FSI Analysis of Francis Turbines Exposed to …660362/FULLTEXT01.pdfSediment erosion is one of the...

Master’s Thesis in

FSI Analysis of Francis Turbines Exposed to SedimentErosion

Sailesh Chitrakar

July, 2013

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 Master’s 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 erosionand 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-wayFSI. 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

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.

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

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

Master’s thesis - FSI analysis of Francis Turbines exposed to Sediment Erosion

3

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


4

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


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

5

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


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


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

8

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

NPSHa Net Positive Suction Head available

NPSHr 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

9

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]

Cθ1 Circumferential absolute velocity component at the inlet [m/s]

Cθ2 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]

ω Rotational speed [rad/s]

∆t Time steps [s]

Q Flow rate (Discharge) [m3/s]

P Power [W]

ηm Mechanical efficiency [-]

η0 Overall efficiency [-]

ηh Hydraulic efficiency [-]

ρ Density [kg/m3]

10

List of symbols

FSI Parameters

µ Dynamic viscosity [N.s/m2]

p Pressure [Pa]

ui Cartesian component of velocity u in direction xi [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]

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

unew Load components transferred at this iteration [-]

uold Load components transferred at the previous iteration [-]

Φmin Convergence criteria in the stagger iteration [-]

e Convergence criteria in the solver [-]

τdisp Mesh stiffness [N/m]

δ Relative displacement of the mesh [m]

Cstiff Model exponent [-]

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

11

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

n Value of exponent

Tabakoff

γ0 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

12

List of symbols

Erosion Parameters

Tsuguo

β 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 factor

x Velocity of eroding particles

y Loss of material

ηr Efficiency after erosion consideration

a, b Empirical constants

13

List of symbols

Units

m Meter

mm Milli meter

rad Radian

MW Mega Watt

Pa Pascal

MPa Mega Pascal

◦C Celsius

kg Kilogram

deg Degree

rev Revolution

min Minute

sec Second

atm Atmosphere

mol Mole

N Newton

14

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 maintenanceperspective 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 themechanical property of these blades.

Turbine Testing Laboratory (TTL) of Kathmandu University has been performing several researchon eroded blades and possible optimization techniques. The present Master’s 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

15

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 thelaboratory 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- turbinessold 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 ofthe 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 anddesign 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 hydraulicdesign of Francis runner for a better sediment handling.


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 bladehaving 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. Chapter 2 consists of some of the introductory part of hydroturbines in general and in the context of Nepal. Chapter 3 contains 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 Chapter 4. Introduction about FSI and strategies of conducting FSI in ANSYS are shownin Chapter 5. Chapters 6, 7 and 8 contains 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 Chapter 9. Finally,future scope in the related field is discussed in Chapter 10.


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 andallows 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

18

CHAPTER 2. HYDRO TURBINES 19

annual precipitation of approximately 1700 mm. The total annual average run-off from the nation’s600 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 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. 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.Cθ2 − U1.Cθ1 (2.1)

Where,Cθ2 : circumferential absolute velocity component at the outletCθ1 : 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 orvariation 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 U2 = U1 :

Htot.g = U.∆Cθ (2.2)

Depending upon the sign of ∆Cθ, the sign of Htot 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 inFigure 2.1. The absolute and the relative velocities at the inlet and the outlet can be split into axialand circumferential components. From the figure, Cθ2 < Cθ1 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 Bernoulli’s



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 normalsituation (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 Figure 2.3. Cavitation in the system can be checked througha measure provided by the manufacturers called as NPSHr (Net Positive Suction Head required).This NPSHr is compared with NPSHa (Net Positive Suction Head available), which is a systemparameter indicating the head surplus at inlet before the saturation pressure is reached.

𝐶1 𝐶2

𝑇 [0𝐶]

𝑃𝑆 [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 staticpressure 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 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 Cθ1 = C1 at the inlet, such kind of arrangement gives themaximum swirl (i.e. negative ∆Cθ), 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 Figure 2.5 whereas, 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.



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 Figure 2.6. 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 casingThe 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 vanesFrom 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 vanesThe 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 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.

RunnerIn 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.

LabyrinthsThe 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 tubeThe 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

ρ.g+V 2

2.g+ z

)penstock

−(p

ρ.g+V 2

2.g+ z

)draft tube

(2.3)



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

work done = ρ.Q(Cθ1 .u1 ± Cθ2 .u2) (2.4)

Where,Q = Discharge through the runner, m3/sWhen Cθ2 = 0, the maximum output is obtained.

Hydraulic efficiency, ηh 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 ρ.g.Q.H. Hence, the followingequation can be achieved:

ηh =ρ.Q(Cθ! .u1)

ρ.g.H.Q(2.5)

or,

ηh =Cθ1 .u1g.H

(2.6)

Mechanical efficiency,

ηm =Shaft power(P )

Power developed by the runner(2.7)

Overall efficiency,

η0 =Shaft power

Water power=

P

ρ.g.Q.H(2.8)

η0 = ηh ∗ ηm (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 inTable 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. Moreabout the erosion problem these turbines are discussed in Chapter 3.


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.

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

27

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 ismore 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



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. Thesecoating 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 tothe 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.



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 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 world’s 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 inmost 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 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. 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 Equation 3.1.

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

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

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 Equation 3.3.

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 Equation 3.4 to calculate erosion in turbines.

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

Where W is loss of thickness per unit time, β 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 terms k1 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 sizecoefficient respectively.



According to [18], the erosion rate was estimated through laboratory tests of various turbine materialsunder different test conditions. Equation 3.5 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 45◦and 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 Equation 3.6 and Equation 3.7.

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

ηr = 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 = kV np f(γ) (3.8)

Where,E is a dimensionless mass,Vp is the particle impact velocity andf(γ) 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.



Model of Tabakoff and Grant

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

E = k1.f(γ).V 2p .cos

2(γ)[1−R2T ] + f(VPN ) (3.9)

Where,

f(γ) = [1 + k2.k1.2sin(γπ/2

γ0)]2 (3.10)

RT = 1− k4.VP sin(γ) (3.11)

f(VPN ) = k3.(VP sin(γ))4 (3.12)

k2 =

{1 if γ ≤ 2γ0

0 if γ > 2γ0(3.13)

Where,γ0 is the angle of maximum erosionk1 to k4, k12 and γ0 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 γ0. An example of these parameters for Quartz-Aluminum is shownin Table 3.1.

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 γ0 25[deg]


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 Table 4.1. 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 donefor 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.

34

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]



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/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 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 Figure 4.5. 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) = ρ.g.h(x) = (ρ.g)(hi −k2.ω2

2.g(r2i − x2))[Pa] (4.1)

p(r) = p(x) = ρ.g.h(x) = (ρ.g)(hp −k2.ω2

2.g(r2p − x2))[Pa] (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



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)

Bla

de

ang

le d

istr

ibu

tio

n r

elat

ive

to t

he

inle

t

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 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.


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 fieldis 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

40

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 singleproduct 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 andCFX). 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 Figure 5.2. 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



ANSYS Master CFX Slave

Do Mapping

Time loop

Stagger loop

End Stagger loop

End Time

loop

Time loop

End Time

loop

Stagger loop

End Stagger loop

Stagger controls(ANSYS to

CFX), Load transfers, Stagger

controls(bidirectional)

Time controls

Time controls

ANSYS

solver

CFX

solver

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.



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

δ

δt(ρui) +∇.ρ.u.ui = −∇p+∇.µ.∇.ui + Ff (t) (5.1)

Where,u = velocity,ρ = density,µ = 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 + CX +KX = Fs(t) (5.3)



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 movement in 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,

CSD

CMD

CFD

dd

𝑡𝑝 = 𝜎𝑓𝑠 𝑜𝑛 𝛤𝑓𝑠

𝑑𝑚 = 𝑑 𝑜𝑛 𝛤𝑓𝑠

𝑢𝑚 = 𝑑 𝑚𝑜𝑛 𝛤𝑓𝑠

𝑡𝑛 → 𝑡𝑛+1

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.


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.

45

CHAPTER 6. CFD ANALYSIS 46

6.1 Sensitivity study

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

where mp is the mass of the particle and N is 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 of kg/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 qualityof 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 terminationof the simulation for finer mesh.



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 targetmesh 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 convergence was decreased from the RMS value of 1E-4 to 1E-6.

• The modification made in the CFX parameter for the inlet angle. This is defined in Appendix-Iin Chapter 11.

This figure also shows the y+ values for various mesh nodes under study. For the most refined mesh,the average value of y+ around the blade was about 37.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2

x 106

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25x 10

−7

Number of Nodes

Ave

rage

Sed

imen

t ero

sion

den

sity

on

the

blad

e

Mesh convergence study

0 0.5 1 1.5 2 2.5

x 106

0

500

1000

1500

2000

2500

X: 2.04e+006Y: 37.44

Number of Nodes

Ave

rage

y+

on

the

blad

eNumber of Nodes vs y+ value

Figure 6.1: Mesh convergence study for the factor ratio of 1.15, RMS of 1E-6 and y+ value on theblade

The second reason can be explained from Figure 6.2, where the erosion pattern on the blade wasconverging for the finer mesh. This contradicts the previous study, where the erosion almost vanishesafter the mesh was made very fine [21]. From these figures, it can be concluded that with the residualtarget of 1E-6, the target mesh of 0.75 million node is sufficient for further study (FSI). However,in order to study the erosion pattern better, the mesh of 1.25 million node was chosen to study andcompare the erosion behavior of the optimized blades.

6.3 Baseline case for the sensitivity analysis

In the sensitivity study, the physical and numerical parameters are varied one at a time, to avoid theeffect of other parameters on the solution. The parameters for the baseline case are selected basedon past experiences and results. Same parameters that were shown in Table 4.1 were used in this



20000 100000 250000

500000 750000

1250000 2000000

Target mesh

Figure 6.2: Sediment erosion pattern for various mesh densities

case. The target mesh of 0.75 million nodes was used for all the sensitivity studies. A mass flow rateof 2.35m3/s was used for the whole passage. The speed and the direction of the flow at the inletwas given from the design program ’Khoj’. Some modifications were made in the inlet angle, whosejustification is provided in Appendix-I in Chapter 11.

6.4 Effect of the physical parameters

6.4.1 Effect of the particle size on the erosion

The diameter of the quartz particle was chosen to be 0.1 mm for the baseline case. The size was variedbetween 0.01 mm to 1 mm to observe the effect of the particle diameter on the erosion pattern. Restof the parameters were made constant during this analysis.

The results of this analysis is shown in Figure 6.3 and 6.4. These figures represent the sedimentpatterns on the blade on the pressure side, but since all of them have the same ‘user specified’ range,the comparison of the results cannot be made numerically. Hence, Figure 6.5 represents the averageerosion rate density and the maximum erosion that occurs at the particular size of the particle. Itcan be seen from these results that when the particles are larger than 0.1 mm in diameter, the erosionpatterns are more concentrated on smaller area. The maximum erosion was found when the diameterof the particle was 0.4 mm. At the diameter of 0.9 mm and 1 mm, the erosion is more concentratedat the outlet region. On the suction side of the blade, no erosion effect was seen in any of the cases



Sediment erosion rate density

R1 Blade

0.1 mm 0.3 mm

0.5 mm 0.7 mm

0.9 mm 1 mm

Figure 6.3: Effect of the size of the particle on the erosion pattern

except when the diameter is 0.01 mm as shown in Figure 6.4. This shows that the size of the particlehas a significant but uneven influence on the erosion pattern.

6.4.2 Effect of the particle shape on the erosion

Particle shape factors defines whether the particles are spherical or elliptical. The X-section areafactor of 1 represents the particle of the spherical shape, which was taken in the baseline study. Theshape of the particles could however have variable shapes. Here, 2 other shape factors were taken into

PS SS

Figure 6.4: The erosion pattern for the particle diameter of 0.01 mm on both Pressure and Suctionside



0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.5

1

1.5

2

2.5x 10

−7

Ave

rage

ero

sion

rat

e de

nsity

on

the

blad

e [k

g/m

2 s]

Particle diameter [mm]

Effect of the particle diameter on the erosion rate density

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.2

0.4

0.6

0.8

1x 10

−3

Max

imum

ero

sion

rat

e de

nsity

val

ue o

n th

e bl

ade

[kg/

m2 s]

Figure 6.5: Average and maximum erosion rate density on the blade for various particle sizes

account. The non-uniformity of the shape was not considered in this study.

The result of this analysis is shown in Figure 6.6. The margin in the legend was made wider in orderto have a better picture of the differences in the results. The spherical particle was seen to have theleast effect on the erosion compared to the elliptical ones. However, there was not much difference inthe overall erosion pattern.

X-Section Area Factor = 1 X-Section Area Factor = 0.5 X-Section Area Factor = 0.25

Ave Erosion rate density = 8.77E-8 Ave Erosion rate density = 2.07E-7 Ave Erosion rate density = 1.92E-7

Figure 6.6: Effect of the particle shape on the erosion pattern

6.4.3 Effect of the particle behavior

The particles inside the domain can be enabled by defining the ‘Particle Behavior’ and specifyingtheir properties on the inflow. Here, the particle velocity, injection position, diameter distributionand mass flow rate need to be specified. By default, the injection of the particles is done randomly.



The direction of the particle is made identical to the direction of the fluid flow. The particle massflow rate was varied between 1 to 50 kg/s per machine. The particle diameter was kept constant (0.1mm). The particles are uniformly injected with 1000 particles at the inlet. This number can also bechosen as ‘Proportional to mass flow rate’ where the number of particles per unit mass flow should bespecified.

The effect of the mass flow rate of the particle on the average erosion rate density on the blade isshown in Figure 6.7. The erosion increases linearly with the mass flow rate. Since other parameterslike the injection position, number of particles and the diameter distribution were made constant, theerosion patterns between these mass flow rate were the same.

0 0.5 1 1.5 2 2.5 30

0.5

1

1.5

2

2.5

3

3.5

4

4.5x 10

−6 Effect of the mass flow rate on Erosion

Mass flow rate per passage (kg/s)

Ave

rage

Ero

sion

rat

e de

nsity

(kg

m− 2s

− 1)

Figure 6.7: Effect of the Mass flow rate on erosion

Similarly, when the mass flow rate of the particle is kept constant and the concentration of the sedimentis increased by increasing the number of particles, the average erosion rate density increased linearly.The mass flow rate and the concentration of the uniformly injected sediment particle have a linearlyproportional influence on the erosion. This can also be justified from Equation 6.1.

6.5 Effect of the numerical parameters

6.5.1 Effect of the residual criteria

The residual measures the local imbalance of each conservative control volume and it indicates whetherthe equations have been solved or not. In CFX, the residuals are normalized to present a consistentmeans of judging the convergence. There are few options in CFX for considering the convergencecriteria. The level of convergence required depends on the purpose of the simulation and can be im-plemented as MAX(maximum) or RMS(root mean square) normalized values of the equation residuals.It is normally chosen between 1E-4 to 1E-6 for the RMS residual level. The comparison between thesetwo results are done by plotting the runner blade loading at 50% span shown in Figure 6.8. This figureindicates that the two residual criteria 1E-4 and 1E-6 provides identical results. However, in the mesh



study, the RMS of 1E-6 shows better results in terms of the mesh independence study. Hence, theRMS of 1E-6 was used as the erosion is more of the interest than other parameters in this project.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4Blade loading at 50% span

Streamwise(0−1)

Pre

ssur

e (M

Pa)

Residual 1E−04Residual 1E−06

Figure 6.8: Effect of the residual criteria for convergence on the blade loading

6.5.2 Effect of the turbulence models

Turbulence models are used to predict the effects of turbulence in fluid flow without resolving thesmall scale turbulent fluctuations. These models are based on RANS (Reynolds Averaged Navier-Stokes) equations. The most common eddy-viscosity models used are k − ε, k − ω and SST models.For general purposes, the k − ε model offers a good combination of accuracy and robustness. Thismodel is, however, not suitable for predicting the boundary layer separation and flows in rotatingfluids. The k − ω based Shear-Stress-Transport(SST) model provides a more accurate prediction ofthe flow separation under adverse pressure gradients. Since this model is developed to overcome thedeficiencies of both k − ε and k − ω model, SST model is more advanced. In Figure 6.9, the result ofthese two models has been compared. The erosion predicted by the k − ε model is less than that ofthe SST model.

6.5.3 Effect of the erosion models and their parameters

Tabakoff erosion model for Quartz-Aluminum was used in the baseline study with the values of the pa-rameters provided by ANSYS-CFX. It also supports Finnie erosion model as well as Tabakoff erosionmodel for Quartz-Steel. These conditions were implemented to observe the variation in the results,which are shown in Figure 6.10.

In the case of Finnie’s model, the erosion is a function of the impact angle and velocity, such that in



SST k-Є

Ave Erosion Rate Density

8.77E-8 8.25E-8

Ave Erosion Rate Density

Figure 6.9: Effect of the turbulence models on erosion

CFX, the only parameter that could be changed explicitly is the value of the velocity power factor(n)as shown in Equation 3.8. It can be seen from Figure 6.10 that the amount of erosion predicted bythis model is massive even when the value of n is 2 (ranges between 2.3 to 2.5 for metals). This showsthat Finnie’s erosion model for this case or the parameters provided is not acceptable.

The Tabakoff’s erosion model seems to be more promising, specially for this application as the coef-ficients which are needed for the implementation of the model are already provided by ANSYS-CFXfor Quartz-Aluminum and Quartz-Steel. It could be seen from the figure that when Quartz-Steel ischosen as the eroding and the eroded material, the amount of erosion is in average about 1.5 timesmore than the Quartz-Aluminum model. This could be because of the higher density of the steelcompared to aluminum. The prediction of the erosion for the stainless steel, which is most commonlyused in the hydro turbines, could be more reliable in this case.



Tabakoff

Quartz-Aluminum

Average Sediment

erosion rate density on

the Blade:

8.77E-8 kg/m2s

Tabakoff

Quartz-Steel

Average Sediment


the Blade:

1.25E-7 kg/m2s

Finnie

Velocity power

factor, n = 2

Reference velocity = 1

m/s

Average Sediment


the Blade:

17.68 kg/m2s

Figure 6.10: Effect of the Erosion models on the results

6.6 Comparison between the optimized and the reference blades

The mesh independent model parameters were used to model all the optimized blades. Here, in orderto study the sediment erosion pattern correctly, the mesh with 1.25 million nodes and the factor ratioof 1.15 was used for all the shapes with a RMS residual convergence target of 1E-6. In this case, tworesults are of interest : erosion and efficiency. The average erosion rate density on the blade with theerosion pattern and the efficiency are compared. The result of this analysis is shown in Figure 6.11.In order to make it possible to plot the two variables in a single graph, the values are normalized withthat of the reference design. This means that the reference shape (shape-3) has the value of 1 forboth efficiency and erosion rate density, whereas the other shapes are in relative to this shape. Forconvenience, their absolute values are also shown above the column, of which the erosion rate densityis in the order of 1E-8 and the unit of kg/m2s. Also, the efficiency in percent is shown in the secondcolumn. The values on the abscissa represent the shape number of the blades under study.



It can be seen from this comparative analysis that the efficiency of the blades does not vary muchwith the change in the shape. However, the erosion rate density varies a lot. The blade shape 2 and 4are the ones which show a decrease in the average erosion rate density on the blade compared to thereference shape. The decrease in this quantity is as much as 21% for the case of shape-4. Hence, theblade shape 4 is the most optimized blade in terms of erosion and efficiency and it is selected for theFSI analysis.

However, it could be inferred from the mesh study that though the mesh convergence study wasperformed on the reference blade, and the results were very sensitive to the type of the mesh generated,it could be interesting to see how the types of mesh vary the results of other blades as well. This willmake the comparison more reliable as each of the CFX model will be independent of the mesh density.

It can be concluded that the erosion predicted by ANSYS CFX is mesh sensitive and requires a highquality and high density to have a converging result. The mesh needs to be refined significantlywithout disturbing the overall quality of the mesh. This was done in this project by reducing thefactor ratio, but making the mesh density large, so that both the criteria are met.



0,0

0

0,2

0

0,4

0

0,6

0

0,8

0

1,0

0

1,2

0

1

2

3

4

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7Structural analysis

The structural analysis was performed in ’Static Structural’ in Workbench. This chapter deals withthe modeling of the 3D geometry of the runner for the structural analysis and the first structuralanalysis setup and results. This chapter primarily focuses on carrying out one-way FSI in AN-SYS. The fully coupled analysis will be carried out in the next chapter. For both the cases inthis report, Structural Steel was chosen as the structural material having following properties :

Density 7850 kg/m3

Young’s Modulus 2E11Pa

Poisson’s Ratio 0.3

7.1 Geometry

The geometry of the blade was made with the help of the curve files in Pro Engineer. The leadingedge and the trailing edge were made from the instruction file of NTNU [27]. The leading edge wasdesigned in such a way that on the pressure side, the edge was rounded with quarter a circle whereason the suction side, it was rounded with an arc of thrice the radius of the leading edge. The trailingedge was designed with a 30 degree angle on suction side with the end part chopped off to prevent thebreaking off due to the pressure fluctuation in the system.

LE TE

Figure 7.1: Leading edge and trailing edge design for FEM [27]

The hub and the shroud were made from the respective curve files, providing the necessary thickness

57

CHAPTER 7. STRUCTURAL ANALYSIS 58

and the place for labyrinths. Before the assembly was made between these three parts, the hub wascut into a single sector containing 1 out of the 17 blades. This was done in Pro-E by the followingsequence,

• Only (360/17)◦ of the total part was modeled. This was done by extruding out the unwantedportion from the hub taking the reference of the blade profile. The blade profile at the firstsection was imported. This was done at a separate datum plane such that the curves could beprojected to and away from the surface of the hub.

• The profile section consists of curve made of points at the pressure side and the suction side ofthe blade. This curve was patterned along the main axis with the value of (360/17 − 4)◦ and4◦ on the direction as shown in Figure 7.3, so the blade lies in the position close to the CFDdomain. By placing the blade in this position gave better mapping with the CFD domain thanwhen placed in the mid position. It can be verified from Figure 7.2, where cases with proper andimproper mappings have been shown. The first figure to the left shows that the fluid domain isshifted upwards compared to the structural domain, whereas in the second figure, the fluid andthe structure are aligned more closely. Important thing to consider is the amount of decimalplaces that needs to be provided in Pro-E, to maintain a consistency with ANSYS. The value of(360/17)◦ is not good in Pro-E because it will round-off the value in lower decimal places thanneeded in ANSYS. The more precise value of 21.17646◦ was used.

• The patterned curves were used to create a closed curve so that the extrude could be made asshown in the figure 7.3. This was done by choosing two curves on the same side (Pressure sidein this case). A circle was made of arbitrary radius, but bigger than the hub diameter. Thiscircle was connected to the two curves tangentially through a line on the inlet side and througha line connecting the center and the final point on the outlet side.

• Similar process was done for the shroud. It was seen that when the sharp edges are included inANSYS while applying the cyclic boundary, the program could not recognize the boundary andit terminated with an error. Hence, the sharp edges had to be cut in both hub and shroud.

• Finally, the blade, the hub and the shroud were assembled together. Also, it was seen that asingle merged part was needed in ANSYS rather than three different parts. This was done byimporting the geometry file of each part as an independent file and saving as a part file ratherthan the assembly file.

Structural domain

Fluid domain

Figure 7.2: Comparison of the two domains with two cases (right one shows better mapping)



Full Hub Full Shroud

Blade Profile

Profile duplicate at (360/17)-4

degree about the centre

Profile duplicate at 4 degree

about the centre

Arbitrary radius circle outside the

boundary

Shroud Sector

Hub Sector

Figure 7.3: The geometry modeling in Pro-E as described in the above procedure



7.2 Boundary condition

Past research works on the Francis turbines have imposed various types of constraints for the structuralanalysis. In some cases, only the runner blade was considered without modeling the hub and the shroudand imposing fixed supports on the surface connecting them with the blade [28], [29]. Whereas, insome cases [30], [31], full geometry of the runner was considered, but the hub and the shroud weremodeled with rigid supports, and their deformation was considered negligible with respect to thedeformation of the blades. However, performing this analysis requires high computational cost andit is difficult to perform the mesh independent study for those models. Because of the symmetricproperty of the structure, it is more convenient to perform the analysis on a single sector in the sameway as the CFD was done. The full analysis of the sector of the model by considering cyclic symmetrycondition and deformation of the whole structure was done in [7]. In the current study, two typesof the boundary conditions were imposed, which are discussed below. In this chapter, one way FSIis done by importing the CFX pressure loads on the boundary walls. The fully coupled analysis arediscussed in Chapter 8 of the report.

7.2.1 Case I

This case consists a single blade of the runner with the following conditions :

• Zero displacement (fixed support) of the surface connecting blade-hub and blade-shroud.

• Rotational velocity about the z-axis with 104,7 rad/s.

• Acceleration due to gravity (g).

• Imported pressure load on the blade surface.

The reason behind conducting this analysis is to check the structural integrity of the blade withoutthe influence of the other stiffer components. This will be easier when the comparison has to be madewith the optimized blade. According to similar studies mentioned above, this type of analysis gives areasonable estimation of the stress induced by the flow on the blade. However, the maximum stresscould be less than the actual value because of the joint between the blade-hub and the blade-shroud.This analysis will be used as a starting solution to see the stress distribution and the deflection ofthe blade due to the pressure load from the flow field, without the influence of the other structuralcomponents and the neighboring blades. The boundary conditions imposed in ANSYS are shown inFigure 7.4.

7.2.2 Case II

This case consists of the following boundary conditions :

• Zero displacement (fixed support) of the surface connecting the shaft and the hub.



Figure 7.4: Boundary conditions used for the case I

• Rotational velocity about the z-axis with 104,7 rad/s.

• Acceleration due to gravity (g).

• Imported pressure load on the blade surface.

• Imported pressure load on the hub and the shroud.

• Cyclic symmetry of the whole component. This property could be defined in two ways.

– From workbench, choosing the symmetry property and selecting the higher and the lowerboundaries of the symmetric body. Doing this requires a new cylindrical co-ordinate systemand the exact geometry on the higher and the lower side so the geometries and the meshare properly mapped.

– By using commands in Mechanical (APDL). This can also be done in workbench itself bywriting the following commands,/prep7cyclic,17/soluTolerances to map the faces can be chosen as per necessity.

Figure 7.5: Boundary conditions used for the case II

This analysis is expected to provide more accurate estimation of the stress distribution consideringthe fact that the influence of the joints and the neighboring blades have been considered.



7.3 FSI mesh study

As the cyclic symmetry option was chosen in the static structural, without using the MechanicalAPDL, the use of the hexagonal mesh was not possible in the current release of ANSYS. Hence, themapped tetrahedron mesh was used to make the structural model of the blade and the unstructuredmesh was used in the other regions. The mesh convergence study was performed on the first caseonly, and a relatively finer mesh was used to generate the results of the second case. The maximumequivalent stress and the maximum total deformation on the blades were studied for the convergencebehavior. The result of this analysis for both the designs is shown in Figure 7.6.

For the reference design, after the mesh node count of 178575, the solution is relatively converging.The change in the maximum stress is about 1% and that of the maximum total deformation is about2%, after this mesh size. Hence, this mesh node, corresponding to the element size of 0.0025 mwas used to make the structural model of this design. On the other hand, for the optimized design,comparatively finer mesh density was needed to have the converged solution. The mesh node count ofthe mesh independent model was 361664 but the element size was only 0.0028 m. For the second case,where the a sector of the full runner was modeled, the element size of 0.004 m was used in both thedesigns. The reason for not conducting the mesh independence study for the second case was becauseof the limitations in the computational capability. Roughly, an estimated mesh node count of morethan 2 millions is needed in order to have the mesh independent FEM model for the second case.

0

2

4

6

8

10

12

0 50000 100000 150000 200000 250000 300000 350000

Mesh node count vs Results

Max Equivalent stress (E6 Pa) Max Total deformation (E-6 m)

Converged solution

2

4

6

8

10

12

0 100000 200000 300000 400000 500000

Mesh node count vs Results (Shape-4)

Max. Equivalent stress(E6 Pa) Max. Total Deformation(E-6 m)

Converged solution

Reference design Optimized design

Figure 7.6: Mesh convergence study for structural analysis



7.4 Results of One-way FSI

7.5 Case-I

The result of the mesh independent model of Case-I for one-way coupling is shown in Figure 7.7.The maximum stress is found to be around 10.95 MPa in the reference design and 10.57 MPa in theoptimized design. The position of the maximum stress is in the trailing edge region connecting theshroud for the reference design and connecting the hub for the optimized design. A comparatively highamount of stress distribution is found on the corners for both the cases. This is because of the fixedconstraint provided to the surface connecting the hub and the shroud. As the hub and the shroudare relatively rigid components, the results of this case is seen to predict the stress distribution veryclosely. However, since the joint between the blade and these components are not considered and alsoloads on these surfaces are not taken into account, the maximum stress on the runner and also on theblade could have been under-estimated by a significant amount. Hence, it is of great importance toconsider the actual section of the runner to match the real condition more accurately. The results ofthis case can be used to compare the structural integrity of the blades of various designs, where thestress is independent of the other components.

7.6 Case-II

The result of the Case-II is shown in Figure 7.8, Figure 7.9 and Figure 7.10. The maximum stressoccurs at the connecting surface of the shaft and the hub, because of the fixed constraint defined onthis surface. The second maximum stress occurs at the leading edge, on the blade-hub region. Oncomparing this result with Case-I, it can be seen that the maximum stress is not on the outlet region,but it is on the inlet blade-hub region. The loads on the hub and the shroud are also imported onthe structure, due to which stress values are more than the previous case. The values of the pressureload is maximum at the leading edge regions, due to which, the stress values are also maximum.Besides, the connection between the blade and the other components induces stress concentrations,which makes these regions prone to failure.

On comparing the results between the reference and the optimized design, it can be seen that the valueof the maximum stress is bigger in the reference design than in the optimized design. The maximumstress on the reference design is around 179.3 MPa whereas 153.8 MPa for the optimized design.Similarly, when only the stress on the blade is considered as shown in the figure 7.9, the maximumstress on the reference design is 123.7 MPa whereas it is 114.9 MPa on the optimized design.

Similarly, in the figure 7.10, the deformation of the runner and the blade is compared. The maximumoverall deformation is seen in the hub towards the inlet due to high pressure load in that region, forboth the designs. The value of the maximum deformation is 0.087 mm for the reference design and0.093 mm for the optimized design. When only the blades are considered, the maximum deformationis towards the shroud-blade connection for both the designs. This value is also higher in the case ofoptimized design, with 0.078 mm than in the case of reference design, with the value of 0.066 mm.



Reference design

Optimized design

Figure 7.7: Result of one-way coupling for Case-I



Reference design

Optimized design

Figure 7.8: Result of one-way coupling (Stress distribution) for Case-II



Reference design

Optimized design

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



Reference design

Optimized design

Figure 7.10: Result of one-way coupling (Deformation) for Case-II


8FSI analysis

ANSYS muti-field solver (MFX) was used to do the two-way FSI. This can be done either in theWorkbench or standalone applications. One example of the project schematic in Workbench forconducting two way FSI is shown in Figure 8.1. Like the one-way FSI technique, two independentmodels are needed for the two domains in this context. An input file is created from ANSYS structural,which is imported in CFX, where all the solver parameters are set. One of the inevitable things whileconducting the two-way FSI is the deformation of the CFD mesh. The deflection of the structureresults in the deformation of the fluid mesh, which changes the flow field surrounding it. Hence, anappropriate model of the mesh displacement and a sufficient value of the mesh stiffness have to bechosen to avoid the folding of the mesh, which is very common in two way FSI. Some of the importantaspects to consider while conducting two-way FSI are discussed below:

8.1 Mesh deformation

Mesh deformation is an important component for problems with moving boundaries or moving sub-domains. It is chosen as ‘None’ when the steady CFD analysis was carried out. In the case of coupledFSI, this motion has to be imposed. It can be done only in the fluid domain. By choosing the option‘Region of Motion Specified’ in the Mesh Deformation option, it is possible to make the mesh outsidethe structural domain move together with its deflection. This motion of the mesh could be determinedby the mesh motion model, which is limited to ‘Displacement Diffusion’ in ANSYS. According to thismodel, the displacements applied on a boundary is diffused to mesh points with the equation,

∇.(τdisp.∇δ) = 0 (8.1)

Where, δ is the displacement relative to the previous mesh locations and τdisp is the mesh stiffness.This equation is solved at the start of each outer iteration. It can be inferred from this equation thatthe relative mesh distribution of the initial mesh has been preserved. This means that the refinementof the mesh at the boundary will remain fine after the deformation at the relative position.

68

CHAPTER 8. FSI ANALYSIS 69

Geometry, mesh and boundary

conditions

Fluid-Structure Interface

Input file (ds.dat) from workbench or

Tools > Write Input file for standalone

applications

Geometry, mesh and boundary

conditions for fluid analysis (Here,

simply .cfx file from the previous CFD

analysis has been imported)

Define Coupling time duration and time

steps

Mesh deformation on the respective

interfaces

Solver control parameters

ds.dat

Figure 8.1: Project schematic of the two-way FSI

The value of the mesh stiffness discussed above can be controlled by choosing an appropriate value.This value can also be chosen such that the stiffness is more at the significant regions, such as nearthe small volumes, or near boundaries. The mesh stiffness value for this case is chosen according tothe following relation,

τdisp =

(1

a∗

)Cstiff

(8.2)

Here a∗ represents either the size of the control mesh volumes, or the distance from the nearestboundary, depending upon the type of the option chosen. In any case, the stiffness of the mesh willincrease when this value will decrease. The rate at which this stiffness increases depends upon thevalue of Cstiff , which represents the model exponent. The default value of this exponent is 10, whichcan be altered according to the need of the problem. In the case when ANSYS Multi-field is chosenfor FSI, the mesh motion can be imposed on the wall boundaries. In this case, the mesh motion hasto be imposed on the blade, hub and shroud regions.

8.2 Interface setup

The load is transferred between the two domains at the interface. This is done through mapping ofthe nodes of one mesh to the local coordinates of an element in the other mesh. In the case of two waycoupling, two mappings are performed; first to map the displacements from solid nodes to fluid nodesand second to map the stresses from fluid to solid. ANSYS surfaces are flagged by interface numbers



(1,2...) and CFX surfaces are flagged by interface name (FSIN 1, FSIN 2...), these numbers and thename on the two domains should represent the same boundary. A typical procedure of setting up theinterface for the blade is listed below :

• In ANSYS Structural, choose ‘Fluid Structure Interface’ and select the blade surface. Thisinterface will be given a number (Starting from 1)

• When the input file is written for the structural case, or when the setup of the structural andCFX are linked, the input from the structural can be read in the CFX in the Analysis type.

• In the domain definition, choose the mesh motion to ‘Regions specified’. This will enable theselection of the mesh motion option on the wall boundaries.

• On blade, select the mesh motion to be ANSYS multi-field. Here, the selection of the appropriateinterface number can be selected. This should correspond to the number provided in structural.

The ANSYS Multi-field solver automatically transfers mesh-based quantities across dissimilar meshes.However, it is better to have similar size meshes between the two fields, to ensure the correct mappingbetween the fields. The quality of the mesh of the two fields is shown in Figure 8.2. The distributionof the mesh is finer near the edges in the case of fluid, as this mesh was created from highly optimizedtopology option from Turbo-grid. Hence, the quality of the mesh is better in the fluid domain.

CFD mesh Structural mesh

Mapping of the two meshes

at the interface

Figure 8.2: Mesh of the two fields and mapping



8.3 Solver Setup

In the case of the coupled-field analysis, the iteration controls and the convergence criteria must beset for each field of the coupled field solvers. A special type of iteration, called stagger iteration isused to ensure the convergence of the quantities transferred between the two fields. At the end ofeach stagger iteration, the ANSYS as the master checks the convergence of the quantities transferredacross the interface and the fields within each field solver. The stagger iteration continues unlessthe maximum number of stagger iteration is reached, or when the convergence has occurred. Theconvergence criteria for the stagger iteration can be chosen in the ‘External Coupling’ tab, by definingthe minimum value of a function Φ, given by the equation:

Φ =

√∑(unew − uold)2√∑

u2new(8.3)

Where uold and unew are the load components transferred at the last and this stagger iteration respec-tively. The quantities are said to be converged when Φ < Φmin. By default, the value of Φmin is setto 0.01 in ANSYS.

In CFX-solver, a new plot called as ANSYS Interface plot appears, which shows the convergence be-havior of the transferred loads after each stagger iteration. The variable value plotted on the y-axisof this graph can be represented by e, where:

e =log(Φ/Φmin)

log(10/Φmin)(8.4)

When Φ < Φmin, e < 0 in the plot and the convergence occurs. A convergence plot used in thisstudy is shown in Figure 8.3. The stagger iteration starts with the start of the simulation. The nextiterations are done as a normal CFD-solver, where the convergence occurs after reaching the RMSresidual criteria, or the maximum number of iterations set in the solver control. After the end of thefirst stagger iteration, a new monitor plot appears, which shows the load transfer from CFD to thestructural. After the load is transferred, the flow field is disturbed and the solver tries to converge themomentum and mass for the new deflected position of the blade. For each iteration, the value of e iscalculated from the Equation 8.4. The stagger iteration continues till the value of the parameter e isnegative. The figure shows that the convergence of the coupled-field analysis occurs after 6 staggeriterations.

8.4 Post processing

The post processing in the two-way FSI can be done in CFD-post. Though CFD-post normally showsresults from the CFD analysis after the solver is finished, the two-way FSI by using ANSYS-CFXfacilitates the post-processing of the results, both from CFD and structural. In this case, the user canchoose to show results of either ANSYS, CFX or both. In the outline tree, two domains are shown,one for the structure, and another for the fluid. However, ANSYS supports only those results fromthe structural, which are stored in CFX results. The deflection of the structure is represented by’Total Mesh Displacement’, which signifies by how much the mesh has been displaced from its initialposition. It can also represent the equivalent Von Mises Stress induced on the structure.



Stagger Iteration (SI) = 1

SI = 2

SI = 3 SI = 4

Figure 8.3: Convergence plot in CFX-solver for the FSI analysis in this study



8.5 Results of Two-way FSI

8.5.1 Case-I

The result of the two way coupling for the first case, when only the blade was considered, is shownin Figure 8.4. Comparing this figure with the same case in one-way coupling, it can be seen that themaximum stress is not towards the outlet region, but it is towards the inlet region, at the shroud-bladeconnection. The value of the maximum stress is 12.45 MPa for the reference design and 16.15 MPafor the optimized design. The value of the maximum stress increased by around 14% for the referencedesign and by around 52% for the optimized design, compared to one-way FSI. The mesh and thecomputational model were the same for this case between one-way and two-way coupling. Though theregion of the maximum stress is different between the two cases, the pattern of the stress distributionlooks similar. A large amount of stresses are induced on the zero displacement regions and also nearthe mid-span of the outlet region as shown in both the figure.

8.5.2 Case-II

The stress distribution of the case-II for two way coupling is shown in Figure 8.5. The region of themaximum stress is towards the blade-hub inlet region. A high stress distribution was found towardsthe joint between the blade-hub and the blade-shroud. The value of the maximum stress is 916.8 MPafor the reference design and 823.9 MPa for the optimized design. Compared to the one-way FSI, thisvalue is about 7 times big. This difference reflects the significance of conducting two way FSI in thisapplication.

In two way FSI, the deflection of the structure is represented by the deformation of the mesh of theflow field surrounding it. Figure 8.6 shows the magnitude of the total mesh displacement around theblade at three different stream-wise positions. It also shows the overall deflection of the CFD meshsurrounding the blade. In the case of the reference design, the deformation of the mesh is maximum inthe shroud region. This figure only shows the local displacement value on the legend. On the runnerblade, the maximum deformation was found to be 0.37 mm. In the case of the optimized design, thepattern of the deformation on the blade is quite different. Maximum deflection occurs towards theinlet and the midspan of the outlet region. Though the maximum deformation on the blade is lessthan the reference design (0.12 mm), the overall deformation of the CFD mesh is similar.



max

8.30E6

7.7E6

3.9E6

Reference design

1.25E7

max

9.61E6

6.12E6

1.25E7

max

9.61E6

6.12E6

Optimized design

Figure 8.4: Stress distribution on the blade from two-way FSI



Reference design

Optimized design

Figure 8.5: Stress distribution on the runner from two-way FSI



Reference design

Optimized design

Figure 8.6: Mesh deformation in the fluid domain from two-way FSI


9Conclusion

The objective of this project work was to carry out the FSI analysis of reference and optimizedFrancis runners exposed to sediment erosion. An optimized runner was chosen between 5 shapesof the blade proposed by earlier studies based on the reduced erosion effect without affecting theefficiency. The erosion effect was imposed in ANSYS-CFX with Tabakoff Erosion Model by buildinga mesh independent model. Some assumptions were chosen to build the CFD parameters, such asshape, size and concentration of the quartz particle in the flow. However, a sensitivity study wasmade, where the effect of changing these parameters were observed. To do this, a baseline case wasinitially established and a single parameter was varied at a time keeping other parameters constant.

The results of CFD were very sensitive to the size and distribution of the mesh. The CFD meshingwas done with the help of the ATM optimized topology in Turbogrid, which is known for generatinga high quality mesh but less freedom of choices. By decreasing the factor ratio, it was seen that theconvergence could be obtained in the results. A target mesh node count of 0.75 million node waschosen for the FSI study, but in order to study the erosion pattern better, a mesh of 1.25 million nodewas chosen for the CFD study. Among the five different runner blades, shape-4 (the physical meaningof the shape was described in the figure 4.6) was seen to have reduced erosion effect by 21% withoutaffecting the efficiency. Hence, it was chosen for the further study.

The structural model of the blade and a sector of the runner was made in Pro-E, with the help ofthe curve files generated from the Matlab Program. While generating the section of the runner, thehub and the shroud regions were trimmed so as to map with the fluid model closely. Two types ofboundary conditions were considered, where the FSI analysis was performed on each of the cases. Inthe first case, a single blade without the hub and the shroud were created, whereas in the second case,the full geometry consisting of a sector with 1/17th of the total runner was developed. The resultsshowed that the stresses, which were plotted as the equivalent Von Mises Stress, were larger in thesecond case than in the first case. This is due to the effect of the joints and the loads imposed on thehub and the shroud, which were not considered in the first case.

One way FSI was conducted in Chapter 7 on both the cases and both the designs. A mesh independentstudy was performed on the first case by considering a mapped tetrahedral mesh around the blade.For the second case, a fixed size mesh was used in both the designs. FSI was imposed by importingthe loads from CFD on the surfaces of the structure. In one way FSI, the cyclic symmetric property

77

CHAPTER 9. CONCLUSION 78

of the blade was established by defining the high and the low periodic boundaries. Other boundaryconditions, such as rotational velocity, gravity, and fixed support on the surface connecting the huband the shaft were imposed. The results of one way FSI showed that the maximum stress on therunner is less in the optimized design compared to the reference design, in both the cases. The valueof the maximum stress on the runner decreased by around 14%. On the contrary, the maximumdeflection of the runner increased by around 6%.

Two way FSI was conducted in Chapter 8 on both the cases and both the designs. This was done bywriting an input file from the structural case consisting of the same boundary condition as one wayFSI, but importing it into CFX on the specified boundaries. The deformation of the mesh on theseboundaries was selected with the provided mesh deformation model. The maximum number of staggeriteration was chosen to be 10 but it was seen that the results converged after maximum 8 iterations.The post processing for both the fields were done in CFX-Post. In the first case of boundary condition,the maximum value of the stress increased by around 29% for the optimized design than the referencedesign. However, in the second case, the value of the maximum stress decreased by around 10%.Compared to one-way FSI, the value of the maximum stress was around 7 times bigger than when twoway FSI was performed. The difference in the results with the same mesh and boundary conditionsshow the significance of conducting the fully coupled analysis in this field. This vast difference alsoresulted because of the different ways of imposing the cyclic symmetry boundary condition to therunner. It was seen that when the APDL command was used to make the cyclic property of thesector, it resulted in mapping problems. This problem could be solved in Workbench Static Structuralby using the model > symmetry > cyclicsymmetry in the outline tree directly and selecting thehigher and the lower periodic boundaries. However, this option was not possible for the two way FSItill the current release of ANSYS. Hence, for the two way FSI, APDL command was used to imposethe cyclic symmetry property. It was seen that using the APDL command not only shows the mappingproblem, but also overestimates the stresses by some amount. In that way, the results of the two-wayFSI could have escalated a bit more than expected, for the second case. A demonstration of thecomparison between the two ways of imposing the cyclic symmetry condition is shown in Appendix-IIin Chapter 12.

One more limitation in the ANSYS release was the restriction in selecting the type of the mesh. Itwas seen that a model with a periodic symmetry property was unable to generate a hexagonal mesh.In order to maintain the consistency in the type of the mesh, tetrahedral mesh was used for all thecases. Creating hexagonal mesh could result in better mapping with the fluid interface because of thesimilar type of the mesh.


10Future scope in the related field

• In the case of the CFD analysis, the mesh convergence study was performed on the referenceblade only. However, performing the study on all the blades will ensure the correctness of thesolutions as all the blades will be mesh independent.

• In the case of the structural analysis, the mesh study was performed on the first case only, whereonly a single blade was considered. It was seen that for the second case, about 2 million meshwas needed to have a mesh independent solution. In order to perform the mesh study for thiscase, a very high computational time is needed. Also, the hexagonal mapped mesh could begenerated from other meshing tools or softwares to have better results.

• A single blade of the runner was considered in this study. The Matlab program which were usedto generate the curve files of the blade can also generate curve files and input parameters of theguide and stay vanes. This can be useful to find erosion information on these regions, along withtheir structural integrity.

• This project still assumed the results to be steady. However, by considering the guide vanes,the transient calculations could be done and the unsteady forces on the runner blades could beknown.

• The material of the structure in this study was chosen to be ’Structural Steel’. However, theanalysis has to be carried out for the exact material from which the manufacturing is done. Themost common materials that are chosen are stainless steel and titanium- and nickel- alloys.

• Perfect mapping of the two domains (fluid and structure) has to be carried out. This will increasethe accuracy of the solution.

79

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BIBLIOGRAPHY 81

[9] Chauhan, A.K., Goel, D.B., Prakash, S.,Erosion behavior of hydro turbine steels,Indian Institute of Technology, 2007.

[10] Wood, R.J.K.,Tribology of thermal sprayed WC-Co coatings,International Journal of Refractory Metals and Hard Materials, 2010, p. 82-94.

[11] Truscott, G.F.,Literature survey of abrasive wear in hydraulic machinery,Wear, 1972, p. 29-50.

[12] Bardal, E., Korrosjon, Korrosjonsvern,Trondheim : Tapir, 1985 (in Norwegian).

[13] Tsuguo, N.,Estimation of repair cycle of turbine due to abrasion caused by suspended sand and determinationof desilting basin capacity,Proceedings of international seminar on sediment handling technique, NHA, Kathmandu,1999.

[14] Thapa, B.S., Thapa, B., Dahlhaug, O.G.,Empirical modelling of sediment erosion in Francis turbines,Journal of Energy, Volume : 41, 2012, pp. 386-391.

[15] Kjolle, A.,Hydropower in Norway, Mechanical Equipment,Survey, Norwegian University of Science and Technology (NTNU), Trondheim, 2001.

[16] Neopane, H.P.,Sediment Erosion in Hydro Turbines,phD thesis, NTNU, 2010.

[17] Thapa, B., Shrestha, R., Dhakal, P., Thapa, B.S.,Sediment in Nepalese hydropower projects,Proceedings of International conference on the great Himalayas: Climate, Health, Ecology, Man-agement and Conservation, Nepal, 2003.

[18] Thapa, B.,Sand Erosion in Hydraulic Machinery,phD thesis, NTNU, 2004.

[19] Gjosaester, K.,Hydraulic Design of Francis Turbine Exposed to Sediment Erosion,Masters Thesis, NTNU, 2011.

[20] Drtina, P., Sallaberger, M.,Hydraulic turbines - basic principles and state-of-the-art computational fluid dynamics applications,Sulzer Hydro AG, Zurich, 1999.

[21] Thapa, B.S.,Hydraulic design of Francis turbine to minimize sediment erosion,Master’s thesis, Kathmandu University, 2011.


BIBLIOGRAPHY 82

[22] Wang, W.Q., He, X.Q., Zhang, L.X., Liew, K.M., Guo, Y.,Strongly coupled simulation of fluid-structure interaction in a Francis hydro turbine,International journal for numerical methods in fluids, Wiley Interscience, 2008, pg: 515-538.

[23] Schmucker, H., Flemming, F., Coulson, S.,Two-way coupled fluid structure interaction simulation of a propeller turbine,25th IAHR Symposium on Hydraulic Machinery and Systems, Voith Hydro GmbH and Co. KG,Germany, 2011.

[24] ANSYS Coupled-Field Analysis Guide,ANSYS Release 10.0, 2005.

[25] Slone, A.K., Pericleous, K., Bailey, C., Cross, M.,Dynamic fluid-structure interaction using finite volume unstructured mesh procedures,Computers and Structures, pg: 371-390, 2001.

[26] Eltvik, M., Thapa, B.S., Dahlhaug, O.G., Gjosaeter, K.,Numerical analysis of effect of design parameters and sediment erosion on a Francis runner,Proceedings of Fourth International Conference on Water Resources and Renewable Energy De-velopment in Asia, Thailand, 2012.

[27] Wei, Z., Finstad, P.H., Olimstad, G., Walseth, E., Eltvik, M.,High Head Hydraulic Machinery, compendium,Water Power Laboratory, NTNU, 2009.

[28] Negru, R., Marsavina, L., Muntean, S.,Analysis of Flow induced stress field in a Francis turbine runner blade,Buletinul Institutului Politehnic Din Iasi (Bulletin of the Technical Institute of Iasi), 2011.

[29] Negru, R., Muntean, S., Marsavina, L., Susan-Resiga, R., Pasca, N.,Computation of stress distribution in a Francis turbine runner induced by fluid flow,Proceedings of the 21st International Workshop on Computational Mechanics of Materials, 2011.

[30] Saeed, R.A., Galybin, A.N., Popov, V., Abdulrahim, N.O.,Modeling of the Francis turbine runner in power stations. Part II:stress analysis,WIT Transactions of the Built Environment, Vol 105, 2009.

[31] Lais, S., Liang, Q., Henggeler, U., Weiss, T., Escaler, X., Eguasquiza, E.,Dynamic Analysis of Francis Runners-Experiment and Numerical Simulation,International Journal of Fluid Machinery and Systems, Vol 2, 2009.


11Appendix-I - Some discrepancies with the design program (Khoj)

The curve files of the blades along with the boundary conditions needed for the CFX simulationswere taken from the Matlab design program called ‘Khoj’. More information about the theories andexecuting the program can be found in the earlier papers [19] and [21]. In this thesis project, theseparameters and files were needed as inputs to conduct the CFD and FSI in later part of the project.The output ‘CFX parameters’ was provided in the following way:

Blades 17.000000

Flow rate 2.350000

Rotational speed -1000.000000

Velocity components:

Between runner and guide vanes:

C_theta 0.976757

C_r 0.214349

C_z 0.000000

Between guide vanes and stay vanes:

C_theta 0.834840

C_r 0.550493

C_z 0.000000

At stay vane inlet:

C_theta 0.855737

C_r 0.517410

C_z 0.000000

These parameters provide information about the inflow conditions, rotational speed of the runner andthe direction of the flow towards the stay vane, guide vane and the runner inflow separately. Theseparameters provide the freedom of modeling the runner independently or together with the stationarycomponents when needed. There have been few concerns raised during the use of these inputs, whichare discussed in this chapter. The results generated in the previous studies and the conclusions havebeen modified accordingly.

83

CHAPTER 11. APPENDIX-I - SOME DISCREPANCIES WITH THE DESIGN PROGRAM (KHOJ) 84

11.1 Direction of the inflow

The Boundary Vector plot at the inlet for the given ‘CFX parameters’ is shown in Figure 11.1. Itshows that the direction of the flow towards the inlet is not aligned properly.

Figure 11.1: Boundary Vector at the inlet with the given flow direction

The explanation of the direction of the flow is explained in Figure 11.2. The co-ordinate axes definedhere are according to the convention used in CFX. It can be seen that the tangential component ofthe velocity should be in the direction of the rotation, which is negative. Also, the radial componentshould be towards the inward direction, which is also negative in this case.

This misalignment was not only seen for the runner inlet, but even when the stationary componentswere modeled, the flow vector was in the opposite direction, as shown in Figure 11.3. Here, both theguide vane and the stay vane have been modeled and the inflow condition was given according to thesame file, but for the stay vane inlet. This can be more clearly understood for the stationary domain,as there is no rotational component and with that, the absolute velocity should be aligned towardsthe direction of the flow. It can be seen that the angle of the inflow looks acceptable, but the directionhas been misaligned.



Hub

Shroud

Outlet Inlet

r

Ɵ

U

W

C

α

β





11.1.1 Modification and influence on the result

The modification was made in the ‘CFX parameters’ file by changing the direction of the tangentialand the radial components. The modified parameters is shown below:

Blades 17.000000

Flow rate 2.350000

Rotational speed -1000.000000

Velocity components:

Between runner and guide vanes:

C_theta -0.976757

C_r -0.214349

C_z 0.000000

Between guide vanes and stay vanes:

C_theta -0.834840

C_r -0.550493

C_z 0.000000

At stay vane inlet:

C_theta -0.855737

C_r -0.517410

C_z 0.000000

A significant effect was seen in the sediment erosion density plot. Major difference was seen when thestationary components were modeled, as shown in Figure 11.4. With the provided information, noerosion effect was seen on the turbine components, which indicates some errors in the CFX parameters.On changing the direction as discussed above, the erosion pattern was seen profoundly and at theexpected places (Guide vane, stay vane inlet and runner outlet). Even when only the runner ismodeled, the erosion was seen in the bigger amount when the directions were modified than whenthey were unmodified.



Modified

Before

No erosion!

Figure 11.4: Result of the two flow directions, unmodified (top) and modified(below)



11.2 Guide vane outlet and runner inlet

The curve files and the boundary parameters in the Matlab code had been designed so as to attainthe best efficiency condition. This suggests that the solution between the two cases, i) when onlythe runner blade is modeled and ii) when the stationary components are modeled together with therunner blade, should not vary much. This was not the case as the results, in terms of head, efficiency,sediment erosion pattern and other results did not seem to match between the two cases, and also thecase when the guide vane and the blade were modeled. This discrepancy is shown in Figure 11.5. Theerosion density of the runner only case is higher than the full stage case. Also, when the stationarycomponents are modeled, the erosion is also seen towards the inlet of the runner. On witnessing otherplots, it was seen that the streamline of the flow in the two cases are different. The streamlines ofthe latter case seems to be distorted which also affected the pressure distribution around the blade.This directly affected the total head as it is mentioned in the figure that the total head was reducedby 75% when the stationary components were modeled. Again, the CFX parameters were taken fromthe same file and the curve files from the same design, which means that the results should not varyby this amount. On further investigating, it was seen that the guide vane of the latter case was notaligned in the correct position, i.e. at the designed condition. The output report file showed that theguide vane was aligned in such a way that the flow at the inlet of the runner was at an angle of 72◦,but in the case when only the runner was modeled, the flow at the inlet of the runner was at an angleof 77◦. This infers that the curve file of the guide vane represents the off-design condition and in orderto obtain the curve files at the best efficiency condition, the Matlab code has to be revised again.



With runner only With Stay vane-Guide vane-Runner

Head : 205.6 m Head : 153.22 m

Figure 11.5: Discrepancy between the results when only the runner and the full stage is modeled


12Appendix-II - Imposing cyclic symmetry boundary conditions in

ANSYS

It was seen that the cyclic symmetry boundary conditions can be imposed in ANSYS Workbench byeither of the two ways :

• From workbench, choosing the symmetry property and selecting the higher and the lower bound-aries of the symmetric body. Doing this requires a new cylindrical co-ordinate system definedand the exact geometry on the higher and the lower side so that the geometries and mesh areproperly mapped.

• By using commands in Mechanical (APDL). This can also be done in workbench itself by writingthe following commands,/prep7cyclic,17/soluTolerances to map the faces can be chosen as per necessity.

The solutions of the two options shown above were apparently different. In the latter case, when theAPDL command was used to impose the cyclic property to the runner, it resulted in some mappingproblems. One solution of removing this problem is to define certain tolerances for the mapped mesh.But since this option could not get the robust solution, the former option was chosen. Here, bydefining the high and the low boundaries of the cyclic region, the problem of the mapping did notpersist. This comparison is shown in Figure 12.1. Also, it can be seen from the comparison that themaximum stress predicted by the latter case is much more than the former case.

Although the results of the former case was adopted for one-way FSI, this option was not valid for thetwo-way FSI till the current release. Hence, the latter option was chosen for that case. Though themapping problems could not be seen in the two way FSI, because the post processing is carried out inCFX-Post, it is expected that the results of the analysis overestimated the stresses by some amount.

90

CHAPTER 12. APPENDIX-II - IMPOSING CYCLIC SYMMETRY BOUNDARY CONDITIONS IN ANSYS 91

Mapping problems

Figure 12.1: Choices of imposing cyclic symmetry property to the sector of the runner


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