Design of Kaplan Turbine

This article discusses the design of a Kaplan turbine for hydro-power generation in Australia. It covers the working principle, methodology, and mathematical models used in the design process. The Kaplan turbine is a reaction turbine that is well-suited for low head sites. It is designed to generate cheap and renewable electrical energy.

Design of Kaplan Turbine 1
DESIGN OF KAPLAN TURBINE
By Name
Course
Instructor
Institution
Location
Date

Design of Kaplan Turbine 2
Executive Summary
The usage of a cheap, clean source of electrical energy has been a big achievement for
most parts of the world including Australia for the last few years, especially the hydroelectric
power since flowing water is free. Basically, electricity is produced from hydropower energy that
is made available due to the potential energy created from the pressure head, hydro sites as well
as water discharge. Grounded on the location of the hydropower several types of hydro turbines
can be developed and designed depending on the requirements of the designers and developers to
produce electric energy. The key concern is to lower the rate of the dependency on the fossil
fuels which are very harmful to our environment and boost the use of cheap and renewable
sources of electrical energy in most parts of Australia both the towns and the rural. In this paper,
we will design a reaction turbine (Francis/Kaplan) for hydro-power generation in Australia.

Design of Kaplan Turbine 3
Table of Contents
Executive Summary.....................................................................................................................................2
CHAPTER 1: Introduction..........................................................................................................................3
1.1 Background.......................................................................................................................................3
1.2 Scope.................................................................................................................................................4
1.3 Objectives..........................................................................................................................................5
CHAPTER 2: Literature Review.................................................................................................................6
CHAPTER 3: Methodology...........................................................................................................................8
3.1: Working Principle.............................................................................................................................8
3.2 Schematic diagram......................................................................................................................9
3.3 Formula Or Theory.....................................................................................................................10
3.3.1 Power.................................................................................................................................10
3.3.2 Specific Speed....................................................................................................................11
3.3.3: Speed of the Runner (N)..........................................................................................................11
3.4 Required mathematical model and design......................................................................................12
3.4.1 Distortion of the Blade..............................................................................................................12
3.4.2: Velocity Triangle......................................................................................................................13
3.4.3 Thickness of Blade Section........................................................................................................15
CHAPTER 4: Result.....................................................................................................................................18
CHAPTER 5: Discussion..............................................................................................................................20
CHAPTER 6: Conclusion and recommendation..........................................................................................21
CHAPTER 7: References.............................................................................................................................23
Appendices................................................................................................................................................24

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Table of tables
Table 1: Showing Classification of Turbines...............................................................................................5
Table 2: Showing the budget for development.........................................................................................18
Table 3: Result Data of Blade Profile.........................................................................................................19
Table 4 Result Data of Forces acting on Blade...........................................................................................20
Table 5: Result Data of Blade Thickness....................................................................................................21
Table of Figures
Figure 1: Showing Basic Layout of a Kaplan Turbine ................................................................................6
Figure 2: general arrangement of a typical Kaplan Turbine ........................................................................8
Figure 3: shows Kaplan Turbine having a different number of blades as 3, 4, and 5 ..................................9
Figure 4: showing the working principle of the Kaplan Turbine ...............................................................10
Figure 5: Showing Schematic diagram 1....................................................................................................10
Figure 6: Showing Schematic diagram 2 ...................................................................................................11
Figure 7: Showing Schematic diagram 3 ...................................................................................................12
Figure 8: Showing Blade section ...............................................................................................................14
Figure 9: Velocity Triangle of Kaplan Blade...............................................................................................16
Figure 10: Showing Blade Section..............................................................................................................17
Figure 11: Showing the Gantt Chart...........................................................................................................19

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CHAPTER 1: Introduction
1.1 Background
Hydropower produced basically from hydroelectric rivers falls and dams are very
sustainable, clear and green sources of electrical energy which generates relatively cheaper
electricity and also reduces the emission of carbon (Hall, 2010). Due to the source`s high energy
density, hydropower is one of the most effective and highly primary available green power
sources that generate electrical energy. For it to have higher efficiency, there must be
installations of the hydraulic turbines in the power plant which are very suitable based on the
head and site discharge (Krivčenko, 2014). There are several hydraulic turbines which can be
employed and these two common types include;
1. Reaction Turbines
2. Impulse Turbines
An impulse turbine is that hydraulic turbine in which all the energy (hydraulic) obtained from
water are converted to the kinetic energy before the water arrived at the turbine runner. While in
the reaction turbine there is some hydraulic energy available which are converted to kinetic
energy before the water strikes the turbine`s runner. The reaction turbine is well suited due to the
head range present at any chosen construction site. There are three well-known reaction turbines
which are ;
1. Pelton
2. Francis
3. Kaplan

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Table 1: Showing Classification of Turbines
Number Type Head Flow rate Specific Speed
1 Kaplan Turbine Low High High
2 Pelton Turbine High Low Low
3 Francis medium Medium Medium
1.2 Scope
In this paper we will make the design on the Kaplan turbine, these turbines have
relatively high specific speed, smaller dimension, therefore, the dimension of the generator are
somehow smaller that always result into the relatively lower cost (Krishna, 2017). Moreover, the
Kaplan turbine has an overload capacity, Water moves via Scroll housing directly into the guide
vane in the radial direction. From this point, it flows making a right angle and then enters the
runner axially. There are as well types of the Kaplan Turbines, that is double and single
regulated, the first one contains just adjustable runner blade while the latter contains both
flexible and adjustable guide vane (Nechleba, 2011). Basically, Kaplan turbine is operational for
a head range of about 2m and 40 m. The double regulated Kaplan operates in a large range of the
designed discharge which is always in 15% - 100 %, but single regulated turbine work at a very
lower range of 30%-100%. The diagram below shows a Kaplan turbine;

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Figure 1: Showing Basic Layout of a Kaplan Turbine (Fielding, 2011).
In this design, we will focus on the low head Kaplan turbine runner since the low head
schemes can be readily executed runoff- rivers and canals. The key focus is on the development
and design of the Kaplan turbine blade for hydro-power generation in Australia. The key features
based on the site will also be calculated during the design.
1.3 Objectives
 To develop a complete case study on hydropower plant (where using reaction turbine)
located anywhere in the world.
 To study the prospect of hydro energy in Australia and identify at least two potential
sites suitable for reaction turbine applications.
 To design (i.e. blade, guide vane, stationary vanes, runner, casing etc.) for an effective
reaction turbine for the selected site.

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 To analyse performance characteristics (i.e. power output, torque, in-out velocity profile,
flow rate, losses, cavitation etc.) of the designated turbine.
CHAPTER 2: Literature Review
The first effort to use the adjustable blades was done in the year 1867 by a scientist by the
name Ludlow O.W who issued the patent of the clue of the design. But now the person who
really made attempts are finally succeeded to develop the Kaplan Turbine was Victor Kaplan
was an Australian engineer. This was done during the early twentieth century actually to be
specific it was Thursday 23rd August 1934 (patent in the public domain, that day the design was
successful). This type of turbine is actually an improvement through modifications from the
Francis Turbine, this was done through the addition of adjustable runner blades. Kaplan is
always installed in large rivers as well as Dams (Zhang, 2010).
The head experienced from this type of Turbine ranges from 1.5 meters to about 50. This
type of Turbine always works best at between heads of 1.5 meters and 15meters. But at a head
over 15, the efficiency of the Kaplan turbine will begin to reduce. This type of turbine can be
vertically or horizontally oriented depending on the flow input. The Kaplan Turbine which are
vertically oriented permits for runner diameter for about 10 meters (Singal, 2012). It is also
possible to increase the efficacy of the Kaplan turbine through adjusting the inlet angle, the
turbine radius, blade pitch angle as well as the exit angle. All these factors are very exceptional
due to the rate of flow for every particular site as well as the scenario of the flow. This type of
the turbine`s efficacy is actually suitable in almost every part of the world since it does not need
much head (Taylor, 2014). The below is a general arrangement of typical Kaplan Turbine;

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Figure 2: general arrangement of a typical Kaplan Turbine (Coutu, 2012).
Bigger Kaplan turbine contains relatively bigger potential energy which generates sufficient
hydroelectric power to help power up to about five million households a year in Australia. And this is
equal to about twenty million oil barrels which are almost about 10 million metric tons of carbon (iv)
oxide emission. Together with the Kaplan variable head, it can generate and also produce an output
which ranges from small KW to about 230 Megawatts. The diagram below shows Kaplan Turbine having
a different number of blades as 3, 4, and 5.
Figure 3: shows Kaplan Turbine having a different number of blades as 3, 4, and 5 (Nechleba, 2011).

Design of Kaplan Turbine 10
CHAPTER 3: Methodology
3.1: Working Principle
The Kaplan Turbine operates as follows, water from the penstock enters the casing scroll, the
casing is constructed in the suitable shape which ensures that the pressure is maintained during the
operation. The water is then directed into the runner blades through the guide vanes (Coutu, 2012). The
vanes are made to be flexible and it is possible to adjust itself in accordance with the specification of
flow rate. Water makes a turn of 90 degrees, thus the direction of the water is axial to runner blades.
The Kaplan blades then start to revolve as water hits due to the reaction force of the moving water
( hence the name reaction turbine).
The blades contain twist along its length so as maintain an optimum angle of attack for all cross-
section of blades to realize greater efficacy. Water then enter into the draft tube from runner blade
immediately, here the pressure of water energy and kinetic energy will reduce. Kinetic energy will be
converted into pressure energy and this results to pressure increase of the water. Therefore the
rotation of the turbine is employed to rotate the shaft to help produce electrical energy. The diagram
below shows the working principle of the Kaplan Turbine
Figure 4: showing the working principle of the Kaplan Turbine (Fielding, 2011).

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3.2 Schematic diagram
Figure 5: Showing Schematic diagram 1 (Nechleba, 2011).
Figure 6: Showing Schematic diagram 2 (Nechleba, 2011).

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Figure 7: Showing Schematic diagram 3 (Nechleba, 2011).
3.3 Formula Or Theory
Some of the basic formulae employed in Kaplan Turbine are illustrated as below;
3.3.1 Power

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The power of the Kapna turbine is a multiplication of the discharge via the turbine and the head of
water, and this can be given mathematically as below;
P= ⍴×g×Q×H×Ƞh ……………………………………………………………………………………………………………. 1
Where g is the gravitational acceleration which is always given 9.81m/S2 , H is the gross head given m, Q
is the discharge in M3/S, ⍴ is the water density in Kg/m3 and Ƞh is hydraulic efficiency (Fielding, 2011).
3.3.2 Specific Speed
Basically, on this parameter, hydraulic turbines are grouped, this is the speed of the Kaplan turbine that
is identical in shape as well as other parameters and it also works in the unit head and generates a unit
power. It can be given mathematically as below;
Ns=
8 85.5
H n
1
4
…………………………………………………………………………………………………………….. 2
Where Ns is the specific Speed and Hn is the Net Head
And also based on the available head, the net head can be calculated from the following equation
Hn= H*Ƞh …………………………………………………………………………………………………………… 3
3.3.3: Speed of the Runner (N)
N= Ns × H n1.25
√ p …………………………………………………………………………………………………………. 4

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3.4 Required mathematical model and design
3.4.1 Distortion of the Blade
Blade of the turbine is viewed to be distorted into some sections always six, the velocity triangle
of these six sections of the blade must be obtained. The angle β α of every section gives the summary of
the blade`s distortion. Before the design is made for every section, velocity triangle, as well as radii of
every section, is determined as below;
Figure 8: Showing Blade section (Nechleba, 2011).
For section 1
In the design radius, R1 and radius of the hub Ri are equal. All the radii of the sections of the blades can
be obtained from the following equations
R1=R2

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For section 2
R2 = Di
2 + 0.00015*De
For section 3
R3=R2+ R 4−R 2
2
For section 5
R4 = De
2 * √1+¿ ¿ ¿
For section 5
R5= R4 + R 6−R 4
2
For section 6
R6= De
2 -0.015*De
3.4.2: Velocity Triangle
For one to know the angle of every section, the velocity diagram must be drawn for every
section. Several velocities like flow velocity, whirl velocity and tangential velocity must be drawn as
shown in the diagram below. The first velocity triangle is witnessed when water just gets into the runner
but another velocity triangle happens when water leaves the runner. The vertical components such as
Wm2 and Wm1 are the flow velocities and they are always equal (Kovalev, 2010). The value t shows the
distance between two adjacent blades while l shows the blade´ length.

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Figure 9: Velocity Triangle of Kaplan Blade (Hall, 2010).
Where w is the relative velocity, c is the absolute velocity while u is the tangential velocity.
The different types of velocities can be obtained below;
Tangential velocity
U= π × d ×n
Absolute velocity
Cu= Hn× g
u
Whirl Velocity
Wu=Cu-u

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Flow velocity
Wm= Q
A
Relative Velocity
W= √ w u2 +w m2 ………………………………………………………………………………………..5
Blade angle
β ∞=arcos Wu
w
3.4.3 Thickness of Blade Section
Figure 10: Showing Blade Section (Zhang, 2010).
An assumption is made that the resultant force will be acting at the tip of the blade but not on the
centre of the blade´s pressure. There will also a consideration of a safety factor of 1.5, therefore there is

Design of Kaplan Turbine 18
no failing in bending during the operation. The thickness can be obtained using the bending stress from
the following equation;
y= √ 6 × Fr × Z
h× σpermissible
Where σpermissible is the stress allowable, y is the thickness of the blade and z is the distance between
the top of the section and the tip of the blade.
σpermissible = σyield
FOS ,
When the material is assumed to be 16Cr5Ni and σyield=6750 ( also assumed ) and the safety factor is
also assumed to be 1.5, then
Z=Re-Rn
Resultant Force
Fr= √ F2 t+ F2 a
Where Fa is the axial force given in N and Ft is the tangential force given in N
Tangential Force
Ft= P
2× π × N × Z ×rcp
Where N is the speed of rotation in rpm, Z is the number of blades and rcp is the radius of the centre
pressure given in m.
The centre pressure is a point where the entire resultant force can be taken to be acting and at a
distance is obtained from the below equation;

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rcp = y= √ R2 e +R2 t
2 …………………………………………………………………………………………………..6
Axial Force
Fa= ⍴*gHn*Ab
Where Ab= Blade area and it is calculated from the equation below
Ab= π × ∝¿ ¿…………………………………………………………………………………………………….7
The diagram below illustrates the Gantt chart for the project development and rolling off
Figure 11: Showing the Gantt Chart
The table below summarizes the budget which would be employed in rolling off the project
Table 2: Showing the budget for development
Number Action Cost in USD

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1 Preliminary design 891
2 Actual Design 2301
3 Purchase of materials 190
4 Testing 23
5 Implementation 32109
CHAPTER 4: Result
The result can be best illustrated using the following tables
Table 3: Result Data of Blade Profile
Parameter Un
it
1 2 3 4 5 6
R m 0.473 0.656 0.839 0.954 1.068 1.102
L m 0.844 0.980 1.226 1.374 1.414 1.414
U m/
s
9.50 13.16 16.83 19.13 21.43 20.86
w m m/
s
10.39 10.39 10.39 10.39 10.39 10.39
w u m/
s
15.79 11.39 8.91 7.84 7.00 6.83

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c u m/
s
18.90 15.42 17.81 13.02 14.78 12.45
w 1 m/
s
12.15 10.54 13.06 15.34 17.78 19.37
w 2 m/
s
14.08 16.77 19.78 21.77 23.82 25.29
w∞ m/
s
13.11 13.66 16.42 18.56 20.80 22.33
β ∞ º 127.55 130.42 140.71 145.92 150.01 152.00
180-β ∞ º 52.44 49.57 39.28 34.07 29.98 28.00
Table 4 Result Data of Forces acting on Blade
Parameter Symbol Value Unit
Yield Stress 750 MPa
Factor of Safety FOS 1.5 -
Allowable Stress 500 MPa
No. of Blades Z 4 -
Radius of Center
r
cp 0.839 m
of Pressure

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Tangential Force F t 74.26 kN
Area of Blade A
b 0.711 m 2
Axial Force Fa 106.84 kN
Table 5: Result Data of Blade Thickness
Parameter Unit 1 2 3 4 5 6
Rn m 0.473 0.656 0.839 0.954 1.068 1.102
z m 0.628 0.445 0.262 0.147 0.033 0.005
y mm 127.85 107.66 82.69 62.04 29.33 20.00
CHAPTER 5: Discussion
From the results given above in table form , it can be easily stated that there was an increase in
tangential velocity with the increase in the number of section employed in the design. For example, the
tangential velocity was 9. 5 m/s when the section was only one and it was 20.86. This can be further
supported from the equation U= × d × n . So when n the number of section increases the tangential
velocity u also increases . But when the section is increased it is so obvious that the distance d will also

Design of Kaplan Turbine 23
increases, this makes the u to increase when the number of sections are increased and it will decrease
when the number of sections are decreased.
The length L and the radius R will also increase when the number of sections is increased this is
because when the number of sections is increased the design become bigger. y is the thickness of the
blade and z is the distance between the top of the section and the tip of the blade.
In table 4 when there was an increase in the number of sections, there was a decrease in the z, this
because z is the is the distance between the top of the section and the tip of the blade. So with the
increase in a number of sections is the distance between the top of the section and the tip of the blade
reduces and this can be clearly stated in the result section. For instance when there was just one section
z was 0. 6 28 but when the number of the section were maximum that is six, then the value of z was
0.005.
The thickness y also reduces with the increase in the number of sections. This is because the
pressure of water is higher and it requires a very strong wall to help maintain it, hence when there was
just one section the thickness of that single section need to be bigger to help maintain the pressure of the
flowing water. But when the sections are increased, every section will increase the thickness of the
overall design therefore individual section can have a reduced thickness and it will still act effectively.
CHAPTER 6: Conclusion and recommendation
In summary, hydroelectric power is very crucial renewable source of energy which is on high
demand in most parts of Australia. Therefore the design for the Kaplan turbine will really help in the
generation of a cheap, green/ clean and reliable source of electricity. Basically, electricity is produced
from hydropower energy that is made available due to the potential energy created from the

Design of Kaplan Turbine 24
pressure head, hydro sites as well as water discharge. Grounded on the location of the
hydropower several types of hydro turbines can be developed and designed depending on the
requirements of the designers and developers to produce electric energy. Therefore this design
will help to reduce the emission of carbon dioxide which would have been emitted if coal was
employed in the generation of electrical energy. Some of the recommendations includes, there
needs to be a perfect selection of construction site where there is a natural waterfall, this is very
important as it makes it easier to realize higher pressure head.

Design of Kaplan Turbine 25
CHAPTER 7: References
Coutu, A., 2012. Flow-Induced Pulsation and Vibration in Hydroelectric Machinery: Engineer’s Guidebook
for Planning, Design and Troubleshooting. 2nd ed. Melbourne : Springer Science & Business Media.
Fielding, L., 2011. Turbine Design: The Effect on Axial Flow Turbine Performance of Parameter Variation.
4th ed. Sydney: ASME Press.
Hall, C., 2010. Fluid Mechanics and Thermodynamics of Turbomachinery. 3rd ed. Liverpool: Butterworth-
Heinemann.
Kovalev, N., 2010. Hydro turbines, design and construction: (Microturbine, konstruktsii i voprosy
proektirovan. 7th ed. Sydney: Program for Scientific Translation.
Krishna, R., 2017. Hydraulic Design of Hydraulic Machinery. 4th ed. Michigan: Avebury.
Krivčenko, G. I., 2014. Hydraulic Machines: Turbines and Pumps. 1st ed. California: Mir.
Nechleba, M., 2011. Hydraulic Turbines: Their Design and Equipment. 3rd ed. Chicago: Artia.
Singal, M., 2012. Hydraulic Machines: Fluid Machinery. 2nd ed. Melbrone: I. K. International Pvt Ltd.
Taylor, C., 2014. Numerical Grid Generation in Computational Fluid Dynamics. 3rd ed. Sydney: Pineridge.
Zhang, J., 2010. Fluid Machinery and Fluid Mechanics. 2rd ed. Sydney: Springer Science & Business
Media.

Design of Kaplan Turbine 26
Appendices
For section 1
In the design radius R1 and radius of the hub Ri are equal . All the radii of the sections of the blades can
be obtained from the following equations
R1=R2
For section 2
R2 = Di
2 + 0.00015*De
For section 3
R3=R2+ R 4−R 2
2
For section 5
R4 = De
2 * √1+¿ ¿ ¿
For section 5
R5= R4 + R 6−R 4
2
For section 6
R6= De
2 -0.015*De

Design of Kaplan Turbine 27
The final design of Kaplan is shown below
The blade section is shown below

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Kaplan during construction
Diagram below illustrates schematic diagram of Kaplan

Design of Kaplan Turbine 29