PEMP
RMD510
Design of Hydraulic
Turbines
Session delivered by:
P f Q.
Prof.
Q H.
H Nagpurwala
N
l
Dept. of Automotive and Aeronautical Engineering
Session-15
@ M.S. Ramaiah School of Advanced Studies, Bengaluru
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Session Objectives
PEMP
RMD510
• To understand the importance of various parameters involved in
the design
g of Pelton,, Francis and Kaplan
p turbines
• To discuss the design guidelines and various empirical design
relations
• To carry out design of a typical low power Pelton turbine, a
Francis turbine and a Kaplan turbine
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RMD510
Design of Pelton Turbine
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Schematic of Pelton Turbines
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RMD510
Pelton turbine with single
g jjet
Pelton turbine with two jets
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Pelton Turbine Installation
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Net Head for Power Generation
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In practice the penstock is
sized so that at rated power the
net head is usually 85-95% of
the total head
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Jet Velocity and Energy Transfer
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RMD510
(Value of  is 165-170°
to avoid interference)
Jet impingement
Double hemispherical shape of bucket
… and from Euler turbine equation,
equation the
energy transferred to the wheel is
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Working Design Proportions
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Working Design Proportions
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Working Design Proportions
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Working Design Proportions
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RMD510
M
M = 1.1 to 1.5d
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Working Design Proportions
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Vertical Pelton Wheel with Six Jets
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Fig 5.11 Vertical Pelton Turbine with 6 jets
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Jet Runner Interaction
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RMD510
Time dependent flow visualization
visualization, taken by a high speed camera in
a typical model Pelton turbine
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Design of a 1.5MW Pelton Turbine
PEMP
RMD510
Given:
Water head = 500 m
Generator power
po er output,
o tp t Pg = 1500 kW
Generator speed, Ng = 750 rpm
Generator efficiency, g = 0.8
Mechanical efficiency, m = 0.85
of turbine:
1. Brake power
p
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2. Absolute velocityy of jet:
j
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Design of a 1.5MW Pelton Turbine
PEMP
RMD510
3. Velocity of bucket:
4. From Euler equation
Assume: K = 0.85, reduction of relative velocity due to friction
 = 165°,
165° vane angle
l
E
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Design of a 1.5MW Pelton Turbine
5. Required flow rate, Q from
power equation:
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6. Nozzle dimensions:
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Design of a 1.5MW Pelton Turbine
7. Diameter of Pelton wheel:
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RMD510
8. Dimensions of bucket
B = 4 Dn = 4 x 0.08367 = 0.3347m
D = 0.9 Dn = 0.9 x 0.08367 = 0.0753m
M = 1.1Dn = 1.1 x 0.08367 = 0.092m
L = 2.4Dn = 2.4 x 0.08367 = 0.2008m
Number of buckets
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Choice of Materials
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1. Manifold
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2. Nozzle
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3. Deflector
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4. Runner
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5. Turbine Shaft
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6. Housing
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RMD510
Design of Francis Turbine
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Francis Turbine
Guide vanes
Runner blades
Rotation
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Work Done and Efficiency
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Euler Turbine Equation
If the flow at runner exit is without swirl then the equation reduces to
Hydraulic
y
Efficiencyy
If c3 = 0, then
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Important Design Relations
PEMP
RMD510
Ratio of width to diameter of the runner,
runner n = b2/D2 = 0.1
0 1 – 0.4
04
Flow ratio, ca2 /sqrt (2gH) = 0.15 – 0.3
Speed ratio, U2 /sqrt (2gH) = 0.6 – 0.9
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Francis Turbine Design
PEMP
RMD510
The following data is given for a Francis turbine.
Net head, H = 60 m
S d N = 700 rpm
Speed,
Shaft power = 294.3 kW
o = 84% ; h = 93%
Flow ratio = 0.20
0 20
Width ratio n = 0.1
Outer diameter of the runner = 2* inner diameter of runner. The thicknesses of
vanes occupy 5% of circumferential area of the runner,
runner velocity of flow is
constant at inlet and outlet and discharge is radial at outlet. Determine:
(i) Guide blade angle
((ii)) Runner vane angles
g at inlet and outlet
(iii) Diameters of runner at inlet and outlet, and
(iv) Width of wheel at inlet
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Francis Turbine Design
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Francis Turbine Design
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Francis Turbine Design
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Francis Turbine Design
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Francis Turbine Design
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Francis Turbine Design
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Francis Turbine Design
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Francis Turbine Design
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Choice of Material
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RMD510
1. Spiral Casing, Stay Ring and Stay Vanes
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2. Covers
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3. Draft Tube Cone
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4. Draft Tube
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5. Guide Vanes
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6. Runner
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7. Labyrinth Seals
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8. Turbine Shaft
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PEMP
RMD510
Design of Kaplan Turbine
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PEMP
RMD510
Definition of Heads of Kaplan Turbine
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Design Specifications
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Power and Specific Speed
PEMP
RMD510
Power
= 97.806
97 806 W = 98 kW
Specific Speed
H = Gross head
Hn = Net head
H
Hence,
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Correlation by
y F. Schweiger
g
and J. Gregory
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Rotational Speed
PEMP
RMD510
E = Specific
p
hydraulic
y
energy
Therefore
Therefore,
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This speed is optimal because it
is synchronous to the generator
speed Thus,
speed.
Thus the turbine can be
directly coupled to the
generator.
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Runaway Speed
PEMP
RMD510
The runaway speed is the max. speed which the turbine can theoretically
attain. It is achieved during load rejection.
The following guideline can be used to determine the runaway speed.
Choosing double regulation for the turbine
turbine,
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Runner Diameter
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RMD510
Hub Diameter
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Suction Head
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RMD510
The suction
Th
i head,
h d Hs, is
i the
h head
h d where
h the
h turbine
bi is
i installed;
i
ll d if the
h
suction head is positive, the turbine is located above the trail water; if it is
negative, the turbine is located under the trail water. To avoid cavitation,
the range of the suction head is limited. The maximum allowed suction
head can be calculated using the following equation:
Where:
patm
pv
ρ
g
c4
σ
Hn
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atmospheric pressure [Pa]
water vapor pressure [Pa]
water density [kg/m3]
acceleration of gravity
outlet average velocity [m/s]
cavitation
it ti coefficient
ffi i t [-]
[]
net head [m]
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Cavitation
PEMP
RMD510
Given:
Suction head,
Therefore,
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Outlet Velocity
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RMD510
 The outlet velocity c4 can be established via the discharge and the
diameter at the outlet of the water ppassage.
g Since the dimensions of
the water passage are not known, the outlet velocity has to be
assumed. An outlet velocity of 2m/s is chosen. Using this velocity, a
ddiameter
a ete of
o 1.38m
.38 would
wou d aarise
se at tthee outlet
out et oof tthee wate
water passage - a
quite realistic value.
 As long as the chosen suction head is below the established suction
head, no cavitation occurs.
 A suction head of 0.45m is chosen.
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Blade Shape
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RMD510
Two different views of a blade
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Velocity Triangles
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RMD510
u tangential velocity [m/s]
c absolute velocity [m/s]
w relative
relati e velocity
elocit [m/s]
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Spanwise Blade Sections
PEMP
RMD510
To define the twist of the blade, the velocity triangles at six different radii
of the blade are determined. The angle β∞ of each radius gives information
on the twist of the blade.
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Analysis of Velocity Triangles
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Analysis of Velocity Triangles
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RMD510
Therefore,
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Analysis of Velocity Triangles
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Analysis of Velocity Triangles
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RMD510
Velocity triangle information at 6 radial locations from hub to tip
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Procedure for Blade Characteristics
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RMD510
Step-1
Lift coefficient at each radius is determined by the following equation:
Where
w2
w∞
patm
Hs
pmin
relative velocity at blade exit [m/s]
medial relative velocity [m/s]
atmospheric pressure [m]
suction head [m]
minimal water pressure [m]
ηs
c3
c4
K
efficiency of the energy change [-]
[]
velocity after the runner [m/s]
outlet velocity [m/s]
profile characteristic number
The values of the following parameters are assumed as per the guidelines:
pmin = 2 - 2.5,
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ηs = 0.88 - 0.91,
K = 2.6 - 3
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Procedure for Blade Characteristics
PEMP
RMD510
Step-2
The ratio l/t is determined using the following relation:
Where:
g
acceleration of gravity [m/s2]
ηh
hydraulic efficiency [-]
H
gross head [m]
cm
meridian velocity [m/s2]
λ
angle of slip [°]
u
tangential velocity [m/s2]
(180-β∞) inflow angle [°]
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The angle of slip λ has to be assumed;
the range for the assumption is as
follows:
λ = 2.5
2 5° - 3
3°
Using this assumption, an approximate
value of the ratio l/t can be established.
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Procedure for Blade Characteristics
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RMD510
Step-3
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
The ratio of the lift coefficients
ζa/ζA can
ζa/ζ
ca be read
ead off
o from
o the
t e
given chart.

Using this ratio the lift coefficient
ζA can be
b established.
bli h d
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Procedure for Blade Characteristics
Step-4
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RMD510
 This figure gives
information on the drag
coefficient ζW of the
different profiles.
 Each of the curves
represents one of the
profiles which are listed
beside the chart.
 First, it has to be decided
which of the profiles
should be chosen;
following this, the drag
coefficient of this profile
can be determined by
y
using the chart.
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Procedure for Blade Characteristics
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RMD510
Step-5
The angle of slip can be calculated using the following equation:
 Check whether the assumed angle of slip and the calculated angle of slip are
similar or not.
 If the difference is too great, repeat the procedure using the angle of slip
calculated from the above equation.
 Steps
p 2 to 5 must be repeated
p
until the angles
g of slipp do not change
g anymore;
y
however, it is necessary to always choose the same profile in Step 4.
 When the angle λ is fixed, it can be assumed that the last calculated values of
Steps 2 to 5 are accurate enough.
 Thus, the ratio l/t and the profile are determined.
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Procedure for Blade Characteristics
PEMP
RMD510
Step-6
The angle of attack δ of the chosen profile
can now be established using the given
figure.
The Steps 1-6 are to be followed for all the
six radial sections of the blade.
blade
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Calculation of Blade Characteristics
PEMP
RMD510
Lift Coefficient
and
Therefore
Therefore,
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and
= 0.08
0 08
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Calculation of Blade Characteristics
PEMP
RMD510
Ratio 1/t
Reciprocal
ec p oca of
o l/t
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Lift Coefficient
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RMD510
From the graph
Therefore,
h f
the
h lif
lifting
i coefficient,
ffi i
A
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Drag Coefficient
PEMP
RMD510
From the graph
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Angle of Slip, 
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RMD510
A l off slip
Angle
li
It can be seen that the calculated value (= 2.7o) of angle of slip is fairly close to
the assumed value (= 3o).
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Angle of Attack and Angle of Twist
PEMP
RMD510
Angle of attack
A l off ttwist
Angle
it
=
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Radial Variation of Blade Parameters
PEMP
RMD510
The listed values in the Table are obtained using the profile 430
To get the accurate angle of distortion, the angle δ has to be subtracted from the
angle (180-β∞).
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Choice of Materials
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RMD510
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1. Spiral Casing
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RMD510
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2. Stay Ring and Stay Vanes
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3. Guide Vanes
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4. Runner
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5. Draft Tube Cone
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RMD510
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6. Turbine Shaft
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Session Summary

Constructional features of hydraulic turbines are briefly
discussed.

Design guidelines and typical working design proportions of
Pelton Francis and Kaplan turbines are explained.
Pelton,
explained

Design examples of the three types of turbines are presented.

Typical materials used in different components of hydraulic
turbines are listed.
Session-15
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RMD510
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PEMP
RMD510
Th k you
Thank
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