfaces. The
meshing of domains for semi-circular and square jets has
been shown in fig.3 and fig.4 respectively. The summery of
mesh data for two cases is given in Table 1.
TABLE 1
MESH DATA
Part Name
Inlet
Jet Back
Jet Half
Opening
Bucket
Fluid Flow
Region
365
Number of Elements
Circular
Rectangular
689
643
10487
10123
5205
3125
51756
52981
28766
28774
7351929
7368493
Element
Type
Triangular
Triangular
Triangular
Triangular
Triangular
Tetrahedral
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 7, July 2012)
C. Common Input Data
The fluid properties and some common input data used
in the two variants are mentioned in Table 2.
III. COMPUTATION OF THEORETICAL FORCE
The bucket placed in front of jet deflects the jet from its
direction at an angle of 170°. As per Newton’s second law
of motion, the theoretical impulse force exerted by the jet
on plate is calculated by neglecting losses as:
TABLE 2
COMMON INPUT DATA
Domain type
Fluid type
Reference pressure
Buoyancy
Domain motion
Mesh deformation
Interphase transfer
Free surface model
Surface tension coeff
Density of water
FT  AV1 (V1  V2 cos )
Fluid Domain
Air and Water
1 atm
-9.81 m/sec2
Stationary
None
Free Surface
Standard
0.072 N/m
997 kg/m3
(1)
Hence actual force experienced by bucket will be less than
theoretical force given by equation (1). The ratio of
computed and theoretical force is expressed as force
coefficient as:
 
FC
FT
(2)
The deviation between theoretical and computed force is
expressed in percentage as
FT  FC
x100
FT
D. Boundary Conditions
The flow parameters like pressure and velocity or mass
flow rate are to be specified in the form of inlet and outlet
boundary conditions to obtain numerical simulation and the
solution of the problem depends on the values given at
boundary conditions.

Inlet boundary condition: This condition has been defined
at inlet in the form of water velocity as 50 m/s and 68 m/s
normal to surface and uniform distribution. The value of
water volume fraction was given as 1 and 0 for air.
The flow simulation has been carried out for two
different shapes of jet of same cross-sectional area (307
mm2) with jet velocity of 50 m/s and 68 m/s. The distance
between jet and bucket (80mm) is also kept same in all
cases. The root mean square (RMS) residual is set to 10 -6
for the termination of iterations. The simulation has
provided water velocity stream lines, pressure distribution
etc. within the flow domain and also on bucket.
The theoretical impulse force by jet on the bucket depends
upon the cross-sectional area of the jet, density of liquid,
velocity of the jet striking the bucket, angle at which the
water is leaving the bucket. The shape of jet is not
considered in theoretical computation but surrounding air
and surface tension will affect the force due to different
surface areas of jets.
(3)
IV. RESULTS AND DISCUSSIONS
Wall conditions: The bucket half is defined as smooth wall
and wall contact angle is taken as 0°.
Symmetry: The section dividing jet into two equal parts was
given as symmetry type boundary condition.
Outlet boundary conditions: As the jet flow is free surface,
hence all boundaries except bucket are defined as opening
type with relative pressure as 0 atmospheric.
366
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 7, July 2012)
Fig 5: Velocity streamlines for semi-circular jet (50 m/s)
Fig 8: Velocity streamlines for square jet (68 m/s)
Fig 6: Velocity streamlines for rectangular jet (50 m/s)
Fig 9: Pressure contour for semi-circular jet (50 m/s)
Fig 7: Velocity streamlines for semi-circular jet (68 m/s)
367
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 7, July 2012)
Fig 10: Pressure contour for semi-circular Jet (68 m/s)
Fig 12: Pressure contour for square jet (68 m/s)
Fig 11: Pressure contour for square jet (50 m/s)
Fig13: Water volume fraction for semi-circular jet (50 m/s)
368
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 7, July 2012)
Fig16: Water volume fraction for square jet (68 m/s)
Fig14: Water volume fraction for semi-circular jet (68 m/s)
It is seen from streamline pattern that jet has parallel
stream lines before striking the plate. The stream lines
diverse near the bucket due to deflection of jet at 170°.
The jet spreads after striking the bucket. It is observed that
more water leaves through the cut-out which leads to
wastage without contribution to impulse force. It is also
observed that more area of bucket surface experiences high
pressure in case of circular jet.
The pressure distributions on the bucket due to jet strike
in the figures 9, 10, 11, 12 indicate that the pressure is
maximum in the sharp curvature zone of the bucket due to
stagnation of jet velocity.
It is observed from figures 13, 14, 15, 16 that water spreads
uniformly over bucket in case of circular jet
TABLE 3
COMPARISON OF THEORETICAL AND COMPUTED FORCES
Jet
Circular- 50 (m/s)
Square- 50 (m/s)
Circular- 68 (m/s)
Square- 68 (m/s)
Fig15: Water volume fraction for square jet (50 m/s)
FT (N)
1518.8
1518.8
2809.1
2809.1
FC (N)
1462.55
1454.25
2640.06
2614.64
ζ
0.963
0.957
0.939
0.931
ϕ
3.70
4.25
6.01
6.92
The theoretical and numerical values of forces are given
in Table 3. The theoretical force in all cases is more than
computed as the losses are neglected in theoretical force. It
is seen that the jet force on bucket is more for circular jet
than the force by the square jet. This is due to the less
surface area of circular jet in contact with air
369
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 7, July 2012)
V. CONCLUSIONS
The force coefficient for circular and rectangular jet are
found to be nearly same for a given jet velocity. As the jet
velocity is increased, force coefficient decreases and
deviation increases indicating more losses. The pressure
distribution over bucket surface is more uniform for
circular jet as compared to rectangular jet. The deviation
between the theoretical and computed within acceptable
limit, CFD can be use to access the flow pattern for
optimization of bucket shape.
REFERENCES
[1] Alexandre Perrig, François Avellan, Jean-Louis Kueny, Mohamed
Farhat. 2006. Flow in a Pelton Turbine Bucket: Numerical and
Experimental Investigations. Transaction of ASME. Journal of Fluid
Engineering. Vol. 128. pp. 350-358
[2] B. Zoppe, C Pellore, T. Maitre, P. Leroy. 2006. Flow Analysis
Inside a Pelton Turbine Bucket. Transaction of ASME. Journal of
Turbomachinery. Vol. 128. pp. 500-511.
[3] M.S. Konnur, Kiran Patel. 2006. Numerical Analysis of Water Jet on
Flat Plate. 33rd National Conference on Fluid Mechanics and Fluid
Power. Raipur. India.
[4] K Patel, B Patel, M Yadav, and T Foggia. 2010. Development of
Pelton turbine using numerical simulation. IOP Conf. Series: Earth
and Environmental Science 12.
[5] V V Barlit. 1974. Fundamentals of the theory of hydraulic turbines.
[6] Parkinson Etienne. 2003. New Developments in CFD Extend
Application to Pelton Turbines. CFX Update.
[7] ANSYS CFX-13 software manuals.
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