FSI analysis of Francis turbines exposed to sediment erosion

FSI Analysis of Francis Turbines Exposed to Sediment Erosion

Sailesh Chitrakar

July, 2013

Sediment erosion is one of the key challenges in hydraulic turbines from a design and maintenance perspective in Himalayas and Andes. Past research works have shown that the optimization of the Francis turbine runner blade shapes can decrease erosion by a significant amount. This study con- ducted as a Master’s Thesis has taken the proposed designs from past works and conducted a CFD analysis on a single passage of a Francis runner blade to choose an optimized design in terms of erosion and efficiency. Structural analyses have been performed on the selected design through one-way and two-way FSI to compare the structural integrity of the designs.

Two types of cases have been considered in this thesis work to define the boundary condition of the structural model. In the first case, a runner blade is considered to have no influence of the joint and other stiffer components. In the second case, a sector of the whole runner has been modeled with necessary boundary conditions. Both one-way and two-way FSI have been performed on the cases for the designs. Mesh independent studies have been performed for the designs, but only for the first case, whereas in the second case, a fine mesh has been used to make the analysis appropriate.

The loads have been imported into the structural domain from the fluid on the interfaces for one-way FSI. In the case of two-way FSI, the Multi-Field Solver (MFX) supported by ANSYS has been used to solve the coupled field analysis. A fully coupled FSI in ANSYS works by writing an input file in the structural solver containing the information about the interfaces in the structural domain, which is imported in the fluid solver. The interaction between the two domains is defined in ANSYS-CFX, including the mesh deformation and solver setups. The results have been post-processed in CFX-Post, where the results from both the fields are included. It has been found that the structural integrity of the optimized design is better than the reference design in terms of the maximum stress induced in the runner. The two-way FSI analysis has been found as an inevitable part of the numerical analysis.

However, with the advancement of the computational capability in the future, there could be a great scope in the research field to carry out a fully-coupled transient simulation for the whole runner to get a more accurate solution.

Keywords: Sediment erosion, one-way FSI, two-way FSI, Francis turbine

I would like to express my gratitude to Professor Michel Cervantes for the continuous support, su- pervision, useful comments, remarks and engagement throughout this master thesis. Furthermore I would like to thank Mr. Biraj Singh Thapa for providing me with all the necessary inputs in this thesis work. His constant support, encouragement and belief towards me and my work made me do the work effectively and punctually. I would also like to thank my program coordinator and lecturer, Professor Damian Vogt for accepting my proposal of doing the thesis in Nepal.

Also, I would like to express my appreciation to all the members of the Turbine Testing Lab, whose continuous care and support made my stay a pleasant one. I would also like to thank Professors Bhola Thapa and Hari Prasad Neopane for their continuous motivation during the project.

Finally, I would like to thank my parents who motivated me and helped me complete my KTM works

while I was away in KU.

List of abbreviations . . . . 9

List of symbols . . . . 10

1 Introduction 15 1.1 Background of the work . . . . 15

1.2 Kathmandu University(KU) and Turbine Testing Lab(TTL) . . . . 16

1.3 Objective of this study . . . . 16

1.4 Study methodology . . . . 17

1.5 Scope of study . . . . 17

1.6 Outline of the thesis . . . . 17

2 Hydro Turbines 18 2.1 Hydropower in Nepal . . . . 18

2.2 Principles of hydro turbines . . . . 19

2.3 Cavitation . . . . 20

2.4 Types of hydro turbines . . . . 21

2.4.1 Pelton turbines . . . . 22

2.4.2 Kaplan turbines . . . . 22

2.4.3 Francis turbines . . . . 23

2.4.4 Work done and efficiency of Francis turbine . . . . 24

2.4.5 Francis turbines in Nepal . . . . 25

3 Sediment Erosion 27 3.1 Materials behavior and coatings . . . . 28

3.2 Sediment erosion in hydraulic machinery . . . . 29

3.3 Sediment erosion in Nepal . . . . 30

3.4 Erosion models . . . . 31

3.4.1 Basic erosion models in ANSYS-CFX . . . . 32

4 Recent works - Review 34 4.1 CFD works . . . . 34

4.2 FSI works . . . . 37

4.3 Other relevant works . . . . 37

5 FSI review 40 5.1 Coupled-Field Analysis . . . . 40

5.1.1 Sequential Method-Physics files . . . . 41

5.1.2 Sequential Method-ANSYS multi-field solver . . . . 41

5.2 Strategy of FSI in ANSYS . . . . 42

5.2.1 Set up ANSYS and CFX models . . . . 42

5.2.2 Flag Field interface conditions . . . . 43

5.2.3 Set up Master Input . . . . 43

5.2.4 Obtain the solution . . . . 43

5.3 Governing equations in FSI . . . . 43

6 CFD analysis 45 6.1 Sensitivity study . . . . 46

6.2 Mesh convergence study . . . . 46

6.3 Baseline case for the sensitivity analysis . . . . 47

6.4 Effect of the physical parameters . . . . 48

6.4.1 Effect of the particle size on the erosion . . . . 48

6.4.2 Effect of the particle shape on the erosion . . . . 49

6.4.3 Effect of the particle behavior . . . . 50

6.5 Effect of the numerical parameters . . . . 51

6.5.1 Effect of the residual criteria . . . . 51

6.5.2 Effect of the turbulence models . . . . 52

6.5.3 Effect of the erosion models and their parameters . . . . 52

6.6 Comparison between the optimized and the reference blades . . . . 54

7 Structural analysis 57 7.1 Geometry . . . . 57

7.2 Boundary condition . . . . 60

7.2.1 Case I . . . . 60

7.2.2 Case II . . . . 60

7.3 FSI mesh study . . . . 62

7.4 Results of One-way FSI . . . . 63

7.5 Case-I . . . . 63

7.6 Case-II . . . . 63

8 FSI analysis 68 8.1 Mesh deformation . . . . 68

8.2 Interface setup . . . . 69

8.3 Solver Setup . . . . 71

8.4 Post processing . . . . 71

8.5 Results of Two-way FSI . . . . 73

8.5.1 Case-I . . . . 73

8.5.2 Case-II . . . . 73

9 Conclusion 77 10 Future scope in the related field 79 Bibliography 80 11 Appendix-I - Some discrepancies with the design program (Khoj) 83 11.1 Direction of the inflow . . . . 84

11.1.1 Modification and influence on the result . . . . 86

11.2 Guide vane outlet and runner inlet . . . . 88

12 Appendix-II - Imposing cyclic symmetry boundary conditions in ANSYS 90

2.1 Co-ordinates and velocity triangles of a typical turbomachinery rotor . . . . 20

2.2 Cavitation due to contraction of a pipe and saturation pressure vs fluid temperature . 21 2.3 Cavitation along a passage with non-uniform area . . . . 21

2.4 Jet impingement into a bucket with corresponding velocity triangles . . . . 22

2.5 Section of a Kaplan turbine[6] . . . . 23

2.6 Some basic components of Francis turbines [4] . . . . 24

3.1 Erosive wear mechanisms [5] . . . . 27

3.2 Erosive wear for various materials at different impingement angles . . . . 28

3.3 Areas exposed to sediment erosion wear in Francis turbines [19] . . . . 30

3.4 Sediment erosion wear in the Francis turbine guide vane and runners in Jhimruk [19] . 31 4.1 Hub, shroud and the blade passage from Turbogrid . . . . 35

4.2 CFX-pre setup file showing the blade passage and the mesh . . . . 35

4.3 Sediment erosion rate density of the reference design[21] . . . . 35

4.4 FSI analysis layout used in the study [7] . . . . 38

4.5 Boundary conditions of the runner used in the study [7] . . . . 38

4.6 Parametric study of the shape of the blades [26] . . . . 39

5.1 ANSYS multi-field solver process [24] . . . . 42

5.2 Schematic of Fluid structure interaction . . . . 44

6.1 Mesh convergence study for the factor ratio of 1.15, RMS of 1E-6 and y+ value on the blade . . . . 47

6.2 Sediment erosion pattern for various mesh densities . . . . 48

6.3 Effect of the size of the particle on the erosion pattern . . . . 49

6.4 The erosion pattern for the particle diameter of 0.01 mm on both Pressure and Suction side . . . . 49

6.5 Average and maximum erosion rate density on the blade for various particle sizes . . . 50

6.6 Effect of the particle shape on the erosion pattern . . . . 50

6.7 Effect of the Mass flow rate on erosion . . . . 51

6.8 Effect of the residual criteria for convergence on the blade loading . . . . 52

6.9 Effect of the turbulence models on erosion . . . . 53

6.10 Effect of the Erosion models on the results . . . . 54

6.11 Sediment erosion results for various shapes of the blade . . . . 56

7.1 Leading edge and trailing edge design for FEM [27] . . . . 57

7.2 Comparison of the two domains with two cases (right one shows better mapping) . . . 58

7.3 The geometry modeling in Pro-E as described in the above procedure . . . . 59

7.4 Boundary conditions used for the case I . . . . 61

7.5 Boundary conditions used for the case II . . . . 61

7.6 Mesh convergence study for structural analysis . . . . 62

7.7 Result of one-way coupling for Case-I . . . . 64

7.8 Result of one-way coupling (Stress distribution) for Case-II . . . . 65

7.9 Result of one-way coupling (Stress distribution on the blade) for Case-II . . . . 66

7.10 Result of one-way coupling (Deformation) for Case-II . . . . 67

8.1 Project schematic of the two-way FSI . . . . 69

8.2 Mesh of the two fields and mapping . . . . 70

8.3 Convergence plot in CFX-solver for the FSI analysis in this study . . . . 72

8.4 Stress distribution on the blade from two-way FSI . . . . 74

8.5 Stress distribution on the runner from two-way FSI . . . . 75

8.6 Mesh deformation in the fluid domain from two-way FSI . . . . 76

11.1 Boundary Vector at the inlet with the given flow direction . . . . 84

11.2 Boundary Vector at the inlet with the given flow direction . . . . 85

11.3 Boundary Vector at the inlet with the given flow direction . . . . 85

11.4 Result of the two flow directions, unmodified (top) and modified(below) . . . . 87

11.5 Discrepancy between the results when only the runner and the full stage is modeled . 89

12.1 Choices of imposing cyclic symmetry property to the sector of the runner . . . . 91

2.1 Major hydropower plants in Nepal . . . . 19 2.2 Technical specification of Francis turbines installed in Hydro-power stations in Nepal . 26

3.1 Coefficients for Quartz-Aluminum using Tabakoff Erosion Model . . . . 33

4.1 Various CFX parameters used in the study[21] . . . . 36

KU Kathmandu University

TTL Turbine Testing Laboratory

FEM Finite Element Method

FSI Fluid Structure Interaction

NORAD Norwegian Agency for Development Cooperation NEA Nepal Electricity Authority

N P SH

Net Positive Suction Head available N P SH

Net Positive Suction Head required

SST Shear Stress Transport

CFD Computational Fluid Dynamics

CSD Computational Structural Dynamics

CMD Computational Multi-body Dynamics

FEA Finite Element Analysis

MFS Multi-Field Solver-Single code MFX Multi-Field Solver-Multiple code

SST Shear-Stress Transport

RANS Reynolds Averaged Navier-Stokes

APDL ANSYS Parametric Design Language

Hydro Turbines Parameters

H

Total Head [m]

g Acceleration due to gravity [m/s

]

C Absolute velocity [m/s]

C

Absolute velocity at the inlet [m/s]

C

Axial absolute velocity component [m/s]

C

Circumferential absolute velocity component at the inlet [m/s]

C

Circumferential absolute velocity component at the inlet [m/s]

U

Tangential velocity of the runner at the outlet [m/s]

U

Tangential velocity of the runner at the inlet [m/s]

W Relative velocity [m/s]

ω Rotational speed [rad/s]

∆t Time steps [s]

Q Flow rate (Discharge) [m

/s]

P Power [W]

η

Mechanical efficiency [-]

η

Overall efficiency [-]

η

Hydraulic efficiency [-]

ρ Density [kg/m

]

FSI Parameters

µ Dynamic viscosity [N.s/m

]

p Pressure [Pa]

u

Cartesian component of velocity u in direction x

[m/s]

F

(t) Transient load vector defined for the fluid [N]

F

(t) Transient load vector defined for the solid [N]

M Mass in the equation of motion [kg]

K Stiffness in the equation of motion [N/m]

C Damping in the equation of motion [N.s/m]

K

A pseudo-structural stiffness matrix which is defined for the whole domain [N/m]

d

Displacement of the mesh [m]

Φ A parameter for checking convergence in a stagger iteration [-]

u

Load components transferred at this iteration [-]

u

Load components transferred at the previous iteration [-]

Φ

Convergence criteria in the stagger iteration [-]

e Convergence criteria in the solver [-]

τ

Mesh stiffness [N/m]

δ Relative displacement of the mesh [m]

C

Model exponent [-]

a∗ Size of the mesh or the distance from the nearest boundary [-]

Erosion Parameters

E, W, E

Erosion Rate

N ˙ Number rate of the particle

m

Mass of the particle

Finnie

V

Particle impact velocity

f (γ) A dimensionless function of the impact angle which is in radian

n Value of exponent

Tabakoff

γ

Angle of maximum erosion

k

− k

, k

Model constants V

− V

Reference velocity

R

, V

Parameters for calculation Bardal

C Concentration of particles

a Size coefficient of particles

K

Material constant

K

Environment constant

V

Velocity of the particle

Erosion Parameters Tsuguo

β Turbine coefficient at eroded part

x Exponent for concentration

y Exponent for size coefficient

m Value of exponent

k

, k

Hardness coefficient of particles

k

Abrasion resistant coefficient of material W Loss of thickness per unit time

Thapa

K

Material factor

K

Hardness factor

K

Flow factor

K

Shape factor

x Velocity of eroding particles

y Loss of material

η

Efficiency after erosion consideration

a, b Empirical constants

Units

m Meter

mm Milli meter

rad Radian

M W Mega Watt

P a Pascal

M P a Mega Pascal

◦

C Celsius

kg Kilogram

deg Degree

rev Revolution

min Minute

sec Second

atm Atmosphere

mol Mole

N Newton

1

Introduction

1.1 Background of the work

Nepal is a land-locked country between India and China, blessed with a massive geographical diversity and water resources. The chances of utilizing these resources in the form of hydropower development are enormous, however, it has been seen that till date, only about 1% of the total feasible hydropower has been harnessed [1]. Not only that different conditions are not supporting the installation of new power plants here, but because of the excessive sediments in the Himalayan River, the damage of the turbine components due to erosion has led to the loss of efficiency and even shut-down of many stations.

Sediment erosion in hydraulic turbines has become a major challenge from a design and maintenance perspective in Nepal. Jhimruk Hydropower plant is one of such hydropower plants in Nepal affected by an extensive amount of sediment erosion reducing the life span of turbine components. Similarly, other power plants such as Marsyangdi, Panauti, Trishuli and Sunkoshi are affected by erosion. Research works have been made to decrease erosion, either by coating or by minimizing the concentration of sediments in the water. These research works are showing possibilities which are either inadequate or unfeasible economically. However, research works based on design optimization of the turbines have shown positive results to some extent. This study will focus on the reference (original) design of the turbine runner and comparison of this with other optimized blades in terms of erosion. Most of the works done previously accounted for the flow field around the blade only, and not the effect of the flow field on the deformation of the blade or the effect of the deformation of the blade on the mesh surrounding it. The results of Fluid Structure Interaction (FSI) could be inevitable in analyzing the mechanical property of these blades.

Turbine Testing Laboratory (TTL) of Kathmandu University has been performing several research

on eroded blades and possible optimization techniques. The present Master’s thesis is an effort to

consolidate the previous works done on the enhanced mechanical design of Francis turbines for better

handling of the sediment erosion by including the effect of FSI. This project is expected to bring

a positive change and advancement in the field of computational solutions of the turbine flow field

and structural integrity considering the sediment erosion damage. Having said the challenges faced

due to sediment erosion and the need of FSI to make a more detailed analysis of the computation,

making a successful FSI analysis is itself a challenge. There are only few studies made about the

one-way coupling techniques in Francis runner and even fewer about the fully-coupled solutions. The

fully-coupled analysis of the Francis runner exposed to sediment erosion will therefore, be a major challenge in this project in terms of carrying out the simulation and validating the results. Thus, this report will also contain some of the basic principles behind FSI and an example of conducting FSI in ANSYS.

1.2 Kathmandu University(KU) and Turbine Testing Lab(TTL)

Kathmandu University is an autonomous, non-profitable, non-governmental institution established on 1991, dedicated to maintain high standards of academic excellence. Turbine Testing Lab (TTL) was established in 2010-2011 inside the premises of KU with a financial support from NORAD and other national industries. With 30 meter open head and 150 meter closed head, TTL is capable of testing different hydraulic turbines up to 300 kW and conduct model tests for larger sizes. This laboratory has strong motives on research, development, training and education sector. The establishment of the laboratory and the various research works have managed to put a step on dealing with the challenges faced by the hydro power stations for making a better future in Nepal in terms of the energy production and efficiency.

The objectives and activities of the TTL according to [2] are :

• Build competence and knowledge in Nepal and South Asia in terms of teaching and learning facilities.

• The laboratory of hydro turbines will carry out the certification of mini- and micro- turbines sold on the regional market and does the model testing of turbines for larger power plant.

• The research works will be held based on sand erosion, turbine and pump and maintenance of the turbines.

• Various projects will be held for students of the university in the related industries.

KU and TTL have been putting its effort into the development of hydro turbines exposed to sediment erosion. They have also been collaborating with various national and international institutions and companies to improve its research standards. Besides, several numerical tools and computational softwares are being used for R and D of hydraulic turbines to characterize sediment particles and design optimization of Francis turbine to minimize sediment erosion. Some of the current research works carried out by this lab is discussed in [2] and [3].

1.3 Objective of this study

The principle objectives of this thesis are summarized below :

• Analyze the results of the ongoing and the past studies focused towards the optimized hydraulic

design of Francis runner for a better sediment handling.

• Introduce the FSI based simulations of the Francis runner through one-way and two-way coupling techniques to establish the mechanical integrity of the design, for both the conventional and the optimized designs.

• Make a comparative analysis of the results between CFD, one-way FSI and two-way FSI and identify the level of significance of FSI in the field of Francis turbines.

1.4 Study methodology

This research work primarily focuses on performing FSI simulation in the premises of ANSYS for the reference and the optimized Francis runners. The optimized runner was proposed in earlier studies [21], which was known to have reduced erosion through CFD analyses, without influencing the efficiency.

These CFD analyses were validated through mesh and various parametric studies and a runner blade having minimum erosion was chosen for structural analysis. The optimized runner blade was then compared with the reference design through one way and two way FSI analysis for two different cases of boundary conditions.

1.5 Scope of study

This study mostly covers the use of numerical tools for the design optimization of Francis runner blades for better sediment handling. The CFD analysis was done in ANSYS-CFX including Turbo-grid for mesh generation. The erosion parameters were used from the models supported by ANSYS whereas validation of the model was done from various parametric studies including a mesh independence study for the reference design. The FSI analysis was done in the static structural part of ANSYS Workbench.

MFX multi-field technique was used for conducting a two way FSI. This study is limited to a steady simulation of a single runner blade by considering cyclic symmetricity of the model. Validation of the results requires experimental data which is not included as a part of this thesis work.

1.6 Outline of the thesis

This thesis is organized in 10 chapters. Chapter 2 consists of some of the introductory part of hydro

turbines in general and in the context of Nepal. Chapter 3 contains a detail review of sediment erosion

in hydraulic machinery and its influence in Nepalese hydro power plants. This chapter also contains

some mathematical formulations of erosion models along with the models supported by ANSYS. The

studies made in the field of numerical analyses of turbines exposed to erosion by past researchers are

discussed in Chapter 4. Introduction about FSI and strategies of conducting FSI in ANSYS are shown

in Chapter 5. Chapters 6, 7 and 8 contains all the numerical analyses performed in this study along

with the results from these analyses. The analyses are divided in such a way that a CFD model was

created in the beginning and the same model was used in further chapters for one way and two way

FSI analyses. The discussion and conclusion from all the results are included in Chapter 9. Finally,

future scope in the related field is discussed in Chapter 10.

2

Hydro Turbines

Hydropower machineries are the machines that convert hydraulic power from the water to the me- chanical power on the machine shaft. Like any other machines, these machines involves various losses that arise partly in the machine itself and partly in the water transfer into and out of the machine such as pipe friction losses, losses due to bends in pipes, gates, valves and losses due to abrupt and gradual expansion and contraction of the pipes [4]. Some of the basic components of a hydropower plant is listed below [4] :

• A water diversion structure like a dam or a weir creating a gross head of water.

• A penstock, which intakes the water from the dam and transports it to the turbines. Screening is done in the intake, to prevent unwanted objects (debris and aquatic animals) entering into the turbine.

• Turbines and governing system.

• Electrical generators, electrical control and switching equipment, equipment housing, transform- ers and electricity transmission lines.

• Some of the other complementary components are the penstock gates, surge tank and a tail race if the turbine exhaust water cannot be discharged directly (through the draft tubes) into the river. Draft tubes are used to utilize the kinetic energy of the water leaving the turbine and allows the turbine to be installed above the tailwater level without decreasing the available head and hence, the available power.

2.1 Hydropower in Nepal

The first hydropower plant was established in Nepal on May 22 1911 in Pharping with the capacity of 500 kW, which was one of the largest hydro-power projects in the south Asia during that time.

Since then up to now, Nepal has been able to harness 698 MW, which is not even 1% of the feasible

power potential of Nepal. Ironically, Nepal is blessed with immense water resources with the average

annual precipitation of approximately 1700 mm. The total annual average run-off from the nation’s 600 rivers flowing from high mountains is over 200 billion m

[1].

Most of the power plants in Nepal are run-of-river type with energy available in excess of in-country de- mand during the monsoon season and deficit during the dry season [1]. Some of the major hydropower stations of Nepal along with the organization and their capacity is given in Table 2.1.

Table 2.1: Major hydropower plants in Nepal

Station Organization/company Capacity

Kaligandaki A Nepal Electricity Authority (NEA) 144 MW

Middle Marsyangdi NEA 70 MW

Marsyangdi NEA 69 MW

Kulekhani 1 NEA 60 MW

Khimti Himal Power Ltd. 60 MW

Bhotekoshi Bhotekoshi Power Company 36 MW

Kulekhani 2 NEA 32 MW

Trishuli NEA 24 MW

Chilime Chilime Hydro Power Company 22 MW

Gandaki NEA 15 MW

Jhimruk Butwal Power Company Ltd. 12 MW

2.2 Principles of hydro turbines

Any turbomachinery rotor can be represented by a system of equation known as Euler equation. In the case of hydro turbines, it gives the relation between the total head (H

) and the velocity triangles in the inlet and the outlet.

H

.g = U

.C

− U

.C

(2.1)

Where,

C

: circumferential absolute velocity component at the outlet C

: circumferential absolute velocity component at the inlet U

: tangential velocity of the runner at the outlet

U

: tangential velocity of the runner at the inlet

This Euler equation implies that in order to have a change in the total head, two ingredients are

necessary : tangential speed of the rotor and the change in the circumferential velocity component or

variation of the circulation between the inlet and outlet of the turbine.

r

x

θ Flow passage

Absolute streamline Relative streamline W1

W2

C2

C1

U1

U2

x(m)

θ

Figure 2.1: Co-ordinates and velocity triangles of a typical turbomachinery rotor

In the case when U

= U

:

H

.g = U.∆C

(2.2)

Depending upon the sign of ∆C

, the sign of H

can be determined. When this value is positive, it means that the energy is added to the fluid and such kinds of hydraulic devices are called pumps.

When this value is negative, it means that the energy is extracted from the fluid and such kinds of devices are called turbines. The velocities triangles of a typical turbomachinery rotor is shown in Figure 2.1. The absolute and the relative velocities at the inlet and the outlet can be split into axial and circumferential components. From the figure, C

< C

i.e. H

< 0, so this is a case of a turbine where the energy is extracted from the fluid.

In the case of radial-axial turbines, the radius at the inlet is not identical to the radius at the outlet.

This means that the tangential speed of the rotor is different at the inlet and the outlet. Also, the axial and the meridional co-ordinates are not the same and instead of the axial co-ordinate (x), meridional co-ordinate (m) has to be referred.

2.3 Cavitation

Cavitation is one of the principle challenges in hydro turbines, which occurs when the local pressure falls below the vapor pressure of the water. This happens due to an increase in velocity or an ambient drop in pressure. The water vapor forms at the area of low pressure in the form of bubbles, which when carried to areas of higher pressure, can collapse violently. This collapse induces high pressures and sets up fatigue stresses in nearby bodies.

A general cavitation phenomenon is shown in Figure 2.2, assuming a section of a pipe where a fluid is

flowing at a certain temperature and pressure with a velocity C

. By entering the contracted region,

from the conservation of mass, the velocity of the fluid C

increases to C

. From the Bernoulli’s

principle, when the velocity of the fluid increases, the pressure in the fluid will decrease to maintain the constant total pressure. This figure also shows the dependency of the saturation pressure on the fluid (water) temperature. As the pressure in the fluid is decreased, the fluid will evaporate at lower temperature, which means the formation of bubbles. When the fluid reaches the normal situation (uncontracted condition) again, the fluid starts to decelerate and the vapor bubbles start to disappear. Because of the increase of the fluid pressure, the vapor bubbles implode sending out small but very high pressure micro jets. These micro jets, when close to the material surfaces, blast away the material. This process is shown in Figure 2.3. Cavitation in the system can be checked through a measure provided by the manufacturers called as N P SH

(Net Positive Suction Head required).

This N P SH

is compared with N P SH

(Net Positive Suction Head available), which is a system parameter indicating the head surplus at inlet before the saturation pressure is reached.

𝐶1 𝐶2

𝑇 [⁰𝐶]

𝑃_𝑆 [𝑘𝑃𝑎]

4.2 101.3

30 100

Saturation pressure

Figure 2.2: Cavitation due to contraction of a pipe and saturation pressure vs fluid temperature

Area of the passage (A)

𝐴₂

𝐴₂ 𝐴₁

𝐴₃

𝐴₁

𝐴₃

Blast of material

m

m 𝐴

Figure 2.3: Cavitation along a passage with non-uniform area

2.4 Types of hydro turbines

Hydraulic turbines can be classified based on their degree of reaction, which is the ratio of the static

pressure drop across the runner to the static pressure drop across the stage. The Pelton turbine is an

impulse stage with all the pressure drop occurring across the stationary components and no pressure drop across the runner. The reaction stages such as Francis and Kaplan turbines have a proportion of the pressure drop in the rotor and a proportion of the pressure drop in the stator.

2.4.1 Pelton turbines

Pelton turbines are particularly suitable for high head applications. The rotor is in the form of a circular disc with buckets which are driven by one or more nozzles delivering a jet perpendicular to the buckets. An example of a jet impingement along with the velocity triangles are shown in Figure 2.4. At the inlet, the flow velocity is C

and the tangential speed of the bucket is U . The relative flow velocity then becomes W

= C

− U . Since C

= C

at the inlet, such kind of arrangement gives the maximum swirl (i.e. negative ∆C

), thus giving maximum total head.

Figure 2.4: Jet impingement into a bucket with corresponding velocity triangles

2.4.2 Kaplan turbines

Kaplan turbines are axial reaction turbines used typically for low head applications. The vanes of the runner are similar to those of axial-flow turbine rotors but designed with a twist in order to have a free-vortex flow at the inlet and an axial flow at the outlet with the number of blades usually small (4-6) [6]. In these type of turbines, the stagger angle can be controlled depending upon the load condition to maintain optimum efficiency conditions. A typical section of a Kaplan turbine is shown in Figure 2.5 whereas, the velocity triangles at the inlet and the outlet are similar to the one shown in Figure 2.1 except that the tangential speed of the rotor at the inlet and the outlet are equal i.e.

U

= U

and also the axial component of the absolute velocity is constant i.e. C

= constant.

Figure 2.5: Section of a Kaplan turbine[6]

2.4.3 Francis turbines

The principal difference between Pelton and Francis turbines is that only a part of the overall pressure drop in Francis turbine occurs in the turbine entry, whereas the remaining pressure drop occurs in the turbine itself. Some of the other characteristic features of the Francis turbines are [6] :

• Unlike the Pelton turbine where only one or two buckets are in contact with the water at a time, the flow in the Francis turbines completely fills all the passage in the runner.

• Presence of pivotable guide vanes to control and direct the flow.

• A draft tube is an integral part of the turbine added to the turbine exit.

The basic components of a vertical Francis turbine is shown in Figure 2.6. In practise, the turbines with comparatively small dimensions are arranged with horizontal shaft whereas the vertical arrangement is used for big dimensions [15]

Components of Francis turbines

In brief, components used in Francis turbines, with their functions.

Spiral casing

The spiral casing, also called as a volute transfers water from the penstock to the runner. The area of cross-section of the volute is decreasing continuously in order to maintain a constant flow velocity.

Stay vanes

From the volute, the water passes through the stay vanes, whose main purposes are to conduct the water towards the guide vanes and absorb the axial forces from the volute. These vanes are given a favorable shape to have a minimum influence on the flow [7].

Guide vanes

The purpose of the guide vane is to regulate the flow into the turbine. This regulating mechanism

Figure 2.6: Some basic components of Francis turbines [4]

is accompanied with vane arms and links which is controlled by a governor system that controls a servo motor connected to the guide vanes [7]. These vanes direct the flow onto the runner at the most suitable angles with the help of this controlled automation.

Runner

In the runner, the angular momentum of the water is reduced and work is supplied to the turbine shaft [6]. Runners with higher head require higher number of blades in order to reduce the individual blade loading and seperation at the runner inlet during low loads [7]. The runners are usually made of stainless steel.

Labyrinths

The leakage losses between the turbine runner and the cover can be minimized by placing labyrinth seals such that the flow of the water from the gap is prevented. The labyrinth consists of a static seal connected to the covers and a rotating part connected to the runner [7].

Draft tube

The draft tube collects the water from the runner and transfers them to the outlet gate. Its main purpose is to convert the kinetic energy at the runner outlet to the pressure energy at the draft tube outlet. It is a diffuser like structure where the flow is decelerating with the increased cross section.

2.4.4 Work done and efficiency of Francis turbine

Euler momentum equation can be used to determine the work done by a Francis turbine. Some of the known quantities needed for this calculation are the gross head which is the difference of water levels between the head race and the tail race (H

) and the loss of head in the penstock (H

). Hence, the net or available head can be calculated through (H

− H

), i.e. difference between the total energy available at the exit from the penstock and the total energy available at the exit from the draft tube.

This is also shown in the following equation [8]:

H =

 p ρ.g + V

2.g + z



penstock

−

 p ρ.g + V

2.g + z



draf t tube

(2.3)

The general expression for the work done according to Euler momentum equation is given by,

work done = ρ.Q(C

.u

± C

.u

) (2.4)

Where,

Q = Discharge through the runner, m

/s

When C

= 0, the maximum output is obtained.

Hydraulic efficiency, η

is given by the total power developed by the runner over the power supplied to the turbine. If H is the net head, then input to the turbine is given by ρ.g.Q.H. Hence, the following equation can be achieved:

η

= ρ.Q(C

.u

)

ρ.g.H.Q (2.5)

or,

η

= C

.u

g.H (2.6)

Mechanical efficiency,

η

= Shaf t power(P )

P ower developed by the runner (2.7)

Overall efficiency,

η

= Shaf t power

W ater power = P

ρ.g.Q.H (2.8)

η

= η

∗ η

(2.9)

Hence, the overall efficiency of the Francis turbine can be deduced as a product of hydraulic and mechanical efficiencies.

2.4.5 Francis turbines in Nepal

Most of the major hydro-power stations in Nepal uses Francis turbines as the main conversion devices.

Kaligandaki ’A’, which is the biggest power station of Nepal (144 MW) uses three 48 MW Francis

turbines with a head of 115 meters. Similarly, other hydro-power stations such as Marsyangdi, Middle

Marsyangdi etc. also uses Francis turbines. The technical specification of these turbines are shown in

Table 2.2.

Table 2.2: Technical specification of Francis turbines installed in Hydro-power stations in Nepal Station No. x Unit Power Head [m] No. of blades[-] Diameter of runner [m]

Kaligandaki A 3 x 48 MW 115 13 2.306 -2.564

Middle Maryangdi 2 x 38 MW 96.5 13 2.256 max.

Marsyangdi 3 x 26 MW - 13 1.93 -2.234

Bhotekoshi 2 x 22 MW 135.5 - -

Jhimruk 3 x 4.2 MW 201.5 17 0.540 - 0.890

The turbines shown in the table above are continuously facing the problem of sediment erosion. More

about the erosion problem these turbines are discussed in Chapter 3.

3

Sediment Erosion

Erosion in general, is one of the many categories of wear caused by the impact of particles of solid or liquid against the surface of an object. The mechanism of the erosive wear is quite similar to the abrasive wear, but in the case of the abrasive wear, the eroding agent is much bigger in size and the angle of impingement is lower. The erosive wear on the other hand, is accompanied with relatively small particles with several number of wear mechanisms. These mechanisms are differentiated based on the impingement angle, size, shape and speed of the particles and the mechanical properties of the base material. The pictoral representation of these mechanisms are shown in the Figure 3.1.

Sa

Particle approaching the material

Impingement angle Base material

Abrasive/cutting erosion at Low impact angle

Fatigue erosion at High impact angle and low speed

Plastic deformation, flakes at high impact angle for ductile material

Brittle fracture at high impact angle, brittle material

Figure 3.1: Erosive wear mechanisms [5]

The figure explains how the erosion takes place depending on the orientation and the properties of the

particles and the base material. These parameters also give the quantitative measure of the erosive wear. For example, a low angle of impingement is favorable for the wear process as the particles are drawn across the surface after the impact. Similarly, if the speed is low, then stresses at impact are insufficient for plastic deformation or brittle fracture. In such cases, the wear by surface fatigue is more probable depending upon the endurance limit of the base material. If the shape of the eroding particle is blunt or spherical, the plastic deformation is more likely to occur, whereas, if the particles are sharp, the cutting wear is more common. It has been seen that for the ductile mode, the maximum erosive wear is generally found close to an angle of 30

whereas, for the brittle mode, the maximum erosive wear is found around 90

of impingement angle [5].

3.1 Materials behavior and coatings

Materials having superior hardness are generally preferred in the context of sediment erosion but it also significantly matters what impingement angles are the particles hitting the material. The most common materials that are chosen are stainless steel and titanium- and nickel- alloys. Formation of the martensites results in the improved hardenability and erosion resistance except at low impingement angles and for the low alloy steels, the ferritic phase with sufficient spheroidal carbide to induce strengthening is very effective against erosive wear. The various materials behavior and the effect of the impingement angles is shown in Figure 3.2.

Figure 3.2: Erosive wear for various materials at different impingement angles

It can be seen from the figure that some materials such as cobalt having a very good erosion resistance at a low impingement angle but one of the worst materials for high impingement angles. According to a study made between a martensitic (13Cr4Ni) and an austenitic (21Cr4Ni) steels, it was seen that the erosion resistance of 21Cr4Ni strengthened with Nitrogen is higher than the former one due to the distribution of hard carbides in the matrix of stabilized austenite [9].

In applications where the working temperature is high, ceramics are gaining a particular interest due

to their excellent high temperature properties. However, these materials are brittle which might result in the brittle fracture.

The prevention of the turbine components can be done by applying a coating on the surface. These coating materials depend upon the exposed environment, for example whether the surrounding is wet or dry (hot). The most common type of coating seen in the hydro turbines is the Tungsten- carbide(WC-Co) coating which typically uses 86-88% WC and 6-13% Co [10]. These coatings have excellent hardness, with better adhesion and large toughness.

3.2 Sediment erosion in hydraulic machinery

The erosion damages in hydraulic machineries can be differentiated for Pelton and Francis turbines.

In the case of Pelton turbines, the high velocity of the particles at the buckets is the main reason of sediment erosion. At the inlet system i.e. manifold and valve, only a moderate effect of the sediment is seen because of the low operating velocity. The effect of the sediment erosion is mostly seen in the needle tip, seal rings in the nozzles and the runner buckets. Specially in the case of high head turbines, the bombardment of the fine particles on the needle surface due to the strong turbulence effect increases the rate of erosion. In the Pelton turbine runner, depending upon the size of particles, the damages are seen in various parts of the runners. For the coarse particles, the damages are in the area where the jet directly hits at the bucket surface and the surface damage is observed primarily due to the hammering action rather than the cutting action. The fine particles on the other hand flow along with the water inside the bucket and strike the surface towards the edge, causing erosion towards the outlet. It is also reported that silts with small grain size damages mostly needles and nozzles whereas the runner buckets have negligible damage. On the other hand, with the coarse particles, the Pelton buckets are mostly eroded while the damage of the nozzles remains less serious [15].

In the case of Francis turbines, the most vulnerable regions to sediment erosion are shown in Figure 3.3. The erosion occurs in the stay vanes because of the secondary flows from the spiral casing causing non-uniform flow angles at the inlet with high absolute velocities. The guide vane system is highly affected by the sediment erosion due to the high absolute velocity and acceleration. The erosion of guide vane can be classified into: turbulence erosion at the outlet region and facing plate due to high velocity of fine particles, secondary flow erosion in the corner between guide vane and facing plates, leakage erosion at the clearance between guide vane and facing plates and acceleration erosion due to the separation of large particles from the streamlines of the main flow due to rotation of water in front of the runner. The vortices generated from the secondary flow and the leakage flow from the guide vane will eventually pass through the runner inlet causing damages at the inlet of the runner. In the runner, the highest relative velocity occurs at the outlet region while the highest absolute velocity and accelerations occurs at the inlet of the blade. Because of the high relative velocity at the outlet, the particles moving towards the outer diameter in the runner will cause more erosion at the outlet.

Inlet region on the other hand is sensitive to incorrect pressure distribution between the pressure and the suction side and any separation caused by this may cause severe local erosion at the inlet [16].

Labyrinth seals having small clearance and coarse particles may have erosion as well as abrasion effect.

Similarly, the area around the draft tube closer to the runner is exposed to high velocity which causes

sediment erosion in that region.

Zones of sediment erosion Runner

blades

Guide vanes

Stay vanes

Figure 3.3: Areas exposed to sediment erosion wear in Francis turbines [19]

3.3 Sediment erosion in Nepal

The climatic and geographical scenarios of Nepal account for the degradation of the hydraulic turbine components from erosion and sedimentation. These scenarios mainly include the tropical climate, immature geology and the intense seasonal rainfall. It has been reported that Southeast Asia alone contributes to two thirds of the world’s total sediment transport to oceans which makes the problem of erosion and sedimentation even more challenging[16]. Ever since the first sediment data collection started in Nepal in 1963 in Karnali river basin, sedimentology has emerged as an important task in most of the recent hydropower projects in Nepal. The vulnerability of the sediments is usually judged by the quartz content, as these materials have enough hardness to erode the turbine material. Results show that the rivers in the Koshi basin have more than 60 percent quartz content in average with more quartz particles in the east compared to the west [17]. Even with the well designed sediment settling and flushing system, power plants like Marsyangdi, Khimti and Jhimruk have severe erosion problem. Some of the erosive damages due to sediment in Jhimruk Power Plant are shown in Figure 3.4. Sediment erosion has not only reduced efficiency in hydro turbines, but has also caused various problems during the operation and maintenance period. Some solutions regarding the change of the material, coatings and the sediment trapping systems have been considered insufficient or unfeasible [15], [16], [17].

The effect of the sediment erosion is not only limited to the context of the Himalayan region, but

it is also significantly seen in the Andes region in South America. A 22 MW Cahua hydro power

plant built in Peru can be taken as an example. It was seen that the sediment concentration exceeded

120,000 tons of sediment only after six weeks of operation with the average quartz content found to be

about 35 percent and feldspar found to be about 30 percent [16]. One of the recent solutions towards

preventing the sediment erosion is to improve the hydraulic design of the runner such that the effect of

the erosion remains minimum. Various studies made regarding the design optimization of the Francis

runner is discussed in Chapter 4.

Figure 3.4: Sediment erosion wear in the Francis turbine guide vane and runners in Jhimruk [19]

3.4 Erosion models

Prediction of the erosion in hydraulic turbines are done with the help of various erosion models. These models can help in the design, operation and maintenance of the turbines for a specific site conditions.

The erosion models are mostly developed through particle dynamics or empirical and statistical rela- tions obtained from experiments and experiences. The most fundamental form of the erosion model is given by Equation 3.1.

Erosion = f (operating condition, properties of the particles, properties of the base material) (3.1)

The expression for erosion was simplified in [11], which is given in Equation 3.2.

Erosion ∝ (velocity)

(3.2)

Where m is the exponent of velocity. According to [12], the most general formula for the pure erosion is give by Equation 3.3.

W = K

.K

.C.V

[mm/year] (3.3)

Where W is the erosion rate in mm/year, K

is the material constant and K

is the environment constant, C is the concentration of the particles and V

is the velocity of the particle.

An erosion prediction was done based on 8 years of erosion data of 18 hydro-power plants in [13]

suggested Equation 3.4 to calculate erosion in turbines.

W = β.C

.a

.k

.k

.k

.V

[mm/year] (3.4) Where W is loss of thickness per unit time, β is turbine coefficient at eroded part, V is relative flow velocity, a is the average grain size coefficient on the basis of unit value for the grain size 0.05 mm.

The terms k

and k

are shape and hardness coefficient of sand particles and k

is the abrasion resis-

tant coefficient of the material. The exponent values x and y are for the concentration and the size

coefficient respectively.

According to [18], the erosion rate was estimated through laboratory tests of various turbine materials under different test conditions. Equation 3.5 gives an empirical relation to predict the erosion rate for 16Cr5Ni, which is the most widely used turbine material.

y = 6E − 5x

[mg/kg] (3.5)

Where x(m/s) is the velocity of eroding particles impinging at the angle of 45

and y is the loss of the material in mg per kg of eroding particles striking the surface.

Recently, an erosion model was proposed in [14] that could estimate both absolute erosion rate (mm/year) and corresponding reduction in efficiency (% per year) of Francis runners due to sus- pended particles. This model was termed as the improved version of the two former models. The final equation yielded by this model was given by Equation 3.6 and Equation 3.7.

E

= C.K

.K

.K

.K

.a.(size)

[mm/year] (3.6)

η

= a.(E

)

[%/year] (3.7)

Where K

is the material factor, K

is the flow factor, K

is the shape factor and K

is the hardness factor. a and b are the empirical constants defined as :

a = 351.35, b = 1.4976 for quartz content of 38%, a = 1199.8, b = 1.8025 for quartz content of 60%, and a = 1482.1, b = 1.8125 for quartz content of 80%.

3.4.1 Basic erosion models in ANSYS-CFX

There are two choices of erosion models in CFX, Finnie and Tabakoff. With a larger number of input parameters, Tabakoff model provides more scope for customization, though the choice between these two models depends on the types of simulation. The equations of these models are discussed below:

Model of Finnie

This model shows that the erosion is affected by the impact angle and the velocity given by:

E = kV

f (γ) (3.8)

Where,

E is a dimensionless mass,

V

is the particle impact velocity and

f (γ) is a dimensionless function of the impact angle which is in radian

n is the value of exponent which is usually in the range of 2.3 to 2.5 for metals.

Model of Tabakoff and Grant

In this model, the erosion rate E is determined from the following relation:

E = k

.f (γ).V

.cos

(γ)[1 − R

] + f (V

) (3.9) Where,

f (γ) = [1 + k

.k

.2sin(γ π/2 γ

)]

(3.10)

R

= 1 − k

.V

sin(γ) (3.11)

f (V

) = k

.(V

sin(γ))

(3.12)

k

=

( 1 if γ ≤ 2γ

0 if γ > 2γ

(3.13) Where,

γ

is the angle of maximum erosion

k

to k

, k

and γ

are model constants and depend on the particle/wall material combination.

The Tabakoff model requires the specification of five parameters : k

constant, 3 reference velocities and the angle of maximum erosion γ

. An example of these parameters for Quartz-Aluminum is shown in Table 3.1.

Table 3.1: Coefficients for Quartz-Aluminum using Tabakoff Erosion Model

Variable Coefficient Value

k

k

0.585

Ref velocity 1 V

159.11 [m/s]

Ref velocity 2 V

194.75 [m/s]

Ref velocity 3 V

190.5 [m/s]

Angle of Maximum Erosion γ

25[deg]

4

Recent works - Review

The damage on hydraulic machineries due to sand erosion was initially studied in [17] and [18] through various design aspects such as material selection, mechanics of material and hydraulics. This research work led the path to carry out further investigations numerically and experimentally, which has now become an integral aspect of the machinery design.

4.1 CFD works

The study of sediment erosion in hydro turbines has been conducted in a phD study in [16] including experimental studies, numerical simulation, and field studies. The erosion rate was predicted for stay vanes, guide vanes, and runner vanes of a Francis turbine for different shape, size and concentration of the particle and operating conditions of the turbine.

The current research project will be based on a previous work regarding the hydraulic design of Francis turbines exposed to sediment erosion [21]. It was shown in the study from CFD analysis that the conventional methods of hydraulic design of Francis turbines can be improved to minimize sediment erosion. The CFD analysis carried out in ANSYS-CFX contains various parameters shown in Table 4.1. The generation of the mesh in Turbogrid, CFX setup and the result showing the erosion rate density for a conventional design is shown in Figure 4.1, 4.2 and 4.3. The simulations were done for a single runner passage,where it was shown that the runner outlet diameter, peripheral velocity at inlet, and blade angle distribution has the highest effect on the sediment erosion of Francis runners.

In order to create and optimize the design of Francis runners, a GUI matlab based program was developed called as ’KHOJ’, which made the optimization process much easier. More information about this program can be found in [21].

Another complementary study was made in [19] where a CFD analysis was performed on a blade

runner. This study showed that the largest reduction of erosion was obtained by decreasing rotational

speed of the turbine. However, this increases the investment cost because of the larger size. An

alternative approach was also made, which showed that the reduction of erosion could also be made

by changing the blade angle distribution, and consequently, the energy distribution.

Figure 4.1: Hub, shroud and the blade passage from Turbogrid

Figure 4.2: CFX-pre setup file showing the blade passage and the mesh

Figure 4.3: Sediment erosion rate density of the reference design[21]

Table 4.1: Various CFX parameters used in the study[21]

Mesh

Mesh elements 268455

Factor ratio 2

Near wall element method y

(Reynolds number = 500000) Sediment

Quartz density 2.65 gm/cm

Particle Molar Mass 1 kg/kmol

Particle Diameter 0.1 mm

Tabakoff erosion parameters

k

0.586

Reference velocity 1 159.11 m/s

Reference velocity 2 194.75 m/s

Reference velocity 3 190.5 m/s

Angle of max. Erosion 25 deg

Particle coupling One way coupling

Rotating domain (R1)

Angular Velocity -1000 rev /min

Turbulence model SST

R1 Blade/Hub/Shroud boundary detail No Slip Wall Inlet components

Mass flow rate 138.235 kg/s

Flow direction(cylindrical components) 0, 0.214349, 0.976757

Turbulence Medium(Intensity = 5%)

Particle mass flow rate 0.07 kg/s

Particle position Uniform injection

Uniform injection 1000 (Direct Specification) Outlet

Relative pressure 1 atm

Pres. Profile Blend 0.05

Solver control

Max. Iterations 100

Residual tolerance 1E-4

4.2 FSI works

The need of FSI was felt when the material strength of the Francis runners was needed to be ana- lyzed together with the hydraulic efficiency. However, the implementation of FSI has not been fully established for the case of Francis turbines, specially when exposed to sediment erosion. A one-way coupling strategy was presented in [7] to compare the structural integrity between the reference and the optimized designs. The FSI analysis layout was made in ANSYS workbench as shown in Figure 4.4. The pressure load from CFX is exported to the structural analysis by defining a Fluid-Structure interface. Also, the boundary conditions of the runner were defined as shown in Figure 4.5. The pres- sure distribution between the inlet and the upper labyrinth on the top side of the hub and underside of the shroud were given by Equation 4.1. The pressure distribution at the surface of the hub between the shaft and upper labyrinth seal is given by Equation 4.2. This unidirectional FSI was inadequate as the deformations in the structure was not taken into account in the flow analysis.

p(r) = p(x) = ρ.g.h(x) = (ρ.g)(h

− k

.ω

2.g (r

− x

))[P a] (4.1) p(r) = p(x) = ρ.g.h(x) = (ρ.g)(h

− k

.ω

2.g (r

− x

))[P a] (4.2) The concept of a fully coupled FSI in Francis turbines has been introduced in a study [22] where a strongly coupled partitioned equations are solved separately using different solvers, but are coupled implicitly into one single module based on a reduced-order model. The proposed model is used to predict the unsteady flow fields of a 3D complete passage, involving in stay, guide vanes, and runner blades of a Francis turbine. Such reduced-order model is based on only a few displacement and stress modes, which not only saves computing time but also enlarge the range of applications in engineering [22]. This study has also shown that the numerical results when considering FSI shows better concordance with the experimental results than when not considering FSI.

A two-way coupled FSI of a propeller turbine is seen to have been made in the premises of ANSYS to determine the mechanical integrity of the turbine blades by varying the stiffness of the blades [23]. A multi-field simulation has been used in this study as CFD and FEA solvers to exchange information at the interface.

4.3 Other relevant works

In the present study, various optimized blades will be investigated, which were studied previously with CFD in [26]. The blades were modified based on the blade angle distribution from inlet to outlet.

The graphical representation of these blades is shown in Figure 4.6. The shape 3 shows the linear

distribution of the blade angle, which is chosen as the reference design. All the other designs and the

results from the CFD are compared with this design. These blade shapes give an indication of how the

hydraulic energy is converted to mechanical energy along the stream-wise direction. A runner blade

design of shape 1 converts half of the hydraulic energy from the middle towards the outlet, whereas

shape 2 will convert the energy at the beginning of the blade till the middle. The result of this study

shows that the blade angle distributions of shape 4 and 5 have reduced erosion effects. Shape 4 will

Figure 4.4: FSI analysis layout used in the study [7]

Figure 4.5: Boundary conditions of the runner used in the study [7]

1 1

0 Stream wise span from inlet(1) to outlet(0)

Blade angle distribution relative to the inlet Shape 1

Shape 2 Shape 3 Shape 4

Shape 5

Figure 4.6: Parametric study of the shape of the blades [26]

have reduced erosion by 60% but the efficiency will be adversely influenced. Shape 5 will have reduced

erosion by 20% without much changes in the efficiency. These shapes will be analyzed in this project,

now also by considering the structural aspect of the design, to see if the designed optimized blades

can sustain equal, more or less pressure loads compared to the reference design.