FSI-Francis-MSthesis (1).pdf

8/9/2019 FSI-Francis-MSthesis (1).pdf

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Masters Thesis in

FSI Analysis of Francis Turbines Exposed to Sediment

Erosion

Sailesh Chitrakar

July, 2013


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Abstract

Sediment erosion is one of the key challenges in hydraulic turbines from a design and maintenanceperspective in Himalayas and Andes. Past research works have shown that the optimization of theFrancis turbine runner blade shapes can decrease erosion by a significant amount. This study con-ducted as a Masters Thesis has taken the proposed designs from past works and conducted a CFDanalysis 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 andtwo-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 thestructural model. In the first case, a runner blade is considered to have no influence of the joint andother stiffer components. In the second case, a sector of the whole runner has been modeled withnecessary boundary conditions. Both one-way and two-way FSI have been performed on the casesfor the designs. Mesh independent studies have been performed for the designs, but only for the firstcase, 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 usedto solve the coupled field analysis. A fully coupled FSI in ANSYS works by writing an input file inthe structural solver containing the information about the interfaces in the structural domain, whichis 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 ofthe optimized design is better than the reference design in terms of the maximum stress induced inthe 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 greatscope in the research field to carry out a fully-coupled transient simulation for the whole runner toget a more accurate solution.

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


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Acknowledgements

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 Iwould like to thank Mr. Biraj Singh Thapa for providing me with all the necessary inputs in thisthesis work. His constant support, encouragement and belief towards me and my work made me dothe 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, whosecontinuous care and support made my stay a pleasant one. I would also like to thank Professors BholaThapa 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 workswhile I was away in KU.


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Contents

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

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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

Masters thesis - FSI analysis of Francis Turbines exposed to Sediment Erosion


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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



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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



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List of Figures

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

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LIST OF FIGURES 6

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 theblade. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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 Suctionside . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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



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LIST OF FIGURES 7

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



11.4 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



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List of Tables

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

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List of abbreviations

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 PSHa Net Positive Suction Head available

N PSHr 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

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List of symbols

Hydro Turbines Parameters

Htot Total Head [m]

g Acceleration due to gravity [m/s2]

C Absolute velocity [m/s]

C1 Absolute velocity at the inlet [m/s]

Cx Axial absolute velocity component [m/s]

C1 Circumferential absolute velocity component at the inlet [m/s]

C2 Circumferential absolute velocity component at the inlet [m/s]

U2 Tangential velocity of the runner at the outlet [m/s]

U1 Tangential velocity of the runner at the inlet [m/s]

W Relative velocity [m/s]

Rotational speed [rad/s]

t Time steps [s]

Q Flow rate (Discharge) [m3

/s]

P Power [W]

m Mechanical efficiency [-]

0 Overall efficiency [-]

h Hydraulic efficiency [-]

Density [kg/m3]

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List of symbols

FSI Parameters

Dynamic viscosity [N.s/m2]

p Pressure [Pa]

ui Cartesian component of velocity u in directionxi [m/s]

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

Fs(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]

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

dm Displacement of the mesh [m]

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

unew Load components transferred at this iteration [-]

uold Load components transferred at the previous iteration [-]min Convergence criteria in the stagger iteration [-]

e Convergence criteria in the solver [-]

disp Mesh stiffness [N/m]

Relative displacement of the mesh [m]

Cstiff Model exponent [-]

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

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List of symbols

Erosion Parameters

E,W,Er Erosion Rate

N Number rate of the particle

mp Mass of the particle

Finnie

Vp Particle impact velocity

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

n Value of exponent

Tabakoff

0 Angle of maximum erosion

k1 k4, k12 Model constants

V1 V4 Reference velocity

RT, VPN Parameters for calculation

Bardal

C Concentration of particles

a Size coefficient of particles

Kmat Material constant

Kenv Environment constant

Vp Velocity of the particle

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List of symbols

Erosion Parameters

Tsuguo

Turbine coefficient at eroded part

x Exponent for concentration

y Exponent for size coefficient

m Value of exponent

k1, k2 Hardness coefficient of particles

k3 Abrasion resistant coefficient of material

W Loss of thickness per unit time

Thapa

Km Material factor

Khardness Hardness factor

Kf Flow factor

Kshape Shape factorx Velocity of eroding particles

y Loss of material

r Efficiency after erosion consideration

a, b Empirical constants

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List of symbols

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 Atmospheremol Mole

N Newton

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1Introduction

1.1 Background of the work

Nepal is a land-locked country between India and China, blessed with a massive geographical diversityand water resources. The chances of utilizing these resources in the form of hydropower developmentare enormous, however, it has been seen that till date, only about 1% of the total feasible hydropowerhas been harnessed [1]. Not only that different conditions are not supporting the installation of newpower plants here, but because of the excessive sediments in the Himalayan River, the damage of theturbine 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 byan extensive amount of sediment erosion reducing the life span of turbine components. Similarly, otherpower plants such as Marsyangdi, Panauti, Trishuli and Sunkoshi are affected by erosion. Researchworks have been made to decrease erosion, either by coating or by minimizing the concentration ofsediments in the water. These research works are showing possibilities which are either inadequate orunfeasible economically. However, research works based on design optimization of the turbines haveshown positive results to some extent. This study will focus on the reference (original) design of theturbine runner and comparison of this with other optimized blades in terms of erosion. Most of theworks done previously accounted for the flow field around the blade only, and not the effect of theflow field on the deformation of the blade or the effect of the deformation of the blade on the meshsurrounding 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 researchon eroded blades and possible optimization techniques. The present Masters thesis is an effort toconsolidate the previous works done on the enhanced mechanical design of Francis turbines for betterhandling of the sediment erosion by including the effect of FSI. This project is expected to bringa positive change and advancement in the field of computational solutions of the turbine flow fieldand structural integrity considering the sediment erosion damage. Having said the challenges faceddue 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 theone-way coupling techniques in Francis runner and even fewer about the fully-coupled solutions. The

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CHAPTER 1. INTRODUCTION 16

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

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

Kathmandu University is an autonomous, non-profitable, non-governmental institution established on1991, dedicated to maintain high standards of academic excellence. Turbine Testing Lab (TTL) wasestablished in 2010-2011 inside the premises of KU with a financial support from NORAD and othernational industries. With 30 meter open head and 150 meter closed head, TTL is capable of testingdifferent hydraulic turbines up to 300 kW and conduct model tests for larger sizes. This laboratoryhas 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 challengesfaced by the hydro power stations for making a better future in Nepal in terms of the energy productionand 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 learningfacilities.

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 sedimenterosion. They have also been collaborating with various national and international institutions andcompanies to improve its research standards. Besides, several numerical tools and computationalsoftwares 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 researchworks 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.



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CHAPTER 1. INTRODUCTION 17

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

Make a comparative analysis of the results between CFD, one-way FSI and two-way FSI andidentify 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 thereference 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 thencompared with the reference design through one way and two way FSI analysis for two different casesof boundary conditions.

1.5 Scope of study

This study mostly covers the use of numerical tools for the design optimization of Francis runner bladesfor better sediment handling. The CFD analysis was done in ANSYS-CFX including Turbo-grid formesh generation. The erosion parameters were used from the models supported by ANSYS whereasvalidation of the model was done from various parametric studies including a mesh independence studyfor 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 steadysimulation of a single runner blade by considering cyclic symmetricity of the model. Validation of theresults 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. Chapter2 consists of some of the introductory part of hydroturbines in general and in the context of Nepal. Chapter3contains a detail review of sediment erosionin hydraulic machinery and its influence in Nepalese hydro power plants. This chapter also containssome mathematical formulations of erosion models along with the models supported by ANSYS. Thestudies made in the field of numerical analyses of turbines exposed to erosion by past researchers arediscussed in Chapter4. Introduction about FSI and strategies of conducting FSI in ANSYS are shownin Chapter5. Chapters6,7and8contains all the numerical analyses performed in this study alongwith the results from these analyses. The analyses are divided in such a way that a CFD model wascreated in the beginning and the same model was used in further chapters for one way and two wayFSI analyses. The discussion and conclusion from all the results are included in Chapter9. Finally,future scope in the related field is discussed in Chapter10.



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2Hydro 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 lossesthat arise partly in the machine itself and partly in the water transfer into and out of the machinesuch as pipe friction losses, losses due to bends in pipes, gates, valves and losses due to abrupt andgradual expansion and contraction of the pipes [4]. Some of the basic components of a hydropowerplant 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. Screeningis done in the intake, to prevent unwanted objects (debris and aquatic animals) entering intothe 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 raceif the turbine exhaust water cannot be discharged directly (through the draft tubes) into theriver. 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 headand 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 capacityof 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 feasiblepower potential of Nepal. Ironically, Nepal is blessed with immense water resources with the average

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CHAPTER 2. HYDRO TURBINES 19

annual precipitation of approximately 1700 mm. The total annual average run-off from the nations600 rivers flowing from high mountains is over 200 billion m3 [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 hydropowerstations 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 MWKhimti 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. Inthe case of hydro turbines, it gives the relation between the total head (Htot) and the velocity trianglesin the inlet and the outlet.

Htot.g= U2.C2 U1.C1 (2.1)

Where,C2 : circumferential absolute velocity component at the outletC1 : circumferential absolute velocity component at the inletU2 : tangential velocity of the runner at the outletU1 : 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 arenecessary : 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.



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r

x

Flow passage

Absolute streamline

Relative streamline

W1

W2

C2

C1

U1

U2

x(m)

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

In the case when U2= U1 :

Htot.g= U.C (2.2)

Depending upon the sign of C, the sign ofHtot 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 ofdevices are called turbines. The velocities triangles of a typical turbomachinery rotor is shown in

Figure2.1. The absolute and the relative velocities at the inlet and the outlet can be split into axialand circumferential components. From the figure, C2 < C1 i.e. Htot < 0, so this is a case of a turbinewhere 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 axialand the meridional co-ordinates are not the same and instead of the axial co-ordinate (x), meridionalco-ordinate (m) has to be referred.

2.3 Cavitation

Cavitation is one of the principle challenges in hydro turbines, which occurs when the local pressurefalls below the vapor pressure of the water. This happens due to an increase in velocity or an ambientdrop in pressure. The water vapor forms at the area of low pressure in the form of bubbles, whichwhen carried to areas of higher pressure, can collapse violently. This collapse induces high pressuresand 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 isflowing at a certain temperature and pressure with a velocity C1. By entering the contracted region,from the conservation of mass, the velocity of the fluid C1 increases to C2. From the Bernoullis



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principle, when the velocity of the fluid increases, the pressure in the fluid will decrease to maintainthe constant total pressure. This figure also shows the dependency of the saturation pressure onthe fluid (water) temperature. As the pressure in the fluid is decreased, the fluid will evaporateat 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 todisappear. Because of the increase of the fluid pressure, the vapor bubbles implode sending out smallbut very high pressure micro jets. These micro jets, when close to the material surfaces, blast awaythe material. This process is shown in Figure2.3. Cavitation in the system can be checked througha measure provided by the manufacturers called as N PSHr (Net Positive Suction Head required).This N PSHr is compared with N PSHa (Net Positive Suction Head available), which is a systemparameter indicating the head surplus at inlet before the saturation pressure is reached.

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

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



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impulse stage with all the pressure drop occurring across the stationary components and no pressuredrop across the runner. The reaction stages such as Francis and Kaplan turbines have a proportionof 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 acircular disc with buckets which are driven by one or more nozzles delivering a jet perpendicular tothe buckets. An example of a jet impingement along with the velocity triangles are shown in Figure2.4. At the inlet, the flow velocity is C1 and the tangential speed of the bucket is U. The relative flowvelocity then becomes W1= C1 U. Since C1 =C1 at the inlet, such kind of arrangement gives themaximum 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 therunner are similar to those of axial-flow turbine rotors but designed with a twist in order to have afree-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 loadcondition to maintain optimum efficiency conditions. A typical section of a Kaplan turbine is shownin Figure2.5whereas, the velocity triangles at the inlet and the outlet are similar to the one shownin Figure 2.1 except that the tangential speed of the rotor at the inlet and the outlet are equal i.e.U1 = U2 and also the axial component of the absolute velocity is constant i.e. Cx= constant.



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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 pressuredrop in Francis turbine occurs in the turbine entry, whereas the remaining pressure drop occurs in theturbine 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 Figure2.6. In practise, the turbines withcomparatively small dimensions are arranged with horizontal shaft whereas the vertical arrangementis 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 ofcross-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 thewater towards the guide vanes and absorb the axial forces from the volute. These vanes are given afavorable 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



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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 aservo motor connected to the guide vanes[7]. These vanes direct the flow onto the runner at the mostsuitable 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 turbineshaft[6]. Runners with higher head require higher number of blades in order to reduce the individualblade loading and seperation at the runner inlet during low loads[7]. The runners are usually madeof stainless steel.

Labyrinths

The leakage losses between the turbine runner and the cover can be minimized by placing labyrinthseals such that the flow of the water from the gap is prevented. The labyrinth consists of a static sealconnected 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 mainpurpose is to convert the kinetic energy at the runner outlet to the pressure energy at the draft tubeoutlet. 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 theknown quantities needed for this calculation are the gross head which is the difference of water levelsbetween the head race and the tail race (Hg) and the loss of head in the penstock (Hf). Hence, thenet or available head can be calculated through (Hg Hf), i.e. difference between the total energyavailable 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.g

+V2

2.g

+zpenstock

p.g

+V2

2.g

+zdraft tube

(2.3)



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

work done= .Q(C1 .u1 C2 .u2) (2.4)

Where,Q = Discharge through the runner, m3/sWhen C2 = 0, the maximum output is obtained.

Hydraulic efficiency,h is given by the total power developed by the runner over the power supplied tothe turbine. If H is the net head, then input to the turbine is given by .g.Q.H. Hence, the followingequation can be achieved:

h= .Q(C! .u1)

.g.H.Q (2.5)

or,

h=C1 .u1

g.H (2.6)

Mechanical efficiency,

m = Shaftpower(P)

P ower developed by the runner (2.7)

Overall efficiency,

0 = Shaft power

W ater power =

P

.g.Q.H (2.8)

0= h m (2.9)

Hence, the overall efficiency of the Francis turbine can be deduced as a product of hydraulic andmechanical 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 Francisturbines with a head of 115 meters. Similarly, other hydro-power stations such as Marsyangdi, MiddleMarsyangdi etc. also uses Francis turbines. The technical specification of these turbines are shown inTable2.2.



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



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3Sediment Erosion

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

Figure 3.1: Erosive wear mechanisms [5]

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

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CHAPTER 3. SEDIMENT EROSION 28

particles and the base material. These parameters also give the quantitative measure of the erosivewear. For example, a low angle of impingement is favorable for the wear process as the particles aredrawn across the surface after the impact. Similarly, if the speed is low, then stresses at impact areinsufficient 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 erodingparticle is blunt or spherical, the plastic deformation is more likely to occur, whereas, if the particlesare sharp, the cutting wear is more common. It has been seen that for the ductile mode, the maximumerosive wear is generally found close to an angle of 30 whereas, for the brittle mode, the maximumerosive 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 italso significantly matters what impingement angles are the particles hitting the material. The mostcommon materials that are chosen are stainless steel and titanium- and nickel- alloys. Formation of themartensites results in the improved hardenability and erosion resistance except at low impingementangles and for the low alloy steels, the ferritic phase with sufficient spheroidal carbide to inducestrengthening is very effective against erosive wear. The various materials behavior and the effect ofthe 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 resistanceat a low impingement angle but one of the worst materials for high impingement angles. Accordingto a study made between a martensitic (13Cr4Ni) and an austenitic (21Cr4Ni) steels, it was seen thatthe erosion resistance of 21Cr4Ni strengthened with Nitrogen is higher than the former one due to thedistribution 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



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to their excellent high temperature properties. However, these materials are brittle which might resultin 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 iswet 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 haveexcellent 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 ofsediment erosion. At the inlet system i.e. manifold and valve, only a moderate effect of the sedimentis seen because of the low operating velocity. The effect of the sediment erosion is mostly seen inthe needle tip, seal rings in the nozzles and the runner buckets. Specially in the case of high headturbines, the bombardment of the fine particles on the needle surface due to the strong turbulenceeffect 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 thearea where the jet directly hits at the bucket surface and the surface damage is observed primarily dueto the hammering action rather than the cutting action. The fine particles on the other hand flow alongwith the water inside the bucket and strike the surface towards the edge, causing erosion towards theoutlet. It is also reported that silts with small grain size damages mostly needles and nozzles whereasthe runner buckets have negligible damage. On the other hand, with the coarse particles, the Peltonbuckets 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 Figure3.3. The erosion occurs in the stay vanes because of the secondary flows from the spiral casing causingnon-uniform flow angles at the inlet with high absolute velocities. The guide vane system is highlyaffected by the sediment erosion due to the high absolute velocity and acceleration. The erosion ofguide vane can be classified into: turbulence erosion at the outlet region and facing plate due to highvelocity 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 frontof the runner. The vortices generated from the secondary flow and the leakage flow from the guidevane will eventually pass through the runner inlet causing damages at the inlet of the runner. In therunner, the highest relative velocity occurs at the outlet region while the highest absolute velocityand 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 andthe 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 causessediment erosion in that region.



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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 turbinecomponents 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 alonecontributes to two thirds of the worlds total sediment transport to oceans which makes the problemof erosion and sedimentation even more challenging[16]. Ever since the first sediment data collectionstarted 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 judgedby the quartz content, as these materials have enough hardness to erode the turbine material. Resultsshow that the rivers in the Koshi basin have more than 60 percent quartz content in average withmore quartz particles in the east compared to the west [17]. Even with the well designed sedimentsettling and flushing system, power plants like Marsyangdi, Khimti and Jhimruk have severe erosionproblem. Some of the erosive damages due to sediment in Jhimruk Power Plant are shown in Figure3.4. Sediment erosion has not only reduced efficiency in hydro turbines, but has also caused variousproblems during the operation and maintenance period. Some solutions regarding the change of thematerial, 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, butit is also significantly seen in the Andes region in South America. A 22 MW Cahua hydro powerplant built in Peru can be taken as an example. It was seen that the sediment concentration exceeded120,000 tons of sediment only after six weeks of operation with the average quartz content found to beabout 35 percent and feldspar found to be about 30 percent [ 16]. One of the recent solutions towardspreventing the sediment erosion is to improve the hydraulic design of the runner such that the effect ofthe erosion remains minimum. Various studies made regarding the design optimization of the Francisrunner is discussed in Chapter4.



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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. Thesemodels 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 modelis given by Equation3.1.

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

The expression for erosion was simplified in [11], which is given in Equation3.2.

Erosion (velocity)m (3.2)

Where m is the exponent of velocity. According to [12], the most general formula for the pure erosionis give by Equation3.3.

W =Kmat.Kenv.C.Vmp [mm/year] (3.3)

Where W is the erosion rate in mm/year, Kmat is the material constant and Kenv is the environmentconstant, C is the concentration of the particles and Vp 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 Equation3.4 to calculate erosion in turbines.

W =.Cx.ay.k1.k2.k3.Vm [mm/year] (3.4)

Where W is loss of thickness per unit time, is turbine coefficient at eroded part, V is relative flowvelocity, a is the average grain size coefficient on the basis of unit value for the grain size 0.05 mm.The termsk1 and k2 are shape and hardness coefficient of sand particles and k3 is the abrasion resis-tant coefficient of the material. The exponent values x and y are for the concentration and the size

coefficient respectively.



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According to[18], the erosion rate was estimated through laboratory tests of various turbine materialsunder different test conditions. Equation3.5 gives an empirical relation to predict the erosion rate for16Cr5Ni, which is the most widely used turbine material.

y = 6E 5x3.13

[mg/kg] (3.5)

Where x(m/s) is the velocity of eroding particles impinging at the angle of 45and y is the loss of thematerial 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 finalequation yielded by this model was given by Equation3.6 and Equation3.7.

Er =C.Khardness.Kshape.Km.Kf.a.(size)b [mm/year] (3.6)

r =a.(Er)b [%/year] (3.7)

Where Km is the material factor, Kf is the flow factor, Kshape is the shape factor and Khardness isthe 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%, anda = 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 inputparameters, Tabakoff model provides more scope for customization, though the choice between thesetwo 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= kVnp f() (3.8)

Where,E is a dimensionless mass,Vp is the particle impact velocity andf() is a dimensionless function of the impact angle which is in radiann is the value of exponent which is usually in the range of 2.3 to 2.5 for metals.



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Model of Tabakoff and Grant

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

E= k1.f().V2p.cos2()[1 R2T] +f(VPN) (3.9)

Where,

f() = [1 +k2.k1.2sin(/2

0)]2 (3.10)

RT = 1 k4.VPsin() (3.11)

f(VPN) =k3.(VPsin())4 (3.12)

k2=

1 if 20

0 if >20(3.13)

Where,0 is the angle of maximum erosionk1 to k4, k12 and 0 are model constants and depend on the particle/wall material combination.

The Tabakoff model requires the specification of five parameters : k12 constant, 3 reference velocitiesand the angle of maximum erosion 0. An example of these parameters for Quartz-Aluminum is shownin Table3.1.

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

Variable Coefficient Value

k12 k12 0.585

Ref velocity 1 V1 159.11 [m/s]



Angle of Maximum Erosion 0 25[deg]



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4Recent works - Review

The damage on hydraulic machineries due to sand erosion was initially studied in[17] and [18]throughvarious design aspects such as material selection, mechanics of material and hydraulics. This researchwork led the path to carry out further investigations numerically and experimentally, which has nowbecome 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]includingexperimental studies, numerical simulation, and field studies. The erosion rate was predicted for stayvanes, guide vanes, and runner vanes of a Francis turbine for different shape, size and concentrationof the particle and operating conditions of the turbine.

The current research project will be based on a previous work regarding the hydraulic design ofFrancis turbines exposed to sediment erosion [21]. It was shown in the study from CFD analysisthat the conventional methods of hydraulic design of Francis turbines can be improved to minimizesediment erosion. The CFD analysis carried out in ANSYS-CFX contains various parameters shownin Table4.1. The generation of the mesh in Turbogrid, CFX setup and the result showing the erosionrate 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 atinlet, 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 wasdeveloped called as KHOJ, which made the optimization process much easier. More informationabout this program can be found in [21].

Another complementary study was made in [19] where a CFD analysis was performed on a bladerunner. This study showed that the largest reduction of erosion was obtained by decreasing rotationalspeed of the turbine. However, this increases the investment cost because of the larger size. Analternative approach was also made, which showed that the reduction of erosion could also be madeby changing the blade angle distribution, and consequently, the energy distribution.

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CHAPTER 4. RECENT WORKS - REVIEW 35

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]



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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/cm3

Particle Molar Mass 1 kg/kmol

Particle Diameter 0.1 mm

Tabakoff erosion parameters

k12 0.586

Reference velocity 1 159.11 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/sParticle 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



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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 fullyestablished for the case of Francis turbines, specially when exposed to sediment erosion. A one-waycoupling strategy was presented in [7] to compare the structural integrity between the reference andthe optimized designs. The FSI analysis layout was made in ANSYS workbench as shown in Figure4.4. The pressure load from CFX is exported to the structural analysis by defining a Fluid-Structureinterface. Also, the boundary conditions of the runner were defined as shown in Figure4.5. The pres-sure distribution between the inlet and the upper labyrinth on the top side of the hub and undersideof the shroud were given by Equation 4.1. The pressure distribution at the surface of the hub betweenthe shaft and upper labyrinth seal is given by Equation 4.2. This unidirectional FSI was inadequateas the deformations in the structure was not taken into account in the flow analysis.

p(r) =p(x) =.g.h(x) = (.g)(hi k2.2

2.g (r2i x

2))[P a] (4.1)

p(r) =p(x) =.g.h(x) = (.g)(hp k2.2

2.g (r2p x

2))[P a] (4.2)

The concept of a fully coupled FSI in Francis turbines has been introduced in a study [22] where astrongly coupled partitioned equations are solved separately using different solvers, but are coupledimplicitly into one single module based on a reduced-order model. The proposed model is used topredict the unsteady flow fields of a 3D complete passage, involving in stay, guide vanes, and runnerblades of a Francis turbine. Such reduced-order model is based on only a few displacement andstress modes, which not only saves computing time but also enlarge the range of applications inengineering[22]. This study has also shown that the numerical results when considering FSI showsbetter 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 todetermine the mechanical integrity of the turbine blades by varying the stiffness of the blades [23]. Amulti-field simulation has been used in this study as CFD and FEA solvers to exchange informationat the interface.

4.3 Other relevant works

In the present study, various optimized blades will be investigated, which were studied previously withCFD 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 lineardistribution of the blade angle, which is chosen as the reference design. All the other designs and theresults from the CFD are compared with this design. These blade shapes give an indication of how thehydraulic energy is converted to mechanical energy along the stream-wise direction. A runner bladedesign of shape 1 converts half of the hydraulic energy from the middle towards the outlet, whereasshape 2 will convert the energy at the beginning of the blade till the middle. The result of this studyshows that the blade angle distributions of shape 4 and 5 have reduced erosion effects. Shape 4 will



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

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



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



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5FSI review

Since the work is intended to be done in ANSYS, ANSYS coupled-field guide [24] is mainly referredin this chapter.

5.1 Coupled-Field Analysis

A coupled-field analysis is a multidisciplinary engineering analysis where various independent fieldscombine and interact together to solve a global engineering problem such that the result of one field

is dependent on the other field(s). The coupling can be either one-way or two-way. In the one waycoupling, the effect of one field is imposed on the other field but not the vice versa. In the fluid-structure analysis, when the stiffness of the structure is too large, the deflection of such structurehas a negligible impact on the flow field. Similarly, in the case of temperature-structure coupling,the temperature field affects the structural field by generating the thermal strains, but the structuralstrains have a negligible or no impact on the temperature field. For these types of applications,a one-way coupling analysis is sufficient. The classical approach towards one-way FSI is that thepressure distribution on the surface is calculated by CFD, which is exported to FEA to calculate thestresses and deflections on the structure. The effect of the deflection of the structure on the flow fieldsurrounding the structure is neglected in the one-way FSI, hence this type of coupling strategy is alsocalled as a partially-coupled or a weak coupled analysis.

A two-way coupling method is a more complex case where all the fields has a significant influence overeach other. In the case of the fluid-structure analysis, when the deflection of the structure cannotbe neglected, or in the case of the induction heating (magnetic-thermal analysis), two-way couplingstrategy is essential.

According to the ANSYS coupled-field guide[24], the coupled-field analysis is of two types: Sequentialand Direct. The sequential method consists of two or more analyses of different fields, which areexecuted sequentially. The direct method on the other hand consists of only one analysis in which acoupled field element is used containing information from both the fields. Direct method is mostlyused when the coupled-interaction is highly nonlinear. Sequential method offers independent solving

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CHAPTER 5. FSI REVIEW 41

of the different fields, providing more flexibility and efficiency when the coupled-interaction does nothave a high degree of nonlinearity. Coupling can be sequentially done either by a physics file or bythe multi-field solver (In the case of ANSYS, ANSYS-Multi field solver).

5.1.1 Sequential Method-Physics files

The physics analysis is based on a single finite element mesh across physics. Using the physicsenvironment, the loads are transferred explicitly external to the analysis. A physics file is read toconfigure the database, a solution is performed, another physics field is read into the database, coupled-field loads are transferred and the second physics is solved.

5.1.2 Sequential Method-ANSYS multi-field solver

Multi-field solver provides a more robust, accurate and easy to use tool than the physics file-basedprocedure. In this case, each physics is created as a field with an independent model and mesh. Thecoupled loads are automatically transferred across dissimilar meshes by the solver. In ANSYS, themulti-field solver can be implemented by two methods.

MFS-Single code

MFS code is used when the small models are used with all the physics field contained within a single

product executable. It uses an iterative coupling where each physics is solved sequentially and eachmatrix equation is solved separately. The solver iterates between each physics until loads transferredacross the physics interface converge.

MFX-Multiple code

MFX code is used when much larger models are needed to be simulated compared to the MFS. It isthe enhanced version of ANSYS multi-field solver used for simulations with physics field distributedbetween more than one product executable (eg. between ANSYS multiphysics or Mechanical and

CFX). A field solver runs different codes involved in the coupled-interaction. These fields are thencoupled using a form of iteration called stagger iteration. The solution loop now consists of twoloops. The multi-field time loop and the multi-field stagger loop. An example of the ANSYS multi-field solver process for Fluid-Structure interaction between ANSYS mechanical and ANSYS CFX isshown in Figure5.2. The solution is divided into two different solvers, of which one is called master andthe other one is called slave. The master performs the coupling setup (reads all the MFX commands,collects the interface meshes from the slave codes, does the mapping) and sends instructions (timeand stagger loop controls) to the slave executable. Contrarily, the slave code receives the couplinginformation from the master code and sends the interface meshes to the master. In MFX, the ANSYScode is always the master, and CFX code is always the slave. In the current study, MFX code will be



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Figure 5.1: ANSYS multi-field solver process [24]

used in order to implement the FSI because of the flexibility and the robustness it provides for thefluid-structure coupling.

5.2 Strategy of FSI in ANSYS

The MFX solution can be carried out in ANSYS with the following sequential strategies :

5.2.1 Set up ANSYS and CFX models

As the MFX procedure consists of two independent solvers, the models needs to be made for each ofthem. It consists of the geometry, the mesh, boundary conditions, analysis options, output optionsetc.



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5.2.2 Flag Field interface conditions

The load transfer between the two fields are done at the interface, where the information is sharedbetween the two different mesh through interpolation. To do this, a particular index is used to specifythe interfaces. In ANSYS, the surfaces are flagged by an interface number, whereas in CFX, thesurfaces are flagged by an interface name (FSIN).

5.2.3 Set up Master Input

Up till now, the set up procedures are done in the individual solvers and the parameters are relatedto them separately. In this part, all the coupled-analysis set up is carried out. This includes, globalMFX controls, interface load transfer, time controls, mapping operations and stagger solutions.

5.2.4 Obtain the solution

After a valid set up is imposed, the program runs successfully and the post processing of the resultscan be done in a similar way, as when the fields are solved independently.

5.3 Governing equations in FSI

The coupled fluid-structure interaction problem may be considered as a three field problem, i.e. fluidflow, structural deformation and the moving mesh. These fields are governed by their respectivegoverning equations [25].

Navier-stokes equation

t(ui) + ..u.ui = p+ ...ui+Ff(t) (5.1)

Where,u = velocity,

= density, = dynamic viscosity,p = pressure,ui = cartesian component of velocity u in direction xi,Ff(t) = transient load vector defined for the fluid.

The equation of continuity for the incompressible flow is given by,

.u = 0 (5.2)

The equation of motion for an elastic structure can be written as :

MX+C

X+KX=Fs(t) (5.3)



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Where,X = displacement,M= Mass matrix,K= Stiffness matrix,

C= Damping matrix,Fs(t) = Transient load vector defined for the solid.

And finally, the mesh movementin the fluid domain may be modelled as a pseudo structural problemwith its own dynamics with a spring based mesh movement, governed by [25],

Km.dm = fm(t) (5.4)

Where,Km = a pseudo-structural stiffness matrix which is defined for the whole domain,dm = displacement of the mesh,

Figure 5.2: Schematic of Fluid structure interaction

The schematic diagram of the representation of FSI is shown in Figure 5.2. The figure shows theinteraction between the three fields and boundary information shared between each domain. Fromthe fluid dynamics, using the Navier-Stokes equation for the incompressible flow, the pressure on theboundaries of the structure is calculated. This pressure is exported to the structural dynamics andusing the equation of motion, the deflection of the structure is known. The deflection of the structureresults in the distortion of the mesh of the flow field surrounding the structure, which affects thecomputation of the fluid dynamics. The displacement of the mesh is transfered to the fluid dynamicsand the pressure field is calculated for the next time step. Other than Computational Fluid dynamics(CFD), CSD and CMD in the above diagram represents Computational Structural Dynamics andComputational Multi-body Dynamics respectively.



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6CFD analysis

The objective of the CFD analysis in the context of this project is to build up a base for the FSIanalysis. This base is made from a detailed CFD analysis, such that the model could be used furtherin the FSI studies. A CFD model independent of the mesh density will be chosen from the meshconvergence study. Then, the same mesh will be used in the sensitivity study, where various physicaland numerical parameters affecting the solution will be tested. This is because most of the parametersused in CFD are based on various assumptions to simplify the solution. The sediment passing throughthe turbine could have various physical properties. By carrying out the sensitivity study, the effectof the variation of the input parameters on the results could be studied. Also, by increasing thetolerance of the residual criteria, the solution could be significantly affected. Following parameterswill be investigated in the sensitivity analysis :

Effect of the particle size (particle diameter)

Effect of the particle shape (particle shape factor)

Effect of the particle behavior (mass flow rate, concentration)

Effect of the erosion model

Effect of the numerical parameters such as convergence criteria and turbulence model

These parameters will undergo independent variations, which will be performed on a baseline case.After performing the sensitivity study, the reference design will be compared with the 4 other optimizeddesigns in terms of blade shape and the blade showing the best erosion resistance without influencingthe efficiency will be chosen for the further studies.

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CHAPTER 6. CFD ANALYSIS 46

6.1 Sensitivity study

In this chapter, the sensitivity study of the various CFD parameters will be performed. The objectives

of this study are :

To create a model whose solution is independent of the mesh density. This model will be usedas a baseline case throughout this chapter.

The baseline case will be subjected to various physical and numerical parameters. The influenceof these parameters on the solution will be studied.

To identify suitable parameters that needs to be used in the future studies. This mainly includesthe numerical parameters such as spatial and temporal distribution.

As the sediment erosion is the principle interest in this context, the comparison between the resultsis done on the basis of the average erosion rate density on the blade. In ANSYS, the erosion of thewall due to a particle is computed from the following relations:

ErosionRate= E N mp (6.1)

wheremp is the mass of the particle and Nis the number rate. The overall erosion of the wall is thenthe sum over all the particles. The erosion rate is in kg/s, but in the CFX-Post Processor, the resultsare in the form ofkg/s/m2 and named as Erosion Rate Density.

6.2 Mesh convergence study

The CFD analysis for determining the sediment erosion rate density is extremely sensitive to the meshdensity. Past studies show and support this fact of difficulty in making the solution independent ofthe size of the mesh[19], [21]. A very small value of y+ is recommended in order to have an accuratesolution. However, to achieve such small value of y+ requires very fine mesh around the boundary,which requires a massive computational time. In Turbo-grid, the near wall mesh refinement allows afiner mesh around the blade, which can be controlled by changing the factor ratio. High value of thefactor ratio makes a finer mesh around the boundary, but it is also seen that it degrades the quality

of the mesh. A factor ratio of 2 was used in the previous studies to create a very low y+ value asrecommended in the studies. However, with this ratio, a very fine mesh was not possible because ofthe very low quality of the mesh. With such large ratio, some of the other parameters, such as thepressure field around the blade were affected.

A good quality mesh could be generated with lower value of the factor ratio, but higher mesh densitywas needed in order to have a mesh independent solution. In this chapter, the factor ratio of 1.15,1.25, 1.5 and 2 were studied. It was seen that the erosion rate density was very sensitive to thechange in the mesh type and size. However, in all the mesh type and size, the average erosion ratedensity on the single blade was in the range of 6E-8 to 1.5E-7. At the factor ratio of 2, though theconvergence behavior was better than other cases, a low quality of mesh resulted in the termination

of the simulation for finer mesh.



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CHAPTER 6. CFD ANALYSIS 47

This problem of mesh convergence for the other cases was treated by decreasing the residual criteria,the RMS value from 1E-4 to 1E-6. The computational time by doing this increased a lot, but itimproved the convergence behavior, as shown in Figure 6.1. Here, the factor ratio was chosen to be1.15 in order to have a better quality of mesh than that of the previous studies. After the target

mesh of 0.75 million node, the solution did not change much even at 2 million nodes. The betterconvergence of the mesh than the previous studies was achieved due to:

The residual criteria for co

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