Relating Slurry Friction with Erosion Rate Using A Toroid ... · 3.11 Distribution of contact load...

$: Relating Slurry Friction with Erosion Rate Using A Toroid ... · 3.11 Distribution of contact load fraction for different concentrations; d 50 = 1 mm.44 3.12 Distribution of contact$
RELATING SLURRY FRICTION WITH EROSION

RATE USING A TOROID WEAR TESTER (TWT)

Lisheng Zhang

A thesis submitted in partial fulfillment of the requirements for the degree of

Master of Science

in

Chemical Engineering

Department of Chemical and Materials EngineeringUniversity of Alberta

© Lisheng Zhang, 2018

Abstract

In the mining industry, high wear rates in slurry pipelines can lead to premature/unplanned

failure, causing operation outages and environmental incidents. Laboratory-scale wear studies and

physics-based modelling are required to predict pipe wear. Recent studies have revealed a strong

relationship between local shear stress and wear rate; so, for heterogeneous (settling) slurries,

evaluation of the Coulombic (contact load) friction is a promising predictor of wear at the pipe

invert. Since studies of wear in pipelines are expensive and time-consuming, this investigation

focuses on Coulombic-friction-based wear prediction for slurry flows in a Toroid Wear Tester (TWT).

The TWT has been found to be a promising apparatus in the study of contact-load-dominated wear.

In this study, a torque sensor system was installed and used to measure the applied torque.

Commissioning tests were performed, which indicated that the torque sensor could generate a

consistent torque signal. The applied torque was measured for a wide range of particle sizes (0.125

mm to 2 mm), solid volume concentrations (10% to 20%), and TWT rotational speeds (10 to 90 RPM).

It has been shown that applied torque, solid volume concentration, and terminal settling velocity

are correlated. Qualitative flow observations were made to better understand the sliding bed

geometry and further to relate the measured torque values to the Coulombic friction component.

Estimation of the torque value was performed using modified equations from the two-layer model.

The agreement between estimated and measured torque values indicates the Coulombic friction

component can be determined. Corresponding erosion wear tests were conducted, and relating

the Coulombic friction component with wear rate was attempted at 30 RPM and 60 RPM. It is

observed that the wear rate grows with increased Coulombic friction. Therefore, it is concluded

that very few tests are required to predict erosion wear rates in TWT. If there is a bridge between

TWT and pipe flow, pipe wear can also be predicted based on a very small number of tests. In

order to developing the bridge, quantitative comparisons between TWT and pipe loop wear results

must be obtained. Also, a broader range of conditions must be tested, including particle types,

wheel speeds, sizes of wear wheel and coupon material to further verify the relationship between

Coulombic friction and wear rates.

ii

Acknowledgements

First of all, it is my great honour to have Dr. Sean Sanders as my supervisor. Without his

excellent guidance and encouragement, it would be impossible for me to complete my

master’s degree. I also would like to thank him not only for teaching me his ethical values

in research but also for sharing his excellent technical abilities with me, which will be a

treasure for the rest of my life.

I would like to thank Terry Runyon for her administrative help, which made my

whole master’s study as smooth as possible. Also, I must express highest gratitude to

my colleagues in the Pipeline Transport Processes Research Group at the University of

Alberta, especially Dr. David Breakey and Nitish Ranjan Sarker for their selfless support

and valuable feedback.

I am also thankful to Imperial Oil Limited (IOL) and NSERC for financial assistance on

my MSc project. The engineering drawings for the TWT used in this study were provided

by Paterson & Cooke. Finally, I would like to thank my parents and friends for their moral

support throughout my master’s studies.

iii

Contents

List of Figures viii

List of Tables xi

List of Symbols xii

1 Introduction 1

1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Toroid Wear Tester . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.4 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.5 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.6 Author’s Contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2 Literature Review 7

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2 Lab-scale Wear Testers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2.1 Pipe loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.2.2 Slurry Pot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.2.3 Jet Impingement Tester . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.2.4 Coriolis Tester . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.3 Wear Measurement Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.4 Current Understanding of Pipeline Wear . . . . . . . . . . . . . . . . . . . . 13

2.4.1 Slurry Erosion Mechanism . . . . . . . . . . . . . . . . . . . . . . . . 13

2.4.2 Hydrodynamic Effect on Slurry Erosion Rate . . . . . . . . . . . . . . 14

2.4.3 Relationship between Slurry Friction and Erosion Wear . . . . . . . 15

2.4.3.1 Two Layer Model . . . . . . . . . . . . . . . . . . . . . . . . 15

2.4.3.2 Slurry Friction Study in Pipe Loop . . . . . . . . . . . . . . 18

iv

CONTENTS

2.5 Toroid Wear Tester (TWT) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.5.1 Historical Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.5.2 Recent Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.5.2.1 Flow Visualization in TWT . . . . . . . . . . . . . . . . . . . 22

2.5.2.2 Parametric Study of Erosive Wear using the TWT . . . . . 24

2.5.2.3 CFD Analysis of the Hydrodynamics of an Air-Water Mul-

tiphase System in a Rotating Toroid Wheel . . . . . . . . . 24

2.5.2.4 TWT Results vs. Recirculating Pipe loop Results . . . . . . 26

2.6 Scope of the Present Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.7 Research Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3 Experimental Method 29

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.2 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.2.1 Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.2.2 Chemicals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.2.3 Test Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.3 Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.3.1 Toroid Wear Tester (TWT) . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.3.1.1 Overall TWT Description . . . . . . . . . . . . . . . . . . . . 31

3.3.1.2 Single Wheel . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.3.2 Torque Sensor System . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.3.2.1 Key elements . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.3.2.2 Torque Sensor Installation . . . . . . . . . . . . . . . . . . . 34

3.3.2.3 Data Acquisition System . . . . . . . . . . . . . . . . . . . . 36

3.4 Experimental Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.4.1 Wear Measurements Procedure Overview . . . . . . . . . . . . . . . 37

3.4.2 Torque Measurements Procedure Overview . . . . . . . . . . . . . . 37

3.4.2.1 Procedure Overview . . . . . . . . . . . . . . . . . . . . . . . 37

3.4.2.2 Sand-related Torque . . . . . . . . . . . . . . . . . . . . . . . 38

3.4.3 Sliding Bed Observation using an Acrylic Toroid Wheel . . . . . . . 39

3.5 Experimental Program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.5.1 Torque Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.5.1.1 Concentration . . . . . . . . . . . . . . . . . . . . . . . . . . 40

3.5.1.2 Wheel Speed . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

3.5.1.3 Particle Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

v

CONTENTS

3.5.2 Wear Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.5.3 Overview of Experimental Program . . . . . . . . . . . . . . . . . . . 43

4 Evaluation of the Torque Sensor System 46

4.1 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

4.2 Commissioning tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.2.1 Signal Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.2.2 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

4.3 Data Repeatability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

4.3.1 Wheel-to-Wheel Repeatability Tests . . . . . . . . . . . . . . . . . . . 53

4.3.2 Test-to-Test Repeatability Tests . . . . . . . . . . . . . . . . . . . . . . 54

4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

5 Results and Analysis 56

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

5.2 The Effect of Particle Size and Wheel Speed on Sand-related Torque . . . . 57

5.3 The Effect of Concentration on Sand-Related Torque . . . . . . . . . . . . . 64

5.4 Converting Measured Torque to the Coulombic Friction . . . . . . . . . . . 66

5.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

5.4.2 Calculation Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

5.4.3 Comparison of Measured and Calculated Torque Values . . . . . . . 74

5.4.4 Force Balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

5.4.5 Obtain the Coulombic Friction . . . . . . . . . . . . . . . . . . . . . . 78

5.5 Relating Coulombic Friction with Erosion Wear Rate . . . . . . . . . . . . . 80

6 Conclusion and Recommendation 83

6.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

6.2 Recommendations for Future Work . . . . . . . . . . . . . . . . . . . . . . . 85

References 86

A Properties of The Test Coupons 91

B Experimental Procedure 92

B.1 Wear Measurements Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . 92

B.1.1 Test Coupon Cleaning . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

B.1.2 Coupon Weighing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

vi

LIST OF FIGURES

B.1.3 Slurry Charging and N2 Purging . . . . . . . . . . . . . . . . . . . . . 93

B.1.4 Starting and Stopping Sequence of the TWT . . . . . . . . . . . . . . 93

B.1.5 Erosive Wear Rate Calculation . . . . . . . . . . . . . . . . . . . . . . 94

B.2 Torque Measurements Procedure . . . . . . . . . . . . . . . . . . . . . . . . . 95

B.2.1 Slurry Charging and Coupon attachment . . . . . . . . . . . . . . . . 95

B.2.2 Torque data collection . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

B.2.3 Torque data processing . . . . . . . . . . . . . . . . . . . . . . . . . . 96

C Moment of Inertia Calculation 97

D The Torque Amplitude of Imbalance and Wobbling 99

E Experiment Results and Sample Calculation 100

E.1 Wear Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

E.2 Sand-Related Torque Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

E.3 Sample Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

F MATLAB Code 105

F.1 Signal Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

F.2 Rotation Angle Measurements (by FUTEK) . . . . . . . . . . . . . . . . . . . 107

F.3 Torque Sensor Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

vii

List of Figures

1.1 Demonstration of TWT rotation . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Wear distribution at circumferential position . . . . . . . . . . . . . . . . . . 4

1.3 Correlation of erosion rate with solid pressure gradient . . . . . . . . . . . . 4

2.1 Schematic diagram of erosion pot tester, dimensions in mm . . . . . . . . . 9

2.2 Slurry pot measured wear rate for stainless steel and abrasive resistance

steel in field and laboratory conditions . . . . . . . . . . . . . . . . . . . . . 10

2.3 Schematic diagram of jet impingement . . . . . . . . . . . . . . . . . . . . . 11

2.4 Schematic diagram of Coriolis tester . . . . . . . . . . . . . . . . . . . . . . . 11

2.5 Wear patterns as slurry flows through . . . . . . . . . . . . . . . . . . . . . . 14

2.6 Idealized velocity distributions and concentration distributions used in the

model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.7 Cross section of a circular pipe . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.8 Actual velocity distributions and concentration distributions for slurry flow

and the two-layer model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.9 Correlation of erosion rate with solid pressure gradient (with best fit line) . 18

2.10 Part of ring pipe used for measuring coal degradation . . . . . . . . . . . . 19

2.11 Demonstration of BHRA’s toroid wheel . . . . . . . . . . . . . . . . . . . . . 20

2.12 Demonstration of PCCE pipeline wear tester . . . . . . . . . . . . . . . . . . 21

2.13 Position terminologies for the ATW . . . . . . . . . . . . . . . . . . . . . . . 22

2.14 Slurry carry-over observation (in monochrome) study in ATW, d50= 0.250

mm, Cs= 30%, N= 95 RPM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.15 Flow observation for 0.250 mm sand at 10% concentration by volume . . . 23

2.16 Data locations considered in the toroid domain . . . . . . . . . . . . . . . . 25

2.17 Comparison of water velocity profiles at Position 0 for N = 30, 60 and 90 RPM 25

2.18 X-direction water velocity profiles at different angular positions, N= 90 RPM 26

2.19 Comparison between the pipe loop experiment and the TWT results . . . . 27

viii

LIST OF FIGURES

3.1 Schematic of key elements of toroid wear tester . . . . . . . . . . . . . . . . 32

3.2 Demonstration of coupon windows on toroid wheel . . . . . . . . . . . . . . 32

3.3 Demonstration of coupon holders . . . . . . . . . . . . . . . . . . . . . . . . 33

3.4 Schematic of N2 purging in the TWT . . . . . . . . . . . . . . . . . . . . . . . 33

3.5 Schematic of key elements of torque sensor system . . . . . . . . . . . . . . 35

3.6 Toroid wear wheel assembly with torque sensor installed . . . . . . . . . . . 35

3.7 Torque sensor assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.8 Schematic of torque data acquisition system . . . . . . . . . . . . . . . . . . 36

3.9 Sliding bed observation for 2 mm gravel; Cs = 15% . . . . . . . . . . . . . . 40

3.10 Sliding bed observation for 0.25 mm Sil 1; Cs = 10% . . . . . . . . . . . . . . 41

3.11 Distribution of contact load fraction for different concentrations; d50 = 1 mm. 44

3.12 Distribution of contact load fraction for different concentrations; d50 = 2 mm. 44

3.13 Distribution of contact load fraction for different wheel speed; Cs = 10%. . 44

3.14 Distribution of contact load fraction for different particle size; Cs = 15%. . . 45

4.1 Unfiltered signal for 2 mm gravel at 60 RPM; Cs = 15% . . . . . . . . . . . . 48

4.2 Frequency-domain signal for 2 mm gravel at 60 RPM; Cs = 15% . . . . . . 49

4.3 Filtered frequency-domain signal for 2 mm gravel at 60 RPM; Cs = 15% . . 50

4.4 Filtered signal for 2 mm gravel at 60 RPM; Cs = 15% . . . . . . . . . . . . . 50

4.5 Best fit line of moment of inertia from the measurements . . . . . . . . . . . 52

4.6 Data repeatability for wheel A, B, and C; Cs = 15% . . . . . . . . . . . . . . 54

4.7 Data repeatability for wheel A; Cs = 5% . . . . . . . . . . . . . . . . . . . . 55

5.1 Flow regimes for 0.250 mm Sil 1 at 10% concentration by volume . . . . . . 57

5.2 Flow observation for 2 mm gravel at 10 % concentration by volume; N = 40

RPM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

5.3 The effect of particle size on sand-related torque; Cs = 15%, N = 60 RPM . 58

5.4 The effect of wheel speed on sand-related torque; Cs = 10% . . . . . . . . . 60

5.5 Sliding bed observation at 10 RPM; Cs = 10% . . . . . . . . . . . . . . . . . . 60

5.6 Sliding bed observation for Sil 1; dp = 0.250 mm, Cs = 10% . . . . . . . . . . 61

5.7 The effect of wheel speed on sand-related torque for LM; Cs = 10%, 15%,

and 20% . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

5.8 Sand-related torque for a variety of particle types with respect to ratio of

TWT speed to particle settling velocity; Cs = 10% . . . . . . . . . . . . . . . 63

ix

LIST OF TABLES

5.9 Sand-related torque for a variety of particle types with respect to ratio of

TWT speed to particle settling velocity; Cs = 10%, 15%, and 20% . . . . . . 63

5.10 The effect of concentration on sand-related torque . . . . . . . . . . . . . . . 65

5.11 Sliding bed observation for 15% gravel at 30 RPM . . . . . . . . . . . . . . . 65

5.12 Sliding bed geometries for 1 mm gravel at 60 RPM . . . . . . . . . . . . . . 66

5.13 Cross section of TWT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

5.14 Demonstrate depth difference on cross section . . . . . . . . . . . . . . . . . 68

5.15 Definition sketch on TWT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

5.16 Sketch for thickness of sliding bed in TWT . . . . . . . . . . . . . . . . . . . 70

5.17 Definition sketch of inclined angle . . . . . . . . . . . . . . . . . . . . . . . . 70

5.18 Demonstration of different normal stress at different point on sidewalls . . 72

5.19 Demonstration of different central angle at different radius on sidewalls . . 72

5.20 Definition of A1 and A2 in the calculation of contact load fraction . . . . . . 73

5.21 Matching between calculated and measured sand-related torque . . . . . . 74

5.22 Force analysis on the sliding bed . . . . . . . . . . . . . . . . . . . . . . . . . 76

5.23 Radial force analysis at bottom wall . . . . . . . . . . . . . . . . . . . . . . . 77

5.24 Definition of key parameter in interpolation equation on sand-related torque

graph; Cs = 10% . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

5.25 Relationship between erosive wear rates and the Coulombic friction . . . . 81

5.26 Additional wear results from Sarkar . . . . . . . . . . . . . . . . . . . . . . . 82

C.1 Demonstration of test coupon with its momentum arm . . . . . . . . . . . . 97

C.2 Demonstration of coupon holder with its momentum arm . . . . . . . . . . 98

D.1 The torque amplitude of imbalance and wobbling . . . . . . . . . . . . . . . 99

E.1 Demonstration of β, θ, and hmax . . . . . . . . . . . . . . . . . . . . . . . . . 103

x

List of Tables

2.1 List of power index from past study . . . . . . . . . . . . . . . . . . . . . . . 15

3.1 Properties and suppliers of particles used in this study. . . . . . . . . . . . . 30

3.2 Properties and suppliers of chemicals used in the this study . . . . . . . . . 30

3.3 Dimension of wheel A, B and C . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.4 List of torque sensor system in the present study . . . . . . . . . . . . . . . 34

3.5 Experimental matrix for torque against concentration . . . . . . . . . . . . . 40

3.6 Experimental matrix for torque against velocity . . . . . . . . . . . . . . . . 41

3.7 Experimental matrix for torque against particle size . . . . . . . . . . . . . . 42

3.8 Experimental matrix for wear measurements . . . . . . . . . . . . . . . . . . 43

4.1 Experiment matrix for wheel-to-wheel repeatability test . . . . . . . . . . . 53

4.2 Experiment matrix for test-to-test repeatability of torque measurements . . 54

5.1 List of drag coefficient and terminal settling velocity for the sands and

gravels studied here . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

5.2 List of conditions where estimated sand-related torque . . . . . . . . . . . . 74

5.3 List of conditions and calculated values for friction coefficient validation . 78

5.4 List of cases using linear interpolation . . . . . . . . . . . . . . . . . . . . . . 80

5.5 Test conditions from Sarker for data points used in the validation . . . . . . 82

A.1 Chemical composition of ASTM A572 GR50 carbon steel specimens . . . . 91

A.2 Mechanical properties of the ASTM A572 GR50 carbon steel specimens . . 91

C.1 Moment of inertial calculation of the test coupon, coupon holder, bolt and nut 98

C.2 Summary of moment of inertial calculation . . . . . . . . . . . . . . . . . . . 98

E.1 Wear results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

E.2 List of sand-related torque results . . . . . . . . . . . . . . . . . . . . . . . . 102

xi

List of Symbols

Symbol Description Units

α Angle measured from central of the sliding bed radian

α1 Angular acceleration radian

αmax Angle boundary limit in torque calculation radian

β Angle defining lower layer radian

µf Dynamic viscosity of carrier flow Pa–s

µs Coefficient of friction –

ρf Density of carrier fluid kg/m3

ρs Density of solid particles kg/m3

ρsteel Density of carbon steel kg/m3

τw Wall shear stress exerted by emulsion Pa

θ Inclined angle radian

A Proportionality in Equation (5.8) –

Ae Eroded surface area mm2

Aouter+wall Total wetted area in TWT mm2

Aouter Wetted area at outer wall in TWT mm2

CD Drag coefficient –

Cpack Packing fraction of the sliding bed –

Cs Volumetric particle concentration –

d50 Mass median particle diameter mm

Dp Diameter of the pipe m

DT Diameter of the TWT m

xii

LIST OF SYMBOLS


dP/dz Solids pressure gradient inside the pipe Pa/m

Ew Wear rate mm/year

Ff,bottom Coulombic friction acting on the bottom wall of the TWT N

Fg Immersed weight of the sliding bed N

FN Normal force N

Fr,bottom Radial force at bottom wall N

Fr Radial force N

Ft,bottom Tangential force at the bottom wall N

Ft,side Tangential force at the side wall N

Ft Tangential force N

g Gravitational acceleration m/s2

h Sliding bed thickness mm

I Moment of inertia kg–m2

L Sliding bed wetted length m

Le Length occupied by emulsion m

m Mass of an object kg

Mc,f Calibration specimen weight after the wear experiment g

Mc,i Calibration specimen weight before the wear experiment g

Mf,A2 Final mass of test coupon A2 g

Mf,A4 Final mass of test coupon A4 g

Mi,A2 Initial mass of test coupon A2 g

Mi,A4 Initial mass of test coupon A4 g

Ml,A2 Material loss on test coupon A2 g

Ml,A4 Material loss on test coupon A4 g

N Wheel speed RPM

r Distance to the centre m

rmax,rmin Radius boundary limit in torque calculation m

xiii

LIST OF SYMBOLS


T Torque N–m

T0 Torque exerted by external friction forces N–m

tETR Total effective time to run the wear experiment Hours

Tf,bottom Torque acting on the bottom wall of the TWT N

Tf,side Torque acting on the side wall of the TWT N

TL,A2 Thickness loss on test coupon A2 mm

TL,A4 Thickness loss on test coupon A4 mm

tSR Total time to stop the TWT due to slurry replacement Hours

tTR Total time to run the wear experiment Hours

v∞ Terminal settling velocity m/s

Vpacked Total packed volume of the sliding bed (particles + voids) m3

Vsand Total volume of particle m3

W Width of TWT channel mm

z Depth measured from sliding bed surface mm

A1 Total contact area mm2

A2 Contact area for settled bed mm2

Mf Final weight of a test coupon g

Mi Initial weight of a test coupon g

xiv

Chapter 1

Introduction

1.1 Background

Slurry pipelines are widely used in various industries such as mining, oil sand, and power

generation to transport raw materials from the place of extraction to the processing plant.

Pipeline transport holds a number of environmental and economic advantages over other

transport methods. For example, slurry pipelines prevent noise and emissions along

with the route as compared to road and railway, and they also cost less on infrastructure

construction and require less labor on daily transportations [1]. However, premature

or unplanned pipeline failure is a significant risk on the reliability of slurry pipelines,

since its failure could lead to operation outages and environmental damage. In Alberta’s

oil sand industry, more than $1 billion is spent each year on pipe reliability related

issues [2]. Pipe erosion wear is defined as pipe materials that are continuously removed by

moving particles due to impact [3–7], and corrosion can also occurs if oxygen or oxidizing

or reducing agents exist. The combination of erosion and corrosion often accelerates

pipeline failures. Therefore, to prevent premature or unplanned pipeline failure, an

erosion model for predicting pipeline wear is very beneficial to industries when making

maintenance strategies. To develop an erosion model for slurry pipelines, in-field wear

tests are impractical to understand various parameters though, since it is often impossible

to measure or control many important parameters, such as solids concentration, slurry

velocity, particle size, pH, and dissolved oxygen (DO) level. Therefore, lab-scale wear tests

are required, and among many lab-scale wear testers, the Toroid Wear Tester (TWT) has

been proposed as a useful apparatus to study pipeline wear in a laboratory setting [3, 7].

A overview of the TWT and its advantages will be discussed in Section 1.2. Past studies

(refer to Section 1.3) indicate slurry friction could be a correlating parameter which help

the author to develop research objectives in this study (refer to Section 1.4). The thesis

outline and author’s contribution will be shown in Section 1.5 and Section 1.6 respectively.

1

1.2. TOROID WEAR TESTER

1.2 Toroid Wear Tester

The TWT has a hollow toroidal wheel driven by a motor. The test materials (also named

test coupons) are attached to the outer circumference of the wheel, and approximately

one-third of the wheel is filled with slurry. As shown in Figure 1.1, under most operating

conditions, a relatively stationary sliding bed is formed at bottom while the wheel rotates.

This apparatus has several advantages over other lab-scale wear testers, such as the

following:

• Small volume of slurry is required, making the wear tests inexpensive.

• For a horizontal slurry pipeline that consists of coarse particles, the highest wear in

pipes is found to occur at the bottom of the pipe owing to the interaction between

contact loads (contact loads means coarse particles, which transmit a portion of

their immersed weight to the pipe wall) and the pipe wall. Since TWT allows the

formation of sliding bed, it can isolate this important wear mechanism.

• Particle degradation for the TWT is less as compared to other wear testers such

as pipe loops (refer to Section 2.2.1 for details). Solid particles are found to lose

their edges and become rounded during wear tests, especially when slurry is used

extensively without replacement. This is termed particle degradation. Particle

degradation causes changes in particle abrasivity [3], which influences the ability to

investigate other wear-related parameters.

Figure 1.1: Demonstration of TWT rotation

2

1.3. PROBLEM STATEMENT

1.3 Problem Statement

A typical oil sands slurry pipeline consists of bitumen, clays, sand, large lumps/rocks and

hot water. Most oil sands slurry contains fine (dp <44µm) and coarse particles. During

transportation, coarse particles tend to form a moving bed (sliding bed). The impact from

moving particles continuously removes the pipe material and causes erosive wear. Since

measuring wear rate is a time-consuming process and wear mechanisms are not well

understood, no accurate model to predict erosion wear rate has been developed so far.

Even though some models such as single-particle based erosion models exist, they cannot

be applied directly to a industrial scale pipelines, since erosive wear generally increases

with increase in solid volume concentration, particle size, and velocity [8]. Moreover, most

of these studies only account for the effect of a single parameter (e.g. velocity) and ignore

the effects of others [5].

A recent study by Schaan et al. [9] illustrates two important points relevant to the use

of the TWT for wear tests. First, in pipelines transporting coarse particles, the maximum

wear rate is found at the pipe bottom which is illustrated in Figure 1.2. The shape of the

profile shows that the peak wear rates occur around 180°, which refers to the pipe bottom,

indicating the sliding bed affects the wear rates. Second, the discrepancy between wear

rates at similar conditions was explained by a reduction in mean particle size and increase

in fines content – two parameters that would strongly affect the properties of the sliding

bed [9]. It is important to note that both of these parameters are reflected in the pressure

drop per unit length of the pipe, which can be well predicted by existing pipeline design

tools. This study shows the importance of both the sliding bed at the bottom of the pipe

and the properties of the sliding bed in predicting wear rate.

Sadighian [5] observed that erosion wear is a strong function of slurry friction, especi-

ally friction from solid particles. In a horizontal recirculating pipe loop carrying coarse

particles, he determined the solid pressure gradient (pressure drop due to solid particles

over certain distance). Sadighian [5] observed a strong correlation between solid pressure

gradient and erosion wear rate (Figure 1.3). The solid pressure gradient strongly depends

on the friction between sliding bed and pipe wall. Therefore, studying the friction is

essential to predict wear rate.

The TWT is a promising apparatus for pipeline erosion wear tests, especially for a

sliding bed study. If a relationship can be derived between friction and erosion wear rate, it

could very much reduce the experimentation necessary to predict pipeline wear. However,

very limited information about friction in TWTs could be found in previous literature. In

order to develop the relationship, both friction and wear measurements are required.

3

1.3. PROBLEM STATEMENT

(a) Schematic illustration ofcircumferential position

(b) Wear distribution at circumferential position

Figure 1.2: Wear distribution at circumferential position, adapted from Schaan et al. [9]

Figure 1.3: Correlation of erosion rate with solid pressure gradient, adapted from Sadighian[5]

4

1.4. OBJECTIVES

1.4 Objectives

The major objective is to develop a relationship to predict erosion wear rate. To achieve

this, the project is divided into two main steps:

Determine the effect of TWT hydrodynamics conditions on sliding bed friction It is ne-

cessary to determine how slurry friction varies with parameters such as wheel velo-

city, solids concentration, and particle type. Shook et al. [10] note that contact loads

vary with slurry velocity and particle size; and further, it is clear that sliding bed

friction, in turn, depends on the contact loads. Also, the goal in this part is to obtain

the value of friction for developing the relationship between friction and erosion wear

rate. Since friction cannot be directly measured, torque will be measured through a

torque sensor and converted into friction.

Develop a relationship between slurry friction and erosive wear rate in the TWT Once

the value of friction due to the sliding bed and wear rate are measured, a relationship

will be developed and then validated with past data.

1.5 Thesis Outline

Chapter 2 provides background information of the lab-scale wear tests, the theory of

wear modelling, as well as the history and development of the TWT, providing the

context necessary to understand the current work. Chapter 3 describes the materials,

procedures, and equipment used in this work. Information regarding the material used

and suppliers is outlined in the material section. The equipment section contains all

information related to the equipment used throughout the thesis, such as their dimensions

and suppliers. A detailed design of torque sensor system is described in this chapter.

The experimental procedures section contains information regarding the wear tests and

torque measurements in the TWT. Due to the unique application of torque sensor, the

torque measurement acquisition procedure is described in detail. Chapter 3 also presents

the experimental program. The experimental program section describes the experimental

matrix done in this study and justification of the test program that was developed. Since

the torque sensor is newly installed in the TWT, evaluation of its performance is discussed

in Chapter 4. Chapter 5 conveys the results and analysis for all tested conditions. The effect

of velocity, concentration, and particle size are summarized and discussed; the methods

that convert torque to friction are described in this chapter as well. Also, the relationship

between slurry friction and erosion wear rate is shown and validated. Chapter 6 discusses

the conclusions of this study and provides recommendations for future work

5

1.6. AUTHOR’S CONTRIBUTION

1.6 Author’s Contribution

In this study, the torque sensor and acquisition system was selected, calibrated, and com-

missioned by the author with the assistance of Dr. David Breakey and Nitish Ranjan Sarker.

The author developed a standard procedure for torque measurements and performed

every experiment related to this thesis, such as torque measurements and wear tests.

MATLAB codes for signal filtering and torque sensor calibration were written by Dr. David

Breakey. The data analysis, including the effect of hydrodynamic conditions (e.g velocity,

particle size, solid volume fraction) on friction due to sliding bed, is the author’s original

work. A unique equation that converts measured torque to the friction due to sliding bed

was derived by the author, based on the two-layer model. Also, the author validated the

equation using force balance. The correlation between friction due to sliding bed and wear

rate was developed by the author as well.

6

Chapter 2

Literature Review

2.1 Introduction

Slurry pipeline transportation is a very important process in industry, and pipe material

loss due to erosion or corrosion or a combination of both can cause significant reduction

in pipeline lifetime. Therefore, a wear model becomes important in predicting wear rates.

Even though many researchers [11–13] have focused on studying wear mechanisms for

many years, they are not yet well understood due to the complexity of wear. In this chapter,

a review of past wear study will be presented in the following perspectives:

• Lab-scale wear testers

• Wear measurements techniques

• Current understanding of pipeline wear

2.2 Lab-scale Wear Testers

As mentioned in Section 1.2, wear experiments are very important in studying wear to

understand wear mechanisms and for testing the performance of new materials. The most

reliable results can be obtained by performing the experiments in an actual operating

pipeline [3]. However, since it is impossible to vary hydrodynamic parameters and since

pipeline owners are unwilling to change the operating conditions [3], laboratory wear tests

are necessary for model development. Several lab-scale wear testers have been developed

and studied, which include pipe loop, slurry pot, jet impingement, and Coriolis testers.

These testers attempt to generate flow behaviour that replicates pipe flow hydrodynamics

to make the wear data valuable. A review of these is provided here.

7

2.2. LAB-SCALE WEAR TESTERS

2.2.1 Pipe loop

This tester consists of a pipe loop and a pump that recirculates the slurry in the loop.

The slurry is stored in the feed tank. The recirculation in the pipe loop significantly

reduces the amount of slurry required, as compared to "once through" experiments such

as actual pipeline tests, especially considering the long experiment duration required for

typical wear tests (frequently >1 week). Also, the diameter of the pipe loop is usually

smaller than the diameter of an industrial slurry pipeline. For example, Sadighian [5]

performed wear experiments with a 3-inch (76.2 mm) diameter pipe, whereas Parent and

Li [14] measured wear loss in a 710 mm diameter operating pipeline from Suncor Energy

Inc and Schaan et al. [9] measured wear loss in a 737 mm diameter operating pipeline

from Syncrude Canada Ltd. Also, different equipment can be installed to obtain in situ

measurements. For example, pressure can be measured by a pressure gauge to ascertain

pressure drops over a certain length, and a flow meter can help monitor slurry velocity in

the pipe. In addition, more in-situ parameters could be measured; for example, Sadighian

[5] measures the in-situ sand concentration at vertical position by using a transversing

gamma ray densitometer. Another example could be that of Shook et al. [15], where an

electrode assembly with the exposed surface of the electrodes was constructed, and the

electrodes flushed with the wall of a 50 mm acrylic pipe to measure particle velocity and

concentration. Another advantage would be that a pipe loop may consist of two test

sections of two different diameters, allowing the study of two different velocities during

each experiment.

Since the slurry recirculates in the pipe and passes through the pump, particles are

degraded. As mentioned in Section 1.2, this phenomenon is called particle degradation.

Henday [16] conducted a pipe loop test using granite chip slurry with 12.5% solid volume

concentration and average particle diameter of 12.5 mm. After 5 hours, the diameter

reduced to 8.6 mm. Particle degradation could change particle abrasivity, making the wear

data less reliable. Furthermore, a pipe loop usually occupies a large area. For example, the

pipe loop used in Sadighian’s [5] study is roughly 35 m to 40 m long, and owing to its

size, the amount of slurry required to be put into the pipe loop is proportionately large. In

Sadighian’s [5] study, the diameter of the pipe loop is 76.2 mm and takes approximately

365 L of slurry. Compared to other lab-scale testers discussed below, it requires a much

greater slurry volume.

2.2.2 Slurry Pot

In a slurry pot tester, the test specimen is placed within a closed pot and exposed to

abrasive slurry. While the specimen rotates, it will be continuously eroded by the slurry

(Figure 2.1). There are many test specimen arrangements. First, a test sample is placed in

8


a rotating shaft and exposed to slurry with simultaneously suspended particle. Figure 2.1

shows a slurry pot that is used in Clark [17]. The vertical cylindrical test specimens are

mounted on the central shaft by nylon cup. The shaft is driven by a electric motor [17].

Examples are Clark [17], Harvey et al. [18], Rajahram et al. [19], Yu et al. [20], Clark [21].

Other arrangements could be stirring the slurry using an impeller at the bottom while

the test specimens rotates. Examples are Tsai et al. [22], Desale et al. [23]. Wear can be

measured by measuring sample weight before and after the test.

Figure 2.1: Schematic diagram of erosion pot tester, dimensions in mm. Reproducedfrom Clark [17]

In this tester, test specimens properties, impact angle, slurry properties, and rotation

speed can be regulated. For example, Desale et al. [23] tested the specimen at different

hardness (91 to 260 HV, HV stands for Vickers Pyramid Number, and the unit is kilograms-

force per square millimetre) to investigate the parameters affecting erosion wear of ductile

materials under normal impact conditions. The mean particle size varies between 363

and 655 µm, and the solid concentration is 10%, 15%, and 20%. The rotating speed varies

between 3 m/s and 8.33 m/s.

Also, a slurry pot occupies less space and requires only a small volume of slurry in

comparison to a pipe loop. Typical, slurry requirements range from 3.8 L (in Ref. [12]) to 5

L (in Ref. [17]).

The fundamental difference between slurry pot testers and pipeline flow is the flow

hydrodynamics, prevents the lab-scale slurry pot results from being scaled up to field. For

example, Madsen [24] performed wear tests using a slurry pot and also collected wear

data in the field. Both tests were conducted at similar conditions (294 K at a slurry speed

of 8 m/s). Significant differences in wear rate were observed, as shown in Figure 2.2.

Even though Gupta et al. [6] showed a good agreement between pipe loop and slurry pot,

9


the difference in flow hydrodynamics between slurry pot testers and pipe flow requires

validation with pipe loop experiments before scale-up can be attempted. Additionally,

since for a slurry pot tester, all particles that come in contact with the specimen are

suspended, it cannot simulate sliding bed wear.

Figure 2.2: Slurry pot measured wear rate for stainless steel and abrasive resistance steelin field and laboratory conditions, adapted from Madsen [24]

2.2.3 Jet Impingement Tester

In a jet impingement tester (Figure 2.3), particles first mix with a liquid or gas phase, then

they are pressurized and shot at the test specimens at high speed. This causes material

loss at the test specimen surface. Examples of using liquid phase can be found in Zu et al.

[25], Benchaita et al. [26], Gnanavelu et al. [27], Hu and Neville [28]. The particle velocity in

liquid phase generally varies from 4.5 m/s (in Ref. [27]) to 18 m/s (in Ref. [28]). Examples

of those using gas phase tests include Wood and Wheeler [29], Oka et al. [30], where the

particle velocity can reach a very high value. For example, Oka et al. [30] performed

erosion wear tests at an impact velocity range of 50 to 130 m/s. Valuable information can

be extracted through surface examination of the specimens. For example, by comparing

the shape of the erosion site and volume of the material removed from the surface [30],

materials can be ranked under identical test conditions. Also, impact angle and particle

velocity can be controlled accurately and can be easily changed. In addition, this tester

occupies less space than a pipe loop. However, particles can be used only once, since

particles may break apart when shot into the test specimen surface. Most importantly, the

flow hydrodynamics are much different than in pipe flow; and since jet impingement does

not allow the formation of sliding bed, a model developed from jet impingement data is

not applicable for heterogeneous flow.

10


Figure 2.3: Schematic diagram of jet impingement. Adapted from Sadighian [5]

2.2.4 Coriolis Tester

The Coriolis wear tester was first developed by Tuzson et al. [31], and has been used in

several subsequent studies [32–35]. As illustrated in Figure 2.4, the slurry is fed to the

centre through a channel. The centrifugal force due to the rotation causes the slurry to flow

along the test specimen through the outer channel. The Coriolis tester is similar to the jet

impingement tester, except that in a jet impingement tester, particle is shot perpendicular

towards (high impact angle) the test specimen surface, whereas in a Coriolis tester, the

particle is shot along (low impact angle) the test specimen surface, allowing the Coriolis

tester to simulate wear conditions in slurry pumps, where particles move rapidly over the

test surface either in isolation or in a bed [33, 36]. Though the Coriolis tester is able to

simulate sliding bed conditions, it is unsuitable for the present study, since it would be

very difficult to measure sliding bed friction in such an arrangement.

Figure 2.4: Schematic diagram of Coriolis tester. Reproduced from Tian et al. [37]

11

2.3. WEAR MEASUREMENT TECHNIQUES

2.3 Wear Measurement Techniques

To evaluate the wear damage in slurry pipelines, several measurement techniques have

been reported [38]. The descriptions, with advantages and disadvantages, are discussed

below:

Weighing is a simple and cost-effective method of lab-scale wear study. However, it only

provides overall wear rate and does not contain information on local wear. In this

study, since local wear is not the main focus, weighing has been implemented to

calculate material loss.

Physical surface profile measurements measure the surface roughness of test specimens

through a solid probe before and after the wear tests. Baker et al. [38] mentioned

that a major problem of this method is that small wear could not be measured due to

irregularities of the surface finish. Therefore, it is necessary to ensure the measuring

probe passes over the exact path of the original measurement to make an accurate

wear measurement.

Optical surface profile measurements measure the local wear by comparing the optical

path difference between test surfaces and a reference surface based on the light wave

properties. Due to non-contact surface measurements, this method is good for very

smooth surfaces. Also, its ability to scan large areas reduces the time spent on surface

measurements compared to physical methods [39].

Permanent magnet gauging requires measuring the required force to separate a magnetic

probe from a coating on a steel pipe. It is suitable for local wear measurements.

However, this method is not suitable for thick coating cases and plastic pipes [38].

Electrical capacitance is a method that measures the electrical capacitance of a length

of non-conducting pipe, and a change in wall thickness will cause change in elec-

trical capacitance. However, Baker et al. [38] indicated that this method requires

considerable development due to problems with sensitivity of the measurement to

wall thickness and water absorption. Also, it has mathematically been proven that

with increase in wall thickness, the expected sensitivity will reduce. Owing to these

problems, this method does not appear to be as reliable as ultrasonic gauging for

use in field or laboratory tests.

Ultrasonic gauging measures the time taken for an ultrasonic wave to pass through the

pipe wall and return to a detector head [38]. It has an accuracy of ±2.4µm and is

suitable for local wear measurement. It can be used for metal and plastic materials

but not for composite material. The ultrasonic technique is very skill-oriented, and

12

2.4. CURRENT UNDERSTANDING OF PIPELINE WEAR

in order to generate repeatable data, the experimental procedure should be followed

meticulously and should preferably be conducted by the same operator [40].

Neutron irradiation requires radioactivating the whole of the test specimen and measu-

ring the change in radiation of the slurry, as the pipe wall is worn away. This method

could provide the desired accuracy but is not applicable to plastic materials and

requires a complicated procedure to calibrate. Moreover, it could result in safety

issues from high radiations [38].

Surface activation is similar to neutron irradiation, except that it makes the surface with

a depth of approximately 100 µm radioactive. The radiation is about 1/100 of that

required in neutron irradiation. However, this method is not applicable to plastic

materials and involves a complicated procedure to calibrate [38].

2.4 Current Understanding of Pipeline Wear

2.4.1 Slurry Erosion Mechanism

As mentioned in Section 1.3, coarse particles in a pipe tends to form a sliding bed. During

transportation, erosion wear occurs as the moving particles impact the inner pipe and

remove pipe material [3–7]. Erosive wear in pipelines results from particle-wall interaction

when local stresses exceed the yield stress of the materials at the points of contact [11].

There are three types of erosive wear process caused by different particle-wall interactions

in heterogeneous flow [11] (Figure 2.5):

1. The directional impingement of solid particles In dilute slurry flow, the velocity

component of the turbulence drives particle to the wall, leading to particle–wall

interaction and causing wear.

2. The random impingement of particles At high concentration, particle-particle

interaction and turbulent motion drive the particles to the wall, leading to particle-

wall interaction and causing wear.

3. The friction of a sliding bed pressing onto the wall The friction force comes from

the immersed weight of large particles sliding on the wall. This friction force is also

termed the Coulombic friction force, and it is related to the normal force and the

coefficient of friction.

13


(a) The directional impingement of solid particles (b) The random impingement of particles

(c) The friction of a sliding bed pressing onto the wall

Figure 2.5: Wear patterns as slurry flows through. Reproduced from Roco et al. [11]

2.4.2 Hydrodynamic Effect on Slurry Erosion Rate

Erosive wear depends on a number of interrelated parameters, such as hydrodynamics and

the properties of the erodent and target materials [7]. Many researchers [6–8, 12, 22, 27, 41]

who performed wear tests in a laboratory setting with the test devices described in

Section 2.2 developed correlations to estimate erosive wear based on particle shape,

particle size, slurry mean velocity, pipe diameter, fluid viscosity, and the properties of the

target material. For example, Gandhi et al. [12] performed experiments in a slurry pot

at various solids concentrations, particle sizes, and velocities, and demonstrated that the

wear increased with increasing solids concentration, particle size, and velocity. They also

concluded that the dependence on velocity is comparatively much stronger than either

solids concentration or particle size. Another example is that of Elkholy [41], where a

systematic study was conducted on abrasion wear in slurry pumps, revealing that wear

is dependent on velocity, solid concentration, particle diameter, impingement angle, and

relative hardness between the particle hardness and eroded material. In many wear studies,

researchers have derived correlations for the prediction of wear rate, and the general form

of their correlation is:

Ew = Kvas db

50Ccs (2.1)

where Ew is wear rate in mm/year, K, a, b and c are the constants whose values depend

on the properties of the material and solid particles. Table 2.1 lists of some values for these

parameters from past studies. It is evident that velocity would have the most impact on

14


wear rates, whereas wear rate would be influenced least by particle size and concentration.

Table 2.1: List of power index from past study

Study Test Device Velocitya

Diameterb

Concentrationc

Notes

Guptaet al. [6]

Slurry pot 2.52.15

0.290.34

0.520.56

For brassFor mild steel

Gandhiet al. [12]

Modifiedslurry pot

2.56 0.85 0.83 Test specimenwas placedtangential to theflow to achieveparallel flow

Karabelas[42]

Pipe loop(3.56 cm ID)

2.322.843.27

— — Top of pipeMiddle of pipeBottom of pipe

Elkholy[41]

Jetimpingement

2.874.83

——

0.616

——

0.682

Cast ironAluminumVarious materials

Jamesand

Broad[13]

Closed loop 0.61.01.2

For 2 m/sFor 4 m/sFor 6 m/s

2.4.3 Relationship between Slurry Friction and Erosion Wear

The importance of studying slurry friction in predicting wear rate has been discussed in

Section 1.3. To better understand slurry friction for pipe flow, the SRC two-layer model is

introduced here. Also, a pipe loop study that relates slurry friction and wear rates will be

discussed to reinforce the possibility of such study in the TWT.

2.4.3.1 Two Layer Model

In order to understand the relationship between slurry friction and erosion wear, it is

critical to understand slurry friction in the pipe. The SRC two-layer model is a very useful

model for predicting slurry friction in a pipe, and it will be used in this study. Generally,

as indicated in Figure 2.6, this model divides solids into two groups [43]: (1) fine particles,

which are those suspended in the water due to fluid turbulence (also called suspended

load); (2) coarse particles, which transmit a portion of their immersed weight to the pipe

wall (also called the contact load). Both of these components contribute to the friction

losses in the pipe. The two-layer model divides these friction losses into 2 groups:

Kinematic friction The velocity-dependent friction caused by the fluid phase and the

15


impact from suspended particles. This friction strongly depends on velocity.

Coulombic friction When the bed slides along the pipe wall, a friction force between

solids and the wall will be generated, which is termed Coulombic friction. The value

of Coulombic friction depends on the weight of the bed that is partially transmitted

to the pipe wall (i.e. a normal load).

Figure 2.6: Idealized velocity distributions and concentration distributions used in themodel. Adapted from Gillies et al. [43]

Shook and Roco [44], for example, show that the by analysis of the geometry of

Figure 2.7, an expression for the Coulombic friction force due to the sliding bed can be

expressed as:

Ff =µsg(ρs − ρ f )D2

pLCpack(sin(β)− β cos(β))

2(2.2)

where Ff is the Coulombic friction force caused by the sliding bed, µs is coefficient of

friction, g is gravitational acceleration, ρs and ρf are the density of the solid and fluid

respectively, Dp is diameter of the pipe, L is the wetted length of the sliding bed, Cpack is

the packing fraction of the sliding bed, and β is the angle defined in Figure 2.7.

The idealized concentration and velocity profiles are shown with dashed lines in

Figure 2.8. In reality, both concentration and velocity change gradually from the top to the

bottom (refer to the solid line in Figure 2.8. Even though the actual particle concentration

distribution and velocity profile (Figure 2.8) are quite different than the ideal case, the

SRC two-layer model works very well in predicting pressure loss in the pipeline. Based

on Equation (2.2), the Coulombic friction could not be directly influenced by velocity and

particle size; but in reality, both velocity and particle size will influence the contact load

fraction (the difference between C1 and C2).

16


Figure 2.7: Cross section of a circular pipe

Figure 2.8: Actual velocity distributions and concentration distributions for slurry flow(solid lines) and the two-layer model (dashed lines). Adapted from Sadighian [5]

17


2.4.3.2 Slurry Friction Study in Pipe Loop

Sadighian [5] performed a quantitative study in a pipe loop and observed that the erosion

wear increased logarithmically with slurry friction, especially friction due to solid particles

(details are discussed in Section 1.3). He has proposed a model to predict the wear rate by

correlating the solids particle-pipe wall stress:

Ew = Ew,0 + k ln(

dP/dz(dP/dz)0

)(2.3)

where Ew is wear rate in cm/year, Ew,0 is the baseline wear rate (acquired experimentally)

in cm/year, k is a constant whose value depends on the type of the solid particles and

pipe material, (dP/dz) is solids pressure gradient inside the pipe in Pa/m, (dP/dz)0 is

the baseline solids pressure gradient inside the pipe in Pa/m (which is the solids pressure

gradient associated with the baseline wear rate).

Based on his experimental data shown in Figure 2.9, k values are 1.05 and 3.26 cm/year

for aluminum oxide and carbon steel respectively. Sadighian [5] validated his model

with existing wear data. For example, he used the data from McKibben [45] in a vertical

loop and Shook et al. [46]. His proposed model and validation results provide significant

confidence on developing a relationship between the Coulombic friction and the erosive

wear rate in a TWT.

Figure 2.9: Correlation of erosion rate with solid pressure gradient (with best fit line),adapted from Sadighian [5]

18

2.5. TOROID WEAR TESTER (TWT)

2.5 Toroid Wear Tester (TWT)

As mentioned in Section 1.2, the TWT has numerous advantages, which include lesser ma-

terial requirements and lesser particle degradation than pipe loop. In addition, compared

to other lab-scale wear testers (i.e. slurry pot, jet impingement tester, and Coriolis tester),

TWT allows the formation of sliding bed (Figure 1.1), allowing the study of contact-load-

dominated wear. In order to properly understand the flow in the TWT and to interpret

wear results, it is necessary to review its history and more recent developments.

2.5.1 Historical Studies

The first use of a TWT was by Worster and Denny [47] in 1955, who termed it a "ring pipe"

and used it to study the degradation of coal travelling through a pipeline. Their TWT

was 4 feet in diameter and had a 6-inch square pipe section with the front face made of

acrylic, allowing the water flow and the coal to be observed. About three-quarters of the

pipe was filled with water and a sample of coal particles (0.91 kg or 1.36 kg weight). They

observed that when the ring was rotating, the water and coal remained approximately

stationary at the bottom, with the linear velocity similar to that of horizontal pipe flow

(Figure 2.10). Traynis [48] studied the hydraulic drag of slurry, particle degradation, and

pipeline wear using three pipe rings. One of the pipe ring was made of glass, to allow

observation of the water flow. One ring had a wheel diameter of 1 m and a 100-mm square

pipe section. The other two pipe rings were made from 200 mm and 300 mm steel pipes

with wheel diameters of 2.6 m and 5.0 m respectively. In the degradation study, Traynis

[48] showed that the amount of fine fraction of coal that formed in horizontal pipes and

the pipe rings was nearly identical. Thus, Traynis [48] concluded that the pipe ring was a

suitable apparatus for simulating pipeline wear based on the agreement between hydraulic

drag and coal degradation in the pipe ring and straight pipe.

Figure 2.10: Part of ring pipe used for measuring coal degradation. Reproduced from Wor-ster and Denny [47]

19


Henday [16] developed a toroidal wheel at the British Hydraulics Research Association

(BHRA) for simulating the wear in straight pipes. The wheel was made of five straight pipe

sections connected by bends with a diameter of 3.2 m, as shown in Figure 2.11. Henday

[16] noticed that wear distributions produced in the toroidal wheel were similar to those

found in real pipelines, as mentioned by Cooke et al. [3] in their review of the TWT. More

importantly, he showed that particles degrade less in both axially rotating pipe and BHRA

toroid wheel than in a recirculating pipe loop. The particle size was found to reduce from

12.5 mm to 9.5 mm in a 100-hour wear test. In a recirculating pipe loop, the particle size

reduces from 12.5 mm to 8.5 mm after a 5-hour test.

Figure 2.11: Demonstration of BHRA’s toroid wheel. Reproduced from Henday [16]

Gillies et al. [49] investigated suitability of heavy oil-in-water emulsions for pipeline

transportation, and used a rotated pipe toroid to simulate the shear process, which

accompanies pipeline flow. Specifically, they measured the applied torque at constant

speed to obtain the shear stress and further investigate the effect of surfactant concentration

on emulsions. The study provided a good example of measuring applied torque on a

rotating wheel, which can be expressed as:

T = τwπDLeR + T0 (2.4)

where T is the applied torque, τw is wall shear stress exerted by the emulsion, D is the

internal diameter of the pipe, Le is the length occupied by emulsion, R is the radius of the

20


toroid, and T0 is torque exerted by external friction forces. This equation is also a good

resource in this study, since it demonstrates mathematically how shear stress is related

to applied torque, which will be helpful while relating Coulombic friction with applied

torque.

2.5.2 Recent Work

In a study by Cooke et al. [3], a small-scale TWT was designed by Paterson and Cooke

Consulting Engineers (PCCE) (Figure 2.12). The wear tester consisted of four square

cross-section toroids mounted on a shaft and driven by an electric motor. Four flat wear

plates were mounted on each toroid using clamps with a polyurethane foam gasket sealed

in between. One major advantage of PCCE’s TWT was that flat wear sample plates were

used, making it is unnecessary to obtain samples of pipe with the correct curvature.

As mentioned in Section 1.2, particle degradation in a recirculating system significantly

reduces particle abrasivity and further reduces the wear during the test. This issue needs

to be taken into account when determining the absolute wear rate. Cooke et al. [3] had

developed a method using slurry replacement interval (SRI) to account for the effect of

particle degradation, then compared with actual field data. The slurry replacement interval

(SRI) defines as how long to replace fresh slurry in TWT. The predicted wear rate for a 100

mm polyethylene pipeline conveying -8 mm quartz tailings was 18.1 mm/year, which is

very close to the actual wear rate (19.3 mm/year).

Figure 2.12: PCCE pipeline wear tester. Reproduced from Cooke et al. [3]

Recently, a modified version of the toroid wheel design of Cooke et al. [3] was fabri-

cated in the Pipeline Transport Processes Research Group at the University of Alberta.

The modified design was used in this study and will be discussed in Section 3.3.1. A

preliminary study was performed by Sarker [7]. Owing to the importance to the present

21


work, the major results from that study are reported below.

2.5.2.1 Flow Visualization in TWT

An Acrylic Toroid Wheel (ATW), similar in dimension to the actual TWT, was used to

reproduce and qualitatively observe the exact flow situation inside the non-transparent

TWT. A typical snapshot of the flow in the ATW is given in Figure 2.13. Sarker [7] observed

that as the wheel speed went beyond 90 RPM (2.9 m/s), a 0.250 mm sand slurry was

carried along the outer wall to the downstream side due to the drag force and all the way

to the upstream side, as shown in Figure 2.14. Therefore, he suggested 90 RPM should be

the upper velocity limit for TWT operation.

He also observed that a sliding bed of particles formed at the bottom at low speeds

(Figure 2.15a). As the speed increased, the flow regime changed from sliding bed to

fully dispersed particles (Figure 2.15b), making the water opaque. Particles become

completely suspended with speeds beyond 60 RPM for small particle (i.e. 0.250 mm Sil 1

in Figure 2.15c). Whenever most of the sand particles are concentrated in the lower layer of

the TWT, it is termed a fully settled case. When a significant portion of the sand particles

disperse in the water at 40 RPM, it is termed as partially settled or partially suspended

case. When all the sand particles disperse in the water, it is termed fully suspended case.

For 0.250 mm Sil 1, the wheel speeds corresponding to these regimes are: (1) N < 20 RPM:

Fully settled, (2) 20 RPM < N < 60 RPM: Partially settled, (3) N > 80 RPM: Fully suspended.

He also observed that the solid particles at the bottom layer would be in contact with the

rotating ATW and move slowly in the direction of the rotation and tumble back into the

middle of the channel at the air-water interface on the downstream side. This occurs for

all the sand particles. In fact, it is worse for smaller ones. Therefore, the relative velocity

between the settled particles and the rotating ATW was not identical to the relative velocity

of a moving sliding bed of particles found in an actual stationary pipeline.

Figure 2.13: Position terminologies for the ATW. Reproduced from Sarker [7]

22


Figure 2.14: Slurry carry-over observation (in monochrome) study in ATW; d50= 0.250 mm,Cs= 30%, N= 95 RPM. Reproduced from Sarker [7]

(a) 10 RPM (b) 40 RPM

(c) 90 RPM

Figure 2.15: Flow observation for 0.250 mm sand at 10% concentration by volume

23


2.5.2.2 Parametric Study of Erosive Wear using the TWT

To verify that TWT is valid for pipeline wear study, it was necessary to ensure that the

results using this TWT, namely the parameters for the general wear model in Equation

(2.1), were consistent with previous results reported in Section 2.4.2. Sarker [7] found

that the average value of the power index for velocity, a, was 2.4. The power index for

concentration, c, varied between 0.30 and 0.37. These indices were close to the ones

discussed in Section 2.4.2 but with some discrepancy. For example, the power indices

for velocity in Gandhi et al. [12] and Gupta et al. [6] were 2.56 and 2.15 (for mild steel)

respectively, while Sarker [7] found a value of 2.4 in the TWT. Sarker [7] suggested the

discrepancy was due to different flow hydrodynamics and the properties of target material

and particles. An example of different flow hydrodynamics would be that of Gandhi et al.

[12] and Gupta et al. [6], who used slurry pots that did not allow the formation of sliding

bed. Overall, he concluded the TWT had the potential to the simulate slurry pipeline wear

mechanisms.

2.5.2.3 CFD Analysis of the Hydrodynamics of an Air-Water Multiphase System in a

Rotating Toroid Wheel

To better understand the flow within the TWT, Sarker [7] performed a Computational

Fluid Dynamics (CFD) analysis of an air-water multiphase system inside the rotating

toroid wheel for predicting the velocity field and wall shear stress distribution in the

water domain. Figure 2.16 defined different locations inside the rotating toroid domain

(clockwise direction). The velocity profiles were shown in Figure 2.17 based on different

RPM. In Figure 2.17, the velocity near the wall was positive, which means the water flows

in the same direction as the rotation. The velocity in the middle was negative, which

means the water flows opposite to the direction of rotation. This phenomenon was referred

to as back flow. The back flow not only happened for all the positions from downstream

to upstream at high speed (refer to Figure 2.18), it also occurred at all wheel speeds (refer

to Figure 2.17).

24


Figure 2.16: Data locations considered in the toroid domain. Reproduced from Sarker [7]

Figure 2.17: Comparison of water velocity profiles at Position 0 for N = 30, 60 and 90 RPM.Reproduced from Sarker [7]

25


Figure 2.18: X-direction water velocity profiles at different angular positions, N= 90 RPM.Reproduced from Sarker [7]

2.5.2.4 TWT Results vs. Recirculating Pipe loop Results

Sarker [7] performed wear tests on 0.425 mm sand particles in the TWT at 60 RPM (1.9

m/s), and the absolute wear rate was calculated using the method in Cooke et al. [3]. The

comparison between the pipe loop [5] and the TWT are shown in Figure 2.19. It was very

clear that the two results had large deviations. Sarker [7] suggested that the difference in

relative velocity between sliding bed and wall in pipe loops and TWT cause the deviation.

Also, he noticed that due to different hydrodynamics, such as the back flow in the TWT,

the contact loads would be different, leading to the deviation. Therefore, he suggested

comparing the wear results based on Coulombic friction.

26

2.6. SCOPE OF THE PRESENT STUDY

H

Figure 2.19: Comparison between the pipe loop experiment and the TWT results.Reproduced from Sarker [7]

2.6 Scope of the Present Study

From the literature review, the motivations for the current study are:

• No accurate model to predict wear rate has been developed yet due to the complexity

of the nature of wear in slurry pipelines.

• The sliding bed has significant effect on wear rate, and a past pipe loop study has

shown the Coulombic friction of that bed is helpful for predicting wear rate (refer to

Section 1.3, and Section 2.4.3.2).

• The TWT has proven to be a promising apparatus to study contact-dominated wear

• An agreeable comparison between TWT and pipe loop results will be required to

predict the wear in actual pipeline using TWT.

Even though the versions of the TWT have been used since 1955, very few studies on

Coulombic friction have been performed in the TWT. The lack of Coulombic friction data

is a major obstacle in developing a relationship between Coulombic friction and erosion

wear rate. To fill the gap, it is necessary to first obtain the Coulombic friction. Based on

Gillies et al. [49] work (refer to Section 2.5), measuring applied torque and converting into

the Coulombic friction seems a good approach to obtain Coulombic friction value, since

(1) the wheel rotates at axial direction, and (2) when at constant speed, the sliding bed

27

2.7. RESEARCH OBJECTIVES

is relatively stationary at the bottom, leading to steady states, and (3) the torque is the

product of force and distance which easy to convert from torque to force. To measure the

applied torque, a torque sensor was used.

2.7 Research Objectives

In view of all of the studies discussed in this chapter and the needs of wear rate modeling

for slurry pipelines, the detailed objectives of this work are the following:

Determine the effect of TWT hydrodynamics conditions on sliding bed friction

• Torque sensor selection, including the use of a case study to forecast performance

before purchasing. The purpose of forecasting the torque sensor performance is

to balance the capacity and the accuracy of the sensor, since a torque sensor with

low capacity could provide high accuracy and resolution, but with high chance of

overload the sensor; whereas, high capacity could reduce the chance of overload, but

it has low accuracy and resolution.

• Performance evaluation (i.e. commissioning and data repeatability) on torque sen-

sor system after installation. Generating reasonable and constant signal output is

essential to this study, since the Coulombic friction will be converted from the torque

value.

• Investigate the effect of solid concentration, flow velocity, and particle size on the

applied torque. Since no research has been conducted on investigating the effect, it

would be helpful to perform this fundamental study.

Develop a relationship between slurry friction and erosive wear rate in the TWT

• Convert from torque to Coulombic friction. It is a very important process in this

study, since the major objective is to relate the Coulombic friction with erosive wear

rate, and one of the major parameters is Coulombic friction.

• Collecting corresponding wear data which allows for Coulombic friction to erosion

relationship development.

28

Chapter 3

Experimental Method

3.1 Introduction

Based on the research objectives in Section 2.7, a torque sensor was need to measure the

applied torque on the TWT; therefore, a torque sensor system was developed and installed

on the TWT. The detailed information regarding the torque sensor and the overview of the

system is described in Section 3.3.2. Also, Section 3.3.1 describes a brief overview of the

TWT that was used in this study. The detailed information of particles and test materials,

including properties and suppliers, are shown in Section 3.2. The experimental procedures

regarding erosion wear tests and torque measurements are presented in Section 3.4. At the

end, a torque experimental matrix that studies the effect of hydrodynamic conditions on

Coulombic friction is described in Section 3.5 with description of wear tests matrix.

3.2 Materials

3.2.1 Particles

Different particle sizes, ranging from 0.125 mm to 2 mm, were used to understand the

hydrodynamic effect on Coulombic friction. The average particle size in this study is

defined as the mass median particle diameter (d50). Table 3.1 lists the detailed properties

and suppliers of the particles.

29

3.2. MATERIALS

Table 3.1: Properties and suppliers of particles used in this study.

Product Name Manufacturer/Supplier Density (kg/m3) d50 (mm)LM 125 Lane Mountain Company

2650

0.125Sil 1

Target Products Ltd.

0.250Sil 4 0.420Silica Gravel 1.0Silica Gravel 2.0

3.2.2 Chemicals

During the torque measurements and wear tests, a gasket with lubricant was applied

between the test materials and the TWT to avoid slurry leakage (See details in Section 3.3.1).

In order to clean the test materials and obtain the wear properly, several cleaning agents

were used; acetone, a multi-purpose cleaning liquid, and toluene were used in this study,

and the properties and suppliers are listed in Table 3.2. An oxygen scavenger was also

used to reduce the level of dissolved oxygen in water and prevent corrosion in the wheel.

The oxygen scavenger used here was HYDROGUARD® I-15 (HG), which contains the

following: water, isopropylhydroxylamine, acetone oxime, and 2-Nitropropane. The details

are also listed in Table 3.2.

Table 3.2: Properties and suppliers of chemicals used in the this study. Entries 1-3reproduced from Sarker [7].

Name Supplier Properties Classification

Fisherbrand Versa – CleanTM Fisher ScientificOdourless,orange in colour

Eye irritant,WHMIS class: D

Acetone, ReagentPlus, ≥99% Sigma-Aldrich

Sweet odour,clear colourlessliquid,volatile

Highly flammable liquid,eye, and nose irritant,WHMIS class: B2, D2B

Laboratory Grade Toluene,Fisher Chemical

Fisher ScientificAromatic,Clear colourlessliquid

Flammable liquid,very toxic,Skin and nose irritant,Storage Code: Red,WHMIS class: B2, D2A, D2B

HYDROGUARD® I-15,Hydroxylamine

Angus ChemicalCompany

Pungent odour,clear colourlessliquid

Nose irritant,WHMIS class: D

30

3.3. EQUIPMENT

3.2.3 Test Materials

In order to retain consistency of the wear data, the test materials that were used for wear

tests were the same as the one in Sarker’s [7] study. The material was made of hot-rolled

ASTM A572 GR50 carbon steel and was purchased from U.S. Steel Canada Inc. The

material was processed into small plates (coupons) with dimensions of 8.0 mm × 100

mm × 80 mm. Detailed chemical composition and mechanical properties are listed in

Appendix A.

3.3 Equipment

3.3.1 Toroid Wear Tester (TWT)

Toroid wear tester (TWT) was built and installed in the Pipeline Transport Processes

Research Lab at the University of Alberta. The TWT used in this study was the same

apparatus as in Sarker’s [7] study along with some modifications. This section will focus

on a brief description of the TWT, and more details can be found in Sarker [7].

3.3.1.1 Overall TWT Description

In Figure 3.1, the TWT consists of four wheels (wheel A, B, C and D), where wheel A,

B, and C have same dimensions, were used in this study. The dimensions are listed in

Table 3.3. Also, in order to observe the flow pattern inside the wheel, a removable acrylic

wheel is attached to the TWT that has same dimension as wheel A to C. All wheels are

mounted to a shaft with a diameter of 38.1 mm and connected to a motor with 3 hp

through a timing belt pulley. In order to maintain the wheel’s rotation at constant speed, a

variable frequency drive (VFD) was used and connected with a computer so that the speed

could be controlled through a software.

Table 3.3: Dimension of wheel A, B and C

Dimensions Wheel A to COuter wall diameter (mm) 608Flow channel height (mm) 60Flow channel width (mm) 65

31

3.3. EQUIPMENT

Figure 3.1: Schematic of key elements of toroid wear tester

3.3.1.2 Single Wheel

For each wheel, there are 5 open windows at the outer circumference, which are named

“coupon windows." (Figure 3.2). The coupons are attached to the coupon window by

coupon holders (Figure 3.3), and the test surface faces are placed toward the coupon

window. A gasket made of rubber and fibre is placed between test coupons and the

coupon window with an additional layer of lubricant to avoid water leakage. Each wheel

has a nitrogen purging and air release port (Figure 3.4). They are placed 180 degree apart

on each wheel to help drive out the remaining air that comes from the gap above the water,

helping avoid corrosion in the wheel.

Figure 3.2: Demonstration of coupon windows on toroid wheel

32

3.3. EQUIPMENT

Figure 3.3: Demonstration of coupon holders

Figure 3.4: Schematic of N2 purging in the TWT

33

3.3. EQUIPMENT

3.3.2 Torque Sensor System

3.3.2.1 Key elements

As mentioned in Section 2.6, the objective in this study is to relate Coulombic friction with

erosion wear rate. The optimum method of obtaining the value of Coulombic friction is

to measure the applied torque on the wheel. Therefore, a torque sensor was selected to

measure the torque applied on the toroid wheel. The key elements are listed in Table 3.4.

Table 3.4: List of torque sensor system in the present study

Name Supplier Description

Torque SensorFUTEKAdvancedSensor Technology, Inc

Capacity: 20 N.m,Non-contact shaft to shaft rotary,With encoder,16 mm shaft

Analog Amplifier

External USB output kit,24-bit resolution,up to 19 bit noise free,Up to 4800 sps

Customized CouplingsCapacity: 80N.m,Diameter: 16 and 38.1 mm

Cable12 Pin Binder,3.05 m long

3.3.2.2 Torque Sensor Installation

In order to measure the applied torque, the TWT was modified to allow the torque sensor

to be installed between the motor and the wheel, allowing it to measure the amount of

torque that the motor provides to the wheel. The schematic figure (Figure 3.5) demon-

strates where the sensor is installed. Since the shaft in the torque sensor has different

diameters (38 mm vs. 16 mm), with the central shaft in the TWT, customized couplings

are required to connect the two shafts together. Additional bearings (i.e. bearings 3 & 4)

are required to avoid unwanted motions (i.e. off-axis rotation). The complete assembly

is shown in Figure 3.6. The figure shows a frame supporting four wheels, and the motor

provides torque to the wheel through the timing belt and pulley drive. After modification,

the entire TWT is approximately 1.8 m long, 0.9 m wide, and 1.1 m high. A close view of

torque sensor system is shown in Figure 3.7.

34

3.3. EQUIPMENT

Figure 3.5: Schematic of key elements of torque sensor system

Figure 3.6: Toroid wear wheel assembly with torque sensor installed

35

3.3. EQUIPMENT

Figure 3.7: Torque sensor assembly

3.3.2.3 Data Acquisition System

The schematic of data acquisition system is shown in Figure 3.8. In order to obtain the

signal, the torque sensor is connected with an analog amplifier through a cable (mentioned

in Table 3.4). There is a strain gauge inside the torque sensor, and the analog amplifier has

an electric source with constant voltage. When both are connected together, it will form a

circuit. The analog amplifier will detect the change of electric current due to change of

resistance of the strain gauge from shaft deformation under a certain torque, then amplify

the signals, and transfer to a computer. The data is collected and stored using a MATLAB

script that interacts with a DLL provided by FUTEK. Further details of this script are given

in Appendix F.2.

Figure 3.8: Schematic of torque data acquisition system

36

3.4. EXPERIMENTAL PROCEDURES

3.4 Experimental Procedures

The major objective in this study is to relate the Coulombic friction with the erosion wear.

Wear measurements and Coulombic friction measurements are required. Since the TWT

used in this study is the same as the one in Sarker’s [7] study. The wear experiment

procedures are almost same except for the use of oxygen scavenger. A overview of wear

experimental procedure will be discussed in Section 3.4.1, and the detailed procedures

are listed in Appendix B.1. As mentioned earlier, Coulombic friction cannot be directly

measured in TWT; an alternative parameter – torque – will be measured through the torque

sensor. Therefore, torque measurement will be performed in this study, and procedures are

discussed in Section 3.4.2 while the detailed procedures are listed in Appendix B.2. Since

torque is a product of friction force and distance, if torque and distance are measured,

then it’s possible to convert torque into Coulombic friction force. In order to measure

the distance from the force acting point to the centre of the rotation, it is necessary to

observe the sliding bed inside the wheel. Therefore, flow observation images using acrylic

wheel could be helpful. A review of procedure from Sarker’s [7] study will be discussed

in Section 3.4.3.

3.4.1 Wear Measurements Procedure Overview

The overall wear experimental procedure can be summarized as the following:

1. Clean and weigh the test coupon to identify initial coupon weight (Mi).

2. Attach the test coupons to the TWT and charge the slurry.

3. Add the Hydroguard and purge N2 to remove dissolved oxygen.

4. Start the VFD and set the wheel speed in the wear wheel software.

5. Start the experiments and run for the set experiment time, replacing the slurry every

24 hours.

6. Clean and weigh the test coupon to determine the final coupon weight (Mf).

Finally, when an experiment is finished, Mi and Mf are compared to determine the amount

of wear during the experiment.

3.4.2 Torque Measurements Procedure Overview

3.4.2.1 Procedure Overview

The overall torque experimental procedure can be summarized as the following:

37

3.4. EXPERIMENTAL PROCEDURES

1. Clean the dummy coupons (The purpose of dummy coupon is only to keep the

wheel sealed and is not for wear tests).

2. Attach the coupons to a single wheel and charge the slurry.

3. Start the VFD and set the wheel speed in the wear wheel software.

4. Start the experiments.

5. Collect torque data for 2 minutes for one set and collect as many sets as possible

until the discrepancy of the mean torque value between the last two sets is less than

0.005 N.m, then get the average torque value base on last two sets.

3.4.2.2 Sand-related Torque

When the wheel rotates at constant speed, the torque measurements are at steady state

condition. There are several contributions to the total torque that need to be considered:

Friction-related torque Since the wear wheels are connected together through a shaft,

and the shaft is supported by four bearings, the bearings will generate friction torque

when the wear wheels rotate.

Water-related torque When only water is added to the TWT, it requires additional torque

against the hydrodynamic friction. This amount of torque caused by the presence of

water is termed water-related torque.

Sand-related torque When slurry (water and solid particles) is added to the wear wheels,

it requires additional torque based on water-related torque against the particles. This

additional amount of torque caused by the presence of particles in the slurry is

termed sand-related torque.

Since four wear wheels are located in between the two bearings, no matter how friction

caused by the particles is measured, the measurements will always incorporate the friction

force caused by the bearings. The way to isolate the sand-related torque is to measure

the total torque for a slurry (solid-water mixture) and the total torque for water only. The

difference will be sand-related torque. The reason to compare to the wheel that contains

water only is that as the wheel rotates, there is a hydrodynamic friction caused by water.

In order to account for this amount of torque, the best way is to compare torque for a

slurry (solid-water mixture) and the torque for water only. This approach is similar to the

isolation of solids-related pressure drop used by Sadighian [5].

38

3.5. EXPERIMENTAL PROGRAM

3.4.3 Sliding Bed Observation using an Acrylic Toroid Wheel

An acrylic toroid wheel was attached to the TWT to observe the sliding bed formation and

measure the sliding bed geometry for all test conditions. The procedure was developed by

Sarker [7], and a brief review is listed below:

1. Attach the ATW to the TWT.

2. Charge the calculated amount of slurry

3. Start the wheel

4. Run the ATW for around 3 minutes to allow particles and water to achieve equili-

brium before any observations.

5. Take video recordings and still images of the ATW’s flow.

3.5 Experimental Program

3.5.1 Torque Measurements

As mentioned in Section 2.4.3, velocity, concentration and particle size have strong effect

on Coulombic friction in the pipe. To be sure, those parameter could also influence the

Coulombic friction in TWT and further influence the torque value. The study of Coulombic

friction in TWT is very new, and there is no quantitative data to help understand the effects

of hydrodynamic conditions on Coulombic friction in TWT. Therefore, it’s necessary to

perform a parametric study of Coulombic friction against hydrodynamics. Considering

Equation (2.2), the value of Coulombic friction force primarily depends on the amount of

particles concentrated in contact load. There are several parameters influencing the amount

of particles that concentrated in contact load. First, if the solid volume concentration is

larger, the Coulombic friction is expected to be bigger. Also, since the particles are

immersed in water, as the rotation induces flow in the TWT, flow turbulence would carry

the particles through the water and thus cause the change the contact-load fraction that

depends on the particle size and the wheel speed. Therefore, the value of Coulombic

friction depends on the combination of concentration, particle size, and wheel speed. In

order to describe the relationship between TWT hydrodynamics and Coulombic friction, it

is necessary to isolate each of these effects. The best way is to change one parameter and

keep the rest unchanged. Therefore, the investigation between TWT hydrodynamics and

Coulombic friction further breaks apart into three sections as discuss below.

39


3.5.1.1 Concentration

The principle effect of concentration in the TWT is a change in the size and shape of the

sliding bed. And understanding how this bed reacts to different TWT speeds is important

in understanding Coulombic friction. However, it has been found from Sarker’s [7] study

that, as speed goes up, more particles will be lifted up by water turbulence, reducing

the particle contact-load fraction. Also, refer to Figure 3.9b, Sarker [7] has found that

large particles (2 mm gravel) concentrated in the lower layer even at relatively high speed

(60 RPM), and the geometry of sliding bed remains similar compared with one at low

speed (Figure 3.9a). Therefore, in order to isolate the effect of concentration on Coulombic

friction at different speeds, large particle sizes are chosen to reduce the change of contact-

load fraction due to velocity as much as possible. Considering Equation (2.2), the value

of Coulombic friction force should be independent of particle size; consequently, 1 mm

gravel are chosen to validate the effect found on 2 mm gravel. The experiment matrix is

listed in Table 3.5.

(a) 30 RPM (b) 60 RPM

Figure 3.9: Sliding bed observation for 2 mm gravel; Cs = 15%

Table 3.5: Experimental matrix for torque against concentration

Particle Size (mm) Solid Volume Concentration Wheel Speed2

10%, 15%, and 20% 10 to 60 RPM1

3.5.1.2 Wheel Speed

As mentioned in Section 2.5, there are three cases (fully-settled, partially settled, and

fully-suspended) as speed goes up. The reason why particles are increasingly suspended

at higher speed is because increasing turbulence levels bring more particles to suspension.

Thus, to investigate the effect of wheel speed, a medium-sized sand particle (0.25 mm Sil

1) was chosen. As Figure 3.10 shown from Sarker’s [7] study, Sil 1 not only concentrated

40


in contact load at low speed (10 RPM), but is also fully suspended at high speed (90

RPM). The experiment matrix is listed in Table 3.6. Sil 4 (0.420 mm) sand particles were

selected to verify the effect for Sil 1. Even through Sarker [7] suggests not to run the wheel

beyond 90 RPM, it is necessary to operate at 100 RPM in order to achieve fully suspended

condition for 0.45 mm Sil 4. Carry-over is not significant when the Sil 4 particles are in

the water. Lane Mountain (0.125 mm) particles were used to explore the happenings for

fully-suspended conditions if the wheel speed goes high. A hypothesis would be that the

sand-related torque become larger as the wheel speed goes higher, since at higher speed,

rapid turbulence will drive more particle-particle and particle-wall collision inside the

wheel. During each collision, kinetic energy of the sand particle will dissipate as heat.

(a) 30 RPM (b) 60 RPM

Figure 3.10: Sliding bed observation for 0.25 mm Sil 1; Cs = 10%. Reproduced from Sarker[7]

Table 3.6: Experimental matrix for torque against velocity

Particle Size (mm) Solid Volume Concentration Wheel Speed0.25

10%, 15%, and 20%10 to 90 RPM

0.42 10 to 100 RPM0.125 10 to 90 RPM

3.5.1.3 Particle Size

Sarker [7] also found that smaller particles are more like to be suspended in the water

than larger particle. Under the same velocity, different particle size would results in

different contact-load fraction, which would further lead to different Coulombic friction

and torque value. Therefore, to understand the effect of particle size on Coulombic

friction, five particle sizes have been selected, keeping the same operating conditions (solid

volume concentration and wheel speed). The experimental matrix is listed in Table 3.7.

A concentration of 15% was chosen for these tests since it provides sufficient difference

on Coulombic friction. 20% volume concentration would be too much, since it would not

41


allow fully suspended conditions without going over the carry-over limit.

Table 3.7: Experimental matrix for torque against particle size

Particle Size (mm) Solid Volume Concentration Wheel Speed2

15% 60, 90 RPM10.420.250.125

3.5.2 Wear Tests

The main objective of this study is to relate Coulombic friction with erosive wear rate.

Thus, corrosion should not occur during wear tests. To achieve purely erosive wear, N2

purging and Hydroguard were used to reduce the dissolved oxygen present in the slurry

and in the air gap. All experiments were conducted by keeping DO level under 0.1 ppm.

The ideal plan is to conduct all the wear tests posted on torque measurements. However,

due to the nature of the TWT, only one wheel speed can be set during the period of test (96

hours), and considering time-effectiveness, it’s impossible to run all the tests. Therefore,

wear experiments are selected based on contact-load fraction. For example, 15% 2 mm

gravel at 60 RPM had been chosen since most of the particles are concentrated in contact

load. 15% 0.25 mm sand at 90 RPM had been chosen since all the sands are suspended in

the water. As mentioned in Section 2.5.2, the slurry replacement interval (SRI) defines as

how long to replace fresh slurry in TWT. The SRI in this study is 24 hours. A summary of

experiment matrix is listed in Table 3.8

42


Table 3.8: Experimental matrix for wear measurements

Wheel Speed(RPM)

Particle Size(mm)

Solid VolumeConcentration

SRI(hour)

Test Period(hour)

30

210%

24 96

15%20%

110%15%20%

0.42010%20%

0.25010%20%

60

1 15%

0.42010%15%20%

0.25010%15%20%

0.125 15%

900.420 15%0.250 15%0.125 15%

3.5.3 Overview of Experimental Program

Overall, the test matrix to investigate the effect of TWT hydrodynamic on Coulombic

friction is selected based on contact load fraction. For example, the rough estimated contact

load fraction in concentration section (refer to Section 3.5.1.1) are shown in Figure 3.11

and Figure 3.12. The estimation method is based on visualization images. When the

slurry is clean, the estimation is based on the ratio of areas (details will be discussed at the

end of Section 5.4.2). It is very clear in Figure 3.11 and Figure 3.12 that the contact load

fraction for the chosen conditions are located near 1, which indicates that most of gravel are

concentrated in contact load and are not influenced by the water turbulence; specifically,

the water turbulence does not lift gravel. The water turbulence strongly depends on

particle size and wheel speed. Therefore, the proposed experiment matrix would help

on the investigation of concentration of Coulombic friction. Whereas, when studying the

effects of particle size and wheel speed on Coulombic friction, the water turbulence caused

43


by different size of particle and wheel speed will lift different portion of sand particles

up and change the contact load fraction differently. Therefore, the experimental matrix

should cover a wider range of contact load fraction. The estimated contact load fraction

for experiment matrix in wheel speed section (refer to Section 3.5.1.2) and particle size

section (refer to Section 3.5.1.3) are shown in Figure 3.13 and Figure 3.14 respectively. It is

very clear that the proposed experiment matrix covers conditions from fully suspended to

fully settled.

Figure 3.11: Distribution of contact load fraction for different concentrations; d50 = 1 mm.

Figure 3.12: Distribution of contact load fraction for different concentrations; d50 = 2 mm.

Figure 3.13: Distribution of contact load fraction for different wheel speed; Cs = 10%.

44


Figure 3.14: Distribution of contact load fraction for different particle size; Cs = 15%.

45

Chapter 4

Evaluation of the Torque SensorSystem

4.1 Objective

The evaluation on the performance of torque sensor system is discussed in this chapter. In

particular, the following parameters are investigated:

• Commissioning test of the torque sensor system

• Data repeatability

The objective of the commissioning part is to test where the sensor could generate a

reasonable signal output. During the commissioning tests, it is expected that the torque

value is constant at constant wheel speed, indicating a flat signal output. However, huge

signal fluctuation (from -1 to 10 N.m) had been found during the tests, which became

a major problem. The reason that causes the signal fluctuation is unwanted noise. The

details of this noise as well as the solutions used to overcome the issues are discussed in

Section 4.2.1. The accuracy of the measured torque value is essential in this study, since

the estimation of the Coulombic friction is derived from the torque value. The sensor was

calibrated by the factory, so the objective of the calibration in this section is only to verify

that the factory calibration is reasonable. The data repeatability part is to verify whether

the torque sensor could generate repeatable output between wheels and tests. At the end,

the conclusion is made based on the results, and the details are shown in Section 4.4.

46

4.2. COMMISSIONING TESTS

4.2 Commissioning tests

4.2.1 Signal Filtering

After the torque sensor system was installed on the TWT, a smooth operation was attemp-

ted and the torque data was collected for 120 seconds. The torque signal is shown in

Figure 4.1. It was operated for 15% 2 mm gravel at 60 RPM. As mentioned in Section 2.6,

when the wheel operates at constant speed, it achieves steady state condition, which

should provide a flat torque signal. However, it is clear that the signal fluctuates in the

figure. Four reasons for the fluctuations were identified:

Wobbling The wobbling mainly occurs from the mechanical couplings, since the couplings

were very sensitive to small misalignment in order to prevent the torque sensor from

damage. It has been observed that a small degree of misalignment appears in the

couplings. The amplitude of the wobbling is about 0.4 mm. The wobbling causes the

flat torque signal to oscillate, and the oscillation repeats with every rotation. This

noise is at the same frequency as the TWT operating speed.

Imbalance of the TWT The TWT is symmetric along its rotational axis, and ideally, the

centre of mass of whole TWT should be located on this axis, so that the angular

position does not affect the torque reading. However, the TWT was not designed

for very tight balancing tolerances, which means that the centre of mass of the TWT

is slightly off its rotation axis. Therefore, as the wheel rotates, it generates a small

amplitude of torque oscillation at the same frequency as the wheel rotation.

Mechanical noise As mentioned in Section 3.3.1, the wheel in the TWT is driven by a

motor through a timing belt pulley. The motor that was used in the TWT is not

designed for low speeds. Thus, when the wheel is rotating at a low speed, the shaft

on the motor does not run smoothly to drive the timing belt; instead, it rotates in a

jerking motion. Therefore, the teeth on the timing belt, due to the jerking motion,

will cause periodic torque oscillation. The magnitude of this fluctuation is much

higher at low RPM (<20 RPM), and is significantly reduced for higher RPM. The

frequency of this oscillation depends linearly on the wheel speed, since the number

of teeth on the timing belt pulley is constant (36 teeth). For example, if the wheel

runs at 10 RPM (1/6 Hz), the frequency of the mechanical noise is 6 Hz.

Electrical noise The largest fluctuation source comes from the electrical noise, specifically

from the variable frequency drive (VFD). Since the frequency is directly related to the

speed in the motor, in order to control the wheel speed, a VFD is required to vary the

frequency from 60 Hz in supply power to a frequency that meets the requirements of

47


the motor’s load. The electrical circuitry that changes the output frequency generates

significant asymmetric electrical noise at many different (mainly higher) frequencies.

During constant TWT rotation, the periodic oscillation of torque signal due to wobbling

and imbalance of the TWT should not influence the mean torque significantly since

the oscillation should be cancelled out. In addition, the amplitude of those oscillation

(wobbling and imbalance) was measured statically by rotating the wheel 5 degrees each

time. The maximum oscillation amplitude was found around 0.3 N.m which is less than

10% of a typical torque signal, but the net effect should be zero. The detailed amplitude

measurements are plotted in Appendix D.

Figure 4.1: Unfiltered signal for 2 mm gravel at 60 RPM; Cs = 15%

In order to eliminate the mechanical and electrical noise, an important point has to be

considered which the frequency of both noise is much higher than the true signal frequency.

Therefore, a signal filter was used in this study to eliminate noise from the motor, signal

filtering using MATLAB, written by Dr. David Breakey, was used in this study. The

code is listed in Appendix F.1. The function of signal filter is to remove unwanted high

frequency signals. For example, if the wheel rotates at 60 RPM, the expected torque signal

frequency is around 1 Hz, and unwanted frequency is defined as three times the expected

frequency. The signal filter works by filtering the time-domain signal (the un-filtered

signal, refer to Figure 4.1) to frequency-domain signal (Figure 4.2), with a low-pass filter

48


implemented by the filtfilt and designfilt function in MATLAB. The low-pass filter

has a passband frequency (cut-off frequency) of three times the expected frequency and a

stopband frequency of 1.5 times the passband frequency. The filter used was a lowpass

finite-impulse-response filter with a stopband attenuation of 30 dB, and the maximum

passband ripple was set to 1 dB. The sample rate for the original data was 300 samples

per second (Hz), and the corresponding Nyquist frequency is 150 Hz. A typical filtered

signal in the frequency domain is also shown in Figure 4.3, and these were the signals

used for determining the mean torque value. The torque signal after filtering (refer to

Figure 4.4) then was obtained by transferring the filtered frequency-domain signal back.

The remaining fluctuation are mainly from the combination of wobbling, imbalance of

the TWT, and the non-smooth motor drive, but it is clear from the fact that the resulting

signal is nearly sinusoidal, where the mean value will not be affected by the remaining

fluctuations. Since it is this mean value that will be used in this work, this demonstrates

that the errors will not affect the present results.

Figure 4.2: Frequency-domain signal for 2 mm gravel at 60 RPM; Cs = 15%

49


Figure 4.3: Filtered frequency-domain signal for 2 mm gravel at 60 RPM; Cs = 15%

Figure 4.4: Filtered signal for 2 mm gravel at 60 RPM; Cs = 15%

50


4.2.2 Calibration

The sensor has been already calibrated from the factory, which shows a torque discrepancy

of around 2%. The purpose of this section is only to verify that the factory calibration

is reasonable. In order to verify the calibration, the following method was used. The

TWT will always experience two stages before any torque measurements: start-up and

constant-speed rotation (steady state condition). In the start-up stage, the motor provides

power to let the wear wheels accelerate and eventually reach and stay at a desired speed.

The start-up torque is the torque required to speed up the wear wheels, and torque value

is the product of the moment of inertia of the TWT wheels and how fast the wear wheels

accelerate. The equation is shown as the following:

T = Iα1 + T0 (4.1)

where T is the applied torque, I is the moment of Inertia, α1 is the angular acceleration, T0

is torque exerted by external friction forces from bearing and air.

In the equation, T0 contains the external torque from wobbling, imbalance of the TWT,

and the non-smooth motor drive. The value of T0 are shown in Appendix D. The torque

and angular acceleration can be measured from the torque sensor system, which allows

calculation of the moment of inertia using Equation (4.1) (refer as measured inertia). On

the other hand, the moment of inertia can be estimated based on the dimension of the

TWT, where contribution to the moment of inertia can be estimated by the following:

I = mr2 (4.2)

where m is the mass of an object, r is the distance between centre of gravity of the object

and the centre of the shaft.

The calibration test can be based on the comparison between measured and estimated

inertia value. Estimation of the moment of inertia of the TWT is complex, since each

part on the wheel should be considered. Instead, two test conditions were considered,

which are the TWT with and without attaching the coupons. That way, only the inertia of

several parts, such as coupons, coupon holders, and its accessories (i.e. bolts and nuts), are

required, since the torque difference between two test conditions are due to the addition

of those parts. The estimation of inertia of coupons, coupon holders, and its accessories is

significantly less complex than the estimation of the whole TWT. Therefore, the calibration

test can be based on comparing the inertia value on the test coupons. Appendix C shows

the estimation of moment of inertia in details.

In order to obtain measured inertia, the torque and the rotation angle were collected by

accelerating the wheel manually using a free weight attached by a string to the TWT. As

51


mentioned in Section 4.2.1, the electrical noise from an operating motor will interrupt the

output signal fluctuation. Even though the electrical noise was acceptable for the torque

signal, it was unacceptable for the rotation angle signal, since the angular acceleration is

calculated from the angle signal. Therefore, it is better not to use the motor as the driving

tool. A MATLAB code modified by Dr. David Breakey from a sample provided by FUTEK

was used in the calibration tests. The code is listed in Appendix F.2. This MATLAB code

collects the applied torque and rotation angle at same time. Once the rotation angle is

obtained, the angular acceleration can be calculated by the second derivative of the rotation

angle. A second MATLAB code written by Dr. David Breakey was used to process the

torque and the rotation angle measurements and obtain the measured inertia. The detailed

code is shown in Appendix F.3. In the code, it takes the second derivative of the rotation

angle by smoothing the rotation angle signal using signal filter and pairs with the torque

signal by downsampling the torque signal to the rotation angle data rates. Then, the code

performs a least-square regression with a linear fit to obtain the inertia value (Figure 4.5).

In the calibration tests, sets of three experiments were conducted for the TWT, with and

without coupons, and the average inertia value was used for comparison. The difference

between measured (0.587 kg.m2)and estimated (0.518 kg.m2) inertia value is around 12%,

which was probably caused by the change in the bearing friction with added weight. The

discrepancy is reasonable in this study, since the objective of the calibration is only to

verify the factory calibration, and 12% is not a huge difference. Therefore, the discrepancy

of 2% from factory calibration is a reasonable value.

Figure 4.5: Best fit line of moment of inertia from the measurements

52

4.3. DATA REPEATABILITY

4.3 Data Repeatability

The performance analysis was done by checking whether the torque sensor could generate

similar results between the three different wheels and between different tests. From

both results, the torque sensor system is able to generate similar torque value within 5%

difference.

4.3.1 Wheel-to-Wheel Repeatability Tests

To examine data repeatability among the wheels, sand-related torque data are collected

under three different speeds. During each test, the slurry will be filled into only one wheel

and the other two wheels are left empty without attaching any coupons. The sampling rate

is 300 samples per second (sps), and test interval is 2 minutes. The experiment matrix for

wheel-to-wheel repeatability test is listed in Table 4.1. Figure 4.6 shows the sand-related

torque value against the wheel speed for wheel A, B, and C. It clearly shows that, at each

speed, the torque values are similar for three wheels. The maximum difference has been

found about 4.5%, which leads to the conclusion that the torque sensor could be able to

generate consistent value between wheels.

Table 4.1: Experiment matrix for wheel-to-wheel repeatability test

Wheel # Wheel Speed (RPM) Particle Size (mm) Solid Volume ConcentrationA

30, 60, 90 2 15%BC

53

4.3. DATA REPEATABILITY

Figure 4.6: Data repeatability for wheel A, B, and C; Cs = 15%

4.3.2 Test-to-Test Repeatability Tests

To evaluate data repeatability among the tests, three tests under same conditions (i.e.

particle size, volume concentration, and wheel speed) were performed on different days.

Table 4.2 shows the detail of the operating condition. Figure 4.7 shows the reproducibility

of sand-related torque data for three different experiments, ‘Run #1’, ‘Run #2’ and ‘Run #3’.

The difference has found approximately 4%, 1.4%, 1.4% for 30, 60, 90 RPM respectively.

Overall, the torque sensor system could produce consistent torque value for the different

tests.

Table 4.2: Experiment matrix for test-to-test repeatability of torque measurements

Wheel # Wheel Speed (RPM) Particle Size (mm) Solid Volume ConcentrationA 30, 60, 90 2 5%

54

4.4. CONCLUSION

Figure 4.7: Data repeatability for wheel A; Cs = 5%

4.4 Conclusion

During the commissioning tests, the torque sensor was able to generate reasonable torque

signal. With the signal filter applied, the electrical noise was successfully removed from the

signal, and the remaining noise, such as wobbling, imbalance of the TWT, and non-smooth

motor drive, are shown as periodic oscillation on torque signal. Since mean torque value

was used in this study, and the amplitude of that noise was relatively small, the effects

of the oscillation were not considered as a issue when measuring the torque. The torque

sensor was calibrated and exhibited a difference of 12%, which has a discrepancy with

factory calibration (2%). It is not considered a problem either, since there could be a change

in bearing friction due to additional weight. In the data repeatability tests, it clearly shows

the torque sensor could generate similar torque value between wheels and tests. Overall,

the torque sensor is ready for collecting torque value for the experiment matrix posted in

Chapter 3.

55

Chapter 5

Results and Analysis

5.1 Introduction

This chapter primarily focuses on results and analysis, and the major results of this work

can be summarized as follows:

The effect of particle size and wheel speed on sand-related torque (Section 5.2) For a gi-

ven concentration, a well-defined trend in sand-related torque is observed, which can

be non-dimensionalized by considering the terminal settling velocity of the particles.

This potentially allows the prediction of sand-related torque for a given particle size

at a known wheel speed, and further, it helps save work on torque measurements

and then obtaining the Coulombic friction value.

The effect of concentration on sand-related torque (Section 5.3) Increasing the solids con-

centration causes increase in normal load and further the Coulombic friction force;

it is clear incremental observation on sand-related torque, which implies that the

torque measurement is a good indicator of Coulombic friction. In addition, for a

fully-settled case, similar sand-related torque at different particle size indicates that

the Coulombic friction is independent on particle size.

Converting measured torque to Coulombic friction (Section 5.4) Good agreement bet-

ween measured and estimated sand-related torque implies that the Coulombic

friction can be estimated using the torque calculation derived in this study.

Relating Coulombic friction with erosion wear rate (Section 5.5) The relationships were

developed for 30 RPM and 60 RPM, and both relationships have shown that the

erosive wear rate grows linearly with Coulombic friction.

56

5.2. THE EFFECT OF PARTICLE SIZE AND WHEEL SPEED ON SAND-RELATEDTORQUE

5.2 The Effect of Particle Size and Wheel Speed on Sand-related

Torque

As mentioned in Section 2.5, there are three regimes inside the TWT as the wheel speed

increases: fully settled (Figure 5.1a), partially settled (Figure 5.1b), and fully suspended

(Figure 5.1c). Also, the speed at which the transition occurs depends on particle size. For

example, both 2 mm gravel (Figure 5.2) and 0.250 mm Sil1 (Figure 5.1b) was operated at

40 RPM, and it was very clear that they were at different regimes; 2 mm gravel was fully

settled and 0.250 mm Sil 1 was partially settled. Based on these observations, the sand-

related torque was also expected to vary with particle size and wheel speed. Therefore,

the effect of particle size and wheel size will discussed together.

(a) Fully settled (b) Partially settled

(c) Fully suspended

Figure 5.1: Flow regimes for 0.250 mm Sil 1 at 10% concentration by volume

The effect of particle size is shown in Figure 5.3. As the speed increases, smaller

particles will suspend into the water earlier than the coarser ones. 60 RPM was selected to

make the torque value more distinct for each particle size. It is obvious that the particle

size has strong impact on sand-related torque in TWT. The reduction of sand-related

torque is due to the reduction of contact load fraction (particles in sliding bed compared

with overall particle volume fraction). With smaller particle sizes, solids are more easily

lifted up by carrier fluid turbulence, and the contact load fraction is reduced.

57


Figure 5.2: Flow observation for 2 mm gravel at 10 % concentration by volume;N = 40 RPM

Figure 5.3: The effect of particle size on sand-related torque; Cs = 15%, N = 60 RPM

To understand the effect of wheel speed on sand-related torque, several tests were

conducted at solid volume concentrations of 10%, 15% and 20%. Sil 4, Sil 1, and LM were

chosen to run at 10 to 90 RPM. Even though the carry-over occurs beyond 90 RPM (refer

to Section 2.5), the maximum wheel speed was set to 100 RPM for 10% sand concentration,

since it is necessary to cover all flow conditions: fully-settled case, partially settled, and

fully suspended. The results are shown separately, where Sil 4 and Sil 1 are in a group.

The results for 10% are shown in Figure 5.4. The sand-related torque at 10 RPM are very

58


similar for both sands, because almost all sand particles remain at bottom (Figure 5.5).

The sliding beds for both particle types are similar in geometry, which causes similar

sand-related torque. As the speed increased, it was found that more sand particles disperse

into the water (Figure 5.6a) and make the water opaque. Dispersed sand particles result

in reducing amount of solids contributing to the contact load fraction and cause the

reduction on torque value. Finally, for the high-speed region (≥80 RPM), nearly all the

sand particles are suspended (Figure 5.6b and Figure 5.6c) and make the water more

opaque. The sand-related torque values in the high-speed region (≥80 RPM) are relatively

constant, indicating a homogeneous slurry. Due to its opacity, it is difficult to determine

if a small amount of sand was left at the bottom. Slurry opacity is the major problem

when converting sand-related torque to Coulombic friction, and this will be discussed in

Section 5.4. Overall, the velocity has strong impact on sand-related torque in TWT. So far,

it is concluded that sand-related torque is strongly affected by wheel speed and particle

size. Both effects are mainly from the change of contact load fraction. The curves for 15%

and 20% show the same trend. It is the evident from the 10%, 15%, and 20% results that

the sand-related torque decreases linearly as wheel speed increases at partially settled

conditions. This observation is very helpful when estimating the Coulombic friction for

partially settled conditions and will be discussed in Section 5.4.5. From the Sil 4 and Sil 1

results, it is not clear how the sand-related torque behaves at fully-suspended conditions.

The results for LM at 10%, 15%, and 20% are shown in Figure 5.7. Both trends clearly

show that sand-related torque increases as the wheel speed increases. As mentioned in

Section 3.5.1.2, as the wheel speed goes higher, more particle-particle and particle-wall

collisions are involved, and each collision will dissipate energy, meaning more energy

would be required to drive the turbulent flow, and increased energy is revealed as an

increase sand-related torque. This graph is helpful and will be discussed in greater detail

when relating Coulombic friction to the erosive wear rate (Section 5.5).

59


Figure 5.4: The effect of wheel speed on sand-related torque; Cs = 10%

(a) Sil 1 (b) Sil 4

Figure 5.5: Sliding bed observation at 10 RPM; Cs = 10%

60


(a) 50RPM (b) 80RPM

(c) 90RPM

Figure 5.6: Sliding bed observation for Sil 1; dp = 0.250 mm, Cs = 10%

Figure 5.7: The effect of wheel speed on sand-related torque for LM; Cs = 10%, 15%, and20%

Gillies et al. [43] developed a correlation to estimate the contact load fraction in pipe

loop based on the ratio of slurry velocity to terminal settling velocity. Terminal settling

velocity measures the speed at which a particle would fall freely in an infinite, stagnant

fluid. An attempt of relating sand-related torque and the ratio of slurry velocity and

terminal settling velocity was conducted. The terminal settling velocity (v∞) is calculated

61


iteratively, using the following equation:

v∞ =

√4gd50(ρs − ρ f )

3CDρ f(5.1)

where g is gravitational acceleration, d50 is particle diameter, CD is the drag coefficient,

and ρs, ρf is the density of solid and fluid, respectively. The values for CD were taken from

the correlations for spheres based on the Reynolds number (Rep):

For Rep ≤ 0.3:

CD =24

Rep(5.2)

For 0.3<Rep ≤ 1000:

CD =24

Rep(1 + 0.15Re0.687

p ) (5.3)

For 1000<Rep<105, CD ≈ 0.445. The Reynolds number is defined as:

Rep =v∞ρ f d50

µ f(5.4)

where µf is the dynamic viscosity of the carrier fluid. The resulting values for each particle

type are given in Table 5.1.

Table 5.1: List of drag coefficient and terminal settling velocity for the sands and gravelsstudied here

Particle Type CD v∞ (m/s)2 mm Gravel 0.54 0.281mm Gravel 0.90 0.16

0.420 mm Sil 4 2.13 0.070.250 mm Sil 1 4.67 0.030.125 mm LM 19.53 0.01

The result shown in Figure 5.8 includes all the sand-related torque at Cs=10%. Note

that the x-axis is in log scale. It is also found in Figure 5.8 that for a given concentration,

the torque is constant up until a certain velocity ratio where it starts to reduce. When the

wheel rotates at low speed, fluid turbulence is not strong enough to lift particles up; all

particles remain at the bottom and form a sliding bed. As the wheel speed increases, the

particles from the sliding bed are dispersed in the water, which causes reduction of the

contact load fraction [7], leading to a reduction in torque value. The linear speed used here

is the tangential speed of TWT wall where it contacts the sliding bed. The results from

15% and 20% (Figure 5.9) also have similar trends as 10%, also three curve seems collapse

together. For this study, In addition, the remarkable feature of this plot in Figure 5.9

62


indicates the sand-related torque is only a function of sand volume concentration and the

ratio between wheel speed and terminal settling velocity which gives the possibility of

predicting sand-related torque of particles at any size and operating at any speed. The

ratio between wheel speed and terminal settling velocity is non-dimensional, which is

beneficial in comparing with different hydrodynamic systems. For example, it gives the

possibility of compare with data from pipe loop (i.e. data in Gillies et al. [43]) using the

non-dimensional parameter.

Figure 5.8: Sand-related torque for a variety of particle types with respect to ratio of TWTspeed to particle settling velocity; Cs = 10%

Figure 5.9: Sand-related torque for a variety of particle types with respect to ratio of TWTspeed to particle settling velocity; Cs = 10%, 15%, and 20%

63

5.3. THE EFFECT OF CONCENTRATION ON SAND-RELATED TORQUE

5.3 The Effect of Concentration on Sand-Related Torque

In the TWT, as concentration increases, the amount of material in the wheel increases,

which should increase the normal force, and consequently, the friction force. At the

same time, the gap through which the back flow travels is decreased, increasing the fluid

force attempting to suspend the particles. To understand the effect of these factors on

sand-related torque, several tests were conducted at different concentrations. Two gravel

sizes (2 mm and 1 mm) were chosen to run from 10 to 60 RPM. As discussed in Section 3.5,

coarser particles were selected to ensure a fully-settled bed at a variety of wheel speeds,

which ensured that the contact-load fraction did not change significantly with velocity. The

slurry concentration was chosen to be 10%, 15%, and 20%, because concentrations above

20% cause excessive solid volume concentration at the down stream position, choking the

water flow [7]. The results are shown in Figure 5.10. For a given concentration, torque

for 1 mm and 2 mm gravel are very similar up until a certain speed (around 40 RPM),

where it starts to differ. This is consistent with the result in Section 5.2 (Figure 5.8), since

the smaller 1 mm particles reach the critical v∞/v ratio, where the particles start to be

suspended before the larger 2 mm particles. The effect can further be explained by flow

observations of the 1 mm and 2 mm gravel at 30 RPM, which are shown in Figure 5.11

for 15% by volume. At this speed, it is clear that almost all particles formed a sliding bed

with a circular-segment shape [7]. Also, the circular segments are similar in dimension for

both cases. To further verify this observation, an image processing program (ImageJ [50])

was used to measure the maximum thickness of sliding bed and central angle (labelled in

Figure 5.11b). By setting the channel height as the reference, the maximum thickness of the

sliding bed was, respectively, 41.5 and 43.5 mm for the 1 mm and 2 mm gravel particles.

The central angle can be used to compare the similarity of circular segments. The central

angles are 64.2°and 63.8°. Thus, it is evident that the sliding bed, at 30 RPM, behave similar

in geometry that cause similar Coulombic friction on the channel wall and similar torque

value. Furthermore, since 1 mm and 2 mm gravel are large enough to be fully settled, the

contact load fraction approaches its maximum value, leading to the conclusion that as the

contact load fraction approaches its maximum, the sand-related torque is independent of

particle size. This is consistent with the result of Shook et al. [15], where erosion wear

should be insensitive to particle size if the contact load fraction approaches its limit.

64

5.3. THE EFFECT OF CONCENTRATION ON SAND-RELATED TORQUE

Figure 5.10: The effect of concentration on sand-related torque

(a) 1 mm (b) 2 mm

Figure 5.11: Sliding bed observation for 15% gravel at 30 RPM

65

5.4. CONVERTING MEASURED TORQUE TO THE COULOMBIC FRICTION

It is also found that the sand-related torque at Cs=20% declines at an earlier speed than

10% and 15%. This can be explained by flow observations of 1 mm at 60 RPM, as shown in

Figure 5.12, for 10% and 20% by volume. As mentioned at the beginning of this section, the

thickness of the sliding bed increases with increasing solid volume concentration. Within

a constant channel height, if the sliding bed is thicker, the gap (illustrated in Figure 5.12a)

between the top of the sliding bed and the upper channel wall will be smaller. Sarker

[7] observed a strong back flow through the gap. Therefore, it is expected that, at the

same wheel speed (60 RPM), the back flow velocity for 20% solid volume concentration is

higher than Cs=10%, thus higher velocity would generate more turbulence, lifting more

particles up at upstream (solids in red circle in Figure 5.12b) and decreasing the contact

load fraction. Therefore, the torque value declines earlier for 20% than 15% and 10%.

(a) 10% (b) 20%

Figure 5.12: Sliding bed geometries for 1 mm gravel at 60 RPM

5.4 Converting Measured Torque to the Coulombic Friction

5.4.1 Introduction

The major objective in this study is to relate Coulombic friction to erosion wear rate. As

mentioned in Section 2.6, measuring sand-related torque could be helpful for obtaining

Coulombic friction. The sand-related torque has been measured so far; therefore, the next

step is to convert the torque value into Coulombic friction. Considering the cross-section

A of the TWT in Figure 5.13, it is clear that particles contact the channel wall at three

places, the bottom wall and the two sidewalls. However, the test coupons are attached

to the outer circumference located at the bottom wall, as shown in the figure. Therefore,

the Coulombic friction force acting on the test coupon is required. In sand-related torque,

both the bottom-wall and side-wall contributions are included. Since both friction forces

occur simultaneously when the wheel starts rotating, to eliminate the friction force from

the sidewalls, a torque calculation is performed. The major goal of the torque calculation

is to predict the sand-related torque at each test condition. The calculation first estimates

66


Coulombic friction acting on the bottom wall and sidewalls using the equations adapted

from the two-layer model, and then the sand-related torque is calculated. If the predicted

sand-related torque is equal to the measured sand-related torque, it is reasonable to

assume that the equation from the two-layer model can be successfully used to predict

the Coulombic friction. The predicted Coulombic friction acting on the bottom wall is

equal to the measured Coulombic friction force acting on the bottom wall. This measured

Coulombic friction force is the one required to relate with erosion wear rate later on.

Figure 5.13: Cross section of TWT

5.4.2 Calculation Method

In the torque calculation, the first step is to estimate Coulombic friction acting at the walls

of the TWT channel. The torque will later be obtained by multiplying these force values

by the appropriate moment arm. As discussed in Section 2.4.3.1, in a circular pipe loop, a

series of steps are performed to estimate Coulombic friction using the two-layer model. A

systematic derivation of the equation that estimates the Coulombic friction is provided by

Shook and Roco [44]. Their derivation started by developing the normal stress gradient

from force balance in the vertical direction (Figure 2.7) between fluid, particles, and the

pipe wall, then integrating along the boundary between the sliding bed and the pipe wall.

Generally, the Coulombic friction force is linearly proportional to the normal load. The

slope is named as the coefficient of friction (µs). Coulombic friction equation for slurry

flow in a pipe is Equation (2.2). However, the equation cannot be directly applied to the

TWT for two reasons: (1) the cross section of the TWT is rectangular instead of circular, and

(2) for different angular positions on the TWT, the height of the particles and water layer

changes (refer to Figure 5.13). Therefore, a modified equation to estimate the Coulombic

friction in TWT is required.

67


In the SRC two-layer model, the Coulombic friction in Equation (2.2) is derived by

integrating the normal stress over the boundary between the sliding bed and the pipe wall.

The normal stress is given as:

σs = g(ρs − ρ f )Cpackz (5.5)

where σs is the normal stress between the particles and the pipe wall, and z is the distance

from a given point to the top of the settled bed. Assuming particles are fully-settled, σs

will be zero at the sliding bed surface, which sets the origin of z. Due to the different

geometry of a circular pipe and the TWT, the boundary between the sliding bed and the

channel wall will be different. For example, by looking through the cross section of a

circular pipe and TWT (Figure 5.14), the depth (z) varies with position in circular pipe,

whereas in the TWT, it still varies with the position on sidewalls but becomes a constant

on bottom-wall. Since the boundary conditions split into two parts, the Coulombic friction

equation derivation, therefore, subdivides into two parts, the bottom wall and the side

walls.

(a) Circular Pipe (b) TWT

Figure 5.14: Demonstrate depth difference on cross section

For the Coulombic friction on the bottom-wall, it is derived by integrating the normal

stress with the boundary, giving the following:

Ff ,bottom = µs

∫g(ρs − ρ f )hCpack dA (5.6)

where Ff,bottom is the Coulombic friction acting on the bottom wall of the TWT channel,

and h is the thickness of the sliding bed. For a given angular position on the TWT, the

depth (z) becomes a constant value (h in Figure 5.15a) when considering the bottom wall.

The boundary (dA) is the contact area between the sliding bed and the channel wall. For

68


the bottom wall, dA is defined as WdL. W is the width of the channel, also the width of

the sliding bed (Figure 5.15a). L is the wetted length (Figure 5.15b). Therefore, Equation

(5.6) becomes:

dFf ,bottom = µsg(ρs − ρ f )hCpackW dL (5.7)

(a) Thickness and width of the sliding Bed (b) Wetted arc length and central angle

Figure 5.15: Definition sketch on TWT

It is evident that the thickness of the sliding bed shown in Figure 5.16 changes with

angular position (hA ̸=hB). Due to the change of thickness of the sliding bed, the normal

stress at the wall changes continuously with position. Therefore, it is necessary to redefine

the parameters. For example, the wetted length (L) can be re-defined as the product of

the TWT radius and sliding-bed central angle (2β). Also, since the particle-water interface

is nearly flat, the sliding bed can be treated as a circular segment, and the thickness of

sliding bed can be represented using polar coordinates. Also, due to the rotation of the

TWT, the whole body of sliding is inclined, and the geometric centre tilted with an angle

of (θ) from vertical (refer to Figure 5.17), which changes the thickness, since the thickness

is measured in z direction. Thus, to account the effect of the inclined angle, the normal

stress after the inclination is assumed to be proportional to the one in Equation (5.5). For

any given position, there will be an angle (α) measured from the central line of the sliding

bed, and the normal stress is obtained after using polar coordinates:

σs ∝ g(ρs − ρ f )CpackDT

2(cos α − cos β) (5.8)

= Ag(ρs − ρ f )CpackDT

2(cos α − cos β)

where A is introduced as the constant of proportionality. Though the value of A is not

immediately obvious, it can be determined from a force balance, which will be shown

in Section 5.4.4, and it is found to be cos θ. Substituting into Equation (5.8) leads to the

69


following:

σs = cos θg(ρs − ρ f )CpackDT

2(cos α − cos β) (5.9)

where DT is the diameter of the TWT. For a small element on the bottom wall, Equation

(5.7) becomes

dFf ,bottom = cos θµsg(ρs − ρ f )DT

2(cos α − cos β)CpackW

DT

2dα (5.10)

To get the sum of the Coulombic friction, an integration is conducted, giving the angle

boundary from −β to +β, giving the following:

dFf ,bottom =∫ +β

−βcos θµsg(ρs − ρ f )

DT

2(cos α − cos β)CpackW

DT

2d α (5.11)

After integration, it becomes:

Ff ,bottom = cos θµsg(ρs − ρ f )D2

T2

(sin β − β cos β)CpackW (5.12)

Figure 5.16: Sketch for thickness of sliding bed in TWT

Figure 5.17: Definition sketch of inclined angle

70


Comparing the derived equation for the TWT in Equation (5.12) with Equation (2.2)

for the pipe loop, the equation is similar except for the inclination of the sliding bed.

Again, the goal of the Coulombic friction derivation is to estimate sand-related torque. The

sand-related torque at the bottom wall can now be estimated with the following equation:

Tf ,bottom = Ff ,bottomDT

2(5.13)

However, for the sand-related torque at the sidewalls, the Coulombic friction and the

moment arm both change simultaneously. Refer to Figure 5.18, the Coulombic friction at

point 2 is expected to be higher than at point 1 due to greater depth (z), and the moment

arm at point 2 is also greater than point 1. To account for these changes, the integration

corresponding to Equation (5.10) becomes:

dFf ,side = cos θµsg(ρs − ρ f )(r cos α − DT

2cos β)Cpackrdαdr (5.14)

where r is the distance from a given point at the side wall to the centre, then integrated as

a double integral covering the whole side wall in contact with the sliding bed:

Tf ,side =∫ rmax

rmin

∫ αmax

−αmax

cos θµsg(ρs − ρ f )Cpackr2(r cos α − DT

2cos β) dα dr (5.15)

where rmax is the maximum radius of the boundary, which is the radius of TWT, rmin is

the minimum radius in the boundary which is equal to 0.5DT − hmax, where hmax is the

maximum thickness of the sliding bed, which can be found at central line of the sliding

bed (when α is zero). Therefore,

rmin = 0.5DT − 0.5DT(1 − cos β) (5.16)

Since the sliding bed surface is flat, αmax depends on radius as:

αmax = cos−1 rmin

r(5.17)

Refer to Figure 5.19, it is evident that the moment arm ra is larger than rb, and a large

portion of sliding bed acts on the moment arm (ra). The total sand-related torque is the

sum of torque at bottom and the sidewalls:

Tf ,total = Tf ,bottom + 2Tf ,side (5.18)

71


Figure 5.18: Demonstration of different normal stress at different point on sidewalls

Figure 5.19: Demonstration of different central angle at different radius on sidewalls

72


In the calculation, several input parameters must be determined: Cpack, hmax, β, and

θ. The best determination of these can be obtained from visualization images. If the

conditions are fully settled and Cpack is guessed as a standard value (such as 0.6), the other

values could also be approximated directly from idealized circular segment geometry,

since the total amount of solids is known. For this work, the measurements from the

visualizations are used. Also, as mentioned in Section 5.2, the strong back flow will lift

particles up at the upstream location when operating at higher speeds, thus reducing the

contact load fraction and causing reduction on Coulombic friction and sand-related torque.

To account that effect in the calculation, the following procedure is used:

1. Measure the total area of sliding bed using ImageJ in Figure 5.20a as A1. A1

represents the total contact area. Also since the width of the channel is constant, A1

also reflects the total volume of the sliding bed (and can be used to calculate Cpack).

2. By looking through the observation video, the suspended particles has larger mo-

vement than the settled ones. Also, most suspended particles are concentrated at

the upstream location and at the top of the sliding bed. By comparing screenshots

between now and 3 seconds later, the area that seems to concentrate in contact loads

can be labelled and measured as A2 (refer to Figure 5.20b). Since the channel width

is constant, A2 could represent the volume of the settled particles.

3. The contact load fraction will be the ratio of A2 over A2.

Since the particles are lifted up by the back flow, it changes both sand-related torque at

the bottom and the sidewalls; so, to obtain a corrected torque, the value for Tf,total can

simply be multiplied by this contact load fraction. A sample calculation is demonstrated

in Appendix E.3.

(a) A1 (b) A2

Figure 5.20: Definition of A1 and A2 in the calculation of contact load fraction

73


5.4.3 Comparison of Measured and Calculated Torque Values

As noted in the previous section, the parameters required to predict torque (Cpack, hmax,

θ,and β) cannot be obtained for flows that are not reasonably settled. Therefore, the

sand-related torque calculations were only conducted for some cases in this study. Those

cases are either for fully-settled condition or conditions where the sliding bed can be

clearly observed. These conditions are listed in Table 5.2. To match the calculated sand-

related torque with the measured one, the friction coefficient (µs) was found to be 0.47.

The matching results between calculated sand-related torque and measured sand-related

torque are shown in Figure 5.21 for 1 mm and 2 mm. It is evident that the calculated torque

is quite similar to measured torque, with an error range of ±10%, which indicates good

agreement. The good agreement indicates the proposed idea of converting sand-related

torque into the Coulombic friction force is reasonable, and furthermore, it demonstrates the

success of using the modified equation from a two-layer model in estimating Coulombic

friction.

Table 5.2: List of conditions where estimated sand-related torque

Particle Size (mm) Solid Volume Concentration Wheel Speed (RPM)2 10%, 15%, and 20% 10-601 10%, 15%, and 20% 10-400.420 10% 10-400.250 10% 10-30

Figure 5.21: Matching between calculated and measured sand-related torque

74


The success of Coulombic friction estimation is essential in this study, since the major

objective is to relate the Coulombic friction with the erosive wear rate, and one of the

major parameters required in this study is the value of the Coulombic friction. Without

obtaining this value, it is impossible to generate this relationship. The comparison shows

a good agreement, indicating the value of Coulombic friction now is obtained, which

the calculated Coulombic friction in Equation (5.12) can be treated as the actual friction

acting on the test coupons. This can be used in developing the relationship with wear

rate. In addition, because of slurry opacity issues, the parameters that were mentioned

at the beginning of this section cannot be obtained for partially settled conditions, which

cause difficulties for Coulombic friction estimation. The Coulombic friction values that

are obtained from the conditions where the sliding bed can be clearly observed could be

helpful on estimating the Coulombic friction for the conditions where slurry opacity issues

are experienced. The details are discussed in Section 5.4.5.

5.4.4 Force Balance

In Section 5.4.3, to match the calculated sand-related torque and the measurements, the

friction coefficient (µs) was found to be 0.47. It is necessary to verify the value, since the

accuracy of this value will directly influence the Coulombic friction and further influence

the relationship between Coulombic friction and erosive wear rates. To verify the friction

coefficient, a force balance on the sliding bed was performed. Since the sliding bed is at

steady state when the wheel rotates at constant speed, the force must be balanced in every

direction. The immersed weight of the sliding bed is supported by the wheel (related to

normal load), and the wheel carries the sliding bed to incline at a certain angle as it rotates

(related to friction). Also, Coulombic friction force is proportional to the normal load, and

the slope is the friction coefficient. Therefore, by applying a force balance, the value of the

friction coefficient can be estimated. The force acting on the gravity centre of the sliding

bed is analyzed in Figure 5.22.

Fr is the force in the radial direction, and the value is the sum of the radial force acting

at every contact point between the channel wall and the sliding bed. Ft is the tangential

force perpendicular to Fr, and the value is the sum of the tangential force acting at every

point of contact between the channel wall and the sliding bed. Fg is the immersed weight

of the sliding bed. Since the sliding bed is at steady state, the sum of forces in the r

direction should be zero, giving the following:

Fr − Fg cos θ = 0 (5.19)

75


Fg is the immersed weight, defined as:

Fg = g(ρs − ρ f )CpackD2

T4

W(β − sin β cos β) (5.20)

where β is the angle referred to Figure 5.15b. The sum of forces in the t direction should

be zero, giving:

Ft − Fg sin θ = 0 (5.21)

Figure 5.22: Force analysis on the sliding bed

As mentioned in Section 5.4.2, the boundary conditions in the TWT consists of two

parts: bottom wall and side walls. Thus, it is necessary to consider Fr as the contribution

from both boundary conditions. Assume there is no force acting on the side wall to push

the sliding bed in radial direction, The radial force at the side wall is zero. And the radial

force is all from the bottom wall. To obtain the sum of radial force at the bottom wall, a

small segment is considered (refer to Figure 5.23). FN is the normal force pointing to the

center of the wheel, and it is the product of the normal stress and segment area. Ff,bottom

is the friction force at bottom, and it is perpendicular to the normal force. The value of the

friction is the product of the normal force and the friction coefficient. The sum of radial

force of the normal force and the friction that contributed to Fr is given by

Fr = Fr,bottom = −∫ β

−βsin α µsdFN +

∫ β

−βcos α dFN (5.22)

76


Figure 5.23: Radial force analysis at bottom wall

By putting Equation (5.8) into Equation (5.22), it becomes:

Fr = Ag(ρs − ρ f )CpackD2

T4

W(−

∫ β

−βsin αµs(cos α − cos β) dα +

∫ β

−βcos α(cos α − cos β) dα

)(5.23)

where A is the proportionality in Equation (5.8). After integration, it becomes:

Fr = Ag(ρs − ρ f )CpackD2

T4


Therefore, by putting Equations (5.24) and (5.20) into Equation (5.19), it becomes:

Ag(ρs − ρ f )CpackD2

T4

W(β − sin β cos β)− g(ρs − ρ f )CpackD2

T4

W(β − sin β cos β) cos θ = 0

(5.25)

By eliminating the same items, the proportionality (A) in Equation (5.8) is cos θ. The

tangential force (Ft) is similar to the radial force, where both boundary conditions should

be considered. For the sum force at the bottom wall, the integration corresponding to

Equation (5.22) becomes

Ft,bottom = −∫ β

−βsin α dFN +

∫ β

−βcos α µsdFN (5.26)

where Ft,bottom is the sum of tangential force at the bottom wall. After integration, it

becomes:

Ft,bottom = cos θµsg(ρs − ρ f )CpackD2

T4


77


When considering the tangential force on the side wall, the normal force points perpendi-

cular to the side wall, since the direction of the tangential force is parallel to the side wall.

Therefore, it is assumed that the normal force does not affect the tangential force at the

side wall. Thus, the tangential force at the side wall (Ft,side) in Figure 5.23 is as follows:

dFt,side = cos αdFf ,side (5.28)

By putting Ff,side in Equation (5.14) into Equation (5.28), it becomes:

Ft,side =∫ rmax

rmin

∫ αmax

−αmax

cos α cos θµsg(ρs − ρ f )Cpackr(r cos α − DT

2cos β) dα dr (5.29)

where rmax, rmin, and αmax refers to Equations (5.15), (5.16), and (5.17) respectively. The

sum of the tangential force will be bottom wall and two side walls, giving:

Ft = Ft,bottom + 2Ft,side (5.30)

The friction coefficient (µs), therefore, can be evaluated using Equation (5.21) with help

from Equation (5.29) and (5.27). Table 5.3 shows the conditions used for friction coefficient

validation, and the estimated friction coefficients, ranging from 0.40 to 0.50. Also, the

friction coefficient used to match the calculated and measured sand-related torque in

Section 5.4.3 was 0.47, which is within this range. Therefore, using 0.47 as the friction

coefficient is a reasonable value in this study. Even though the discrepancy of estimated

friction coefficient from Table 5.3 seems a little bit large (0.1 difference), it is mainly due to

the discrepancy from the measurements (e.g. θ, β, and Cpack) on the visualization images.

Table 5.3: List of conditions and calculated values for friction coefficient validation

RPM Particle size (mm) Solid Volume Concentration Calculated µs

30

110% 0.4415% 0.4920% 0.41

210% 0.4215% 0.4720% 0.42

5.4.5 Obtain the Coulombic Friction

As mentioned in Section 5.4.3, the slurry opacity problems for partially settled conditions

make it impossible to estimate the Coulombic friction for those conditions. However, many

wear experiments were conducted on partially-settled conditions. If only fully-settled

78


conditions are considered when relating the Coulombic friction to wear rates, there will

be less data pairs when developing the relationship and the relationship will be less

convincing. Therefore, in order to make more data pairs, it is necessary to obtain the

Coulombic friction for partially settled conditions. From Figure 5.4, it is clear that sand-

related torque decreases linearly as the wheel speed increases. Also, since torque is the

product of force and distance, and the distance is constant, it is a reasonable assumption

that the Coulombic friction also reduces linearly with the wheel speed, and the ratio of

reduction of Coulombic friction (outer-wall contribution) will be the same as the sand-

related torque (outer + side-wall contributions). Therefore, the Coulombic friction for

partially settled conditions can be estimated using linear interpolation, if the initial and

final value of sand-related torque and Coulombic friction are known. As mentioned in

Section 5.3, when all the particles concentrate in contact load, sand-related torque remains

constant and so does Coulombic friction, which can be treated as the initial value. The

Coulombic friction for fully-suspended condition is assumed as the final value, since there

is no particles left at the bottom that leads to friction forces. The interpolation equation is

shown as follows:T − Tf

Ti − Tf=

Ff − Ff , f

Ff ,i − Ff , f(5.31)

where Tf is the final sand-related torque; it is also the sand-related torque when it just

reaches fully suspended condition. Due to slurry opacity problem, it is difficult to define

the wheel speed when it just reaches fully suspended condition, but it was found that

sand-related torque goes up in fully suspended condition as the wheel speed increases.

Therefore, Tf is chosen as the lowest torque value, and the speed at which it occurs is taken

as the fully-suspended speed. Ti is the initial sand-related torque, and it is also the torque

at fully-settled conditions. Among the particles that were used to develop the relationship

between the Coulombic friction and the erosive wear rates, the sand-related torque at

10 RPM was selected as the initial torque. Ff,i is the Coulombic friction corresponding

to Ti. The method that estimates Coulombic friction for fully-settled conditions using

sand-related torque was introduced from Section 5.4.1 to Section 5.4.3. T is the sand-related

torque for any particular case, and Ff is the Coulombic friction corresponding to T. Ff,f

is the Coulombic friction that just reaches the fully-suspended conditions, and it can be

assumed that the torque are evenly contributed from the wetted wall (outer + side-wall

+ inner); then, the friction force at the outer wall from torque and known distance is

calculated as follows:

Ff , f =Tf

r∗(

Aouter

Aouter+wall

)(5.32)

where Aouter is wetted area at outer wall, Aouter+wall is the total wetted area. Figure 5.24

gives an example how to define Ti, Tf, and Ff,i. The linear interpolation method works

79

5.5. RELATING COULOMBIC FRICTION WITH EROSION WEAR RATE

particularly well for partially settled conditions, where the dimension of the sliding bed

cannot be defined due to slurry opacity problems. In this study, the method described

above was used to obtain the Coulombic friction for the cases shown in Table 5.4.

Figure 5.24: Definition of key parameter in interpolation equation on sand-related torquegraph; Cs = 10%

Table 5.4: List of cases using linear interpolation

Particle size (mm) Concentration RPM0.42

10%, 15% 20%30, 60, 90

0.25 30, 60, 90

5.5 Relating Coulombic Friction with Erosion Wear Rate

The erosive wear experiments were conducted for a period of 96 hours. During the

experiments, the slurry was replaced every 24 hours. For each of the conditions, there were

two test coupons attached to the wheel. By comparing the wear between test coupons and

checking the discrepancy, it allows the identification of any errors during the experiments.

If the wear for both coupons is similar, the wear rates for this condition are taken as

the average. To eliminate any corrosion during the tests, HG was added to the slurry

to remove dissolved oxygen. The erosive wear rates are listed in Appendix E. Once the

Coulombic friction and the wear rates are obtained, the next step is to relate them. The

relationships are shown separately for 30 RPM and 60 RPM (Figure 5.25). The reason to

relate them at different wheel speeds is because it is known from wear studies that wear

80


increases with vb, where b is typically in the range of 2 to 3.5 (Refer to Section 2.4.2), but

the two-layer-based model does not account for this effect. A part of this difference can be

explained by the different impact energy from dispersed particles at different speeds. The

correlations from both wheel speeds were obtained using the best fit line. By assuming

the wear rates grow linearly with Coulombic friction and forcing the y-intercept for both

best fit lines to pass through the origin, the results for 30 RPM and 60 RPM are shown in

Figure 5.25.

Figure 5.25: Relationship between erosive wear rates and the Coulombic friction

It is very clear that the data points could collapse into one curve per speed. That leads

to a conclusion where there is a relationship between erosive wear rates and Coulombic

friction in the TWT. The relationship directly leads to the success of achieving the main

objective that relates the erosive wear rates to the Coulombic friction. This relationship

would also be very helpful in wear rate prediction in the TWT. Sarker [7] showed the

ability that the TWT could simulate pipe wear conditions by comparing the power index

of velocity, particle size, and concentration (refer to Section 2.4.2). However, it is not

possible to compare the wear rates between the TWT and the pipe loop under similar

hydrodynamic conditions. The success of developing the relationship between the erosive

wear rates and the Coulombic friction indicates the Coulombic friction could be a new

comparable parameter.

To further test those relationships, wear rates from Sarker [7] using the same TWT at

different conditions were selected. When Sarker [7] was performing the preliminary study

on the TWT, he had done some wear tests under different conditions. Table 5.5 lists those

conditions. The good agreement between measured and calculated sand-related torque

in Section 5.4.3 indicates the success of obtaining Coulombic friction using the modified

81


equation (refer to Equation (5.12)). The Coulombic friction for the conditions in Table 5.5

was estimated directly using Equation (5.12). In the equation, β was calculated from the

total volume of particles by assuming an idealized circular-segment sliding bed, and Cpack

was 0.6. θ was calculated based on the average θ value for 10% 2 mm gravel at the same

speed. The additional results are shown in Figure 5.26 for 30 RPM. It is clear that wear

data from Sarker [7] (the open circle points) collapse to the correlations obtained here,

which support the success of the relationships. However, since there are only two points

available in the past study, more wear data is required to fully validate the relationship.

In conclusion, the relationship between the erosive wear rates and the Coulombic

friction was successfully developed. Therefore, the main objective for this study has been

achieved. The correlations will be helpful in the erosive wear rate predictions made for the

TWT.

Table 5.5: Test conditions from Sarker [7] for data points used in the validation

Particle size (mm) Concentration RPM

26% 3012% 30

Figure 5.26: Additional wear results from Sarker [7], N = 30 RPM

82

Chapter 6

Conclusion and Recommendation

6.1 Conclusion

In many industries, wear-related issues in pipelines could lead to pipeline failure, causing

increased costs along with safety and environmental issues. Therefore, it is necessary

to develop a model to predict wear rates to develop maintenance strategies and reduce

premature or unplanned pipeline failures. It has been found in past that erosive wear was

strongly influenced by the sliding bed, and specifically by Coulombic friction. Developing

a model based on the erosive wear rates and the Coulombic friction could be a possible

approach in wear prediction. The Toroid Wear Tester (TWT) has been proposed as a useful

apparatus to study sliding-bed dominated wear due to several advantages, such as less

particle degradation, and has been used in this study. Therefore, the major objective of

this study is to relate erosive wear rates in a TWT with the Coulombic friction from sands

and gravel in sliding-bed dominated wear. In order to achieve this objective, there are two

parameters measured through the experiments:

Coulombic friction Since Coulombic friction cannot be measured directly in the TWT,

an alternative parameter, torque, is measured with a torque sensor. A torque

sensor system was designed, installed in the TWT, and calibrated. The effect of

hydrodynamic conditions on the Coulombic friction in the TWT was investigated to

understand how the friction varies with wear-related parameters.

Erosive wear rate Wear rates under the same conditions were measured to develop the

relationship.

The torque sensor was installed on an existing TWT setup. Though the signal suffered

from both high- and low-frequency noise, the high frequencies were successfully filtered,

and the low frequencies were shown not to affect the results. With the data repeatability of

torque sensor, the discrepancy of sand-related torque value between wheel-to-wheel and

83

6.1. CONCLUSION

test-to-test is within 5%, which confirms that the torque sensor would generate consistent

results during torque measurements.

The effect of particle size, sand volume concentration, and wheel speed on the Cou-

lombic friction was investigated. Based on the torque measurements for 1 mm and 2 mm

gravel, it has been found that when all the sand particles are concentrated in the lower

layer (fully-settled condition), the sand-related torque is independent of particle size. As

the wheel speed goes up, the sand-related torque starts to decrease, as some fraction of

the sand particles disperse into the water. It decreases more rapidly for small particles

than for large particles, since small particles disperse more easily. By normalizing the

wheel speed with the terminal settling velocity of each particle size, and relating it with

the sand-related torque, the torque data collapses to a single relationship depending only

on solids concentration and the ratio of particle settling velocity to wheel speed. This

correlation is important, since it gives a possible bridge when comparing TWT results with

a pipe loop.

To convert the measured sand-related torque into the Coulombic friction, a torque

calculation has been performed by estimating the Coulombic friction using modified

equation from the two-layer model, then multiplying by the moment arm. With the input

parameters of the dimensions of the sliding bed, an estimated torque value has been

calculated. By fitting a friction coefficient of 0.47, a comparison between the measured

sand-related torque and estimation was conducted, and it showed an agreement within

10% for all data points. That indicates the success of applying the modified equation from

the two-layer model to estimate the Coulombic friction, and thus the estimated Coulombic

friction can be taken as the actual Coulombic friction. To check the accuracy of friction

coefficient of 0.47, a force balance was performed on the sliding bed which showed the

friction coefficient varied from 0.4 to 0.5, indicating that the friction coefficient of 0.47 is a

reasonable value when matching the estimated sand-related to the measurements.

Relating the erosive wear rates and the Coulombic friction was attempted for 30 RPM

and 60 RPM. It is very clear that the data points could collapse onto one curve per speed,

indicating a relationship between the erosive wear rates in a TWT with the Coulombic

friction from sands in sliding-bed dominated wear. By assuming linear growth and forcing

the intercept to pass through the origin, the wear rate for 30 RPM increases at a constant

of 0.131, and it grows at the rate of 0.705 for 60 RPM. Those correlations would be very

helpful in wear rate prediction in the TWT. Since Sarker [7] compared wear results between

the TWT and pipe loops under the similar hydrodynamic conditions and showed a poor

agreement. He indicated comparisons based on Coulombic friction may improve the

agreement. The success of developing the relationship between the erosive wear rates

and the Coulombic friction indicates that Coulombic friction could be a new comparable

parameter.

84

6.2. RECOMMENDATIONS FOR FUTURE WORK

6.2 Recommendations for Future Work

At this point, very limited wear data is available to further verify the relationship; thus, a

broader range of conditions must be tested, including particle diameter and particle shape.

Specifically, in this study, only a relatively narrow size distribution of particles was used in

each test; however, there is a broad range of particle size in an actual pipeline. Therefore,

it is necessary to perform tests on the combination of different particle sizes.

Furthermore, the motivation of this study is to predict the wear rate in pipelines, and

quantitative comparisons between TWT and pipe loop wear results must be obtained. In

this study, Coulombic friction has been proved as a new comparable parameter that could

be used for quantitative comparisons.

Moreover, it is recommended to conduct tests in a larger TWT, since the maximum

wheel speed of the TWT in this study is 90 RPM which corresponding to a linear speed

of 3 m/s, and the operating slurry speed in an industrial slurry pipeline is greater than

that. It is necessary to generate similar conditions. In addition, it is necessary to verify the

independence of the linear relationship between Coulombic friction and erosion wear rate

in different TWT sizes.

Since Coulombic friction is calculated using the parameters measured from visualiza-

tion images, errors from measurements could affect the accuracy of calculated Coulombic

friction. Therefore, it is recommended to conduct error analysis to better improve the

accuracy of calculated Coulombic friction.

The fitted parameters from the relationship between erosive wear rates and Coulombic

friction in this work apply only to one coupon material and the TWT set-up. To explore

this relationship, wear tests with different coupon materials are required.

Particles are assumed to be spherical in the calculation of terminal settling velocities in

this study. However, it becomes more realistic if assume these particles are angular, and a

past study (refer to [44]) has already developed a correlation for such particles.

A correlation has been found between the sand-related torque and sand volume

concentration and terminal settling velocity (refer to Section 5.2), which reduces the work

required to obtain torque measurements. In this study, the input parameters required to

calculate the Coulombic friction (Cpack, θ,and β) have to be measured from the visualization

image, which requires experimental testing. But in many cases, the sliding bed has

essentially the shape of a circular segment, indicating that the input parameters can be

obtained without measurements. Therefore, a recommendation would be to correlate the

input parameters with test conditions, such as sand volume concentration.

85

References

[1] H. Bhabra. Slurry pipeline now goes the distance. World Pumps, 2013(6):38–40, (2013).

[2] B. Fotty, M. Krantz, J. Been, and J. Wolodko. Development of a pilot-scale facility

for evaluating wear in slurry pipeline systems. In 18th International Conference on

Hydrotransport, pages 431–443, Rio de Janeiro, Brazil, (2010).

[3] R. Cooke, G. Johnson, and P. Goosen. Laboratory Apparatus for Evaluating Slurry

Pipeline Wear. In Economics of Wear Materials, pages 1–17. South African Institute of

Tribology, (2000).

[4] I. R. Kleis and P. Kulu. Solid particle erosion: occurrence, prediction and control. Springer,

London, UK, (2008). ISBN 978-1-84800-028-5.

[5] A. Sadighian. Investigating Key Parameters Affecting Slurry Pipeline Erosion. PhD thesis,

University of Alberta, Edmonton, Canada, (2016).

[6] R. Gupta, S. N. Singh, and V. Sehadri. Prediction of uneven wear in a slurry pipeline

on the basis of measurements in a pot tester. Wear, 184(2):169–178, (1995).

[7] N. R. Sarker. A preliminary study of slurry pipeline erosion using a toroid wear tester. MSc

thesis, University of Alberta, Edmonton, Canada, (2016).

[8] B. E. A. Jacobs and I. G. James. The Wear Rate of Some Abrasion Resistant Materials.

In 9th International Conference on Hydraulic Transport of Solids in Pipes, pages 331–344,

Rome, Italy, (1984).

[9] J. Schaan, N. Cook, and R. S. Sanders. On-line wear measurements for commercial-

scale, coarse-particle slurry pipelines. In 17th International Conference on Hydrotransport,

pages 291–300, Cape Town, South Africa, (2007).

[10] C. A. Shook, R. G. Gillies, and R. S. Sanders. Pipeline hydrotransport: with applications

in the oil sand industry. SRC Pipe Flow Technology Centre, Saskatoon, Canada, (2002).

ISBN 978-1-895880-20-5.

86

http://doi.org/10.1016/S0262-1762(13)70155-X

https://www.researchgate.net/publication/267423118_Laboratory_Apparatus_for_Evaluating_Slurry_Pipeline_Wear

https://www.researchgate.net/publication/267423118_Laboratory_Apparatus_for_Evaluating_Slurry_Pipeline_Wear

https://doi.org/10.7939/R3GX45041

http://dx.doi.org/10.1016/0043-1648(94)06566-7

http://dx.doi.org/10.1016/0043-1648(94)06566-7

http://doi.org/10.7939/R3C824K8X

REFERENCES

[11] M. Roco, P. Nair, and G. Addie. Test Approach for Dense Slurry Erosion. In J. E.

Miller and F. Schmidt, editors, Slurry Erosion: Uses, Applications, and Test Methods,

volume 946, pages 185–210. American Society for Testing and Materials, Philadelphia,

USA, (1987).

[12] B. K. Gandhi, S. N. Singh, and V. Seshadri. Study of the parametric dependence of

erosion wear for the parallel flow of solid–liquid mixtures. Tribology International, 32

(5):275–282, (1999).

[13] J. G. James and B. A. Broad. Wear in Slurry Pipelines: Experiments with 38mm

Diameter Specimens in a Closed-loop Test Rig. Technical Report SR773, Transport

and Road Research Laboratory, Great Britain, (1983).

[14] L. Parent and D. Li. Wear of hydrotransport lines in Athabasca oil sands. Wear, 301

(1-2):477 – 482, (2013).

[15] C. Shook, M. Mckibben, and M. Small. Experimental Investigation of Some Hydrody-

namic Factors Affecting Slurry Pipeline Wall Erosion. The Canadian Journal of Chemical

Engineering, 68(1):17–23, (1990).

[16] G. Henday. A comparison of commercial pipe materials intended for the hydraulic transport

of solids. British Hydromechanics Research Association, Fluid Engineering, Cranfield,

UK, (1988). ISBN 978-0-947711-59-7.

[17] H. M. Clark. On the impact rate and impact energy of particles in a slurry pot erosion

tester. Wear, 147(1):165–183, (1991).

[18] T. Harvey, J. Wharton, and R. Wood. Development of synergy model for erosion-

corrosion of carbon steel in a slurry pot. Tribology - Materials, Surfaces & Interfaces, 1

(1):33–47, (2007).

[19] S. S. Rajahram, T. Harvey, and R. Wood. Evaluation of a semi-empirical model in

predicting erosion–corrosion. Wear, 267(11):1883–1893, (2009).

[20] B. Yu, D. Li, and A. Grondin. Effects of the dissolved oxygen and slurry velocity on

erosion-corrosion of carbon steel in aqueous slurries with carbon dioxide and silica

sand. Wear, 302(1-2):1609–1614, (2013).

[21] H. M. Clark. Specimen diameter, impact velocity, erosion rate and particle density in

a slurry pot erosion tester. Wear, 162-164(Part B):669–678, (1993).

[22] W. Tsai, J. A. C. Humphrey, I. Cornet, and A. V. Levy. Experimental measurement of

accelerated erosion in a slurry pot tester. Wear, 68(3):289–303, (1981).

87

http://dx.doi.org/10.1016/S0301-679X(99)00047-X

http://dx.doi.org/10.1016/S0301-679X(99)00047-X

http://doi.org/10.1016/j.wear.2013.01.039

http://doi.org/10.1002/cjce.5450680102

http://doi.org/10.1002/cjce.5450680102

http://dx.doi.org/10.1016/0043-1648(91)90127-G

http://dx.doi.org/10.1016/0043-1648(91)90127-G

http://dx.doi.org/10.1179/175158407X181471

http://dx.doi.org/10.1179/175158407X181471

http://dx.doi.org/10.1016/0043-1648(93)90065-T

http://dx.doi.org/10.1016/0043-1648(93)90065-T

http://dx.doi.org/10.1016/0043-1648(81)90178-2

http://dx.doi.org/10.1016/0043-1648(81)90178-2

REFERENCES

[23] G. R. Desale, B. K. Gandhi, and S. C. Jain. Slurry erosion of ductile materials under

normal impact condition. Wear, 264(3):322–330, (2008).

[24] B. W. Madsen. A Portable Slurry Wear Test for the Field. Journal of Fluids Engineering,

111(3):324–330, (1989).

[25] J. B. Zu, I. M. Hutchings, and G. T. Burstein. Design of a slurry erosion test rig. Wear,

140(2):331–344, (1990).

[26] M. T. Benchaita, P. Griffith, and E. Rabinowicz. Erosion of Metallic Plate by Solid

Particles Entrained in a Liquid Jet. Journal of Engineering for Industry, 105(3):215–222,

(1983).

[27] A. Gnanavelu, N. Kapur, A. Neville, and J. F. Flores. An integrated methodology for

predicting material wear rates due to erosion. Wear, 267(11):1935–1944, (2009).

[28] X. Hu and A. Neville. The electrochemical response of stainless steels in liquid-solid

impingement. Wear, 258(1):641–648, (2005).

[29] R. J. K. Wood and D. W. Wheeler. Design and performance of a high velocity air-sand

jet impingement erosion facility. Wear, 220(2):95–112, (1998).

[30] Y. I. Oka, H. Ohnogi, T. Hosokawa, and M. Matsumura. The impact angle dependence

of erosion damage caused by solid particle impact. Wear, 203-204(Supplement C):

573–579, (1997).

[31] J. Tuzson, J. Lee, and K. Scheibe-Powell. Slurry Erosion Tests with Centrifugal

Erosion Tester. In M. C. Roco, editor, Liquid-Solid Flows and Erosion Wear in Industrial

Equipment, volume 13, pages 84–87. American Society of Mechanical Engineers, Fluids

Engineering Division, New Orleans, USA, (1984).

[32] H. M. Clark, J. Tuzson, and K. K. Wong. Measurements of specific energies for erosive

wear using a Coriolis erosion tester. Wear, 241(1):1–9, (2000).

[33] H. M. Clark, H. M. Hawthorne, and Y. Xie. Wear rates and specific energies of some

ceramic, cermet and metallic coatings determined in the Coriolis erosion tester. Wear,

233-235(Supplement C):319–327, (1999).

[34] Y. Xie, H. M. Clark, and H. M. Hawthorne. Modelling slurry particle dynamics in the

Coriolis erosion tester. Wear, 225-229(Part 1):405–416, (1999).

[35] K. Pagalthivarthi and F. Helmly. Applications of Materials Wear Testing to Solids

Transport via Centrifugal Slurry Pumps. In R. Divakar and P. J. Blau, editors, Wear

Testing of Advanced Materials, volume 1992, pages 114–126. American Society for

Testing and Materials, Philadelphia, USA, (1992).

88

http://dx.doi.org/10.1016/j.wear.2007.03.022


http://dx.doi.org/10.1115/1.3243647

http://dx.doi.org/10.1016/0043-1648(90)90093-P

http://dx.doi.org/10.1115/1.3185891

http://dx.doi.org/10.1115/1.3185891





http://dx.doi.org/10.1016/S0043-1648(98)00196-3

http://dx.doi.org/10.1016/S0043-1648(98)00196-3

http://dx.doi.org/10.1016/S0043-1648(96)07430-3

http://dx.doi.org/10.1016/S0043-1648(96)07430-3

http://dx.doi.org/10.1016/S0043-1648(00)00327-6

http://dx.doi.org/10.1016/S0043-1648(00)00327-6

http://dx.doi.org/10.1016/S0043-1648(99)00213-6

http://dx.doi.org/10.1016/S0043-1648(99)00213-6

http://dx.doi.org/10.1016/S0043-1648(99)00016-2

http://dx.doi.org/10.1016/S0043-1648(99)00016-2

REFERENCES

[36] H. H. Tian and G. R. Addie. Experimental study on erosive wear of some metallic

materials using Coriolis wear testing approach. Wear, 258(1):458–469, (2005).

[37] H. H. Tian, G. R. Addie, and K. V. Pagalthivarthi. Determination of wear coefficients

for erosive wear prediction through Coriolis wear testing. Wear, 259(1):160–170, (2005).

[38] P. J. Baker, S. T. Bonnington, and B. E. A. Jacobs. A guide to slurry pipeline systems.

British Hydromechanics Research Association, Fluid Engineering, Cranfield, England,

(1979). ISBN 978-0-906085-38-7.

[39] N. A. Feidenhans’l, P.-E. Hansen, L. Pilný, M. H. Madsen, G. Bissacco, J. C. Pe-

tersen, and R. Taboryski. Comparison of optical methods for surface roughness

characterization. Measurement Science and Technology, 26(8):085208, (2015).

[40] R. M. Summer. A Review of Pipeline Slurry Erosion Measurements and Research

Recommendations. In J. E. Miller and F. Schmidt, editors, Slurry Erosion: Uses,

Applications, and Test Methods, volume 946, pages 91–100. American Society for Testing

and Materials, Philadelphia, USA, (1987).

[41] A. Elkholy. Prediction of abrasion wear for slurry pump materials. Wear, 84(1):39–49,

(1983).

[42] A. Karabelas. An experimental study of pipe erosion by turbulent slurry flow. In 5th

International Conference of Hydraulic Transport of Solids in Pipes, pages E2. 15–E2. 24,

Hannover, Germany, (1978).

[43] R. G. Gillies, C. A. Shook, and K. C. Wilson. An improved two layer model for

horizontal slurry pipeline flow. The Canadian Journal of Chemical Engineering, 69(1):

173–178, (1991).

[44] C. A. Shook and M. C. Roco. Slurry flow: principles and practice. Butterworth-

Heinemann, Boston, USA, (1991). ISBN 978-0-7506-9110-9.

[45] M. J. McKibben. Wall erosion in slurry pipelines. PhD thesis, University of Saskatchewan,

Saskatchewan, Canada, (1992).

[46] C. Shook, D. Haas, W. Husband, and M. Small. Relative Wear Rate Determinations

for Slurry Pipelines. Journal of Pipelines, 1(4):273–280, (1981).

[47] R. C. Worster and D. F. Denny. Hydraulic Transport of Solid Material in Pipes.

Proceedings of the Institution of Mechanical Engineers, 169(1):563–586, (1955).

[48] V. V. Traynis. Parameters and flow regimes for hydraulic transport of coal by pipelines.

Terraspace, Rockville, USA, (1977). ISBN 978-0-918990-01-3.

89





http://dx.doi.org/10.1088/0957-0233/26/8/085208

http://dx.doi.org/10.1088/0957-0233/26/8/085208

http://dx.doi.org/10.1016/0043-1648(83)90117-5

http://dx.doi.org/10.1002/cjce.5450690120


http://dx.doi.org/10.1243/PIME_PROC_1955_169_064_02

REFERENCES

[49] R. G. Gillies, R. Sun, and C. A. Shook. Laboratory investigation of inversion of heavy

oil emulsions. The Canadian Journal of Chemical Engineering, 78(4):757–763, (2000).

[50] ImageJ: Image Processing and Analysis in Java, (2018).

http://imagej.nih.gov/ij/index.html.

90



http://imagej.nih.gov/ij/index.html

Appendix A

Properties of The Test Coupons

Table A.1: Chemical composition of ASTM A572 GR50 carbon steel specimens. Adaptedfrom Sarker [7]

Material Concentration Material ConcentrationC 0.06 Mn 0.58Ti 0.002 Cb 0.034P 0.009 Mo 0.007

Ca 0.0002 S 0.009Cu 0.058 Al 0.037V 0.002 B 0.0002Si 0.011 Cr 0.062Ni 0.026

Table A.2: Mechanical properties of the ASTM A572 GR50 carbon steel specimens. Adaptedfrom Sarker [7]

Tensile strength (MPa) 520Yield Strength (MPa) 442

Elongation 25

91

Appendix B

Experimental Procedure

B.1 Wear Measurements Procedure

B.1.1 Test Coupon Cleaning

Since liquid lubricant between test coupon and coupon window is used to avoid water

leakage, it’s very important to remove the lubricant after the experiment. Also, the lab-scale

experiments are usually done in shorter time, and the material loss (approximately 0.1 g

loss) is much less than in an actual pipe. Therefore, it’s necessary to keep it clean before

the experiment as well. The steps for cleaning the coupons are listed below:

1. Rinse the test coupons by tap water and remove the dirt (i.e. sand particles after the

experiments)

2. Place the test coupons into a cleaning solution for 30 minutes. The cleaning solution

is made of Versa-Clean TM and tap water at a mixing ratio of 1:10.

3. After 30 min, scrub the test coupon gently to remove the lubricants.

4. Sonicate the test coupons in an ultrasonic De-Ionized (DI) water bath for 5 minutes.

5. After sonication, wipe the coupons, move them quickly to a fume hood, and rinse the

coupon surfaces using acetone. Wait for 2 minutes to allow the acetone to evaporate.

6. Rinse the coupon surfaces with toluene. Wait for 5 minutes to allow the toluene to

evaporate.

B.1.2 Coupon Weighing

Weigh measurement is a cost-effective and simple method, as discussed earlier. In this

study, An electronic weighing scale (Brand: A&D Corporation Ltd., Model: FX-3000i) was

used, and it has a resolution of 0.01mg. The steps for coupon weighing are listed below:

92

B.1. WEAR MEASUREMENTS PROCEDURE

1. Start the weighing scale, set the sensitivity to medium, and re-zero the scale. Calibrate

the scale by measuring a 500g standard calibration weight on the scale.

2. Measure the test coupon and record the weight when stable. Measure each coupon

thrice to reduce the uncertainties.

3. Re-measure the 500g standard weight to ensure the consistency of the measured

weight data.

B.1.3 Slurry Charging and N2 Purging

Once the test coupons are clean and the initial masses are recorded. The next step is to

fill the slurry and hydroguard and purge the N2. The steps for slurry charging and N2

purging are listed below:

1. Attach four (out of five) coupons to the coupon window in the following manner:

• For all the wheel: Attach test coupons 1,2,3, and 5

2. Place the open window (#4) at the top in order to fill the slurry.

3. Fill the wheel with calculated water, sand particles, and hydroguard to each wheel.

4. Attach the final test coupons to window 4.

5. Secure a TWT in a way (using the metal rod) that the inlet of N2 purging port of a

targeted wheel is just above the slurry level.

6. Open the air release port and N2 charging port for wheel A, purge N2 with 5 psi

pressure for 1 minute. Then rotate the wheel and purge N2 from the opposite side.

The wheel should be gently agitated during the purging to ensure no air (O2) is

trapped in a blind spot inside the wheel.

7. Close the air release port and N2 charging port tightly

8. Repeat step 5 to 7 for wheel B, C, and D.

9. Close the N2 cylinder tightly after filling all wheels.

B.1.4 Starting and Stopping Sequence of the TWT

The steps for starting the TWT are shown below:

1. Before switching on the main power, move to the safety zone (the zone outside the

fenced Wear Wheel area) to avoid mishaps during the operation and maintenance of

the TWT.

93

B.1. WEAR MEASUREMENTS PROCEDURE

2. Make sure the control status is set to “Remote” status using the on-board toggle

switch near the VFD. Switch on the main power supply for the VFD.

3. Start the TWT control software. Make sure that the VFD is operating without

showing any fault code in the control software.

4. Ensure the speed variation alert system is on for safety monitoring.

5. Click “RUN” to start the wheel.

The steps for stopping the TWT are shown below:

1. Ensure the speed variation alert system is off.

2. Click “STOP” to stop the wheel. Once the wheel is fully stopped, turn off the main

power supply.

3. Take out the coupons from the wheels, and clean and weight the coupons as discussed

earlier.

4. Finally, clean the wheels for future tests.

B.1.5 Erosive Wear Rate Calculation

A sample of erosive wear rate calculation is performed in the following. The experiment

was performed in Wheel A, and there are two coupons involved in this experiments, which

are A2 and A4. The sand volume concentration is 15%, the particle size is 1 mm, and the

wheel speed is 30 RPM.

• Time:

Total time to run the wear experiment, tTR = 96 hours

Total time to stop the TWT due to slurry replacement, tSR = 11.8 hours

Total effective time to run the wear experiment, tETR = 84.2 hours = 9.61e−3 years

• Initial Mass (before the experiment):

Calibration specimen weight before the wear experiment, Mc,i = 501.94 g

Initial mass of test coupon A2, Mi,A2 = 497.28 g

Initial mass of test coupon A4, Mi,A4 = 490.87 g

• Final Mass (after the experiment):

Calibration specimen weight after the wear experiment, Mc,f = 501.94 g

Final mass of test coupon A2, Mf,A2 = 497.23 g

Final mass of test coupon A4, Mi,A4 = 490.82 g

94

B.2. TORQUE MEASUREMENTS PROCEDURE

• Material loss:

Material loss on test coupon A2, Ml,A2 = Mi,A2 - Mf,A2 + (Mc,f - Mc,i) = 0.05 g

Material loss on test coupon A4, Ml,A4 = Mi,A4 - Mf,A4 + (Mc,f - Mc,i) = 0.05 g

• Convert to thickness loss:

Density of the carbon steel test coupons, ρsteel = 0.0078 g/mm3

Eroded surface area, Ae = 65*65 = 4225 mm2

Thickness loss on test coupon A2, TL,A2 =Ml,A2

Aeρsteel= 1.52e−3 mm

Thickness loss on test coupon A4, TL,A4 =Ml,A4

Aeρsteel= 1.52e−3 mm

Average thickness loss, TL,avg = 0.5 ∗ (TL,A4 + TL,A2) = 1.52e−3 mm

• Wear rates: Erosive wear rates, Ew = f racTL,avgtETR = 0.16 mm/year

B.2 Torque Measurements Procedure

B.2.1 Slurry Charging and Coupon attachment

• The procedure to attach coupon and charge slurry is same as step 1 to 4 in Appen-

dix B.1.3

• However, it’s required to remove the test coupons from other wheels in torque

measurement for safety

B.2.2 Torque data collection

Once the wheel is filled with slurry, next step is to collect torque data. A computer

software, SENSIT (by Futek), was used for collection. The steps for collecting torque data

are listed below:

1. Open SENSIT at desktop, set sampling rate (300SPS) and test duration time (120s).

Also set the file path (i.e. C:\Users\lisheng\Desktop)

2. Start the wheel and run to desired speed (refer to Starting in previous section)

3. Once the wheel rotates at constant speed, click Start Test.

4. After 120s, an excel file will automatically show on the screen, save the file name in

the computer (i.e. dl600_10RPM_300SPS_120s_10%250umSil1_1).

95

B.2. TORQUE MEASUREMENTS PROCEDURE

B.2.3 Torque data processing

Due to the imbalance of TWT, electrical noise, and non-smooth movement in the timing-

belt at low speed, the torque value fluctuates during the measurements. In order to get a

representative mean value, signal filtering using MATLAB was used in this study (code in

Appendix F.1). The step to process the torque data are shown below:

1. Open the MATLAB code, set the file path and file name as following:

• File path: C:\Users\lisheng\Desktop

• File name: dl600_10RPM_300SPS_120s_10%250umSil1_1

2. Run the MATLAB code, and collect the mean value from the Command Window.

96

Appendix C

Moment of Inertia Calculation

Figure C.1: Demonstration of test coupon with its momentum arm

97

Figure C.2: Demonstration of coupon holder with its momentum arm

Table C.1: Moment of inertial calculation of the test coupon, coupon holder, bolt and nut

Coupon # Weight (g) r (mm) I (kg.m^2)A1 487.65 304.10 0.045Nut 4.65 291.73 0.0004Bolt 17.47 299.86 0.0018

holders 515.78 308.1814 0.049

Table C.2: Summary of moment of inertial calculation

Parts # I (kg.m^2)Nuts and Bolts *20 0.046Coupon Holders *5 0.247

Coupons 0.225Total 0.518

98

Appendix D

The Torque Amplitude of Imbalanceand Wobbling

Figure D.1: The torque amplitude of imbalance and wobbling

99

Appendix E

Experiment Results and SampleCalculation

100

E.1. WEAR RATES

E.1 Wear Rates

Table E.1: Wear results

Wheel Speed(RPM)

Particle Size(mm)

Sand VolumeConcentration

SRI(hour)

Test Period(hour)

Wear Rates(mm/year)

30

210%

24 96

0.19015% 0.519, 0.32920% 0.596, 0.475

110% 0.20015% 0.199, 0.14320% 0.480

0.42010% -0.03220% 0.08

0.25010% -0.03220% 0.286

60

1 15% 1.399

0.42010% 0.07515% 0.13620% 0.128

0.25010% 0.01515% 0.19620% 0.36

0.125 15% 0

900.420 15% 0.2330.250 15% 0.1870.125 15% 0.016

101

E.2. SAND-RELATED TORQUE RESULTS

E.2 Sand-Related Torque Results

Table E.2: List of sand-related torque results

Calculated Measured

Cs d50 N Cpack β θ hmaxA2

A1Ff Tf,bottom Tf,side Tf,total

Sand-relatedtorque

(%) (mm) (RPM) – (rad) (rad) (m) (–) (N·m) (N·m) (N·m) (N·m) (N·m)

10

1

10 0.573 0.473 0.520 3.29E-02 1 1.525 0.458 0.205 0.663 0.67320 0.559 0.478 0.518 3.36E-02 1 1.541 0.462 0.201 0.663 0.66630 0.568 0.477 0.538 3.35E-02 1 1.567 0.470 0.205 0.675 0.66140 0.519 0.491 0.508 3.54E-02 1 1.553 0.466 0.187 0.653 0.641

2

10 0.545 0.495 0.500 3.60E-02 1 1.695 0.508 0.199 0.708 0.64720 0.550 0.486 0.560 3.47E-02 1 1.553 0.466 0.192 0.658 0.64230 0.556 0.486 0.528 3.47E-02 1 1.595 0.479 0.198 0.677 0.65940 0.526 0.487 0.540 3.49E-02 1 1.510 0.453 0.186 0.639 0.66150 0.553 0.500 0.550 3.67E-02 1 1.696 0.509 0.193 0.702 0.66460 0.540 0.491 0.540 3.54E-02 1 1.764 0.529 0.195 0.724 0.644

15

1

10 0.584 0.542 0.589 4.29E-02 1 2.221 0.666 0.351 1.017 1.15520 0.568 0.552 0.585 4.46E-02 1 2.230 0.689 0.342 1.031 1.08030 0.563 0.548 0.620 4.39E-02 1 2.170 0.651 0.334 0.985 1.05040 0.554 0.550 0.609 4.42E-02 1 2.176 0.653 0.333 0.986 1.010

2

10 0.588 0.546 0.610 4.37E-02 1 2.263 0.679 0.379 1.058 1.08120 0.594 0.545 0.590 4.35E-02 1 2.303 0.691 0.383 1.075 1.05130 0.569 0.546 0.604 4.37E-02 1 2.148 0.644 0.352 0.997 1.07240 0.568 0.545 0.601 4.34E-02 1 2.181 0.654 0.352 1.006 1.03550 0.580 0.543 0.529 4.32E-02 1 2.310 0.693 0.362 1.055 1.00660 0.578 0.544 0.581 4.33E-02 1 2.238 0.671 0.349 1.020 0.984

20

1

10 0.596 0.609 0.550 5.39E-02 1 3.282 0.985 0.578 1.562 1.72520 0.595 0.605 0.546 5.32E-02 1 3.280 0.984 0.578 1.562 1.71330 0.598 0.609 0.569 5.39E-02 1 3.253 0.976 0.613 1.589 1.62740 0.591 0.609 0.509 5.39E-02 1 3.331 0.999 0.586 1.586 1.539

2

10 0.590 0.600 0.580 5.24E-02 1 3.128 0.938 0.567 1.505 1.54520 0.580 0.605 0.585 5.32E-02 1 3.062 0.919 0.550 1.468 1.62530 0.600 0.603 0.576 5.29E-02 1 3.156 0.947 0.572 1.519 1.62540 0.569 0.606 0.590 5.34E-02 1 3.010 0.903 0.538 1.441 1.54350 0.590 0.600 0.584 5.24E-02 0.937 2.839 0.852 0.522 1.374 1.43260 0.600 0.603 0.570 5.29E-02 0.855 2.674 0.802 0.485 1.287 1.381

102

E.3. SAMPLE CALCULATION

E.3 Sample Calculation

Figure E.1: Demonstration of β, θ, and hmax

The sample calculation is for 10% 2 mm gravel at 30 RPM.

• Cpack:

Total contact area, A1 (refer to Figure 5.20a) = 6.36e−3 m2

Width of the TWT channel, W = 0.065 m

Total packed volume of the sliding bed (sands + voids), Vpacked = 0.065 ∗ 6.36e−3 =

4.1e−4 m3

Total volume of sands, Vsand = total slurry volume* particle volume concentration =

2.3 liter * 0.1 = 2.3e−4 m3

Cpack = VsandVpacked

= 0.556

• Calculate Tf,bottom

Density of carrier fluid, ρf = 1000 kg/m3

Density of sands, ρs = 2650 kg/m3

β = 0.486; θ = 0.528

103

E.3. SAMPLE CALCULATION

Ff,bottom (refer to Equation (5.12))= 0.35 * 9.81 * 1650 * 0.62 * sin(0.486)−0.486cos(0.486)2cos(0.528) *

0.556 * 0.065 = 1.592 N

According to Equation (5.13), Tf,bottom = Ff,bottom* 0.5 * DT = 1.726 * 0.5 * 0.6 = 0.478

N.m

• Calculate Tf,side

rmin (refer to Equation (5.16)) = 0.5 * 0.6 - 3.47e−2 = 0.265 m

αmax (refer to Equation (5.17)) = cos−1( 0.265r )

Tf,side (refer to Equation (5.15)) =

0.35 ∗ 9.81 ∗ 1650 ∗ 0.556cos(0.528)

∗∫ 0.3

0.265

∫ cos−1( 0.265r )

− cos−1( 0.265r )

r2(r cos α − 0.3 cos(0.486))d α d r (E.1)

Tf,side = 0.35 * 9.81 * 1650 * 0.556 * 2.71e−5cos(0.528) = 0.099 N.m

• Calculate Tf, total:

Tf, total = Tf,bottom + 2 * Tf,side = 0.676 N.m

104

Appendix F

MATLAB Code

F.1 Signal Filtering

1 %This s c r i p t f i l t e r s data obtained from a FUTEK torque sensor to removehigh−frequency noise and to obta in the mean torque

2 %3 % ( c ) David Breakey4 % Last updated : 2017−Jun−285

6 %Input path7 path = ’C:\ Users\l i sheng\Google Drive\Torque\Brad\Commissioning on

August\August 11 th 2017\15_ 2mm gravel in B 30 60 90RPM\ ’ ;8 %Input f i l e9 f i l e = ’ dl600_60RPM_300SPS__120s_15%2mmgravel_1 ’ ;

10

11 fbase = 0 ;12

13 rpmind = s t r f i n d ( lower ( f i l e ) , ’rpm ’ ) ;14 rpmMax = str2double ( f i l e ( rpmind−2:rpmind−1) ) ;15 rpmToHz = 1/60;16 hzMax = rpmMax*rpmToHz ;17

18 f s = 3 0 0 ;%Hz19 dt = 1/ f s ;%s20

21 data = x ls read ( [ path f i l e ] ) ;22

23 ncol = s i z e ( data , 2 ) /6;24

25 nrow = min (65535 , s i z e ( data , 1 ) ) ;

105

F.1. SIGNAL FILTERING

26 [ t_d , s i g ] = deal ( zeros ( nrow* ncol , 1 ) ) ;27 f o r c i = 1 : ncol28 s i g ( ( c i −1) *nrow + ( 1 : nrow ) ) = data ( : , 2 + ( c i −1) * 6 ) ;29 t_d ( ( c i −1) *nrow + ( 1 : nrow ) ) = data ( : , 1 + ( c i −1) * 6 ) * dt ;30 end31

32 s i g ( isnan ( s i g ) ) = [ ] ;%Signa l data33 t_d ( isnan ( t_d ) ) = [ ] ;34

35

36 s i g = s i g ( 1 : length ( s i g )−mod( length ( s i g ) , 2 ) ) ;37 t_d = t_d ( 1 : length ( t_d )−mod( length ( t_d ) , 2 ) ) ;38

39

40 N = length ( s i g ) ;%Number of samples41 t = ( 0 :N−1) * dt ;42

43

44 %F i l t e r params45 f c = 3*hzMax ;%Hz46 f i l t e r f i l e = s t r r e p ( s p r i n t f ( ’ f i l t _ d a t a _ f s %05.0 f _ f c %05.2 f ’ , f s , f c ) , ’ . ’ , ’− ’

) ;47 i f ~ e x i s t ( [ f i l t e r f i l e ’ . mat ’ ] , ’ f i l e ’ )48 F = d e s i g n f i l t ( ’ lowpass f i r ’ , ’ PassbandFrequency ’ , fc , ’

StopbandFrequency ’ , 1 . 5 * fc , ’ PassbandRipple ’ , 1 , ’StopbandAttenuation ’ , 30 , ’ SampleRate ’ , f s ) ;

49 save ( f i l t e r f i l e , ’ F ’ )50 e l s e51 load ( f i l t e r f i l e )52 end53

54 s i g _ f = f i l t f i l t ( F , s i g ) ;55

56 %P l o t f i l t e r e d and u n f i l t e r e d57 f i g u r e (2+ fbase )58 p l o t ( t , s ig , t , s i g _ f )59 ylim ([−1 5 ] )60 x l a b e l ( ’ t ’ )61 y l a b e l ( ’T (Nm) ’ )62

63 %Spectra64 df = f s /N;65 f = ( 0 :N/2−1) * df ;

106

F.2. ROTATION ANGLE MEASUREMENTS (BY FUTEK)

66 SIG = f f t ( s i g ) ;67 SIG_f = f f t ( s i g _ f ) ;68 f i g u r e (3+ fbase )69 loglog ( f , abs ( SIG ( 1 :N/2) ) . ^ 2 , f , abs ( SIG_f ( 1 :N/2) ) . ^ 2 )70 x l a b e l ( ’ f (Hz) ’ )71 y l a b e l ( ’ FFT ( s i g ) ’ )72

73 %%74

75 %PSD76 NFFT = 2^( nextpow2 ( f s ) +4) ;77 fp = ( 0 : NFFT/2−1) * f s /NFFT ;78 nblocks = f l o o r (N/NFFT) ;79 [PSD , PSD_f ] = deal ( zeros (NFFT , 1 ) ) ;80 f o r ni = 1 : nblocks81 PSD = f f t ( s i g ( ( 1 : NFFT) + ( ni −1) *NFFT) , NFFT) + PSD ;82 PSD_f = f f t ( s i g _ f ( ( 1 : NFFT) + ( ni −1) *NFFT) , NFFT) + PSD_f ;83 end84 PSD = 2* abs (PSD ( 1 : NFFT/2) . ^ 2 ) /nblocks/NFFT^2;85 PSD_f = 2* abs ( PSD_f ( 1 : NFFT/2) . ^ 2 ) /nblocks/NFFT^2;86 f i g u r e (4+ fbase )87 loglog ( fp , PSD , fp , PSD_f )88 x l a b e l ( ’ f (Hz) ’ )89 y l a b e l ( ’PSD ’ )90

91 rpmp = fp/rpmToHz ;92 f i g u r e (5+ fbase )93 loglog (rpmp , PSD , rpmp , PSD_f )94 x l a b e l ( ’RPM’ )95 y l a b e l ( ’PSD ’ )96

97 t r impoints = 5/dt ;98

99 f p r i n t f ( ’Mean @ %i RPM: %5.3 f N−m\n ’ ,rpmMax, mean( s i g _ f ( t r impoints +1: end−t r impoints ) ) )

F.2 Rotation Angle Measurements (by FUTEK)

1 %% Clear Var iab les and Open FUTEK USB DLL Assembly2

3 c l e a r v a r i a b l e s ;4 pause ( ’ on ’ ) ;5

107


6 %Net . addAssembly r e q u i r e s the f u l l f i l e path to a c c e s s p r i v a t e . d l lf i l e s

7 %such as the FUTEK USB DLL .8 %With the current f o l d e r s e t as where both t h i s s c r i p t and the . d l l f i l e9 %are located , the which ( ) funct ion re turns the f u l l f i l e path .

10

11 %The included copy of FUTEK_USB_DLL . d l l has been compiled f o r e i t h e r 32b i t

12 %or 64 b i t plat forms . I f you are running MATLAB 32 b i t use only the 32b i t

13 %. d l l f i l e and i f you are using MATLAB 64 b i t use only the 64 b i t . d l l14 %f i l e .15

16 %F u l l . d l l f i l e API a v a i l a b l e here : ht tp ://www. futek . com/ f i l e s /docs/API/FUTEK_USB_DLL/webframe . html

17

18 %Requires . Net 4 . 0 and Windows19 NET. addAssembly ( which ( ’FUTEK_USB_DLL . d l l ’ ) ) ;20 import FUTEK_USB_DLL . *21 import FUTEK_USB_DLL . USB_DLL . *22

23 %S e r i a l Number in ’ ’ f o r your Instrument or USB Output Kit24 serialNumber = ’ 702997 ’ ;25

26 %% I n i t i a l i z e Var iab les27

28 i n s t r = USB_DLL ( ) ;29 channel = 0 ;30 samples = 2 0 0 ;31 deviceHandle = ’ ’ ;32 devi ceS ta t us = 0 ; %#ok<NASGU>33 deviceStatusChr = ’ ’ ;34 temp = 0 ;35 o f f s e t V a l u e = 0 ;36 f u l l S c a l e V a l u e = 0 ;37 f u l l S c a l e L o a d = 0 ;38 decimalPoint = 0 ;39 normalData = 0 ;40 calculatedReading = 0 ;41 unitCode = 0 ;42 unitChr = ’ ’ ;43 unitCodeData = { ’ atm ’ ; ’ bar ’ ; ’dyn ’ ; ’ f t−H20 ’ ; ’ f t−lb ’ ; ’ g ’ ; ’g−cm ’ ; ’g−

mm’ ; ’ in−H20 ’ ; ’ in−lb ’ ;

108


44 ’ in−oz ’ ; ’ kdyn ’ ; ’ kg ’ ; ’ kg−cm ’ ; ’ kg/cm2 ’ ; ’ kg−m’ ; ’ k lbs ’ ; ’kN ’ ; ’ kPa’ ; ’ kpsi ’ ;

45 ’ l b s ’ ; ’Mdyn ’ ; ’mmHG’ ; ’mN−m’ ; ’MPa ’ ; ’MT’ ; ’N’ ; ’N−cm ’ ; ’N−m’ ; ’N−mm’ ;

46 ’ oz ’ ; ’ ps i ’ ; ’ Pa ’ ; ’T ’ ; ’mV/V ’ ; ’uA ’ ; ’mA’ ; ’A ’ ; ’mm’ ; ’cm ’ ;47 ’dm’ ; ’m’ ; ’km ’ ; ’ in ’ ; ’ f t ’ ; ’yd ’ ; ’mi ’ ; ’ug ’ ; ’mg ’ ; ’LT ’ ;48 ’mbar ’ ; ’ ?C ’ ; ’ ?F ’ ; ’K ’ ; ’ ?Ra ’ ; ’kN−m’ ; ’g−m’ ; ’nV ’ ; ’uV ’ ; ’mV’ ;49 ’V ’ ; ’kV ’ ; ’NONE’ } ;50 c a l c u l a t e d T a b l e = c e l l ( samples , 4 ) ;51

52 %% Open Connection and Begin Data Capture Run53

54 %I n t i a l i z e s the connect ion to instrument with the s p e c i f i e d S e r i a lNumber .

55 %Fetches Device S t a t u s to determine i f connect ion i s s u c c e s s f u l orre turns

56 %the e r r o r code and e x i t s57 i n s t r . Open_Device_Connection ( serialNumber ) ;58 devi ceS ta t us = i n s t r . DeviceStatus ( ) ;59 i f dev iceS ta tus == 060 disp ( ’ Device loaded s u c c e s s f u l l y . Measuring . . . ’ )61 e l s e62 deviceStatusChr = num2str ( dev ice S ta tus ) ;63 disp ( [ ’ Device Error ’ deviceStatusChr ] )64 re turn ;65 end66

67 %Fetches the device handle needed to r e t r i e v e s tored values used in load68 %c a l c u l a t i o n69 deviceHandle = i n s t r . DeviceHandle ( ) ;70 save ( ’ devHandleStorage . mat ’ , ’ deviceHandle ’ ) ;71

72 %% Capture Var iab les73

74 %Uses the FUTEK USB DLL to r e t r i e v e values f o r load c a l c u l a t i o n75 %The . d l l re turns these values as a System . S t r i n g76 %This i s then converted to a char value and then a number77 %L a s t l y i f there was a r e t r i e v a l e r r o r the . d l l re turns ’ Error ’ which78 %converts to an empty value . isEmpty ( ) t e s t f o r t h a t and cont inues79 %r e t r i e v a l u n t i l a number i s returned .80

81 % O f f s e t Value82 while t rue

109


83 temp = str2num ( char ( i n s t r . Get_Offset_Value ( deviceHandle ) ) ) ; %#ok<*ST2NM>

84 i f ~( isempty ( temp ) )85 break86 end87 end88 o f f s e t V a l u e = temp ;89

90 %F u l l S c a l e Value91 while t rue92 temp = str2num ( char ( i n s t r . Get_Ful l sca le_Value ( deviceHandle ) ) ) ;93 i f ~( isempty ( temp ) )94 break95 end96 end97 f u l l S c a l e V a l u e = temp ;98

99 % F u l l S c a l e Load100 while t rue101 temp = str2num ( char ( i n s t r . Get_Ful lscale_Load ( deviceHandle ) ) ) ;102 i f ~( isempty ( temp ) )103 break104 end105 end106 f u l l S c a l e L o a d = temp ;107

108 % Decimal Point109 while t rue110 temp = str2num ( char ( i n s t r . Get_Decimal_Point ( deviceHandle ) ) ) ;111 i f ~( isempty ( temp ) )112 break113 end114 end115 decimalPoint = temp ;116 %Test to see i f decimal point returned i s outs ide defined decimal point117 %values118 %See here f o r more information :119 %http ://www. futek . com/ f i l e s /docs/API/FUTEK_USB_DLL/webframe . html#

DecimalPointCodes . html120 i f decimalPoint >= 6121 disp ( ’ Decimal Point Out of Range/Undefined ’ )122 re turn ;123 end

110


124

125 % Get Unit Code and Convert to Actual Load126 while t rue127 temp = str2num ( char ( i n s t r . Get_Unit_Code ( deviceHandle ) ) ) ;128 i f ~( isempty ( temp ) )129 break130 end131 end132 unitCode = temp + 1 ;133 unitChr = unitCodeData { unitCode , 1 } ;134

135 boardType = i n s t r . Get_Type_of_Board ( deviceHandle ) ;136 FWversion = i n s t r . Get_Firmware_Version ( deviceHandle ) ;137

138 %Begin loop to c o l l e c t samples139 [ tnow , angle ] = deal ( zeros ( samples +1 ,1) ) ;140 blocks = repmat ( char ( ’ ’ ) , samples +1 ,3000) ;141 f s = 1 0 ;142 sps = 1 0 0 ;143 dt = 1/ f s ;144

145

146 x = 1 ;147 t i c148 while t rue149 i f ( toc * fs >=x +1)150 data = char ( i n s t r . Fast_Data_Request ( deviceHandle , 0 , 0 , boardType , ’

9 ’ , FWversion , channel ) ) ;151 blocks ( x , 1 : length ( data ) ) = data ;152 i n s t r . Get_Rotation_Values ( deviceHandle ) ;153 angle ( x ) = i n s t r . AngleValue ;154 tnow ( x ) = toc ; %Retr ieve Current Time155 x = x +1;156 i f x>=samples+1+1%We w i l l throw away the f i r s t ( b u f f e r i s bigger

)157 break ;158 end159 end160 end161 t = tnow ( 2 : end ) − tnow ( 2 ) ;162 blocks = blocks ( 2 : end , : ) ;163 angle = angle ( 2 : end , : ) ;164 %% Close Connection

111


165

166 % Close the connect ion to properly disconnect device and allow a c c e s s by167 % other programs , otherwise you must disconnect drive from USB port .168 i n s t r . Close_Device_Connection ( deviceHandle ) ;169

170 %% Ca l c u l a te Read Out and Display171 % times = d a t e s t r ( tnow , ’ dd−mm−yyyy HH:MM: SS FFF ’ ) ;172 % t = ( tnow ( 2 : end ) − tnow ( 2 ) ) *24*60*60 ;% Times in seconds173

174 %% Assemble blocks175 normalData = i n f ( round ( 1 . 1 * sps *max( t ) ) , 1 ) ;176 normalDataTS = repmat ( char ( ’ ’ ) , round ( 1 . 1 * sps *max( t ) ) , 2 1 ) ;177 x i = 0 ;178 e r r o r s = f a l s e ( samples , 1 ) ;179 f o r x =1: samples180 i f ~conta ins ( lower ( blocks ( x , : ) ) , ’ e r r o r ’ )181 commas = s t r f i n d ( blocks ( x , : ) , ’ , ’ ) ;182 cpdp = 8 ;%commas per data point183 f o r s i = 1 : s t r2double ( blocks ( x , commas ( 1 ) +1:commas ( 2 ) −1) )184 normalData ( x i +1) = str2double ( blocks ( x , commas( 2+ ( s i −1) *

cpdp ) +1:commas( 3+ ( s i −1) * cpdp ) −1) ) ;185 TS = blocks ( x , commas( 6+ ( s i −1) * cpdp ) +1:commas( 7+ ( s i −1) * cpdp )

−1) ;186 normalDataTS ( x i + 1 , 1 : length ( TS ) ) = s t r t r i m ( TS ) ;187 x i = x i + 1 ;188 end189 e l s e190 e r r o r s ( x ) = true ;191 i f x<3192 e r r o r ( ’ Error rece ived during f i r s t two blocks . ’ ) ;193 e l s e194 warning ( ’ Error rece ived during measurement . There w i l l be

NaNs in time s i g n a l . Estimated samples l o s t : %i ’ , s i ) ;195 normalData ( x i + ( 1 : s i ) ) = NaN;196 e r r o r s ( x ) = true ;197 x i = x i + s i ;198 end199 end200 end201 normalDataTS ( i s i n f ( normalData ) , : ) = [ ] ;202 normalData ( i s i n f ( normalData ) ) = [ ] ;203 tn = ( 0 : length ( normalData ) −1)/sps ;204

112

F.3. TORQUE SENSOR CALIBRATION

205 normalDataTS = mat2ce l l ( normalDataTS , ones ( s i z e ( normalDataTS , 1 ) , 1 ) , s i z e (normalDataTS , 2 ) ) ;

206

207 % Use r e t r i e v e d v a r i a b l e s to c a l c u l a t e measured load c e l l output208 calculatedReading = normalData − o f f s e t V a l u e ;209 calculatedReading = calculatedReading /( f u l l S c a l e V a l u e − o f f s e t V a l u e ) ;210 calculatedReading = calculatedReading * f u l l S c a l e L o a d ;211 calculatedReading = calculatedReading /10^ decimalPoint ;212

213 T = calculatedReading ;214 deg = ( angle−angle ( 1 ) ) /40;215

216 f i g u r e ( 1 0 * channel +1)217 p l o t ( tn , T )218 f i g u r e ( 1 0 * channel +2)219 p l o t ( t , deg )

F.3 Torque Sensor Calibration

1 %This s c r i p t performs a s e n s o r _ c a l i b r a t i o n f o r a torque sensor bycomparing

2 %the angular r o t a t i o n ’ s second d e r i v a t i v e ( angular a c c e l e r a t i o n ) to the3 %measured torque value4 %5 % ( c ) David Breakey6 % Last updated : 2018−Feb−267

8 c a l i n d s = 1 : 6 ;%S e l e c t s which c a l i b r a t i o n f i l e to use9 warning o f f

10

11 f o r c a l i n d = c a l i n d s12

13 %Folder and f i l e to process14 currd = [pwd ’\ ’ ] ;15 c a l f i l e s = c e l l ( 6 , 1 ) ;16 c a l f i l e s { 1 } = ’ dl300sps_40s_nocoupons_June13th_1_4errors . mat ’ ;17 c a l f i l e s { 2 } = ’ dl300sps_40s_nocoupons_June13th_2_4errors . mat ’ ;18 c a l f i l e s { 3 } = ’ dl300sps_40s_nocoupons_June13th_3_1errors . mat ’ ;19 c a l f i l e s { 4 } = ’ dl300sps_40s_5coupons_June13th_1_2errors . mat ’ ;20 c a l f i l e s { 5 } = ’ dl300sps_40s_5coupons_June13th_2_3errors . mat ’ ;21 c a l f i l e s { 6 } = ’ dl300sps_40s_5coupons_June13th_3_1error . mat ’ ;22

23 c a l f i l e = c a l f i l e s { c a l i n d } ;

113


24

25 %f e s t i s an es t imate of the f r i c t i o n torque at zero angular v e l o c i t y26 %f e s t was obtained by running the code s e v e r a l t imes to minimize

f e s t _ e r r ,27 %which i s c a l c u l a t e d from the e r r o r between the torque and I * alpha

curves28 %in the d e c e l e r a t i n g s tage of r o t a t i o n29 f e s t = 0 . 5 3 ;%Nm30

31 %f o r c e _ i n t e r c e p t causes the i n t e r c e p t of the l i n e a r f i t to pass throughthe

32 %o r i g i n . I f f e s t i s c o r r e c t , t h i s should be the case .33 f o r c e _ i n t e r c e p t = 1 ;34

35 %Load data36 data = load ( c a l f i l e ) ;37

38 %%39

40 %Get data r a t e of Torque s i g n a l41 dtT = data . tn ( 2 )−data . tn ( 1 ) ;42 fsT = 1/dtT ;43

44 %Get data r a t e of angle s i g n a l45 dtdeg = mean( d i f f ( data . t ) ) ;46 fsdeg = 1/dtdeg ;47

48 %Get data49 t t = data . tn ’ ;50 T = data . T ;51 deg = data . deg * pi /180;%now in radian52 tdego = data . t ;53

54 %Find the i n i t i a l and f i n a l torque value f o r the s i g n a l55 navg = 2 5 ;56 T_i = mean( T ( 1 : navg ) ) ;57 T_f = mean( T ( end−navg +1: end ) ) ;58 deg_i = mean( deg ( 1 : navg ) ) ;59 deg_f = mean( deg ( end−navg +1: end ) ) ;60

61 %These f i t parameters come from a zero−load s t a t i c measurement of torquea t d i f f e r e n t angular p o s i t i o n s ( F r i c t i o n Torque Vs . Angle . x l s x )

62 A = 0 . 2 2 5 ;

114


63 B = 8 0 ;64 C = 0 . 1 3 ;65 Tcorr = @( theta , phase ) A* s i n ( t h e t a − B* pi /180 + phase ) + C;66 %Any i n i t i a l torque value could be obtained at one of two d i f f e r e n t

angles67 %( phase a or phase b )68 %The only way to choose which i s to use the f i n a l torque value as well

to69 %check which gives a b e t t e r guess70 phaseguess = ( as in ( ( T_i − C) /A) − deg_i + B* pi /180) ;71 phaseguessb= ( ( pi−as in ( ( T_i − C) /A) ) − deg_i + B* pi /180) ;72

73 %Find the phase option t h a t gives the bes t guess of the f i n a l torque74 ra = abs ( T_f−Tcorr ( deg_f , phaseguess ) ) ;75 rb = abs ( T_f−Tcorr ( deg_f , phaseguessb ) ) ;76 f p r i n t f ( ’ Phase c o r r e c t i o n (Nm) . Option A: %5.3 f Option B : %5.3 f F i l e : %s

\n ’ , ra , rb , c a l f i l e ) ;77 i f ra < rb78 phase = phaseguess ;79 e l s e80 phase = phaseguessb ;81 end82

83 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%84 %%% Process ing option B : Downsample torque s i g %%%85 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%86 %%87 f s r a t = round ( fsT/fsdeg ) ;88 convF = ones ( 1 , f s r a t ) / f s r a t ;89 Tcv = conv ( T , convF , ’ va l id ’ ) ;%T has already been c o r r e c t e d f o r angle90 Tcv = Tcv ( 1 : f s r a t : end ) ;91 t t c v = t t ( f s r a t : f s r a t : end ) ;92 tdeg = tdego ;93 degs = deg ;94

95 t t c v = t t c v ( t t cv >=min ( tdeg ) ) ;96 Tcv = Tcv ( t t cv >=min ( tdeg ) ) ;97 tdeg = tdeg ( 1 : length ( t t c v ) ) ;98 degs = degs ( 1 : length ( t t c v ) ) ;99

100 Tcv = Tcv − Tcorr ( degs , phase ) ;101

102 %Apply gaussian f i l t e r i n g to f i x f i n i t e p o s i t i o n r e s o l u t i o n

115


103 degs = conv ( degs , f s p e c i a l ( ’ gaussian ’ , [ 5 1 ] , 2 ) , ’ same ’ ) ;104 degs = degs ( 1 : end−10) ;105 tdeg = tdeg ( 1 : end−10) ;106

107 %Orig ina l s i g n a l%108 f i g u r e ( 1 1 )109 p l o t ( t t , T , t t cv , Tcv , tdeg , degs )110 x l a b e l ( ’ t ( s ) ’ )111 y l a b e l ( ’T (Nm) and Angle ( rad ) ’ )112

113 %Angular v e l o c i t y%114 f i g u r e ( 1 2 )115 omega = d i f f ( degs ( 1 : end−1) ) /dtdeg ;%Omega = ddeg/dt116 to = tdeg ( 1 : end−2)+ d i f f ( tdeg ( 1 : 2 ) ) /2;117 p l o t ( t t cv , Tcv , to , omega )118 x l a b e l ( ’ t ( s ) ’ )119 y l a b e l ( ’T (Nm) and Omega ( rad/s ) ’ )120

121 %Angular a c c e l e r a t i o n%122 f i g u r e ( 1 3 )123 alpha = d i f f ( omega ( 1 : end−1) ) /dtdeg ;%Alpha = domega/dt124 t a = to ( 1 : end−2)+ d i f f ( tdeg ( 1 : 2 ) ) /2;125 p l o t ( t t cv , Tcv , ta , alpha )126

127 %%%Set ROI − Region of i n t e r e s t %%%128 f i g u r e ( 1 4 )129 ROI = [ to ( f ind ( omega > 0 . 0 5 , 1 , ’ f i r s t ’ ) ) ta ( f ind ( alpha <0.2 & omega ( 2 : end−1)

>0 .5 ,1 , ’ f i r s t ’ ) ) ] ;130 ROI2= [ to ( f ind ( alpha < −0.2 ,1 , ’ f i r s t ’ ) ) t a ( f ind ( ta >ROI ( 2 ) & omega ( 2 : end−1)

<0 .5 ,1 , ’ f i r s t ’ ) ) ] ;131 alphaROI = alpha ( ta >ROI ( 1 ) & ta <ROI ( 2 ) ) ;132 taROI = ta ( ta >ROI ( 1 ) & ta <ROI ( 2 ) ) ;133 tkeep = t tcv >ROI ( 1 ) & t tcv <ROI ( 2 ) ;134 s h i f t = 0 ;135 tkeep = [ tkeep ( s h i f t +1 : end ) tkeep ( 1 : s h i f t ) ] ;136 TROI = Tcv ( tkeep ) ;137 ttROI = t t c v ( tkeep ) ;138 TROI = TROI ( 1 : length ( alphaROI ) ) ;139 ttROI = ttROI ( 1 : length ( alphaROI ) ) ;140 p l o t ( ttROI , TROI , taROI , alphaROI )141

142 % Angular a c c e l e r a t i o n in region of i n t e r e s t %143 i f ~ f o r c e _ i n t e r c e p t

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144 pM = [ alphaROI ones ( s i z e ( alphaROI ) ) ] ;145 p = pM\(TROI−f e s t ) ;146 e l s e147 pM = alphaROI ;148 p = [pM\(TROI−f e s t ) ; 0 ] ;149 end150 p l o t ( alphaROI , TROI−f e s t , ’ x ’ , [ 0 max( alphaROI ) ] , polyval ( p , [ 0 max( alphaROI )

] ) )151 x l a b e l ( ’ Alpha ( rad/s$^2$ ) ’ )152 y l a b e l ( ’T (Nm) ’ )153

154 %Estimate f e s t by looking at e r r o r in d e c e l e r a t i o n stage155 Test = alpha *p ( 1 ) +p ( 2 ) + f e s t ;156 a1 = Tcv ( t t cv >ROI2 ( 1 ) & t tcv <=ROI2 ( 2 ) ) ;157 a2 = Test ( ta >ROI2 ( 1 ) & ta <=ROI2 ( 2 ) ) ;158 a1 = a1 (~ isnan ( a1 ) ) ;159 a2 = a2 (~ isnan ( a1 ) ) ;160 f e s t _ e r r = mean( a1 − a2 ) /2;161

162 %Add the new torque es t imate to the e a r l i e r p l o t163 f i g u r e ( 1 3 )164 hold on165 p l o t ( ta , Test , t t c v ( t t cv >ROI2 ( 1 ) & t tcv <ROI2 ( 2 ) ) , Tcv ( t t cv >ROI2 ( 1 ) & t tcv <

ROI2 ( 2 ) ) , ’ . ’ , t a ( ta >ROI2 ( 1 ) & ta <ROI2 ( 2 ) ) , Test ( ta >ROI2 ( 1 ) & ta <ROI2( 2 ) ) , ’ . ’ )

166 hold o f f167

168 %P r i n t the r e s u l t s169 f p r i n t f ( ’METHOD B − Slope : %5.3 f Nm/( rad/s ^2)=>kg *m^2 I n t e r c e p t : %5.3 f (

Nm) f e s t _ e r r : %5.3 f (Nm) F i l e : %s\n ’ ,p , f e s t _ e r r , c a l f i l e )170

171 end

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Relating Slurry Friction with Erosion Rate Using A Toroid ... · 3.11 Distribution of contact load...

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Transcript of Relating Slurry Friction with Erosion Rate Using A Toroid ... · 3.11 Distribution of contact load...