Transcript
In the name of god, the merciful
WIRE-ARC SPRAYING SYSTEM: Particle Production, Transport, and Deposition
by
AmirHossein Pourmousa Abkenar
A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy Graduate Department of Mechanical and Industrial Engineering University of Toronto
© Copyright by AmirHossein Pourmousa Abkenar 2007
ISBN: 978-0-494-39723-7
Abstract
WIRE-ARC SPRAYING SYSTEM: Particle Production, Transport, and Deposition
AmirHossein Pourmousa Abkenar Doctor of Philosophy Graduate Department of Mechanical and Industrial Engineering University of Toronto 2007
Protective coatings are important to metal working. Thermal spray is a rapidly growing market, and wire-arc spraying is gaining a significant share of this market because of its low operating/equipment costs and high material/energy efficiency. Although wire-arc spraying is widely used, many of its underlying processes are not yet fundamentally understood. This work examines and explains different aspects of a wire-arc system. In wire-arc spraying, two consumable wires are continuously fed into the gun. An electric arc is struck between the tips of these two wires and continuously melts their material. A crossflow gas removes the molten material from the wire-tips and accelerates them towards a substrate, over which the detached particles form a protective coating layer. An imaging system was developed to take pictures of the arc, and determine its length and shape. Using the information extracted from such pictures, a computational fluid dynamic model of the wire-arc torch was developed to estimate the shear stresses on the wire-tips and also sizes of primary breakups from the two electrodes.
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Shortly after primary breakups, the detached particles break up into smaller particles (secondary atomization). The size and velocity of such particles were measured in-flight using a DPV-2000 system for a range of operating parameters. A technique was developed to identify and separate the size distributions of particles produced by atomization of molten metal at either the anode or cathode by assuming that both follow a log-normal distribution. (This assumption was also verified experimentally). It was shown that particles produced by the anode are almost two times larger than those originating from the cathode. Furthermore, effect of operating parameters on size distribution of anodic and cathodic particles was investigated. Experiments were also conducted to study the effect of impact velocity and substrate temperature on the properties of individual wire-arc splats and coatings. Aluminum was sprayed onto polished stainless-steel coupons maintained at temperatures ranging from 25°C to 450°C. At low substrate temperature, droplets splashed, forming irregular splats; at higher temperatures there was no splashing and splats formed circular disks. The temperature at which the transition occurred decreased with increasing impact velocity.
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To my love, Malahat …
without whom this work could have never been done, or could have been done much sooner...
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Acknowledgements
I would like to take this opportunity to acknowledge my supervisors and mentors, Professor Javad Mostaghimi and Professor Sanjeev Chandra, for their invaluable guidance, encouragement, and support throughout this study. I would like to express my sincere appreciations to Professor Javad Mostaghimi for his patience and understanding. His concise but insightful comments fueled me with ideas. I extend thanks to my supervisory committee members, Professor Bendzsak, Professor Sullivan, Professor Ashgriz, and Professor Bussmann for their advice and helpful suggestions. I am also grateful to Dr. Larry Pershin and Mr. Tiegang Li for their assistance in the lab, and Ms. Brenda Fung for her excellent administrative support at the office of graduate studies. In addition, I would like to thank all my colleagues at the Center for Advanced Coating Technologies for making this journey enjoyable. My special thanks goes to Ali Abedini, my lab partner, Hanif Montazeri, my numerical handyman, Rajeev Dhiman, my heat transfer expert, Hamid Salimi, my industrial advisor, Fardad Azarmi, my political rival, Hamed Samadi, my financial advisor, and many more including Liming, Libing, Michelle, Bob, Ken, Ala, Mehdi, Afsoon, Nikoo, Andre, Reza, and many more friends in the department. I am grateful to my family, especially my parents for their never ending love and support. I would like to extend my special thanks to my father-in-law who was not only my teacher, but also my mentor in difficult times. To my wife, Malahat: Without you, your energetic essence, enthusiastic support, and unconditional kindness, I could have never completed this work. I love you and I gladly dedicate this thesis to you.
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Table of Contents
ABSTRACT ................................................................................................................................................................II ACKNOWLEDGEMENTS .......................................................................................................................................V CHAPTER 1
INTRODUCTION ..............................................................................................................................1
1.1 BACKGROUND, MOTIVATION, AND LITERATURE SURVEY ...............................................................................1 1.1.1 Thermal spray.......................................................................................................................................1 1.1.2 Twin-Wire-Arc Spray............................................................................................................................5 1.1.2.1
Description of the Wire-Arc spraying process.................................................................................. 5
1.1.2.2
Operating parameters........................................................................................................................ 8
1.1.3 Brief Literature Review ......................................................................................................................10 1.1.3.1
Previous Work on Droplet Production and Transport..................................................................... 10
1.1.3.2
Previous Work on Bimodal Size Distribution of In-flight Particles................................................ 12
1.1.3.3
Previous Work on Particle Deposition............................................................................................ 13
1.2 STATEMENT OF OBJECTIVES ..........................................................................................................................14 1.3 SCOPE OF THE PRESENT WORK .......................................................................................................................15 1.4 OUTLINE OF THE THESIS .................................................................................................................................16 CHAPTER 2
EXPERIMENTAL APPARATUS AND PROCEDURES.............................................................17
2.1 COATING AND PROCESS DIAGNOSTICS ...........................................................................................................17 2.1.1 Coating Characterization...................................................................................................................17 2.1.2 Process Characterization ...................................................................................................................18 2.2 VALUARC 200 SPRAYING SYSTEM AND ITS CHARACTERISTICS .....................................................................26 2.2.1 Volume-Flow-Rate..............................................................................................................................32 2.2.2 Arc Current.........................................................................................................................................33
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CHAPTER 3
PARTICLE BREAKUP: THERMAL SPRAY GUN ....................................................................38
3.1 EXPERIMENTAL STUDIES ...............................................................................................................................38 3.1.1 Imaging system ...................................................................................................................................39 3.1.2 Current and Voltage Fluctuations......................................................................................................45 3.2 NUMERICAL STUDIES .....................................................................................................................................49 3.2.1 Flow dynamics of the nozzle geometry ...............................................................................................49 3.2.2 Simplified Arc Solution.......................................................................................................................61 3.2.3 Arc Heating in a cross flow ................................................................................................................66 3.3 SIMPLIFIED BREAKUP MODEL ........................................................................................................................72 CHAPTER 4
PARTICLE TRANSPORT: IN-FLIGHT PARTICLES...............................................................75
4.1 BACKGROUND................................................................................................................................................75 4.2 SPATIAL CHARACTERISTICS OF THE SPRAY ...................................................................................................77 4.3 BIMODAL PARTICLE SIZE DISTRIBUTION AND SEPARATION TECHNIQUE .......................................................82 4.3.1 Size Distribution of Anodic and Cathodic Particles...........................................................................84 4.3.2 Separation Technique.........................................................................................................................86 4.3.3 Error Estimation.................................................................................................................................87 4.3.4 Effect of Varying Wire-Arc Parameters .............................................................................................92 4.4 AXIAL VARIATION OF PARTICLE PROPERTIES .................................................................................................96 4.4.1 Drag Force and Force Balance Relation ...........................................................................................97 4.4.2 Heat Transfer and Exothermic Oxidation of Particles .......................................................................97 CHAPTER 5
PARTICLE DEPOSITION: SPLAT AND COATING FORMATION.....................................102
5.1 EFFECT OF SUBSTRATE TEMPERATURE ON SPLAT FORMATION....................................................................102 5.1.1 Experimental Procedure...................................................................................................................104 5.2 SPLAT MORPHOLOGY ..................................................................................................................................108
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5.3 MODEL FOR TRANSITION TEMPERATURE .....................................................................................................112 5.4 COATING PROPERTIES ..................................................................................................................................118 CHAPTER 6
CLOSURE.......................................................................................................................................122
6.1 CONCLUSIONS ..............................................................................................................................................122 6.2 RECOMMENDATIONS FOR FUTURE WORK .....................................................................................................124 REFERENCE ..........................................................................................................................................................125 APPENDIX A: METAL PROPERTIES ...............................................................................................................132 APPENDIX B: TRANSPORT PROPERTIES OF AIR.......................................................................................133
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List of Figures
Figure 1.1 Basic principles underlying the thermal spray processes: Production, Transport, and Deposition of molten particles. ......................................................................................3 Figure 1.2 Schematics of wire-arc spraying system and its major components .................................5 Figure 2.1 (a) Picture of DPV-2000 scanning unit alongside the wire-arc spraying gun detecting the in-flight particles (b) The computer system containing the DPV-2000 operating system and CPS-2000 modules; the two are connected to the scanning unit via fiber-optic cables. ...................................................................................................19 Figure 2.2 Schematic diagram of the DPV’s optical sensing head and its field of view [9] .............20 Figure 2.3
(a) A schematic diagram showing the signal sensed by the DPV-2000 sensing head when a particle passes through its field of view. (b) Picture of the two slits in P4590170 photo mask...........................................................................................................20
Figure 2.4 Wire-arc sprayed stainless-steel particles are approximately spherical. ........................20 Figure 2.5 Size distribution of particles was measured using two additional methods (optical picture measurements, and PSA measurements) to calibrate DPV’s particle size measurements. ......................................................................................................................23 Figure 2.6 Pyrometer’s calibrated reference curve. High voltages on λ = 780 nm and λ = 850 nm photomultipliers were 700 V and 1000 V, respectively...............................................24 Figure 2.7 Surface profile of polished AISI 304L stainless steel substrate obtained using a Surface Profiling Microscope (Wyko Optical Profilometer, Veeco Instruments Inc., Woodbury, NY). Surface roughness is 7.90 nm.................................................................25 Figure 2.8 Picture of ValuArc 200 Twin Wire Arc spray system and the spray gun manufactured by Sulzer-Metco. Picture is adapted from [63].........................................27 Figure 2.9 Picture of ValuArc 200 Twin Wire Arc spray system during operation.........................28 Figure 2.10 Schematics of ValuArc 200 Twin-Wire-Arc Spraying System and its components. Picture is adapted from [2,72].............................................................................................28 Figure 2.11 Exploded rear view of the ValuArc 200 twin-wire-arc gun and its components. The gun can be mounted on the handle and hand operated, or on a separate mount or robot and remotely operated. Picture is adapted from [72] .............................................29 Figure 2.12 Exploded front view of the ValuArc 200 twin-wire-arc gun and its components. Picture is adapted from [72]................................................................................................30
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Figure 2.13 Standard volumetric flow-rate of the atomizing gas (dry air) as a function of the upstream pressure. The data points represent 20 psig (239 kPa), 30 psig (308 kPa), 40 psig (377 kPa), 50 psig (446 kPa), and 60 psig (515 kPa) in the system’s pressure setting. ...................................................................................................................................32 Figure 2.14 Current-voltage characteristic of the arc for different wire-feed-rates and pressures. Dry-air as the atomizing gas and aluminum wires were used. The errorbars represent current fluctuation and standard deviation of 5 to 10 measurements. ..34 Figure 2.15 Current that passes through the arc increases when the feed rate of aluminum wires is increased. Solid curves represent quadratic fits to the datapoints.....................36 Figure 2.16 Current that passes through the arc increases when the feed rate of copper wires is increased. Solid curves represent quadratic fits to the datapoints. .................................36 Figure 2.17 Input power versus feed rate of aluminum wires. Slope of 39.5V, 32.1V, and 25V curves represent 7.90, 7.01, and 4.53 MJ/kg (mega joules per kilogram of aluminum), respectively. Solid curves represent quadratic fits to the datapoints. ........37 Figure 2.18 Input power versus feed rate of copper wires. Slope of 39.8V, 32.1V, and 26.9V curves represent 3.01, 2.40, and 1.54 MJ/kg (mega joules per kilogram of copper), respectively. Solid curves represent quadratic fits to the datapoints. .............................37 Figure 3.1 Pictures of the wire-tip region and the arc during operation of the wire-arc spraying system. These pictures are taken using a visible-wavelength Nikon E3 camera with different optical filters. ..................................................................................40 Figure 3.2 Black body radiation curves at different temperatures, scaled to a maximum of one. The presented curves represent radiation at the melting and boiling temperatures of Stainless Steel, Copper, and Aluminum. ................................................41 Figure 3.3 Optical system used to transmit laser beam from the laser system to the region to be photographed: (a) Laser beam output, (b) coupler, and (c) fiber optic cable............43 Figure 3.4 Schematic diagram of the position of the UV-intensified CCD camera and illuminating laser beams. Laser beams are coupled into and transmitted through the optical fibers along positive and negative Y axes. Cylindrical lenses focus the beams onto the YZ plane. The CCD camera, attached to the lens system and aligned with the X axis, takes a picture of the wire tips....................................................43 Figure 3.5 Photographs of the two wires and the detached particles. These pictures are the negative of what was captured by the UV-intensified COHU camera. Two lasers illuminate the area from top and bottom simultaneously. Aluminum wires and a High-Velocity cap were used; wire-feed-rate = 8 m/min, voltage = 29.1 V, pressure = 45 psig (412 kPa)................................................................................................................44 Figure 3.6 The average period of arc voltage fluctuations versus wire-feed-rate for aluminum wires, atomizing gas (air) pressure of 45 psig (412 kPa), Voltage of 29.4 V. The data was collected by taking several snapshots of the voltage fluctuations and counting/averaging the number of cycles in a time interval of about 10 or 20 milliseconds. The error bars are the standard deviation of the collected data...............47
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Figure 3.7 Average volume of metal detachment, calculated from equation (3-1) and data in Figure 3.6, presented as a function of wire-feed-rate. Material vaporization is neglected in this analysis......................................................................................................48 Figure 3.8 Volume of the gun in which atomizing gas flows. Four tubular inlets carry pressurized atomizing gas (mainly dry air) into the gun chamber. The opening on top (and its bottom mirror-image) is where contact tips and wire guides are located....................................................................................................................................50 Figure 3.9 Inner components of the ValuArc 200 wire arc gun. Contact-tips guide the wires towards the nozzle. Diameter of the wires is 1.6 mm.........................................................50 Figure 3.10 Contours of gas velocity (a) and pressure (b). Numbers are in m/s and Pa, respectively. Mass-flow-rate of air is 12.3 gr/s. κ-ε turbulent modeling.........................52 Figure 3.11 Reduced geometry of the gun included contact-tips and wire-tips..................................53 Figure 3.12 Contours of gas velocity (a) and pressure (b) for mass-flow-rate of 25.3 gr/s. Numbers are in m/s and Pa, respectively. κ-ε turbulent model. Arc heating is not considered. ............................................................................................................................54 Figure 3.13 Contours of gas temperature (a) and mass-flux density (b) for mass-flow-rate of 25.3 gr/s. Numbers are in K and kg m-2s-1, respectively. κ-ε turbulent model. Arc heating is not considered......................................................................................................55 Figure 3.14 Fluid streamlines parallel to YZ (a) and XZ (b) planes in the vicinity of wire-tips. Streamlines are coloured by Y-component (a) and X-component (b) of gas velocity. Mass-flow-rate of gas is 25.3 gr/s. Arc heating is not considered.....................................56 Figure 3.15 Contours of shear stress on the wire tips. Numbers are in Pa. Mass-flow-rate of air is 12.3 gr/s. Arc heating is not considered. .........................................................................57 Figure 3.16 Numerical predictions of volumetric-flow-rate of air as a function of atomizing gas pressure compare relatively well with experimental measurements. Experiments correspond to pressure settings of 20, 30, 40, 50, and 60 psig. Numerical results of κ-ε model under-predict the flow rate by about 8%. Dash-line takes into account the pressure drop in the connecting hose. LES data points and their error-bars represent time-averaged and RMS values of time-dependent flow-rate. ........................59 Figure 3.17 Shear stress on the surface of the wire-tips for different mass-flow-rates of air. Arc heating is not considered. LES turbulence modeling........................................................60 Figure 3.18 Grayscale picture of arc, taken at P = 30 psig (a) and P = 40 psig (b), wfr = 7 m/min, V = 30.1 V, with aluminum wires, and air as atomizing gas. Radiation intensity is translated to grayscale intensity (a number between 0 and 255). The region of higher radiation intensity is then found by stratifying the picture. Shutter speed setting: 750 (a) and 500 (b). .................................................................................................62 Figure 3.19 Grayscale picture of arc, taken at P = 45 psig (a) and P = 60 psig (b), wfr = 7 m/min, V = 30.1 V, with aluminum wires, and air as atomizing gas. Radiation intensity is translated to grayscale intensity (a number between 0 and 255). The region of
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higher radiation intensity is then found by stratifying the picture. Shutter speed setting: 500 for both (a) and (b). .........................................................................................63 Figure 3.20 At each pressure setting, arc length from different images was measured and averaged. The error bars represent the standard deviation of the measurements. .......64 Figure 3.21 Arc radius, current density, and electric field as functions of axial distance in a 4mm long arc with current of 200A. .....................................................................................65 Figure 3.22 Contours of gas velocity (a) and pressure (b) for mass-flow-rate of 25.3 gr/s. Numbers are in m/s and Pa, respectively. κ-ε turbulent model. Arc heating is considered. ............................................................................................................................68 Figure 3.23 Contours of gas temperature (a) and mass-flux density (b) for mass-flow-rate of 25.3 gr/s. Numbers are in K and kg m-2s-1, respectively. κ-ε turbulent model. Arc heating is considered. ...........................................................................................................69 Figure 3.24 Fluid streamlines parallel to YZ (a) and XZ (b) planes in the vicinity of wire-tips. Streamlines are coloured by Y-component (a) and X-component (b) of gas velocity. Mass-flow-rate of gas is 25.3 gr/s. Arc heating is considered. Divergence of gas flow is more than that in Figure 3.14, where arc heating was not considered. .......................70 Figure 3.25 Shear stress on the surface of the wire-tips for different mass-flow-rates of air, with the consideration of arc heating. Turbulence was modeled using κ-ε. ............................71 Figure 4.1 Optical (a) and SEM (b) pictures of aluminum particles collected by spraying into water; P=30 psig (308 kPa), V=32.1 V, wire-feed-rate=7 m/min ......................................78 Figure 4.2 Velocity, diameter and Mass-flow-rate of the spray particles as a function of y and x, with z = 50mm. Center of the spray is located at x = y = 0mm. The error-bars in the graphs represent the standard deviation of 3 to 5 measurements. ............................79 Figure 4.3 Frequency-distribution (a) and volumetric-distribution (b) histograms of measured particle diameter are shown by grey histograms; P=60 psig (515 kPa), V=37.9V, and wire-feed-rate=7m/min. The curve in (a) is a Log-Normal function (μ=56μm, σ=0.451) matching the maximum and full-width-half-maximum of the measured distribution. The curve in (b) is the volumetric Log-Normal function with same μ and σ as in (a) and scaled with the same scaling factor as the measured volumetricdistribution. The black bar-histogram represents the difference between the measured volumetric-distribution and the volumetric log-normal function. .................83 Figure 4.4 An optical picture of magnetically-agglomerated stainless-steel particles before being demagnatized..............................................................................................................85 Figure 4.5 A log-normal function fits well within the error-bars of the size-distribution of anodic particles. Stainless steel and copper wires were used as anode and cathode, respectively. The error bars represent the systematic error of the size measuring device. ....................................................................................................................................86 Figure 4.6 The separation technique was applied to the addition of two known log-normal functions (LN1: µ1=50µm, σ=0.45 and LN2: µ2=90µm, σ=0.45) to reconstruct the original functions. (a) frequency-distribution (b) volumetric-distribution.....................90
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Figure 4.7 Two peaks in the measured diameter distribution were separated and presented in frequency (a) and volumetric (b) forms. LN1 and LN2 represent log-normal distribution functions of cathodic and anodic particles respectively. vLN1 and vLN2 are the volumetric representation of LN1 and LN2. Experimental particle size statistics was obtained by DPV-2000 system at a stand-off distance of 50 mm, voltage of 32.1 V, wire-feed-rate=7 m/min, and P = 60 psig (515 kPa). These distributions represent statistics of about 8000 aluminum particles. ..............................91 Figure 4.8 Mean-Diameter and Mass-Mean-Diameter of cathodic and anodic particles decrease as the pressure of the atomizing gas increases. Anodic particles are more significantly affected by atomizing gas pressure than the cathodic particles. Errorbars represent standard deviation of 3 to 5 measurements of about 8000 particles. Operating parameters: Aluminum wires, V=32.1V, wire-feed-rate=7m/min, standoff distance=50mm. ..............................................................................................................93 Figure 4.9 Mean-Diameter and Mass-Mean-Diameter of cathodic and anodic particles as a function of the wire-feed-rate. Error-bars represent standard deviation of 3 to 5 measurements of about 8000 particles. Operating parameters: Aluminum wires, P = 60 psig (515 kPa), V = 32.1V, stand-off distance = 50 mm. ............................................94 Figure 4.10 Mean-Diameter and Mass-Mean-Diameter of cathodic and anodic particles as a function of the applied voltage. Error-bars represent standard deviation of 3 to 5 measurements of about 8000 particles. Operating parameters: Aluminum wires, P = 60 psig (515 kPa), wire-feed-rate = 7 m/min, stand-off distance = 50mm.....................95 Figure 4.11 Axial velocity profile of particles in the spray. ..................................................................96 Figure 4.12 Axial temperature profile of particles in the spray with air and nitrogen as atomizing gas. Temperature of aluminum particles sprayed with nitrogen increases by about 130°C as they travel a distance of 20 cm. ...........................................................97 Figure 4.13 Average temperature of aluminum particles in the spray as a function of lateral distance from the centerline of the spray. Axial distance from the gun is 3" (76 mm). V=31V, wfr = 7 m/min, P=30 psig (308 kPa)............................................................100 Figure 5.1 Experimental setup to obtain distinct splats on the substrate........................................106 Figure 5.2 Splat morphology and corresponding coating microstructure of wire-arc sprayed aluminum deposited onto polished stainless steel (type AISI304L) held at various temperatures. ......................................................................................................................109 Figure 5.3 Frequency of disk-shape splats increases with increasing substrate temperature. High-velocity and low-velocity data are adapted from [1] and [2]. Mid-velocity data are measured solely by the author of this thesis. .............................................................111 Figure 5.4 Degree of splashing decreases with increasing substrate temperature. Adapted from [1]................................................................................................................................112 Figure 5.5 Experimental and theoretical spread factor values for both high velocity (143 m/s) and low velocity (109 m/s) tests. The curves are the theoretical predictions from equation (5-6)......................................................................................................................114
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Figure 5.6 Prediction of transition temperature for aluminum droplets impacting a stainless steel surface. The three experimental data points do not necessarily have similar contact resistances due to the growth of an oxide layer on the substrate......................116 Figure 5.7 Plot of elemental composition of the stainless steel substrates heated to various temperatures. Adapted from [1]. ......................................................................................117 Figure 5.8 Effect of substrate temperature on porosity of the produced coating. ..........................118 Figure 5.9 Measured deposition efficiency for high velocity (143m/s) and low velocity (109m/s) test conditions. Curves represent the best fit. ..................................................................120 Figure 5.10 Measured coating adhesion versus substrate temperature for particles having an average velocity of 143m/s. [1,2] .......................................................................................121
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Chapter 1 Introduction
This opening chapter introduces the concepts of thermal spray as well as the twin-wirearc spray process and its spraying gun. A summary of the scientific literature on this topic, and also the motivation behind the current work are presented. The scope of the work is defined and an outline for the structure of the thesis is provided.
1.1 Background, Motivation, and Literature Survey
1.1.1 Thermal spray Thermal spraying is a group of elevated-temperature, high-velocity material processing techniques in which molten or semi-molten particles are accelerated towards and deposited onto a prepared surface, on which the deposited particles are solidified or sintered and form a protective coating layer. The particles in this process are either introduced in the form of solid ceramic or metallic particles that are heated/melted in a hot flame, or, are atomized off the molten tip of an electrically-conductive metallic wire. The coating layer that is formed in a thermal spray process is a collection of many individual solid flattened particles, splats, that pile on top of each other. The coating layer formed, depending on its microstructure, can be used in various industries (including electronic, automotive, aeronautic, and aerospace) to provide: 1
• Resistance to wear, abrasion and erosion • Thermal barrier coating to protect structures and materials • Corrosion resistance in air and marine environments • Protection against high temperature oxidation, erosion and corrosion • Electrical resistance, electrical conductivity, or electro-magnetic shielding • Layer-by-layer manufacturing of shaped components • Dimension restoration for worn surfaces • Building composite structures of metals and ceramics • Adhesive base for bone ingrowth in medical implants Because protective coatings are becoming a widespread part of metal working, thermal spray is a rapidly growing market. The methods classified under thermal spraying include flame spraying, plasma spraying, High-Velocity-Oxyfuel (HVOF), and twin-wire-arc spraying, all of which share the following common features: 1) Production of molten particles: molten particles are formed in the spraying gun region 2) Transport of molten particles: molten particles are propelled towards the substrate to be coated 3) Particle deposition: molten particles are deposited and flattened on the substrate, forming solidified or sintered splats that form the coating layer. These three common features are the basic principles underlying the thermal spray process and are schematically shown in Figure 1.1.
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Figure 1.1 Basic principles underlying the thermal spray processes: Production, Transport, and Deposition of molten particles.
Despite these common features, there are major differences between thermal spraying methods; namely: • Type of feedstock: the spray material can be introduced as powder, wire, suspension, or solution. • Heating method: the spray material can be heated with an electric arc or a flame. • Cost: The equipment and operation costs involved vary from one method to another. • Microstructure of the coating produced: Microstructure of the coating produced varies from one thermal spraying method to another, making them suitable for different applications, such as in corrosion protection or wear-resistant coatings. • Heat transfer to the substrate: Deposition and solidification of molten particles on a solid substrate warms up the substrate. (This may even cause melting and resolidification of a layer of the substrate). In some applications, where heat treatment of the substrate changes its desired mechanical properties, it is required that the heat transfer to the substrate be minimized by proper selection of spray technique.
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Table 1.1
Comparison of three thermal spray processes [8, 33, 66] Thermal Spray Processes
Criteria
Wire-Arc
HVOF
Atmospheric Plasma
Type of feedstock
Wire
Powder
Powder, suspension, solution
Choice of material
Restricted to electricallyconductive wires: metals, metal alloys, metallic composites
Metallic alloys, carbides and composites; Limitation for refractory materials
Metallic alloys, carbides, ceramics, composites, and refractory materials
Versatility in the choice of material
Low
Medium
High
Reliability
Medium
High
High
Heat transfer to the substrate
Low
Very High
Medium
Process Cost
Low
Medium
High
Capital Cost
20000$
100000$
100000$
Deposition Rate
1 – 50 kg/hr
1 – 10 kg/hr
0.5 – 10 kg/hr
Adhesion Strength
Low
High
High
Coating Porosity
10% – 25%
0.5% – 5%
0.5% – 10%
Maximum Temperature
4000oC – 6500oC
2600oC – 3100oC
Up to 20000oC
Particle Temperature Low
Medium
High
Particle Velocity
80 – 150 m/s
550 – 1000 m/s
100 – 300 m/s
Particle Diameter
30-50 μm
Powder (10-100 μm)
Powder (10-100 μm)
Surface Roughness
2 - 10 μm
1 - 4 μm
1 - 4 μm
Wire-Arc, HVOF, and Atmospheric Plasma spray systems are extensively used and compared against each other in industrial applications. For example, Barbezat [8] has compared the performance of these systems in deposition of protective coating layers on engine cylinder bores. Table 1.1 summarizes such results and compares coating characteristics for these three thermal spray processes. Twin-Wire-Arc Spray, also termed as Wire-Arc Spray, is one of the most cost-effective methods of thermal spraying and is described in more detail in the next section. 4
1.1.2 Twin-Wire-Arc Spray Twin-wire-arc spraying is an economical technique of thermal spraying and has become popular in the industry because it combines low operating and equipment costs with high material and energy efficiencies. The coatings produced in the wire-arc spraying process usually have a greater porosity and lower adhesion strength than those obtained from other thermal spray processes, making them of relatively poorer quality. Nevertheless, in some applications, higher amounts of porosity are acceptable or even desired (e.g. to hold lubricants [23]). Twin-Wire-Arc spray has a wide range of industrial applications, many of which are listed in [56], categorized according to different wire materials and coating thicknesses. 1.1.2.1 Description of the Wire-Arc spraying process Figure 1.2 schematically shows the twin-wire-arc spraying process and the spraying system. The material that is used in this process is introduced into the process in the form of two electrically-conductive consumable wires. The wires commonly used in industry are usually made of electrically-conductive materials, such as Aluminum, Zinc, Stainless Steel, and Copper. In some recent wire-arc developments, intermetallic compound coatings and metal-ceramic composite coatings were prepared by using pre-alloyed wires [25,68] and cored wires [18,30,60], in which non-conductive materials are used as the core of a conductive wire.
Figure 1.2 Schematics of wire-arc spraying system and its major components
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In this process, the two electrically-conductive consumable wires are continuously fed into the wire-arc spray gun. The gun geometry is designed such that the wire tips are separated by a distance of about a few tenths of a millimeter from one another. An electric voltage of about 40 V, applied on the two wires, causes an arc in the gap between the wire tips. The arc heats the tips of the wires, and produces a thin layer of molten material. A stream of atomizing gas, as shown in the figure, strips the molten layer off the wire tips and propels it towards the substrate. The detached molten droplets will not only accelerate, but also undergo further atomization and produce smaller droplets. The molten droplets are then deposited on the substrate one over another, where they solidify and form a coating layer. Some of the advantages that make wire-arc spraying an attractive process to industrial users are [23, 26]: 1) The simple design of the equipment, the low cost of producing wires, and the low cost of electrical power, makes this process cost-efficient. The capital and the operation costs of a typical wire-arc spraying gun are respectively five times and nine times less than those of a typical plasma spraying system. [33,58]. Besides, because of its light weight and portable design, wire-arc system is an ideal tool for on-site application of coatings. 2) The use of non-flammable gases and the possibility of using dry-air as the atomizing gas make the process safer and even more cost-efficient. 3) Since the gas heating region is very small, the atomizing gas has a relatively low temperature, reducing the rate of heat transfer to the substrate. Keeping the substrate temperature at a low level prevents damage, distortion, and metallurgical changes to the substrate surface.
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4) The materials introduced to the system are entirely melted and consumed in the process. Complete melting of the input material makes the wire-arc spraying a material- and energy-efficient process. This also eliminates the problems caused by partially-melted particles. (Incomplete melting of particles is associated with almost all other thermal spray processes that use solid particles or powder as feedstock. In such processes, heating and melting starts from the periphery of the particle and the inner portion may not reach the melting temperature). 5) It has been experimentally shown that the wire-arc spraying process has the highest coating rate among all other thermal spray processes. Also, the deposition efficiency (mass ratio of coated material to fed material) of this process is shown to be comparable and, in some cases, better than that of other thermal spray processes. Despite the advantages that make wire-arc spraying an attractive process to industry, it has certain disadvantages too. Its major disadvantage is the poor quality of the coatings produced: Wire-arc coatings are usually characterized by their high porosity and low adhesion strength, which are undesirable in most applications. Another disadvantage of wire-arc spraying is the lack of control over the size of the produced particles. In most thermal spray processes, the molten droplet sizes are determined by solid particle sizes in the fed powder, whereas, the molten droplet sizes in wire-arc are determined by the operating parameters. It should be noted that particle size controls dynamic and thermal behavior within the spray and the splashing and spreading behavior during deposition. Therefore, lack of control over particle size effectively limits the ability to adjust coating characteristics according to wide range of industrial requirements, thereby narrowing the range of wire-arc applications.
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1.1.2.2 Operating parameters The industrial wire-arc spraying systems that are designed and manufactured by different companies are all based on concepts discussed in section 1.1.2.1. However, they differ in the geometry of the torch, the wire-diameter, the feed mechanism for the wires, and the location where the tips of the wires are located with respect to the torch geometry. In this study, the ValuArc 200 Twin-Wire-Arc Spraying Gun, manufactured by Sulzer-Metco (Westbury, NY) was used. Detailed engineering drawings of this gun are presented in Chapter 2, section 2.2. The parameters that can be controlled in most wire-arc spray systems and affect the microstructure of the produced coatings include [54, 55, 70]: 1) Material of the fed wires: The wide range of materials being used in industry include aluminum, copper, stainless steel, tin, titanium, and zinc. Each one of these materials or a combination of two of them can be used for different applications. In some applications, cored wires are used, in which non-conductive materials, such as carbide, nitride, or cermet, are wrapped inside an electrically conductive outer layer. 2) Type of the atomizing gas: The types of the atomizing gas used in industrial applications include dry-air, nitrogen, and argon. The atomizing gas strips molten material off the tips of the wires and therefore needs not be flammable. Use of gas mixtures that do not contain oxygen reduces the oxide content in the coating produced. 3) Pressure of the atomizing gas: The upstream pressure of the atomizing gas determines the volume-flow-rate and the velocity of the atomizing gas. The gas velocity directly affects the velocity of detached droplets. 4) Voltage applied on the wires: The applied voltage controls the input power of the arc and indirectly affects the rate at which the tips of the wires are heated and melted. 8
5) Wire-feed-rate (only in type 1 systems), also termed as wfr: This parameter determines the rate at which material is introduced into the system, which is equivalent to the rate at which the introduced material is melted. In type 1 systems that allow control over wire-feed-rate, there is no control over the arc-current. Arc current, which is directly proportional to the input power, is determined based on melting rate and other system settings. An example of a type 1 spraying system is the ValuArc system (manufactured by Sulzer-Metco). 5) Arc current (only in type 2 systems): This parameter controls the input power of the arc, affecting the rate at which the tips of the wires are heated and melted. In type 2 systems, there is no control over the wire-feed-rate. It is therefore determined based on other system settings, including the arc current. An example of a type 2 system is TAFA 9000 Wire Arc (manufactured by Praxair/Tafa, Inc.).
In addition to the abovementioned control parameters, there are other factors that may affect the coating quality or its characteristics which are not controlled by the knobs and switches on the spraying system: The state of the ambient gas (e.g. oxygen and moisture content), and the state of the substrate (e.g. temperature and roughness) may affect the coating characteristics.
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1.1.3 Brief Literature Review The idea of wire-arc spraying was first introduced by Schoop in 1910 and quickly found commercial applications in Germany, France and United States [26]. Since then, there have been many improvements in its design in accordance with its rapidly expanding applications. However, due to the relatively poor coating quality (as compared to other thermal spray processes) and its high-efficiency high-deposition-rate, it has mostly been used in applications that require thick coatings and are less-demanding, such as corrosion or wear protection coatings [33]. With its increasing applications in the industry in the last decade [19], the wire-arc spray process is seeing an upswing in terms of research interest. However, the research work done in this field is mainly experimental and little work has focused on fundamental modeling. In this section, previous experimental and numerical work on production of molten droplets using the wire-arc technique is summarized first, and studies on in-flight particle characteristics and droplet deposition follow. 1.1.3.1 Previous Work on Droplet Production and Transport One of the earliest studies on the performance of wire-arc spray was conducted by Steffens in 1966, in which he used an oscilloscope and high speed cinematography to show 1 to 2 kHz fluctuations in the spray process and that the process is unsteady in nature [33]. The high speed photographs also revealed asymmetric melting of anode and cathode material: while localized melting was observed in cathode, the molten material of the anode formed a sheet before breaking up. A complete explanation of this phenomenon, however, was not given. Later, Marantz in 1974 showed that size of the sheets produced at the anode decreased with increasing pressure of the atomizing gas.
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The past two decades have witnessed more research studies on wire-arc. However, most of these studies have focused on relating coating properties with operating parameters of wirearc, and few of them focused on improving the process design. One of the major improvements in the design of the wire-arc system was suggested by Russ in 1993: he proposed using a converging-diverging nozzle (instead of the conventional straight bore nozzle) to increase gas velocities in the spray. Using converging-diverging nozzle results in a much weaker diamond shock structure in the gun, and results in a higher gas flow velocity, and therefore, higher particle velocity. One of the earliest theoretical descriptions of arc heating is given by Steffens in 1990 for single-wire-arc process, in which molten metal is directly transferred from the consumable wire (that acts as one electrode) to the substrate (that acts as the second electrode). In this process, gravity, rather than an external gas flow, is used to transport molten particles to the substrate. In another study, Varacalle et al [64] modeled the arc, jet, and particle transport and heating in the plume of a wire-arc system using already developed codes. These codes solved two-dimensional simplified models of an arc with a parabolic laminar cross-flow. They did not model particle breakup and assumed a single size for the molten droplets. The most comprehensive attempt to date to model the wire-arc spraying process has been performed by Kelkar [33-35] and Hussary [28], in which they modeled both the fluid flow and the arc in presence of fluid flow. Assuming the traditional particle breakup model of Amson [4] and Arai [5], they modeled primary and secondary atomization. In a separate study, Hussary et al [29] studied the mechanisms involved in primary atomization of molten metal from the wire tips and the effect of process parameters on these mechanisms. In their study, they presented quantitative results about sheet, extrusion and membrane lengths, and breakup times.
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1.1.3.2 Previous Work on Bimodal Size Distribution of In-flight Particles It has long been known that the anode and cathode are heated differently in a wire-arc process. The arc attaches to the anode over a larger area than the cathode where heating is more localized at the cathode spot [67, 28]. At the tip of the anode-wire a large area is heated due to diffuse arc-anode attachment, melting a layer of metal that is pushed off the edge of the wire-tip by the atomizing gas, creating an “anode sheet”. At the cathode, constricted arc attachment causes much more localized heating and melting. Also, since the current passes through a smaller area the current density (j) at the cathode surface is much higher, producing a large magnetic
uv v uv pinch force (or j × B force, where B is the induced magnetic field). Molten metal droplets ejected into the arc from the cathode due to both drag and magnetic forces are observed to be smaller than those that detach from the anode. Using laser strobe photography Hussary et al [28] and Watanabe et al [68,69] clearly illustrated the differences between molten metal detachment at the tips of the anode and cathode wires. To date, no numerical work has been performed to model the size and shape of droplets from anode and cathode. Kelkar et al [33,34,35], who numerically modeled the wire-arc process, used a simple breakup model and a simplified secondary atomization model to determine the particle size distribution in a wire-arc plume. Although they showed a bimodal distribution for particle size, their graphs do not predict equal mass-feed-rates of anode and cathode material. Inhomogeneity in the microstructure of wire-arc coatings was also observed by Zhu et al [72]. By spraying two different materials as anode and cathode, they demonstrated that particles originating from anode and cathode are distributed in an asymmetric way about the centerline of the wire-arc spray.
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1.1.3.3 Previous Work on Particle Deposition Determining the effects wire-arc operating parameters have on coating characteristics is the most practical part of research on wire-arc spraying. Such practical studies have been conducted using a wide variety of techniques. Wang et al [66], for example, used optical microscopy and Auger electron spectroscopy to study the effect of the atomizing gas pressure on porosity and oxide content of the produced coating. Their work indicated an increase in oxide content and decrease in porosity with increasing atomizing gas pressure. They also sprayed wirearc particles into an ice block to freeze the molten particles with minimal deformation, and measured in-flight particle size distribution, in which they found two peaks. Other work by Varacalle et al [63,64] involved a systematic experimental design along with two-color pyrometry technique and image analysis to study and determine the effects arc voltage, gas pressure and spray distance have on roughness, oxide content and porosity of the produced coating. They found that increasing arc current, lowering atomizing gas pressure, and shortening spray distance results in higher coating roughness, lower oxide content and lower porosity. Another subject that has captured the interest of researchers in the field of thermal spraying is the effect of substrate conditions (e.g. temperature, roughness, and contaminants) on the quality of the produced coatings. However, most studies have focused on plasma spray particles. Pershin et al [50], for example, have shown that by increasing the substrate temperature from 20oC to 650oC, the adhesion strength of plasma-sprayed nickel powder increases by almost an order of magnitude. Also, effect of substrate temperature on the shape of individual splats has been studied by several researchers and has been summarized by Fauchais
et al [19]: A thermal spray particle landing on an unheated surface will splash and form a fragmented splat. A particle landing on a heated surface, however, forms a circular disk with no 13
irregular edges. Fukumoto et al [20] introduced a “transition temperature” (Tt) for the substrate above which most of the deposited droplets are disk-shape splats. In another attempt, Jiang et al [32] showed that removing contaminants from the surface of the substrate increases the probability of obtaining a disk-shape deposit. Therefore, it can be seen that, to date, there has not been a single comprehensive numerical treatment of the wire-arc spray system. The development of an acceptably complete model of the wire-arc process requires that all parts of this complicated process, including particle production, particle transport, and particle deposition, be analyzed and modeled.
1.2 Statement of Objectives Advantages of wire-arc spray system, including its low costs and high material/energy efficiency, have made its market grow rapidly in the thermal spray industry. Despite its simple design, the physical phenomena underlying its operation are very complex and have yet to be understood. Fundamental understanding of the wire-arc spray process is needed to better control the spray particle properties and optimize its performance for different industrial applications. Better understanding of the wire-arc spraying process will also provide us with some guidelines as to how existing wire-arc spray equipment designs can be modified to improve the quality of the produced protective coating layers. The objective of this research is to quantitatively analyze and model how the wire material is heated, melted, atomized, transported, and deposited onto the substrate: Knowledge of fluid flow in the wire-arc gun is necessary to predict the size and shape of the primary detachments from the wire-tips. Knowledge of particle properties and their distributions is needed because it directly affects the quality of the produced coating. Knowledge of individual
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particle deposition (and splat formation) is necessary because it determines the microstructure of the produced coating layer. As different industrial applications of thermal sprays require different ranges of particle velocities, particle temperatures, and particle sizes, the ultimate goal of this research is to use the obtained knowledge and suggest methods of controlling/enhancing the wire-arc process and make it more suitable for each application.
1.3 Scope of the present work Due to the complex physical phenomena underlying the operation of the wire-arc system, certain simplifications have to be made:
• Although the particle detachment, arcing, and therefore, arc heating are highly oscillatory, all processes are assumed to occur at their average properties. In other words, time dependence is not considered.
• The arc is modeled with a simplified semi-2D model, originally developed by Lowke [38].
• Pictures of the arc are used to identify the shape of the arc. Pictures are then used to prescribe arc info in the CFD solution of the fluid flow in the gun.
• The arc is solved independent of the cross-flow, except that the arc shape/length is determined from the arc pictures.
• A simplified model of primary atomization is used to determine the size of primary molten metal detachments from the wire-tips.
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1.4 Outline of the thesis This thesis presents the results obtained from numerical and experimental investigations of three main segments of a wire-arc spraying process: Particle production, Particle transport, and Particle deposition. Chapter 2 introduces the experimental apparatus and procedures used in this research work, including coating-characterization and process diagnostics tools. Section 2.2 of this chapter analyzes the experimentally measured arc current to estimate metal evaporation rate. Chapter 3 introduces the imaging system used to take pictures of the arc and wire-tips during operation. It also presents the post-processed pictures of the arc, which are used in solving simplified arc-equations. It also describes how this arc solution is used in modeling arc-heating in the wire-arc gun. Finally, a simplified model of liquid metal breakup is used to estimate the size of primary molten metal detachments from electrodes. Chapter 4 discusses the size-distribution of particles in the wire-arc spray. A method is presented to identify and distinguish the size-distribution of particles originating from anode from those originating from cathode. Oxidation of aluminum particles and its effect on axial temperature profile is also discussed. Chapter 5 summarizes the experiments conducted to study the effect of substrate temperature on splat formation and coating properties. Chapter 6 summarizes the conclusions drawn from the findings of this study and presents recommendations for future work.
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Chapter 2 Experimental Apparatus and Procedures
This chapter describes the experimental apparatuses used in this study for experimentation and characterization of the wire-arc spraying process. The major experimental setup that was used in this study included a wire-arc spraying system (ValuArc 200, Sulzer Metco, Westbury, NY), a metallic substrate (placed in front of the spray gun), a heater (to heat the substrate), and diagnostic tools (to monitor the process parameters during operation). Operating this spraying system produced a coating layer on the substrate. Diagnostics methods were also employed to characterize the properties of the produced coating layer.
2.1 Coating and Process diagnostics Process characterization and product characterization are essential steps in all industrial applications. In thermal spray processes, in-flight particle characteristics, as well as coating characteristics can be determined using well-developed methods that are briefly described here.
2.1.1 Coating Characterization Coating characterization is a well-established and well-documented field of science [30, 33, 63]. Different material properties, e.g. density, porosity, oxide content, and elemental composition, can be obtained for any thermal spray coating.
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In a typical procedure for determining the microstructure, a cross-section of the coating is obtained by cutting the coating and mounting it into epoxy. The cross-section is then finely polished to expose its microstructure. Pictures of the microstructure can be taken with either an optical microscope or a Scanning Electron Microscope (SEM). The pictures that can be easily digitized are then imported into an image analysis program, with which the porosity of the microstructure is determined. A typical procedure for determining the elemental composition in a coating layer is to use X-Ray Photoelectron Spectroscopy (XPS), described in detail in [24]. In this technique, which is carried out in ultra high vacuum conditions (UHV, P < 10-9Pa), surface contaminants are first removed from the surface of sample by means of argon-ion-sputtering. The sample is irradiated with a beam of X-Rays, resulting in electron excitations and ejection of electrons from the material (photoelectric effect). The energy signature of the emitted electrons (counts per energy intervals, magnitude and width of the peaks in its spectrum) is then translated to elemental composition of the sample. Coating densification can be easily evaluated by measuring its weight in air and in distilled water. This method, recommended by American Society for Testing and Materials, is coded as ASTM B 311-93. [7]
2.1.2 Process Characterization Real-time monitoring of in-flight particle characteristics (such as temperature, velocity, and size) provides a useful tool for the operator of a thermal spray system to control the quality of the produced coating as it is being produced. The apparatus used for in-flight particle characterization in the present work is the DPV2000 system (manufactured by Tecnar Automation Ltd., Montreal, QC, Canada). This optical 18
monitoring device has a sensing head that consists of a focusing lens, a two-slit photomask, and optical fibers (Figure 2.2). This sensing head is aimed perpendicular to the spray particle flow (Figure 2.1) and can be moved (with two degrees of freedom) to scan a cross section of the spray plume. This device measures properties (velocity, temperature and size) of individual particles by analyzing the infrared radiation emitted by each particle passing through the field-of-view of its sensing head. A photomask with two vertical slits is fixed in front of the optical sensor so that two peaks are recorded whenever a particle is detected. (Figure 2.3). Two photomasks are supplied with the device allowing to measure particle velocities below and over 400 m/s. The low velocity mask, P4590170, was used in these experiments.
(a)
(b)
Figure 2.1 (a) Picture of DPV-2000 scanning unit alongside the wire-arc spraying gun detecting the in-flight particles (b) The computer system containing the DPV-2000 operating system and CPS2000 modules; the two are connected to the scanning unit via fiber-optic cables.
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Figure 2.2 Schematic diagram of the DPV’s optical sensing head and its field of view [9]
(a)
Figure 2.3
(b)
(a) A schematic diagram showing the signal sensed by the DPV-2000 sensing head
when a particle passes through its field of view. (b) Picture of the two slits in P4590170 photo mask.
Figure 2.4 Wire-arc sprayed stainless-steel particles are approximately spherical.
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The following information can then be deduced from the recorded signal [53]:
• Particle velocity is measured by recording the time taken for a particle to traverse the known distance between the two slits (multiplied by magnification of the lens); Measurable range: between 10 m/s and 1500 m/s depending on the photomask. Error of accuracy of velocity measurements is less than 0.5%. [36, 53]
• Temperature is determined using principles of two-color-pyrometry. Temperature is directly related to the ratio of the strength of emission at one wavelength to the other. It is assumed that the detected particle is a spherical (see Figure 2.4 as an example) gray-body emitter. Minimum measurable temperature depends on the emissivity and size of the particle. For a typical wire-arc-sprayed aluminum particle ( ε ≈ 0.3 , d p ≈ 50μ m ), this minimum temperature is about 1500 ̊C. Temperature
measurements are 3% accurate. [36, 53] • Diameter is determined by measuring the total radiation emitted by each particle. (The total emission is proportional to the square of diameter). Diameter measurement range is between 10µm and 300µm [53, 62]. Although relative values of diameter measurements are precise (about 1% precision, [53]), the error of accuracy associated with its measurement can be as much as 7%. [36] To correctly measure the above properties, it is essential that the device be properly calibrated by modifying the calibration factors in the DPV software. The velocity calibration factor has to be modified each time the two-slit photomask is changed. The diameter calibration factor has to be calibrated whenever a new material (with new emissivity) is being measured. Temperature measurements are calibrated using a supplied calibration module (consisting of a pre-calibrated lamp) whenever the filters of the two-color-pyrometer are replaced.
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To calibrate the diameter measurements of DPV, wire-arc particles were frozen and captured by spraying them into a dry-ice block or water. After washing and drying the particles with acetone, they were spread on a white piece of paper and their pictures were taken using an optical microscope and a digital camera. Measuring diameters of several hundred particles provided an estimate of size distribution of wire-arc particles (histogram in Figure 2.5). The size distribution of such collected particles were also found by using MasterSizer S (Malvern Instruments, UK) Particle Size Analyzer (PSA), which is a single lens laser diffraction system that evaluates the size distribution of a powder (of solid particles) by measuring its laser scattering data. Particle-size detection range of this device is from 0.05µm to 880µm. The size-distributions obtained from these two methods (optical picture measurements and PSA measurements) were then used to modify the diameter factor in the DPV software and calibrate the device. Figure 2.5 compares these size distributions after calibration for aluminum particles. It shows that DPV diameter-measurements satisfactorily matched measurements of the other two methods (except for very small particles, d p < 10μ m ). Furthermore, Mauer et al [40] compared DPV-2000 in-flight particle measurements against Accuraspray-g3 diagnostics system and have confirmed the measurement accuracy of both systems. On the other hand, Vaidya [62] has reported that DPV is unable to accurately measure properties of very small particles (less than 5µm) and Biancaniello [9] discusses that the gray-body assumption introduces some errors in measuring temperature of particles whose emissivity is highly dependent on wavelength of the emitted beam (such as Molybdenum). However, these shortcomings of the DPV-2000 system will not be of great importance to this study.
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Figure 2.5 Size distribution of particles was measured using two additional methods (optical picture measurements, and PSA measurements) to calibrate DPV’s particle size measurements.
In addition to particle properties, it is also necessary to measure the temperature of the stationary wire tips during operation. Since this temperature cannot be measured using the pyrometer system of the DPV, a separate custom-made two-color pyrometer system was used. It consists of two photomultiplier tubes measuring the intensity of thermal radiation at two different wavelengths, and finds the intensity ratio using an electronic circuit. In theory, the intensity ratio is related to the temperature of the object, following Wien’s law: hc
hc
2 B
1 B
− λ5 = 25 e λ k T λ k T R (T ) = λ1 Iλ
I λ1
(2-1)
2
where kB , h and c are the Boltzmann constant, Planck’s constant and the speed of light in vacuum, respectively. The pyrometer output signal, however, depends on the voltages that are applied on the photomultipliers, and has to be calibrated. The pyrometer output signal was therefore measured and plotted against different temperatures of a heating element (Figure 2.6).
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The obtained plot was then used as the calibrated reference curve to measure the unknown temperature of the wire-tips by aiming the pyrometer at the wire-tips during operation and measuring the pyrometer’s output signal voltage.
Figure 2.6 Pyrometer’s calibrated reference curve. High voltages on λ = 780 nm and λ = 850 nm photomultipliers were 700 V and 1000 V, respectively.
Another factor that greatly influences the coating quality is the state of the substrate on which the coating is being applied. Substrate temperature, its elemental composition, and its surface roughness, are shown to have huge effects on the coating microstructure and physical properties [19]. Therefore, it is necessary to characterize the substrate properties before and during the spraying process. To measure and control the substrate temperature, two or three J-type thermocouples were attached to the substrate: one on top of the substrate (on its exposed face), and one behind the substrate, where it was attached to a controlled-temperature heater block. A custom-designed 24
temperature controller unit [2] controlled the substrate temperature based on the temperature of the unexposed surface of the substrate (because the temperature measurement of exposed surface was unreliable, due to extreme air flow around it). Surface roughness measurements were done prior to spraying using PDI Surfometer Series 400 (Precision Devices, Inc., Milan, MI), which records the surface profile of a component by running a stylus over it. This instrument then gives an average surface roughness value, which will be denoted as Ra. Also, substrate surface profile was looked at using a Surface Profiling Microscope (Wyko Optical Profilometer, Veeco Instruments. Inc., Woodbury, NY). A sample surface profile is illustrated in Figure 2.7.
Figure 2.7 Surface profile of polished AISI 304L stainless steel substrate obtained using a Surface Profiling Microscope (Wyko Optical Profilometer, Veeco Instruments Inc., Woodbury, NY). Surface roughness is 7.90 nm.
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Another characterizing parameter that was measured for the wire-arc-spraying process in this study was the deposition efficiency, which was calculated as follows. The mass of the substrate was measured prior to spraying (mi) and after the spraying (mf). Also, prior to any testing, the wire-feed-rate setting on the wire arc was measured and calibrated to the desired setting. With the wire-feed-rate known, and by measuring the duration for which the wire-arc was sprayed, the mass of the material of the two consumed wires (mc) was determined: mc = 2 ρ ⋅ wfr ⋅ π r 2 ⋅ t
(2-2)
In equation (2-2), ρ is the density of the wire material sprayed, wfr is the calibrated wirefeed-rate, r is the radius of the wire, and t is the measured spray duration (time in seconds). Subsequently, the deposition efficiency is given by:
eff =
m f − mi mc
× 100%
(2-3)
Numerous tests were carried out at each setting and each time the efficiency was calculated.
2.2 ValuArc 200 Spraying System and Its Characteristics The ValuArc 200 Twin-Wire-Arc Spraying System manufactured by Sulzer-Metco (Westbury, NY) was used to conduct all the experimental work presented in this dissertation. Figure 2.8 and Figure 2.9 show pictures of this system and Figure 2.10 schematically shows its components: This system is comprised of • Power supply and control unit:
The ValuArc 200 system uses Sulzer-Metco’s
LCARE power supply, which is a constant-voltage SCR (Silicon Controlled Rectifier) controlled DC voltage supply. It requires a three phase 440 V 50/60 Hz 26
electrical input. This power supply is installed inside a control unit with switches, control knobs, indicator lights and digital voltage/current readout. The back of the control unit contains an air pressure gauge and a regulator to adjust the pressure and flow-rate of the atomizing gas. • Wire spool tower to hold the wire spools • Wire-feed chassis with a mechanism to push the wires towards the gun • Spraying gun (front and rear views are shown in Figure 2.11 and Figure 2.12). The front of the gun houses the arc shield, air cap, contact tips and tubes, electrode posts, and DC power cable connections on the bottom. The rear gun body houses the wire feed cable connections and the air hose connection. A handle (Figure 2.11) was also supplied with the system to mount and hand-operate the gun. However, for the purpose of this study, this handle was removed and the gun was mounted on an adjustable bracket at the desired positions. The handle was then used to operate the gun from outside the spraying booth.
Figure 2.8 Picture of ValuArc 200 Twin Wire Arc spray system and the spray gun manufactured by Sulzer-Metco. Picture is adapted from [61]
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Figure 2.9 Picture of ValuArc 200 Twin Wire Arc spray system during operation.
Figure 2.10 Schematics of ValuArc 200 Twin-Wire-Arc Spraying System and its components. Picture is adapted from [2,70].
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Figure 2.11 Exploded rear view of the ValuArc 200 twin-wire-arc gun and its components. The gun can be mounted on the handle and hand operated, or on a separate mount or robot and remotely operated. Picture is adapted from [70]
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Figure 2.12 Exploded front view of the ValuArc 200 twin-wire-arc gun and its components. Picture is adapted from [70]
The gun is connected to the control unit with a hose and cable package that includes two wire-feed cables, two DC power cables (anode and cathode connections), and an air hose. The wire-feed cables are used to guide the consumable wires from the wire-spool to the gun. The DC power cables transmit the voltage supplied by the power supply and apply it on the consumable wires. The air hoses are used to deliver the pressurized atomizing gas intake (dry-air or nitrogen) from a primary compressor unit (Airtower26, KAESER) or a nitrogen tank to the back of the control unit, where it is regulated, and also to deliver the regulated gas from there to the gun. In addition to the above components, an external flow-meter (MEM Thru View, manufactured by Meter Equipment Manufacturing Inc., OH, USA), and a pressure gauge were installed upstream of the gas-inlet hose of the spaying gun to measure the volume-flow-rate and pressure of the atomizing gas. The pressure gauge was installed downstream of the flow-meter and upstream of the spraying gun. The spraying system is setup inside an industrial sized spray booth equipped with a programmable robotic arm (to control the motion of the gun with respect to the substrate), a large exhaust hood and ventilation system. The sound-proof walls of the booth are designed to reduce
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the noise level during operation. Since wire-arc operates at 116 dBA noise level and produces large quantities of harmful dust, fumes and particulates, ear protection and respiratory protection are required during operation inside the booth. Parameters that can be directly or indirectly controlled in this system and their operating range for stable spray conditions are listed here: 1) Material of the fed wires: The following 14-gauge wires (diameter = 1.63 mm) supplied by Sulzer-Metco (NY, USA) were primarily used in this study: • Stainless Steel Metcoloy® 2: Fe 13Cr 0.5Si 0.5Ni 0.5 Mn 0.35C • Stainless Steel Metcoloy® 5: Fe 18Cr 8.5Mn 5Ni 1Si 0.15C • Metco Al: 99% aluminum • Metco Copper AW: 99.8% copper 2) Type of atomizing gas: In this study, dry air and nitrogen were used. 3) Pressure of the atomizing gas: The pressure of the atomizing gas determines its volume-flow-rate and thereby its velocity in the nozzle region. The maximum gas pressure that can be used is limited by the laboratory’s air compressor unit (Airtower26, KAESER). The minimum gas pressure is restricted by the stability of the spray system. Overall, the gas pressure in the ValuArc 200 spray system can be varied between 20 psig (239 kPa) and 65 psig (550 kPa). 4) Voltage applied on the wires: The applied voltage in the ValuArc 200 spraying system can be varied from 20 V to 40 V. 5) Wire-feed-rate: wfr in ValuArc 200 spray system can be varied from 3 m/min to 11 m/min. (5 cm/s to 18 cm/s)
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6) Arc current (indirectly controlled): The current that passes through the wires and maintains the arc, ranges from about 150 Amperes to about 300 Amperes in the ValuArc 200 spraying system. This current is determined by other operating parameters. The next two sub-sections discuss how these operating parameters interrelate.
2.2.1 Volume-Flow-Rate Volume-flow-rate of the atomizing gas and its pressure were measured using the external flow-meter (MEM Thru View, Meter Equipment Manufacturing, Inc., OH) and pressure gauge installed between the flow-meter and the gun. These measurements are plotted in Figure 2.13 for air as the atomizing gas. It can be observed that volume-flow-rate increases linearly with pressure. Since the arcing occurs downstream of the nozzle, this relationship is not significantly affected by other operating parameters (i.e. voltage, wfr, wire material).
Figure 2.13 Standard volumetric flow-rate of the atomizing gas (dry air) as a function of the upstream pressure. The data points represent 20 psig (239 kPa), 30 psig (308 kPa), 40 psig (377 kPa), 50 psig (446 kPa), and 60 psig (515 kPa) in the system’s pressure setting.
32
2.2.2 Arc Current Although the voltage applied on the wires can be directly set using the voltage knob on the control unit, the current that passes through the arc depends on other operating parameters, namely, voltage, gas pressure, wfr, and wire material. Increasing arc voltage increases the electric field within the arc plasma, causing more current to flow. Increasing gas pressure increases the velocity of the cross-flow gas, increases the cooling rate of the arc region, decreases the arc temperature and conductivity, and thereby decreases the current that passes through the arc. Increasing wire-feed-rate shortens the arc length, increases the electric field within the arc plasma, and thereby increases the current that passes through the arc. Besides, increasing the wire-feed-rate increases the amount of heat required to melt the fed material and that is generated by the increased current that passes through the arc. (This is one of the factors that stabilize the spray operation). Moreover, changing the wire material can affect the arc current: a material with a higher specific heat or latent heat of fusion requires more power to melt, thereby the spray gun draws more current from the power supply. Figure 2.14 shows the voltage-current characteristic relationship of the arc for different operating conditions when aluminum (Metco Al) wires and dry-air (as the atomizing gas) are used. It can be observed that increasing voltage or wire-feed-rate significantly increase the current through the arc. It can also be observed that increasing the atomizing gas pressure decreases the current, but the change in current is insignificant (less than 4%) and of the same order of magnitude as the current fluctuations.
33
Figure 2.14 Current-voltage characteristic of the arc for different wire-feed-rates and pressures. Dryair as the atomizing gas and aluminum wires were used. The error-bars represent current fluctuation and standard deviation of 5 to 10 measurements.
Figure 2.15 and Figure 2.16 show that current through the arc changes linearly (approximately) with wire-feed-rate for different operating voltages, and for both aluminum and copper wires. Changes in arc current due to higher gas pressures are, as stated earlier, insignificant and therefore not plotted. To understand the trend of Figure 2.15 and Figure 2.16, one should notice that more power is required to melt material that is fed at a higher rate: This is why the system draws more current. Figure 2.17 and Figure 2.18 show the input power (voltage multiplied by current) as a function of wire-feed-rate, which is the same as the rate at which material is melted. The slopes of these graphs determine the additional power required to heat and melt an extra 1 m/min of fed wire. These graphs can be used for an energy balance analysis of the system. The main source of energy input into the system is joule heating of arc. A small fraction (less than 2%) of this energy is propagated in the form of electromagnetic radiation, a 34
considerable portion increases the temperature of the atomizing gas, and the rest heats up (and melts) the wire-material. Increasing the rate at which wire-material is introduced to the system, requires more power to melt it, whereas the power required to maintain the arc (by heating the gas) is approximately constant (and its variation can be neglected). Therefore, any additional power for an increased wire-feed-rate is approximately equal to the power required to heat up the additional wire-material. In mathematical terms, the energy required to heat up solid aluminum (at room temperature) to molten aluminum at its boiling point is: Q& = csolid (Tmelting − Troom ) + Lf + cliquid (Tboiling − Tmelting ) = 3.10MJ / kg m&
(2-4)
where, Lf is the latent heat of fusion of aluminum and c is the average specific heat of solid and liquid aluminum. This means that 3.1 MJ is required to heat up 1 kg of solid aluminum to its boiling point (liquid form). However, the additional energy provided by the arc is 4.53 MJ/kg (for V = 25 V; see caption of Figure 2.17). It is speculated that the difference (4.5 – 3.1 = 1.4 MJ/kg) vaporizes a fraction of the fed aluminum. Percentage of the vaporized material can be estimated from the following relation: csolid (Tmelting − Troom ) + Lf + cliquid (Tboiling − Tmelting ) + f Lv = 4.53MJ / kg or
(2-5)
3.10MJ / kg + f Lv = 4.53MJ / kg
where Lv and f are latent heat of vaporization and fraction of material that is vaporized, respectively. Equation (2-5) estimates f to be about 13%. The fraction of vaporized material at higher applied voltages, 32.1 V and 39.5 V, is estimated at 36% and 44%, respectively. These estimated fractions explain the considerably large quantity of white powdery-form fume produced during operation of wire-arc spray with aluminum wires. For copper material, this estimated fraction of vaporization is considerably smaller (e.g. f = 3% for V = 26.9 V). 35
Figure 2.15 Current that passes through the arc increases when the feed rate of aluminum wires is increased. Solid curves represent quadratic fits to the datapoints.
Figure 2.16 Current that passes through the arc increases when the feed rate of copper wires is increased. Solid curves represent quadratic fits to the datapoints.
36
Figure 2.17 Input power versus feed rate of aluminum wires. Slope of 39.5V, 32.1V, and 25V curves represent 7.90, 7.01, and 4.53 MJ/kg (mega joules per kilogram of aluminum), respectively. Solid curves represent quadratic fits to the datapoints.
Figure 2.18 Input power versus feed rate of copper wires. Slope of 39.8V, 32.1V, and 26.9V curves represent 3.01, 2.40, and 1.54 MJ/kg (mega joules per kilogram of copper), respectively. Solid curves represent quadratic fits to the datapoints.
37
Chapter 3 Particle Breakup: Thermal Spray Gun
This chapter discusses the physical phenomena of arc heating and particle breakup in a wire-arc spray gun. The custom-made laser-illumination visualization technique used to visualize the process is discussed first, numerical modeling of fluid dynamics of the gun is presented next, and discussions on breakup mechanisms (from anode and cathode) and secondary atomization follow.
3.1 Experimental Studies One of the most influential components in any thermal spraying process is the production of small molten droplets. In most thermal spraying processes, solid particles, in the form of powder, are introduced to the high-temperature high-velocity stream of gas or plasma. The hightemperature ensures that the particles melt in the process and the high-velocity of gas ensures that the particles reach a proper speed before impacting the substrate. In the wire-arc process, however, the small particles are produced throughout the process. The material is introduced in the form of two solid wires that are continuously fed into the system and act as anode and cathode for a DC circuit. The tips of the two wires are positioned close to each other and form an angle ranging from 30 degrees to 45 degrees [26]. The DC voltage applied on the wires causes an electric current to flow between the tips of the two wires and produces an arc. The heat generated by the electric arc heats the tips of the two wires and 38
melts a thin layer on them. The shear force due to the cross-flow atomizing gas strips the molten material off the tip of the wires. The detached molten material that is produced in the wire-arc spray system will then accelerate and undergo secondary atomization.
3.1.1 Imaging system A custom-made high-speed imaging system was developed to take pictures of the wire tips and identify mechanisms of particle detachment. Any imaging system requires a light source to illuminate the region to be photographed, and a light capturing device to record the reflected light. However, excessive amounts of high-intensity radiation at visible wavelengths exist in the wire-tip region that are emitted from the arc and high-temperature metal. Therefore, it is not possible to discern the borders of the wire-tips in a picture taken with a visible-wavelength camera. However, such pictures can be used to determine the general shape of the arc. Examples of such photographs are shown in Figure 3.1.
39
(a)
(b)
Figure 3.1 Pictures of the wire-tip region and the arc during operation of the wire-arc spraying system. These pictures are taken using a visible-wavelength Nikon E3 camera with different optical filters.
40
To avoid the effect of thermal radiation on the imaging system, two pulsed nitrogen lasers ( λ = 337nm , UV radiation) were used to illuminate the wire-tip region, while a UVintensified CCD camera (Cohu 4910 RS-170, COHU Inc.), originally used by Masri [39], captured the reflected beam behind a narrow-band filter at 337 nm. To show that the thermal emission at this wavelength is negligible, Planck radiation of a gray body material is plotted as a function of wavelength in Figure 3.2. These curves are plotted at the melting and boiling temperatures of the materials used as the fed wires in this study (stainless steel, copper, and aluminum). Since the temperature of the wire material lies somewhere between its melting and boiling temperatures (closer to the melting point), it can be observed, from the curves, that its radiation at 337 nm is relatively small. Therefore, the CCD camera will mostly capture the reflected laser beam, rather than the thermal radiation.
Figure 3.2 Black body radiation curves at different temperatures, scaled to a maximum of one. The presented curves represent radiation at the melting and boiling temperatures of Stainless Steel, Copper, and Aluminum.
41
Other obstacles were also addressed in developing this imaging system: • The shutter of the CCD camera has to be synchronized with the laser pulse; the shutter has to be opened before the laser pulse is fired and has to remain open while the laser pulse is illuminating the region. Synchronizing the lasers with the CCD camera was done by using the parallel port of a personal computer and parallel-port programming: consecutive TTL pulses (+5V square wave) were sent to different pins of the parallel port of a desktop computer by assigning 0 or 1 to the corresponding port number. The parallel port, connected to the lasers and the CCD camera, could then fire the lasers and open/close the shutter on the CCD camera at the programmed times. • There was a time delay between the sent signal and the actual laser pulse (about 750 ns [39]), and also between the sent signal and the closing/opening of the shutter (about 100 ns [39]). These delays were considered in programming the parallel port signal. • Since the laser system was relatively large in size, the laser beam was transmitted from the laser exit to the wire-tip region through an optical fiber. Figure 3.3 shows the laser output, the optical fiber, and the coupler used to transmit the laser beam into the fiber. • Since the CCD camera with its lens system attachment was relatively large in size, it was not possible to illuminate the region (with the laser) and shoot (with the CCD camera) from the same angle. Therefore, the two lasers were positioned to illuminate the region simultaneously from top and bottom (Figure 3.4). Improved illumination and visibility were obtained.
42
(a)
(b)
(c)
Figure 3.3 Optical system used to transmit laser beam from the laser system to the region to be photographed: (a) Laser beam output, (b) coupler, and (c) fiber optic cable.
Figure 3.4 Schematic diagram of the position of the UV-intensified CCD camera and illuminating laser beams. Laser beams are coupled into and transmitted through the optical fibers along positive and negative Y axes. Cylindrical lenses focus the beams onto the YZ plane. The CCD camera, attached to the lens system and aligned with the X axis, takes a picture of the wire tips.
Figure 3.5 shows a picture of the two wires and the detached particles. The main reason for the poor quality of the picture is that the output of the COHU camera was analog and could only be recorded on a VCR tape. Still, it is possible to clearly see the detached particles and the anode sheet.
43
30º
1.63 mm
1.63 mm Figure 3.5 Photographs of the two wires and the detached particles. These pictures are the negative of what was captured by the UV-intensified COHU camera. Two lasers illuminate the area from top and bottom simultaneously. Aluminum wires and a High-Velocity cap were used; wire-feed-rate = 8 m/min, voltage = 29.1 V, pressure = 45 psig (412 kPa).
Originally, we planned to use the imaging system to measure particle velocities based on Particle Image Velocimetry (PIV) methodology. However, it was later decided to measure the particle properties using the DPV-2000 system, and therefore, the pictures taken with the imaging system were only analyzed for observation of the detachment mechanisms. 44
3.1.2 Current and Voltage Fluctuations In the wire-arc spray gun, melting of the wires occurs at the wire tips, where they are attached to the arc. When the molten material is pushed by the atomizing gas and breaks away, the arc extinguishes and then reignites between the points of closest distance between the two electrodes. This periodic behavior translates into fluctuations of arc voltage and current, because a change in the distance between the wire-tips results in a change in the arc voltage/current. The effects of the flow rate of atomizing gas and the arc current on the amplitude and the peak frequency of the arc voltage fluctuations (with different nozzle configurations) has been studied by several researchers [46,51,60,65,69]. Steffens and Sheard experimentally showed that there is a relationship between metal atomization from the wire tips and voltage fluctuations [26]. It was shown that molten metal atomization occur shortly after a minimum voltage is reached. Steffens and Babiak [60] measured the arc voltage fluctuations and identified frequencies between 500 Hz and 2 kHz in its power spectrum. Watanabe et al [69] found this frequency peak to be between 500 Hz and 1 kHz. Newbery and Grant [46], also, analyzed the FFT (Fast Fourier Transform) of the voltage fluctuation signal. Furthermore, they correlated the frequency of such fluctuations to the operating parameters of the wire-arc gun and showed that this frequency increases with increasing atomizing gas pressure and increasing wire-feed-rate. Planche et al [51] also analyzed the amplitude of voltage fluctuations and found that it decreases with increasing atomizing gas pressure. Wang et al [67] used a laser strobe high speed vision system to record images of metal detachment from the wire tips, synchronized with arc voltage measurements. They used those images to correlate the fluctuating voltage trace to various stages of metal detachment. Finally, Hussary et al [27,29] studied synchronized detachment images and identified
different mechanisms of primary breakup: membrane, axisymmetric, and non-
45
axisymmetric. They clearly illustrated that primary particle breakup mechanisms from the anode and cathode are different, which results in a bimodal (dual peak) particle size distribution. To further understand primary atomization in the wire arc gun and to focus on the bimodal particle size distribution, the voltage trace of the ValuArc 200 spray system was recorded and analyzed in this study. If particles are detached from the anode and cathode with different average sizes, the rate of detachment from the anode and cathode should be different, and therefore, theoretically, the power spectrum (FFT) of the voltage trace should contain two peaks. To investigate the possibility of having two or more peaks in the power spectrum of the arc voltage fluctuations, the signal was traced on a TDS 220 Tektronix Oscilloscope (Beaverton, OR, USA). The observed cyclic signal was then analyzed using the Fast Fourier Transform (FFT) utility of the same oscilloscope. The FFT spectrum of the signal showed several peaks; however, these peaks moved back and forth in the frequency domain. This uncertainty in the peak frequency can be attributed to: 1) the voltage signal noise level, 2) the randomness in the time the arc is extinguished or reignited, and 3) the inherent errors in estimating the power spectrum with FFT analysis (with limited sampling rate). Therefore, it was technically impossible to distinguish frequency peaks. Instead, the average period of these not-so-uniform voltage fluctuations was calculated by taking several snapshots of the voltage signal and measuring the time duration of about 100 cycles, several times. The average period of voltage fluctuation provides an estimate of the time interval between consequent metal detachments. This time period is of the order of half a millisecond. The dependence of the average period of fluctuation on the operating parameters of the wire-arc spray system was also studied. Changing the applied voltage did not cause a 46
considerable change in the main period of the voltage fluctuations. In contrast, this period decreases with increasing wire-feed-rate or increasing pressure of the atomizing gas (Figure 3.6). 0.7
main period of fluctuation (ms)
0.6 0.5 0.4 0.3 0.2 0.1 0 6
6.5
7
7.5 8 Wire Feed Rate (m/min)
8.5
9
9.5
10
Figure 3.6 The average period of arc voltage fluctuations versus wire-feed-rate for aluminum wires, atomizing gas (air) pressure of 45 psig (412 kPa), Voltage of 29.4 V. The data was collected by taking several snapshots of the voltage fluctuations and counting/averaging the number of cycles in a time interval of about 10 or 20 milliseconds. The error bars are the standard deviation of the collected data.
Based on the abovementioned hypotheses and applying conservation of mass, the average period of arc voltage fluctuations can be related to the wire-feed-rate (wfr) and the average size of detached molten droplets: Neglecting vaporization of material during primary atomization, the total volume of detached molten droplets is equal to the volume of metal that is fed into the gun in the form of wires: d w2 ⋅t Vi = NV = wfr ⋅ π ∑ 4 i =1 N
⇒ ⇒
d w2 t ⋅ V = wfr ⋅ π 4 N d2 V = wfr ⋅ π w ⋅ T 4
(3-1)
where d w , Vi, V , and N are, respectively, wire diameter, volume of the ith detached molten
47
particle, the average volume of detached particles, and the number of detached particles during sampling time interval t. T is the average period of the main oscillation of the arc voltage fluctuation. 1.6E-10
Expected average volume of metal detachments (cubic meters)
1.4E-10 1.2E-10 1.0E-10 8.0E-11 6.0E-11 4.0E-11 2.0E-11 0.0E+00 6
6.5
7
7.5 8 Wire Feed Rate (m/min)
8.5
9
9.5
10
Figure 3.7 Average volume of metal detachment, calculated from equation (3-1) and data in Figure 3.6, presented as a function of wire-feed-rate. Material vaporization is neglected in this analysis.
Using equation (3-1) and the measured average period of voltage fluctuations (presented in Figure 3.6), the average volume of molten metal detachments can be estimated. The results are presented in Figure 3.7. This figure suggests that the size of the molten metal droplets detached in the primary atomization stage has a maximum in the mid-wfr values, although it is not significantly affected by wire-feed-rate. Although slightly overestimated, the calculated sizes of the metal droplets (due to primary atomizations) are of the same order of magnitude as the sizes of metal droplets observed via the CCD camera. It should be noted that the size of the particles downstream of the arc is reduced due to secondary atomizations. Due to unreliability of the voltage fluctuation analysis in identifying the dual-peak particle-size-distribution, no further work was conducted on this method. Instead, the dual peak nature of particle-size-distribution was extensively studied using another method that will be discussed in Chapter 4. 48
3.2 Numerical Studies One of the most powerful tools available today for design and diagnostics of technical systems is numerical modeling and it was therefore used in this study to estimate the size of primary metal detachments from the wire tips in the twin-wire-arc spray system. The numerical modeling was conducted using FLUENT software (finite-volume based code; FLUENT Inc., Lebanon, NH). Solution of fluid flow without consideration of arc-heating is presented first, an approximate arc solution and the effect of arc-heating on the shear stresses on the wire-tips is discussed next, and a breakup model to predict the size of primary detachment follows.
3.2.1 Flow dynamics of the nozzle geometry The geometry of the ValuArc 200 wire-arc gun was created in GAMBIT software (Fluent Inc., Lebanon, NH, USA) based on the engineering drawings provided by the Sulzer-Metco Inc. [70] and measurements of the components of the gun. The created geometry was then meshed and introduced to FLUENT. Figure 3.8 and Figure 3.9 show the outer and inner components of the meshed geometry. This geometry consists of four tubular inlets that carry pressurized atomizing gas into the main torch chamber. There is a regulating rod around which the atomizing gas flows and reaches the nozzle exit. Also, the two contact-tips shown in Figure 3.9 guide the wires towards the nozzle, where the tips are kept at a distance of about 1 mm. Although the wires are constantly moving (because they are consumed), their motion is not modeled in this study.
49
24 mm
Figure 3.8 Volume of the gun in which atomizing gas flows. Four tubular inlets carry pressurized atomizing gas (mainly dry air) into the gun chamber. The opening on top (and its bottom mirrorimage) is where contact tips and wire guides are located. Contact-tip
Wire-tips
Tubular inlets
Regulating Rod
Figure 3.9 Inner components of the ValuArc 200 wire arc gun. Contact-tips guide the wires towards the nozzle. Diameter of the wires is 1.6 mm.
In addition to the shown geometry, a cylindrical volume (or a frustum) was attached to the numerical domain downstream of the nozzle to study the flow downstream of the nozzle exit. It also increases the distance of the nozzle region (which is of primary importance to this study) from the boundaries, and therefore, reduces the numerical errors associated with boundary conditions. The boundary conditions assigned for the model geometry included:
50
• No-slip boundary condition for the solid surfaces in the geometry, including the wire surfaces and contact tips. • Pressure-Inlet for the four tubular inlets • Pressure-Outlet boundary condition was used for the faces exposed to ambient atmosphere. Turbulent fluid flow was solved within the chamber and also downstream of the nozzle (in the attached cylindrical region). Since the Mach number of the gas flow in the gun exceeds 0.3, compressible flow equations were solved. Arc heating was not considered at this stage. Turbulence in the flow was initially modeled using the κ-ε model and turbulent intensities of 10% were assigned to the inlets. Since the κ-ε solution in this geometry is symmetric with respect to YZ and XZ planes, only one quarter of the geometry was introduced to the FLUENT software. Also, since the transport properties of air are strongly dependent on temperature, this dependence was manually assigned in FLUENT. The flow was then solved with second-order solvers and numerical results were obtained with residual levels below 10-5%. Some of these results are presented in Figure 3.10 for a mass-flow-rate of 1.23×10-2 kg/s: Figure 3.10 shows pressure and velocity contours in a cross section of the gun, parallel to the jet. The pressure contours clearly illustrate that most of the pressure drop occurs in the nozzle region and, that pressure is almost constant upstream of the contact-tips. Gas velocity and temperature are also observed to be approximately constant upstream of the contact-tips. Hence, there is no need to include this region in the numerical domain, as only the shear stresses on the wire-tips are of concern to this study.
51
Contact-tip
Wire-tip
Velocity (m/s)
Regulating Rod
Pressure (Pa)
(a)
(b)
Figure 3.10 Contours of gas velocity (a) and pressure (b). Numbers are in m/s and Pa, respectively. Mass-flow-rate of air is 12.3 gr/s. κ-ε turbulent modeling.
52
A new reduced geometry (Figure 3.11) was therefore created, meshed with a finer mesh, and solved with similar boundary and flow conditions: “Pressure-Inlet” for the inlet; “pressureoutlet” for the outlet, no-slip velocity boundary condition for the solid walls, contact tips and wires.
Figure 3.11 Reduced geometry of the gun included contact-tips and wire-tips.
A cross-section of this new geometry and contours of the solved flow properties (velocity, pressure, temperature, and mass-flux density) are shown in Figure 3.12 and Figure 3.13. As shown, supersonic velocities create shockwaves (that are captured by the refined mesh), and a sudden temperature drop of 130K (arc-heating is not yet considered). It is also observed that maximum velocity occurs few millimeters downstream of the nozzle exit. This high velocity region also accommodates local minima of pressure and temperature. Figure 3.14 shows the fluid streamlines in YZ and XZ planes, which clearly demonstrate that, without consideration of arc-heating, divergence of the atomizing gas stream is almost zero.
53
Velocity (m/s) Pressure (Pa)
(a)
(b)
Figure 3.12 Contours of gas velocity (a) and pressure (b) for mass-flow-rate of 25.3 gr/s. Numbers are in m/s and Pa, respectively. κ-ε turbulent model. Arc heating is not considered.
54
Temperature (K) Mass-Flux density (kg m-2s-1)
(a)
(b)
Figure 3.13 Contours of gas temperature (a) and mass-flux density (b) for mass-flow-rate of 25.3 gr/s. Numbers are in K and kg m-2s-1, respectively. κ-ε turbulent model. Arc heating is not considered.
55
Vy (m/s) Vx (m/s)
(a)
(b)
Figure 3.14 Fluid streamlines parallel to YZ (a) and XZ (b) planes in the vicinity of wire-tips. Streamlines are coloured by Y-component (a) and X-component (b) of gas velocity. Mass-flow-rate of gas is 25.3 gr/s. Arc heating is not considered.
56
Figure 3.15 Contours of shear stress on the wire tips. Numbers are in Pa. Mass-flow-rate of air is 12.3 gr/s. Arc heating is not considered.
Figure 3.15 illustrates the distribution of shear stress on the surface of the wire tip. It can be observed that when arc heating is not considered, the shear stress (skin friction) on the wiretips has a maximum that is located on the side that is facing away from the other wire-tip, a region that is not directly heated by the arc. This can be explained by the fact that the flow area between the two wire-tips is much smaller that the opening between the wires and the nozzle. This limits the amount of flow that passes between the wire tips, and therefore, decreases the flow velocity in that region. Consequently, velocity gradients and shear stresses will be lower than those in the rest of the nozzle cross section. The second approach used to model turbulence in the gun was LES. As powerful computers become more affordable, Large Eddy Simulation (LES) is emerging as a viable and powerful alternative tool in turbulence computations. In recent years, LES has been applied to an increasing number of problems in the field of engineering. This is made possible through the use of parallel computing over under-utilized distributed machines in an industry setting, and the availability of relatively cheap processors. The challenge in carrying out LES is that a three57
dimensional, unsteady calculation must be carried out on a grid capable of resolving the larger scales of the motion. For flow geometries and Reynolds numbers of engineering interest, this implies that the mesh-file is usually large. Hence, the CPU time required to perform the calculation is substantially larger than that for an analogous RANS calculation. Unlike κ-ε, implementation of LES turbulence modeling technique in FLUENT has not been extensively tested by independent researchers. Therefore, a benchmark case, based on [21] was created, meshed and solved in FLUENT. The case involved a rectangular channel, open on two ends. FLUENT satisfactorily predicted the velocity profile in the channel, and was therefore used in evaluating the shear stresses on the wire-tips of the ValuArc 200 gun. To be able to resolve relatively large scales of motion, the full geometry of the gun was meshed with a finer grid, and LES equations were solved in the domain. Pressure-inlet and pressure-outlet boundary conditions were assigned to the inlet and outlet of the domain. Timeaveraged flow properties were found, and also time-variations of pressure, velocity, and shearstress at a few points in the domain were tracked. The FFT spectrum of the time-variations revealed a few strong peaks between 40 kHz (for 201 kPa pressure setting) and 88 kHz (for 351 kPa pressure setting). It should be noted that an estimate of the frequency of vortex shedding can also be found using the Strouhal-Reynolds relation: St = 0.198 (1 − 19.7 / Re ) [15]; the main frequency of vortex shedding of a flow of 250 m/s past a cylinder of diameter 1.6 mm is estimated to be 31 kHz, which is of the same order of magnitude as that predicted by LES modeling. It can be concluded that the frequency of vortex shedding (about 40 kHz) is about 20 times the frequency of particle detachment from the wire-tips (about 2 kHz). This means that a molten droplet will experience about twenty oscillations of shear stress; therefore, molten particle atomization can be modeled using a time-average turbulent model (such as κ-ε). 58
To verify that the numerical calculations correctly solve the fluid flow in the experiments, the total pressure drop in the gun+hose system was numerically calculated and experimentally measured for different pressure settings. The experimental and numerical findings are plotted and compared in Figure 3.16. It can be observed that the numerical model provides an acceptable estimate of the total pressure drop.
Figure 3.16 Numerical predictions of volumetric-flow-rate of air as a function of atomizing gas pressure compare relatively well with experimental measurements. Experiments correspond to pressure settings of 20, 30, 40, 50, and 60 psig. Numerical results of κ-ε model under-predict the flow rate by about 8%. Dash-line takes into account the pressure drop in the connecting hose. LES data points and their error-bars represent time-averaged and RMS values of time-dependent flow-rate.
Furthermore, shear stresses were determined on the surface of the wire-tips. The results are shown in Figure 3.17 for different mass-flow-rates of air. Increasing the mass-flow-rate of atomizing gas (air) increases the shear stress on the wire-tip surfaces, and without consideration of arc heating, the maximum shear stress on the wire-tip surface occurs at a point that will not be heated by the arc. This reduces the effectiveness of the current design of the wire-arc gun in atomizing the molten material off the wire-tips. 59
(a) 0.008 kg/s
(b) 0.012 kg/s
(c) 0.018 kg/s
(d) 0.025 kg/s
(e) 0.032 kg/s
(f) 0.038 kg/s
Figure 3.17 Shear stress on the surface of the wire-tips for different mass-flow-rates of air. Arc heating is not considered. LES turbulence modeling.
60
3.2.2 Simplified Arc Solution To incorporate the effect of arc heating in the fluid flow, the arc was solved theoretically with some simplifying assumptions, and based on the experimentally observed shape of the arc. About five pictures of the arc were taken at different system settings (P= 30, 40, 45, and 60 psig) using a visible-wavelength Nikon E3 camera with different optical filters. These digital pictures, as shown in Figure 3.18 and Figure 3.19, were processed in MATLAB software (The MathWorks Inc., Natick, MA): the radiation intensity at all points were translated to grayscale level (a number between 0 and 255), and the grayscale levels were stratified to identify the region of maximum intensity. Then, the arc-shape information (including the length and bending angle of the centerline of the arc) were extracted from the processed pictures. It should be noted that these pictures were taken with different shutter speeds to optimally use the sensitivity range of the camera pixels (sensors). Therefore, maximum grayscale intensities will not indicate maximum radiation level. The presented pictures of arc (Figure 3.18 and Figure 3.19), clearly illustrate that the arc is deflected in the downstream direction (due to convective effects of the cross-flow air). Also, it can be observed that the bending angle and length of the arc increase with increasing atomizing gas pressure. The bending angle and length of the arc were measured from the processed pictures, and then averaged at each pressure setting (Figure 3.20). The average arc length and shape, along with a simplified 2-D arc solution were used to model the arc-heating in FLUENT.
61
(a)
(b)
Figure 3.18 Grayscale picture of arc, taken at P = 30 psig (a) and P = 40 psig (b), wfr = 7 m/min, V = 30.1 V, with aluminum wires, and air as atomizing gas. Radiation intensity is translated to grayscale intensity (a number between 0 and 255). The region of higher radiation intensity is then found by stratifying the picture. Shutter speed setting: 750 (a) and 500 (b).
62
(a)
(b)
Figure 3.19 Grayscale picture of arc, taken at P = 45 psig (a) and P = 60 psig (b), wfr = 7 m/min, V = 30.1 V, with aluminum wires, and air as atomizing gas. Radiation intensity is translated to grayscale intensity (a number between 0 and 255). The region of higher radiation intensity is then found by stratifying the picture. Shutter speed setting: 500 for both (a) and (b).
63
Average Arc Length (mm)
6 5 4 3 2 1 0 20
30
40 Pressure (psi)
50
60
Figure 3.20 At each pressure setting, arc length from different images was measured and averaged. The error bars represent the standard deviation of the measurements.
In order to obtain a simplified solution to the arc in cross-flow, a simple theory of freeburning high-current arcs, developed by Lowke [38], was used and the following simplifying assumptions were made: • The arc was considered two dimensional: although the arc is deflected due to convective effects of the cross-flow, the arc was considered symmetrical about its maximum-temperature centerline. The arc was solved as if it was stretched along a straight line. • Arc radius (radius of the current carrying column) was assumed to be the same as the radius of the radiating column (this radius can be measured from the arc images). • The arc plasma was assumed to be in local thermodynamic equilibrium (LTE). • Transport properties of air at atmospheric conditions were used [12] and gas compressibility effects were neglected. Lowke’s method [38] solves for the centerline temperature, electric field, plasma velocity, and voltage as functions of location along the arc axis, while considering that temperature is constant in the radial direction within the arc. It also assumes that pressure and 64
axial plasma velocity profiles are parabolic in the radial direction. An approximate arc solution can be obtained using the resultant simplified electromagnetic and Navier-Stokes equations. However, due to strong energy convection effects of the atomizing gas, the simplified energy equation will not be a proper approximation of the physics of the arc in cross-flow. Therefore, only the simplified electromagnetic equations were used. Such equations were coded and solved in MATLAB for different current settings and arc lengths (measured from the processed arc images). Results are presented in Figure 3.21 for a current of 200 A and an arc length of 4 mm.
Figure 3.21 Arc radius, current density, and electric field as functions of axial distance in a 4-mm long arc with current of 200A.
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3.2.3 Arc Heating in a cross flow The simplified arc model that was introduced in the previous section provides an approximate solution to current density and electric filed within the arc region. It is therefore
r r possible to estimate the “joule heating” term ( j .E ) in the general energy equation. To estimate the arc-heating term in the arc region, it was assumed that the arc centerline is aligned with the curved centerline obtained from images (local maximum intensity points on the arc pictures). It was also assumed that at any point on the centerline, the arc has a circular cross-section on a plane that is normal to the centerline at that point. Such a simplified arc shape allows determination of the local rate of heating at any point in the arc region. FLUENT was again used to solve the fluid flow equations in the wire-arc-gun geometry. This time, however, an additional volume source of energy, corresponding to the local rate of heating, was added to the energy equation by means of a User Defined Function (UDF) script. A UDF is a C-language routine (programmed by the user) that can be invoked at each iteration of the FLUENT solver. At each iteration of the energy-equation, FLUENT executed a UDF that determined the heat source terms: the amount of energy generated by joule heating, and also the energy loss due to radiation. The new model of fluid flow in the wire-arc-gun, with these heat sources, was run and solved in FLUENT. The resultant velocity, pressure, temperature, and mass-flux density contours are shown in Figure 3.22 and Figure 3.23. It can be observed that due to the increased temperature, the supersonic shockwave effects have subsided. This is mainly because the speed of sound increases with the square root of temperature, and therefore Mach number decreases substantially when arc-heating is considered.
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In addition, as shown in Figure 3.24, the fluid streamlines in YZ and XZ planes are significantly different than those obtained without the effect of arc-heating (Figure 3.14). Arc heating causes the atomizing gas stream to diverge by an angle of about 15 degrees in YZ plane and 20 degrees in XZ plane. This divergence is expected to affect the initial velocity of the produced particles. Furthermore, the resultant shear stresses on the surface of the wire-tips were found at different pressure settings. Figure 3.25 shows the distribution of the shear stress on the wires with the consideration of arc heating. It can be observed that inclusion of arc-heating increases the maximum value of shear-stress on the wire-tip (compare with Figure 3.17). In addition, the point of maximum shear-stress is no longer on the outside face of the wire-tip: it is located between the wires, and moves forward with increasing atomizing gas pressure.
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Velocity (m/s) Pressure (Pa)
(a)
(b)
Figure 3.22 Contours of gas velocity (a) and pressure (b) for mass-flow-rate of 25.3 gr/s. Numbers are in m/s and Pa, respectively. κ-ε turbulent model. Arc heating is considered.
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Temperature (K) Mass-Flux density (kg m-2s-1)
(a)
(b)
Figure 3.23 Contours of gas temperature (a) and mass-flux density (b) for mass-flow-rate of 25.3 gr/s. Numbers are in K and kg m-2s-1, respectively. κ-ε turbulent model. Arc heating is considered.
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Vy (m/s) Vx (m/s)
(b)
Figure 3.24 Fluid streamlines parallel to YZ (a) and XZ (b) planes in the vicinity of wire-tips. Streamlines are coloured by Y-component (a) and X-component (b) of gas velocity. Mass-flow-rate of gas is 25.3 gr/s. Arc heating is considered. Divergence of gas flow is more than that in Figure 3.14, where arc heating was not considered.
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(a) 0.008 kg/s
(b) 0.012 kg/s
(c) 0.018 kg/s
(d) 0.025 kg/s
(e) 0.032 kg/s
(f) 0.038 kg/s
Figure 3.25 Shear stress on the surface of the wire-tips for different mass-flow-rates of air, with the consideration of arc heating. Turbulence was modeled using κ-ε.
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3.3 Simplified Breakup Model The surface of the wire-tips, where they are in contact with the arc, is heated by the arc and therefore, a layer of molten material is formed at this contact region. This molten layer experiences several forces: • Shear stress by the atomizing gas, which was estimated in the previous section. • Pressure drag (form drag): this force is due to existence of high pressure gradients in the region.
v uv • Magnetic pinch force ( j × B ), which, for a particle of diameter d detaching from a
μ0 d 4 2 wire of diameter d w is estimated to be I by Amson [4]. This force becomes 4π d w4 very small in the anode region, because
v v j anode < j cathode
(size of arc-anode
attachment is much bigger than the size of arc-cathode attachment).
• Surface tension force • Weight of the molten layer: this force is about two orders of magnitude smaller than other forces and, therefore, is neglected. Although, theoretically, it may be possible to use a multi-phase fluid code (such as FLUENT) to track the surface of the molten layer and model the primary breakup from the wiretips, FLUENT was not used because of two reasons: poor performance, and high accumulated errors. Numerical studies conducted in FLUENT were found to produce an unacceptable prediction of interface motion in a two-phase fluid flow. Besides, interface tracking becomes particularly difficult (and inaccurate) at high flow velocities.
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In addition, even with a validated numerical code, the errors in shear stresses, magnetic pinch forces, and pressure drag forces, are too high to produce an adequately accurate particle shape and size during primary atomization process. Therefore, it was decided to use the simplified primary-breakup model developed by Amson [4], and used by Kelkar and Heberlein [34]. In this model, a force balance equation is solved to determine the size of the detached material:
μ0 d 4 2 I + FD cos(θ ) − πσ d = 0 4π d w4
(3-2)
where σ is the surface tension constant and θ is the angle between the aerodynamic drag force ( FD ) and the direction of current flow (normal to wire-tip’s surface). The aerodynamic drag force, FD , can be estimated by multiplying the average shear stress on the wire-tip (in the arcelectrode attachment region) by the surface area of a hemisphere of size d. This equation was solved for droplets detaching from aluminum wires (dw = 1.6 mm), for a wire-arc spraying gun operating at a current I = 202 A at different pressure settings. The results are summarized in Table 3.1.
Table 3.1
Size of primary metal detachments from wire-tips, using the simplified model of
Amson [4]. Pressure Setting
20 psig (239 kPa) 30 psig (308 kPa) 40 psig (377 kPa) 50 psig (446 kPa) 60 psig (515 kPa)
Droplet Diameter (μm) (primary atomization) Cathode 480 355 280 220 210
Droplet Diameter (μm) (primary atomization) anode 510 365 285 225 210
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The estimated size of the primary droplets can be used to determine a Weber number We = ρ gU 2 d / σ , where ρ g , U , and σ are gas density, relative gas-droplet velocity, and surface
tension of the liquid metal. The Weber number for the above particles varies between 20 and 50. Metallic droplets with Weber numbers above a critical Weber number Wecrit ≈ 13 , are unstable and subject to secondary atomization [71]. Since the range of Weber numbers of the primary droplets in the wire-arc spray is estimated to be more than Wecrit , all of the primary droplets are subject to secondary atomizations. Particle sizes after secondary atomization and their distribution functions are discussed in the next chapter.
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Chapter 4 Particle Transport: In-flight Particles
The previous chapter of this thesis considered the physical phenomena of arc heating and particle breakup in a wire-arc spray gun. This chapter discusses the characteristics of these detached particles as they are transported in the spray plume. The results presented in this chapter have been summarized and published in the Journal of Thermal Spray Technology [55].
4.1 Background The quality of thermal sprayed coatings is directly related to the properties of the in-flight molten particles, namely, size, temperature and velocity [30,52,54,67]. These properties are interdependent because the diameter of a particle determines the magnitude of both heat transfer and the drag force acting on it, and hence its temperature and velocity. In powder based spray techniques, such as plasma spraying or HVOF, particle size is determined by the size distribution of the powder fed into the gun. Wire arc spraying is different since no powder is used; rather, the heating of the wire tips by the arc, and the detachment of molten metal droplets due to drag and magnetic forces determines the shape and size of spray particles. The heating of the anode and cathode in a wire-arc process, and the difference between them, were extensively discussed in Chapter 3: The arc attaches to the anode over a larger area than the cathode, and so heating is more localized at the cathode spot [28,67]. At the tip of the 75
anode wire a large area is heated due to diffuse arc-anode attachment, melting a layer of metal that is pushed off the end of the wire-tip by the atomizing gas, creating an “anode sheet”. At the cathode, constricted arc attachment causes much more localized heating and melting. Also, since the current passes through a smaller area the current density (j) at the cathode surface is much
v uv uv higher, producing a large magnetic pinch force (the j × B force, where B is the induced magnetic field). Molten metal droplets ejected into the arc from the cathode due to both drag and magnetic forces are observed to be smaller than those that detach from the anode. Using laser strobe photography Hussary et al [28,29] and Watanabe et al [68,69] clearly illustrated the differences between molten metal detachment at the tips of the anode and cathode wires. Inhomogeneity in the microstructure of wire-arc coatings was also observed by Zhu et al [72]. They demonstrated that particles originating from anode and cathode are distributed in an asymmetric way about the centerline of the wire-arc spray. It is interesting to note that although several different researchers have observed and discussed the bimodal size distribution of wire-arc spray particles [28, 34, 35], no attempt has been made to quantitatively analyze the particle-size-distribution graph and observe its variation with different operating parameters. This chapter addresses this issue and includes the following:
• Spatial variation of average particle properties (temperature, size, and velocity) are presented and discussed.
• The dual peak feature of the size distribution of wire-arc particles is analyzed. A new technique to separate the individual peaks of the size distribution of in-flight particles (pertaining to anodic and cathodic particles) is presented. The effect of process parameters on the size distribution is also presented.
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• The temperature distribution within particles and heat production due to exothermic oxidation are discussed for in-flight aluminum spray particles. A numerical model of the heat transfer and temperature distribution within a particle is also presented.
• The drag force and acceleration of particles in the plume are also discussed.
4.2 Spatial Characteristics of the Spray The DPV-2000 monitoring system (Tecnar Ltd., Montreal, QC, Canada) was used to measure particle characteristics at different spatial locations during the time of traversing their path from the wire-arc spray gun towards the substrate. DPV particle size measurements were calibrated by spraying wire-arc particles into water, drying them and washing with acetone. Figure 4.1 shows a typical sample of such particles. The size distribution of the powder collected was measured using a particle size analyzer (MasterSizer S; Malvern Instruments, UK) with a detection range from 0.05µm to 880µm, and then fitted to the DPV-2000 size distribution by varying the assumed diameter coefficient of the DPV software, a factor that takes the effect of material emissivity into account [53]. Particle size distributions were plotted as both frequencyhistogram and volumetric-histogram of particle diameter, assuming particles were spherical.
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(a)
(b)
Figure 4.1 Optical (a) and SEM (b) pictures of aluminum particles collected by spraying into water; P=30 psig (308 kPa), V=32.1 V, wire-feed-rate=7 m/min
The wire-arc spraying system with a high-velocity air cap has a divergence angle of about 15o, giving a coated area of 50 mm × 50 mm when the substrate is placed 200 mm away from the gun. The deposited coating is not a perfect circle; rather the spray pattern is in the shape of an oval whose shorter radius lies in the plane of the two wires. For example, the minor and major radii of the coated area are 25mm and 30mm respectively for a substrate at a stand-off distance of 200 mm (with V=32.1 V, P = 30 psig (308 kPa), wire-feed-rate=7 m/min). As discussed in Chapter 3, this is because the atomizing gas stream is diverted by the wires producing a larger spray divergence along the x-axis than the y-axis (the coordinate system is shown in Figure 4.2a).
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Figure 4.2 Velocity, diameter and Mass-flow-rate of the spray particles as a function of y and x, with z = 50mm. Center of the spray is located at x = y = 0mm. The error-bars in the graphs represent the standard deviation of 3 to 5 measurements.
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Particle properties were measured at different positions in the spray to examine the uniformity of the spray. Figure 4.2 shows the variation of particle velocity (Figure 4.2-a) and diameter (Figure 4.2-b) at different x and y positions in the spray at a distance of 50 mm from the spray nozzle. Results are shown for aluminum particles with the operating parameters of the gun kept constant with a gas pressure of 30 psig (308 kPa), arc voltage of 32.1 V, and wire-feed-rate of 7 m/min. The points in Figure 4.2 represent the average of 3 to 5 measurements of 7000 to 10000 particles in the spray and the error bars show the standard deviation of the values recorded. Particle velocity diminished with distance from the centerline of the spray (see Figure 4.2-a), following the gas velocity profile as discussed in Chapter 3 and in [11]. The average particle diameter increased with increasing radial distance from the centerline of the spray (Figure 4.2-b). This is because the larger/heavier particles that gain their initial momentum at a region with diverging gas flow (Figure 3.24), tend to retain their momentum for a longer period of time, and therefore are deposited farther from the centerline of the spray. Particle temperatures (not plotted here) were practically constant in the x-y plane (about 2433 K) and any variations were within the experimental error range. Particle temperature was much higher than the melting point of aluminum, indicating that surface oxidation produced a highly exothermic reaction on the surface of particles. Mass flow-rate of particles ( m& ) at any axial location in the plume can be calculated as:
⎛ v ⋅π d 3 ⎞ Average ⎜ ⎟ ⎝ 6 ⎠ m& = n& ⋅ ρ ⋅ Average ( v )
(4-1)
where d and v are diameter and speed of a particle, ρ is the density of the particles, and n& is the number flow-rate (number of particles per second that pass through the field of view of the DPV80
2000 sensing head). Since the DPV-2000 system only records a certain fraction of particles (depending on the settings and detection criteria) passing through its sensing volume, the number flow-rate of particles that is measured is proportional to the actual value. Therefore, the calculated mass-flow-rate will be a relative (or scaled) value. Figure 4.2c illustrates the relative mass-flow-rate profile of the in-flight particles at a cross-section of the spray. A measure of the spatial dispersion of particles is the full-width-half-maximum (FWHM) of the mass-flow-rate curve, defined as the distance between points on the mass-flow-rate curve at half the peak value. The full-width-half-maximum of particle mass-flow-rate in the y-direction is about 28 mm and 35 mm in the x-direction (Figure 4.2-c), producing the elliptical deposit on the substrate observed in experiments. When calibrating the DPV-2000 the size of particles sprayed into water was matched to those measured by the DPV along the axis of the spray. Radial variations of particle size, such as shown in Figure 4.2a were ignored in this process. Neglecting particle size variations does not create a large error because the particle density in the spray is concentrated along the spray axis (see Figure 4.2-c). It was estimated that the error in total mass-flow-rate introduced by assuming uniform particle size distribution was less than 4%. The variation of particle properties along the axis of the spray gun was also investigated. Velocity of particles decreased with distance form the nozzle, falling from 160 m/s at z = 70 mm, to about 100 m/s at z = 200 mm. Particle size distribution and temperature showed no variation in the z-direction. It is speculated that the heating of aluminum particles due to surface oxidation offsets the cooling due to convection and radiation to the surroundings.
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4.3 Bimodal Particle Size Distribution and Separation Technique In the wire-arc spraying system, the arc attaches differently to the anode and cathode [28,31,34,35,57,67,68,69], so that the two wires do not melt in the same way. Photographs of arcs have shown that cathode heating is confined to a small area (cathode spot) while the anode is heated more uniformly, though in both cases the area of arc attachment is smaller than the diameter of the wire [28,29,69]. Droplets detaching from the anode are therefore typically larger than those from the cathode [28, 68], producing a dual-peak particle size distribution. In some recent studies [28, 34], bimodal size-distributions have been reported when operating with low atomizing gas pressures. However, at higher pressures the two peaks overlap so that it is not easy to distinguish between them. Figure 4.3a shows the diameter frequency-histogram of aluminum particles produced with atomizing gas pressure 60 psig (515 kPa), arc voltage 37.9 V and wirefeed-rate=7 m/min. The same data is presented as a volumetric-histogram (volume fraction) in Figure 4.3b. The y-axes in the size distributions are shown with arbitrary units since only a fraction of all particles in the spray were recorded by the DPV-2000. Only one peak is obvious in both cases. The technique used to separate cathodic and anodic particles is described below.
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(a)
(b)
Figure 4.3 Frequency-distribution (a) and volumetric-distribution (b) histograms of measured particle diameter are shown by grey histograms; P=60 psig (515 kPa), V=37.9V, and wire-feedrate=7m/min. The curve in (a) is a Log-Normal function (μ=56μm, σ=0.451) matching the maximum and full-width-half-maximum of the measured distribution. The curve in (b) is the volumetric LogNormal function with same μ and σ as in (a) and scaled with the same scaling factor as the measured volumetric-distribution. The black bar-histogram represents the difference between the measured volumetric-distribution and the volumetric log-normal function.
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4.3.1 Size Distribution of Anodic and Cathodic Particles The size distribution of particles produced by atomization of liquid jets typically follows a log-normal probability distribution function defined by [37]: dN 1 1 − 12 ( ln( D )σ−ln( μ ) )2 f ( D) = e = dD 2πσ D
(4-2)
where σ and μ are the geometric standard deviation and geometric mean drop size [37, 22]. This curve fits best to the experimental data of Figure 4.3a with μ=56 μm and σ=0.451. However, there are more than expected large particles in the experiments (see Figure 4.3a, d>100 μm). The difference becomes more obvious when the volumetric log-normal probability distribution function defined as: vdf ( D) =
1 ln( D ) − ln( μ ) 2 ) − ( dV π D 3 1 σ = f ( D) = D 2e 2 dD 6 72π −1σ
(4-3)
is plotted on the experimental volumetric-distribution data in Figure 4.3b. In this figure the volumetric log-normal function is produced with same μ and σ as in Figure 4.3a and is scaled in the same way as the experimental data. Here the difference between the number of large particles measured and those expected from typical atomization theory becomes obvious. The difference (black bar-histograms in Figure 4.3b) is evidence of there being two sets of particle, produced by the cathode and anode, respectively, which have different but overlapping size distributions. Since particles in each of the two sets are produced by simple atomization process from one electrode, their individual size distributions are expected to follow a log-normal function. To confirm that particles produced by melting and atomization of each of the wire tips follow a log-normal probability distribution function it was necessary to physically separate the anodic and cathodic particles. For this purpose, Stainless Steel Metcoloy 2 and Metco Copper wires were used as anode and cathode, respectively. After spraying into water, particles were 84
collected, dried, washed with acetone, and then separated using a magnet. Stainless steel and copper are distinguishable by their color under a microscope and inspection showed that the number of copper particles present in the stainless steel particles after separation was less than 1%. To avoid particle agglomeration (see Figure 4.4), stainless steel particles were placed in a demagnetizer, (DEMAG, Nortronics, NY).
Figure 4.4 An optical picture of magnetically-agglomerated stainless-steel particles before being demagnatized.
Size distribution of stainless steel particles was measured using a Particle Size Analyzer™. Figure 4.5 shows the size distribution of anodic stainless steel particles. A lognormal distribution curve fits the data well; discrepancies were less than the uncertainty of the measuring instrument (represented by error bars in Figure 4.5). The experiment was repeated with the polarity of wires switched so that the cathode was stainless steel. Cathodic stainless steel particles, too, follow a log-normal distribution function. 85
Figure 4.5 A log-normal function fits well within the error-bars of the size-distribution of anodic particles. Stainless steel and copper wires were used as anode and cathode, respectively. The error bars represent the systematic error of the size measuring device.
4.3.2 Separation Technique The size-distribution of wire-arc particles can be represented by superposing two lognormal distribution functions. Since anode and cathode wires are fed into the spray gun at the same rate in experiments the total mass of cathodic and anodic particles in any sample collection are equal. Therefore, even though the volumetric-distribution curves of anodic and cathodic particles are different, the area under the curves must be the same. Since cathodic particles are smaller they must be more numerous than the larger anodic particles. A method for determining the size distributions of anodic and cathodic particles produced by a wire-arc spray is summarized in the following steps: 1. Plot the experimental volumetric-distribution of particles and determine the area (A0) under the curve;
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2. Fit a log-normal function, using the least square method, to the ascending portion of the experimental frequency-distribution curve of particle diameter (from 0 to the most frequent particle diameter - e.g., from 0 to 45 μm in Figure 4.3a). Since this fit represents the frequency-distribution of cathodic particles, the area under its volumetric-distribution curve must equal A0/2. We assume here that the anodic particles are larger and much fewer in number and hence contribute little to the population of small particles. 3. Subtract the fitted cathodic distribution curve from the measured distribution to obtain the distribution of anodic particles. 4. Fit a log-normal function through the calculated diameter frequency-distribution of anodic particles using method of least-squares. The area under its volumetric-distribution curve must also be A0/2. 5. Add the cathodic and anodic distributions and compare with the experimental size distribution to evaluate errors.
4.3.3 Error Estimation To estimate the errors associated with the experimental instrumentation for measuring powder size distributions, we mixed two powders of known size distribution, measured the size distribution of the mixture and then calculated the size distribution of one of the original powders. Metco 54NS-1 powder (Al 99%, particle size: -75+45µm) was sieved to isolate batches with diameter ranges of -53+45µm and -75+63µm. A particle size analyzer (MasterSizer S; Malvern Instruments, UK) was used to measure the size distributions of both samples. Equal weights of both powders were then mixed and the size distribution of the mixture determined. Since the volume of the mixture was twice the volume of the samples, their size distributions were scaled similar to steps 1 and 2 of the algorithm outlined above. By subtracting the size 87
distribution of the smaller particle sample from that of the mixture, the size distribution of the larger powder was determined. The relative error ( ε ) was calculated from
ε=
∫ y− y ∫ y dx
reconst
dx
(4-4)
where y and yreconst are the experimental and calculated size distribution of the larger diameter powder respectively. The relative error in reconstructing the size distribution was less than 4%. To estimate the errors associated with the proposed technique for separating anodic and cathodic particle size distributions, we reconstructed two peaks from the mathematical sum of two known log-normal functions. Typical values of μ1=50μm and σ1=0.45 were assumed for the cathodic log-normal particle size distribution function and μ2=120μm and σ2=0.45 for the anodic distribution function. These curves and their summations are shown in Figure 4.6, both as frequency-distribution (Figure 4.6a) and volumetric-distribution (Figure 4.6b) of particle diameter. Following the procedure outlined above the anodic and cathodic particle diameter distributions were reconstructed from the combined curve; the calculated size distributions are also shown in Figure 4.6. The relative errors of both reconstructed functions were calculated to be less than 0.5%. This error varies with the shape and peak-to-peak spacing of the anodic and cathodic distribution curves. Table 4-1 lists five different anodic log-normal functions and the error in reconstructing them while holding the cathodic particle size distribution constant. Errors increase when the peaks are closer together and there is greater overlap of the two distribution curves.
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Table 4-1
Different log-normal functions and the relative error in reconstructing them from
their sum. Cathodic log-normal function μ1 (μm) σ1 50 0.45 50 0.45 50 0.45 50 0.45 50 0.45
Anodic log-normal function μ2 (μm) σ2 150 0.45 120 0.45 90 0.45 80 0.45 70 0.45
Relative error 0.2% 0.4% 1.6% 3% 8%
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(a)
(b)
Figure 4.6 The separation technique was applied to the addition of two known log-normal functions (LN1: µ1=50µm, σ=0.45 and LN2: µ2=90µm, σ=0.45) to reconstruct the original functions. (a) frequency-distribution (b) volumetric-distribution.
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(a)
(b)
Figure 4.7 Two peaks in the measured diameter distribution were separated and presented in frequency (a) and volumetric (b) forms. LN1 and LN2 represent log-normal distribution functions of cathodic and anodic particles respectively. vLN1 and vLN2 are the volumetric representation of LN1 and LN2. Experimental particle size statistics was obtained by DPV-2000 system at a stand-off distance of 50 mm, voltage of 32.1 V, wire-feed-rate=7 m/min, and P = 60 psig (515 kPa). These distributions represent statistics of about 8000 aluminum particles.
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4.3.4 Effect of Varying Wire-Arc Parameters To investigate the effect of wire-arc operating parameters such as atomizing gas pressure, wire-feed-rate and operating voltage on particle size distribution, a series of experiments was done in which each of these was varied. Particle size distributions were measured using the DPV-2000 and anodic and cathodic particles identified using the separation technique described above. Figure 4.7 shows a typical result for a spray gun operated with gas pressure 60 psig (515
kPa), wire-feed-rate 7 m/min and arc voltage 32.1 V. Particle sizes are shown as both a frequency-distribution (Figure 4.7a) and volumetric-distribution (Figure 4.7b) and calculated anodic and cathodic particle size distributions are also shown. Similar experiments were done for atomizing gas pressures ranging from 20 psig (239 kPa) to 60 psig (515 kPa), wire-feed-rates of 6 to 10 m/min and arc voltages of 25 to 40 V. Repeated experiments were done at each setting. The results shown are the average of 4 measurements and error bars represent the standard deviation. Figure 4.8 shows the variation of both mean-diameter and mass-mean-diameter of both anodic and cathodic particles with gas pressure. Mass-mean-diameter is defined as MMD = (∑ mi di ) / ∑ mi where mi and di are mass and diameter of i th particle, and the
summation is over all particles [28]. Anode particles were always significantly larger than cathodic particles. Particle size increased as gas pressure was reduced. Drag forces exerted by the gas are the main reason for atomization of molten material from the wire tips. Droplets of molten metal are formed when the drag and magnetic forces that tear liquid off the wire tip exceed surface tension forces attaching it to the wire. As gas pressure decreases so does its velocity and therefore drag forces. Molten metal droplets grow larger before detaching from the wire tip when drag forces diminish. Moreover, secondary atomization that breaks the molten material into smaller droplets tends to produce smaller particles with increasing gas flow velocity [71]. 92
Figure 4.8 Mean-Diameter and Mass-Mean-Diameter of cathodic and anodic particles decrease as the pressure of the atomizing gas increases. Anodic particles are more significantly affected by atomizing gas pressure than the cathodic particles. Error-bars represent standard deviation of 3 to 5 measurements of about 8000 particles. Operating parameters: Aluminum wires, V=32.1V, wire-feedrate=7m/min, stand-off distance=50mm.
The primary dimensionless parameter on which secondary atomization depends is the gas Weber number defined as We = ρ g ΔU 2 D / σ , where ρ g , U , and σ are gas density, relative gasdroplet velocity, and surface tension of the liquid metal. For all metallic melts, there exists a critical Weber number ( Wecrit ≈ 13 ) below which droplets remain stable [71]. Weber number in the nozzle region of the spraying gun, where the primary breakups occur, is estimated to be 70 (assuming typical values for gas velocity and spherical drop diameter as in [34]). Thus the metallic detachments are unstable and subject to further disintegration. However, five centimeters downstream from the nozzle exit, the Weber number dramatically drops to an approximate low value of 0.5, below the critical value. Therefore, the effect of secondary disintegrations can be neglected in the spray region. This is confirmed by the experimental
93
measurements of the average size of particles that showed no significant variation along the spray plume. Since the size of droplets resulting from a secondary breakup is proportional to the size of the original particle [71], and since the primary breakups from anode and cathode are different in size [34], the size of anodic and cathodic droplets after the secondary atomization should be distinct.
Figure 4.9 Mean-Diameter and Mass-Mean-Diameter of cathodic and anodic particles as a function of the wire-feed-rate. Error-bars represent standard deviation of 3 to 5 measurements of about 8000 particles. Operating parameters: Aluminum wires, P = 60 psig (515 kPa), V = 32.1V, stand-off distance = 50 mm.
Figure 4.9 shows the variation in particle size with wire-feed-rate. There was a small increase in particle diameter as feed rate increases, though it was so small that it was difficult to see the effect on mass mean diameter. Increasing the wire-feed-rate shortens the arcing distance, which results in an increase in the current that passes through the arc, and therefore the heat flux to the electrodes. In the case of the cathode, where heating is localized at the cathode spot, an increase in heat flux results in faster detachment of same size droplets from the wire material that 94
is fed at a higher rate. In the anode region, where heating is spread over a larger area, the increased heat flux results in a thicker layer of molten material, which is pushed away by the drag force of the gas flow. The drag force, however, does not increase with the thickness of the anode sheets and therefore slightly larger particles are produced in the anode. Varying operating voltage, too, had only a small effect on particle size. Figure 4.10 shows the variation of mean particle diameter with voltage. A mid-value voltage, at about 32V, appeared to maximize particle size. A full explanation of this behavior will likely require a detailed analysis of changes in heat transfer and magnetic forces at the wire tip caused by varying voltage.
Figure 4.10 Mean-Diameter and Mass-Mean-Diameter of cathodic and anodic particles as a function of the applied voltage. Error-bars represent standard deviation of 3 to 5 measurements of about 8000 particles. Operating parameters: Aluminum wires, P = 60 psig (515 kPa), wire-feed-rate = 7 m/min, stand-off distance = 50mm.
95
4.4 Axial variation of particle properties As discussed earlier in this chapter, aluminum particle properties (temperature, velocity and size) produced by the ValuArc200 twin-wire-arc spray were measured at different stand-off distances from the gun. The experimental results showed that while the velocity of wire-arc aluminum particles diminishes along the axis of particle spray, particle temperature does not noticeably change along the axis of particle spray. The behavior exhibited by the velocity profile (Figure 4.11) is explained in accordance with the velocity profile of the atomizing gas. The behavior exhibited by the temperature profile (Figure 4.12) is explained by the exothermic oxidation of the aluminum surface. 140
Particle Velocity (m/s)
120 100 80 60 40 20
y = 135.03e
-3.6867x
0 0
0.05
0.1 0.15 Distance (m)
0.2
0.25
Figure 4.11 Axial velocity profile of particles in the spray.
96
2450
Temperature (K)
2400 2350 2300 2250 Sprayed with Air Sprayed with Nitrogen
2200 0
0.05
0.1 0.15 Distance (m)
0.2
0.25
Figure 4.12 Axial temperature profile of particles in the spray with air and nitrogen as atomizing gas. Temperature of aluminum particles sprayed with nitrogen increases by about 130°C as they travel a distance of 20 cm.
4.4.1 Drag Force and Force Balance Relation Upon primary atomization of molten material from the wire-tips, the molten detachments are exposed to transonic flow of the atomization gas. This gas flow produces a positive drag force on the particles and accelerates them towards the substrate. A few centimeters downstream, the gas velocity reaches its maximum and then decelerates due to its expanded flow area (see Figure 3.10). This causes the relative gas-particle velocity to become negative and therefore the spray particles decelerate. This deceleration is experimentally measured and presented in Figure 4.11.
4.4.2 Heat Transfer and Exothermic Oxidation of Particles In order to model the heat transfer processes during and after primary particle breakup in the wire-arc spray gun, it is necessary to have an estimate of the timescales involved in such processes. It is also useful to distinguish between dominant and negligible terms in the heat balance equation. This section qualitatively describes the variation of particle temperature based on some theoretical calculations and experimental results. 97
As shown in Figure 4.12, the surface temperature of aluminum particles, when sprayed with air, is about 2400K, which is below the boiling point of aluminum, and slightly above the melting point of aluminum oxide. Therefore, due to rapid oxidation of aluminum, a typical inflight aluminum particle will have a liquid shell of aluminum oxide containing a mixture of molten aluminum and molten aluminum oxide. Formation of the aluminum oxide layer is a very rapid process. The thickness of the oxide layer has a parabolic behavior with time: Depth of the oxide layer can be estimated by δ=(Dt)1/2, where D is the effective diffusion coefficient. During the typical particle-travel-time (from the gun to the substrate), which is about 2ms, the depth of the oxide level can reach a few nanometers, at room temperature. Diffusion rate at elevated temperatures is probably much higher (no reference was found for this data), and therefore, the oxide layer on the in-flight wirearc particle is likely much thicker. In addition, the motion of molten aluminum inside the particle can mix the aluminum and aluminum oxide, which increases the oxide content of the particle even further. Oxidation of aluminum is an exothermic process and produces 399kcal of heat per mole. The released energy can be calculated by estimating the number of aluminum oxide molecules and the heat capacity of the particle: H = ΔG ρ Al2O3 π d 2δ / M
(4-5)
where ΔG , ρ Al2O3 , d, δ, and M are molar heat of formation, density of aluminum oxide, diameter of in-flight particle (about 50μm), thickness of oxide layer (considered to be 10nm), and the molar mass of aluminum oxide (102 gr/mol), respectively.
98
A heat balance equation can then be used to relate the released energy to the temperature increase experienced by the particle (assuming that this energy will completely dissipate within the particle):
ΔT = H / (cp ρ Al πd3/6)
(4-6)
where cp and ρ Al are specific heat and density of aluminum. For a typical aluminum particle, this temperature increase can be expressed as:
H = 1.7 × 1011 d 2δ ≅ 4.2 × 10−8 J ΔT = 1.16 × 105 δ / d ≅ 23K
(4-7)
This ΔT likely underestimates the actual increase in temperature and can be orders of magnitude higher if the diffusion rate at the high temperatures (@ 2400K) and the mixing of aluminum and aluminum oxide were considered. To further investigate the effect oxidation has on the temperature of a particle, the atomizing gas (usually dry air) was replaced with nitrogen. If exothermic oxidation counteracts the convective cooling effects of the surrounding gas, eliminating oxidation should reduce the particle temperature. Figure 4.12 shows the experimental measurements of particle temperature at different axial locations for two cases of air and nitrogen as atomizing gas. It can be observed that for the case of nitrogen (as the atomizing gas), the temperature of aluminum particles immediately downstream of the gun is about 150 K lower than when dry-air is used. As the particles move towards the substrate, air is entrained in the particle+nitrogen plume, and oxidation starts to occur. This is more evident from the lateral variation of particle temperature shown in Figure 4.13; Off-center nitrogen-sprayed particles in the plume are more exposed to the oxygen molecules in the ambient air, and therefore, oxidize more (and will have a higher temperature than the centerline particles). It is interesting to note that the average temperature of
99
particles sprayed with air and nitrogen both reach a value of 2350 K in the outer layer of the spray. 2450 Sprayed with Air Sprayed with Nitrogen Temperature (K)
2400 2350 2300 2250 2200 -30
-20 -10 0 10 20 Distance from centerline of the spray (mm)
30
Figure 4.13 Average temperature of aluminum particles in the spray as a function of lateral distance from the centerline of the spray. Axial distance from the gun is 3" (76 mm). V=31V, wfr = 7 m/min, P=30 psig (308 kPa).
Relaxation Times for Heat Transfer: Since formation of the protective aluminum-oxide
layer is a rapid process (about 1ns at room temperature, and less than 1ns at elevated temperatures), oxidation can be assumed as an instantaneous process (compared to the typical inflight time of about 2 ms). During and after the oxidation process, the produced heat will be conducted to the center of the particle in a very short time, causing it to reach an equilibrium temperature. The characteristic time during which the generated heat is dissipated through the spherical particle can be estimated using temperature-response-time [15]:
τ=
ρcpd 2 12k
(4-8)
where τ , k , c p , and d are characteristic temperature-response-time, thermal conductivity, heat capacity, and diameter of the particle, respectively. This characteristic time for aluminum particles is about 2μs which is much less than the in-flight time period. This characteristic time 100
would be the same for any other process that changes the temperature on the surface of the particle. For example, heat conduction from the surface will cool down the whole particle in a time interval that is much shorter than the in-flight time. Detached Aluminum Particles: The above discussion provides us with a clearer view of
in-flight particles. Roughly speaking, every 1 ms, the atomizing gas strips molten material off the wire tips. In just a couple of nanoseconds, when the molten material (an undetached drop) is still in the process of detachment, its outer layer will be oxidized. In addition to the heat gained from the arc, the exothermic process of oxidation will also contribute to the heating of the outer layer of the particle. Shortly after detachment (in few microseconds), the particle reaches thermal equilibrium: convective heat transfer and radiation losses cool down the particle, while the exothermic oxidation counteracts these effects and maintains the temperature of particles.
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Chapter 5 Particle Deposition: Splat and coating formation
Previous chapters of this thesis considered heating, melting, atomization and transport of wire-arc particles. This chapter discusses how these particles are deposited on the substrate. The results presented in this chapter have been summarized and published in Journal of Surface and Coating Technologies [1] Generally, a thermal spray particle is partially or fully melted before deposition. Upon touching the substrate, it spreads on the substrate and starts to cool down and solidify. This solidified splat (or deposit) and the ones that will be deposited on top of it, will form the building blocks of the produced coating layer. The quality of the coating depends on the shape, size and material of these splats and also on how strong they are attached together and to the substrate. Shape and size of the solid deposits depend on substrate condition and also on in-flight particle properties, which, in turn, depend on operating parameters of the spray system. Effects of substrate temperature and particle velocity on shape of the deposited splat are discussed first, and their effects on coating quality follow.
5.1 Effect of Substrate Temperature on Splat Formation Increasing substrate temperature is shown to have a strong effect on the properties of the thermal spray coating that is applied on it: Pershin et al [50] plasma sprayed nickel powder onto 102
a stainless steel plate and found that coating adhesion strength increased by almost an order of magnitude as surface temperature was raised from room temperature to 650°C. Several explanations were proffered: heating the surface clears volatile contaminants adsorbed on the surface, improving contact between impinging particles and the substrate; reducing the cooling rate and solidification time of droplets allows them to flow into surface cavities before freezing, enhancing mechanical bonding. The most visible effect of increasing substrate temperature, though, was to change the shape of splats formed by solidified droplets after impact on the surface. The effect of substrate temperature on splat shape has been well established in a number of studies, reviewed in detail by Fauchais et al [19]. Typically, a thermal spray particle landing on an unheated surface will splash, forming a fragmented splat with irregular edges. If surface temperature is increased splat shape changes, so that impacting droplets form circular discs with no evidence of splashing. Fukumoto et al [20] did a statistical analysis of splat shapes deposited on a surface and defined a “transition temperature” (Tt) as the substrate temperature where equal numbers of splat and disk splats were visible on the surface. Surface temperature, though, is not the only factor affecting splat shape. Jiang et al [32] plasma sprayed ZrO2 particles onto polished stainless steel coupons and found that the presence of condensates/adsorbates on the substrate enhanced splashing; removing adsorbed volatile compounds on the surface reduced splashing. Computer simulations of impacting molten metal droplets [43,47] provide insight into a mechanism for solidification induced splashing. A spreading drop begins to freeze along its edges, where it first contacts the colder substrate. The solid rim formed obstructs further flow, forcing liquid to jet off the surface so that it becomes unstable and breaks up into satellite droplets. The rate of solidification depends on both properties and temperatures of the substrate and droplet, and also the thermal contact resistance between the two (which varies with surface 103
roughness and the presence of any surface contaminants). The transition temperature is therefore a complex function of all these parameters. Dhiman and Chandra [16,17] proposed a simple criterion to determine if solidification induced splashing will not occur: a droplet will form a disk splat if the solid layer in the droplet does not grow as thick as the splat, in the time the droplet takes to spread. A one-dimensional heat conduction analysis was used to develop a model to predict the transition temperature. Most studies on the effect of surface temperature on the properties of single splats and coatings have investigated plasma spraying [10,44], and little work has been done on splats generated by wire-arc spraying. This section of the thesis focuses on the morphology of the splats formed by wire-arc spraying aluminum droplets onto stainless-steel substrate.
5.1.1 Experimental Procedure ValuArc 200 wire-arc spray system (Sulzer-Metco, Westbury, NY, USA) with HighVelocity cap and air as its atomizing gas was used to spray aluminum (Metco Al wires) onto polished stainless steel substrates for the purpose of determining the effects in-flight particle properties have on the splat formation The experimental results presented in Chapter 4 showed how in-flight particle properties (velocity, temperature, and diameter) and their distributions are affected by operating parameters of ValuArc 200 wire-arc spray system: Although average particle velocity inhibits a significant change when operating parameters are altered, average temperature and diameter inhibit only a slight change. Experiments also showed that particle velocity is strongly dependent on the atomizing gas pressure (and not voltage or wfr). Therefore, arc voltage and wire-feed-rate were kept constant in the experiments presented in this section of the thesis (for the purpose of finding the effects of particle properties on the splat formation). Voltage and wire-feed-rate were held at 104
32.1 V and 7 m/min, respectively, while atomizing gas pressures of 30, 45, and 60 psig were used. Table 5.1 summarizes particle diagnostics in the spray at these three pressure settings. Since increasing pressure of the atomizing gas increases particle velocity, these settings are hereafter referred to as low-velocity, mid-velocity, and high-velocity settings, respectively.
Table 5.1
Wire-Arc Operating Parameters and Particle Properties High velocity setting (V=143 m/s)
Voltage (V)
Mid Low velocity setting velocity setting (V=131 m/s) (V=109 m/s)
32.1
32.1
32.1
7
7
7
60 , 515
45 , 411
30 , 308
Gas Flow Rate (scfm)
64
53
40
Arc Current (A)
202
205
212
Mean Velocity (m/s) Standard deviation (m/s)
143 ± 3 36
131 ± 3 36
109 ± 2 28
Mean Temperature (oC) Standard deviation (oC)
2132 ± 10 131
2135 ± 12 133
2140 ± 7 120
Mean Diameter (μm) Standard deviation (μm)
71 ± 3 42
70 ± 3 40
71 ± 3 40
wire-feed-rate (m/min) Operating Gas Pressure (psig , kPa)
Substrates were 16-gauge AISI 304L stainless steel coupons, 75 mm × 40 mm × 2.5 mm in size. These coupons were polished to a mirror finish (Ra = 0.01-0.04 μm), using progressively finer grades of emery paper and finishing with alumina suspension applied with a soft cloth. As shown schematically in Figure 5.1, the prepared substrates were mounted 200 mm from the spray gun exit on a heater block whose temperature could be controlled with an accuracy of ±5°C. A steel restriction plate with a 1.6 mm opening was placed approximately 125 mm downstream from the gun, the hole aligned with the centerline of the spray. A second blocker plate was used to close the opening while the gun was started until the spray process 105
stabilized. It was then removed very briefly (for about 1 to 2 seconds), to allow a few particles to pass through the hole, land on the substrate and form distinct splats. Removing the restriction/blocker plates for 3 to 5 seconds allows a coating layer with 200 μm to 400 μm thickness to build up.
Figure 5.1 Experimental setup to obtain distinct splats on the substrate.
DPV-2000 diagnostics system (described in 2.1.1) was used to measure size, velocity, and temperature distribution of in-flight particles. Although DPV-2000 measures the properties of individual particles, it was not possible to relate each splat with its corresponding in-flight particle. (Obtaining such information requires a more sophisticated setup similar to [41]). Instead, a statistical approach was taken: mean and mode diameter of in-flight particles were compared to mean and mode diameter of splats.
106
Optical analysis of splats and coating cross-sections was done using Clemex Vision Pro image analysis software (Clemex Technologies Inc., Longueuil, QC, Canada). The area (Asplat) and the length of the periphery (Psplat) of each splat were determined using the software. An equivalent splat diameter (Dmax) was then calculated using the relation: Dmax =
4 Asplat
π
(5-1)
For irregular splats a “degree of splashing” (DS) was also calculated, as defined by Sampath et al [58] DS =
2 Psplat 4πAsplat
(5-2)
For perfectly circular splats DS = 1 and the value increases as splat splashing increases. Coating deposition efficiency was measured by recording the difference in coupon weight before and after spraying, and dividing that by the weight of the wire sprayed. Adhesion strength of the wire-arc sprayed aluminum coatings onto stainless steel substrates have been previously measured by Abedini [2]: He used the procedure recommended by ASTM standard C633-01 (Standard Test Method for Adhesion or Cohesion Strength of Thermal Spray Coatings). Coatings were deposited on the flat ends of cylindrical coupons, 50 mm long and 24.7 mm in diameter, held in a heater block. Adhesion strength was measured by attaching another identical coupon to the coating using epoxy, after which an Instron Model 1331 hydraulic tensile test machine used to pull the coating off the substrate. Coating adhesion strength was defined as the force required to detach the coating, divided by the cross-sectional area of the coupon. X-ray Photoelectron Scanning (XPS) was used to determine the elemental composition of the stainless steel substrates and to detect how much oxidation was caused by increasing surface temperature. A PHI 5500 Multi-Technique System (Physical Electronics, Eden Prairie, 107
Minnesota, USA) was used to measure the fraction of oxygen, iron and chromium and other elements present on substrates. Prior to XPS analysis the test specimens were argon-ion sputtered to remove surface contaminants.
5.2 Splat Morphology Figure 5.2 shows images of aluminum splats formed on stainless steel substrates held at temperature (Ts) ranging from 25°C to 300°C, and corresponding cross-sections through coatings formed at the same conditions. The two columns on the left show splats and coatings formed with a higher atomizing gas pressure, where mean particle velocity was 143 m/s, while those on the right were formed with a lower gas pressure and mean impact velocity of 109 m/s. At surface temperatures below 100°C splats showed signs of having undergone extensive splashing, with long fingers radiating out from a central core of solidified metal. Computer simulations of droplet splashing [43, 47] have shown that solidification starts at the periphery of the spreading droplet, creating a solid rim that forces the liquid to jet off the surface, where it becomes unstable and breaks into fingers. Voids between fragments of the drop and in the central splat itself create pores in the coating: cross-sections through coatings formed on surfaces at 25°C show large voids and pores (see Figure 5.2). The voids were largest at the lower impact velocity (V=109 m/s), especially at the substrate-coating interface, and decreased when impact velocity increased to 143 m/s.
108
Figure 5.2 Splat morphology and corresponding coating microstructure of wire-arc sprayed aluminum deposited onto polished stainless steel (type AISI304L) held at various temperatures.
109
Increasing substrate temperature produced a change in splat shape. As Ts was increased above 100°C splats became rounder and fingers became shorter until they disappeared almost entirely. The change was progressive, but there was a sharp transition in the range 100°C150°C: at lower substrate temperatures, below the transition temperature, there was too much splashing and loss of mass (not accounted for in the model) to obtain meaningful splat diameters. Equation (5-6) predicts disk splat diameters with reasonable accuracy.
Figure 5.5 Experimental and theoretical spread factor values for both high velocity (143 m/s) and low velocity (109 m/s) tests. The curves are the theoretical predictions from equation (5-6).
The criterion postulated for formation of disk splats [16, 17] is that s ≤ h during the spreading time, tc. The transition temperature, Tt , is the lowest substrate temperature at which this will happen; for Ts>Tt the droplet spreads fully before the solid layer has grown sufficiently to obstruct flow. Combining equations (5-3) to (5-6) we obtain an explicit expression for the transition temperature:
114
⎡ 4 We ⎤ (1− cosθ a ) + ⎢ 3 Re ⎥ Pe A H f ⎢ ⎥ Tt = Tm − ⎡ ln(1+ Bi A) ⎤ ⎢ 2(We + 16)C p ⎥ ⎢1− ⎥ ⎥⎦ Bi A ⎦ ⎢⎣ ⎣
(5-7)
where A=
ρ d kd Cd 8π ρ s ks Cs 3Pe
(5-8)
The transition temperature depends on the properties of the impinging droplet and the substrate, impact velocity and contact resistance. Figure 5.6 shows the variation of transition temperature with impact velocity for aluminum droplets impacting stainless steel surfaces. Results are shown for four different values of Rc= 0, 10-7, 1.4x10-7, and 1.7x10-7 m2K/W, as well as the three experimentally determined values of Tt. Transition temperature decreased significantly with increasing contact resistance. For Rc=0 there was little effect of impact velocity on transition temperature; at higher values of contact resistance transition temperature decreased with impact velocity.
115
Figure 5.6 Prediction of transition temperature for aluminum droplets impacting a stainless steel surface. The three experimental data points do not necessarily have similar contact resistances due to the growth of an oxide layer on the substrate.
As impact velocity increases droplet spreading time and splat thickness both decrease. As a consequence of shorter droplet spreading time the solid layer has to grow faster to obstruct flow, resulting in a lower transition temperature. However, reduced splat thickness means that the solid layer has to grow less to obstruct flow, which increases transition temperature. The contact resistance determines the relative magnitude of these two competing effects. For Rc=0, solidification progresses rapidly and changes in spreading time have little impact; for higher Rc, solid layer growth is slow and therefore transition temperature decreases with increasing droplet velocity. The experimentally observed decrease in transition temperature, from 230°C at Vo=109 m/s to 140°C at Vo=143 m/s, was more than that predicted by the model if Rc was assumed the same at all three temperatures. However, it seems quite likely that contact resistance changes with surface temperature due to the growth of an oxide layer when steel plates are heated in air [13]. Heating test coupons to 300ºC changed their color to a golden hue, which turned brown 116
under further heating. Figure 5.10 shows the surface composition of coupons heated in air to a given temperature and then allowed to cool. The oxygen content increased from 35% of the total at room temperature to over 60% at 350°C, indicating increased oxidation.
Figure 5.7 Plot of elemental composition of the stainless steel substrates heated to various temperatures. Adapted from [1].
Prolonged heating in air can create a significant amount of oxide scale at the surface, sufficient to increase not only thermal contact resistance but also surface roughness. A mirrorpolished substrate, initially with Ra=0.01 μm, was found to have surface roughness as high as 0.40 μm after being heated for 25 min at 350°C. Increased roughness also promotes splashing of molten metal droplets [59]. Figure 10 shows images of splats collected on coupons at 350°C. The first (Figure 10a) is a disk splat formed on a surface heated for 7 min, in which time the surface roughness did not show significant change. In the second (Figure 10b), the surface was held at the elevated temperature for over 20 min, increasing surface roughness significantly. Splats collected on this surface showed clear evidence of splashing. The mechanism for this is different, being caused not by solidification, but by fluid instabilities at the edges of the spreading liquid droplet, which are promoted by surface roughness [42].
117
5.4 Coating Properties Figure 5.8 and Table 5-3 show the porosity, determined using optical analysis, in coatings produced at various substrate temperatures, for both impact velocities. All coatings had less than 5% porosity. Coatings produced at low substrate temperatures frequently showed voids at the substrate-coating interface; both their number and size reduced significantly for Ts>100°C and were no longer detectable for substrate temperatures of about 200°C. Conversely, it was observed that increasing the substrate temperature above 200°C increased the porosity level. Although both velocity conditions illustrated similar patterns, the presence of large experimental errors in porosity measurements makes it impossible to draw definitive conclusions about porosity behavior from this study.
Figure 5.8 Effect of substrate temperature on porosity of the produced coating.
118
Table 5-3 Microstructure Analysis Substrate Temperature (ºC)
High velocity setting (V=143 m/s) Porosity % Pore Size [μm]
Low velocity setting (V=109 m/s) Porosity % Pore Size [μm]
25
2.4 ± 1.1
5.3
2.6 ± 1.1
4.8
100
1.8 ± 1.7
5.8
1.7 ± 0.8
3.0
150
-
-
1.9 ± 1.2
3.3
200
1.1 ± 0.2
2.5
1.9 ± 1.7
4.1
250
1.9 ± 1.1
2.6
2.8 ± 1.0
2.8
300
2.3 ± 0.1
2.3
3.3 ± 0.8
4.2
Average
1.9 ± 0.8
3.7
2.4 ± 1.1
3.7
Measurements of the cross-sectional hardness (10 from each sample) were also taken for each coating using a micro hardness tester (Zwick Hardness Tester, Zwick, Germany) applying 500 g-force. Neither substrate temperature nor spray impact velocity had a significant effect on hardness. The average hardness (Vickers) for the 109 m/s coatings was 51.2 ± 4.2, while the average hardness for the 143 m/s coatings was 52.1 ± 4.0. Coating roughness was measured with a Surfometer (Precision Devices Inc., Milan, Michigan, USA) that ran a stylus over the surface. An average of 10 measurements was made for each sample. Again, substrate temperature and spray velocity did not have a measurable effect on coating roughness, which was Ra=15±2 µm in all cases. Coating deposition efficiency increased with substrate temperature. Figure 5.9 shows the variation of deposition efficiency, determined by weighing the coupons before and after spraying, with substrate temperature. Deposition efficiency was lowest (approximately 40%) when the substrate was at room temperature and increased with substrate temperature, reaching a maximum value of 52% at Ts=300ºC. Further increases in substrate temperature did not result in greater deposition efficiency. It was also shown that within the velocity range of these experiments, impact velocity had little effect on deposition efficiency. 119
Figure 5.9 Measured deposition efficiency for high velocity (143m/s) and low velocity (109m/s) test conditions. Curves represent the best fit.
Figure 5.10 shows the variation of coating adhesion strength with substrate temperature. Each data point on the figure shows the average of five measurements and error bars represent their standard deviation. Average spray velocity in all tests was 143 m/s. For coatings produced at room temperature the average coating strength measured was approximately 9.5 MPa, increasing to 12.1 MPa at approximately 100ºC. Raising substrate temperature to almost 200ºC – above the transition temperature – increased adhesion strength by 86% to an average value of 17.9 MPa. Further increases in substrate temperature led to a rise in adhesion strength, though not by as great an amount.
120
Figure 5.10 Measured coating adhesion versus substrate temperature for particles having an average velocity of 143m/s. [1,2]
121
Chapter 6 Closure
This concluding chapter summarizes the major results, findings, and contributions of the present work. Also, some ideas are suggested as to how this research topic can be explored in more details.
6.1 Conclusions In a wire-arc spray system (such as Sulzer-Metco’s ValuArc 200, which was used in this study), particles are formed by atomization of molten metal from the tips of two consumable wires between which an electric arc is struck. A cross-flow atomizing gas accelerates the detached particles towards a substrate on which a protective coating is formed by deposition of these particles. In this study, arc voltage and arc current were experimentally measured at different operating conditions. The measured data were analyzed to find the energy delivered to unit mass of the fed material, and to estimate aluminum evaporation. Arc voltage fluctuations were also looked at, and analyzed to obtain an estimate of the size of primary atomizations from the wires. It is well known that the arc attaches to the anode over a much larger area that the cathode and, consequentially, particles separating from the anode are larger than those from the cathode. The sizes of these primary detachments were estimated using computational fluid 122
dynamics and simplified models of arc and particle-breakup. These simplified models were based on the information obtained from pictures of the arc (taken with Nikon E3 digital camera) and pictures of metal detachment (taken with a custom-made UV camera with Nitrogen laser illumination). Shortly after primary atomization, the detached particles break up into smaller particles (undergo secondary atomizations). These in-flight particles are a mixture of cathodic and anodic particles. Although mixed, an algorithm was presented to identify the size distributions of the two sets of particles. The presented algorithm assumes that both anodic and cathodic particles follow a log-normal distribution. This assumption was also validated by spraying magnetic and non-magnetic materials (as anode and cathode), and separating the resultant particles. The presented separation-algorithm provides a tool to study effects of operating parameters on each of the anodic or cathodic set of particles. Experiments showed that increasing the atomizing gas pressure decreased the size of both anodic and cathodic particles, while changing wire-feed-rate and operating voltage did not change particle size significantly. Axial variations (along the spray plume) of particle velocity and temperature were also investigated. While aluminum particles decelerate as they move towards the substrate (as expected), their temperature remains almost constant. This was explained by analyzing the exothermic oxidation of the surface of aluminum particles. The presented explanation was also verified by spraying aluminum with nitrogen as atomizing gas (to prevent oxidation). Also, effects of substrate temperature and spray velocity on the properties of aluminum splats and coatings deposited on mirror-polished steel surfaces were studied. As substrate temperature was increased droplets no longer splashed, but formed disk shaped splats. Aluminum particles sprayed with an average velocity of 109 m/s had a transition temperature of 230°C; particles sprayed with an average velocity of 131 m/s had a transition temperature of 123
200°C; particles sprayed with an average velocity of 143 m/s had a transition temperature of 140°C. In addition, coating porosity levels were measured (less than 5% for all coatings produced). Raising substrate temperature reduced the size and density of voids at the coating/substrate interface, and also increased deposition efficiency and adhesion strength of coatings. By conducting the studies on a mirror-polished surface, the effect of surface roughness on splashing was eliminated, allowing focusing on other phenomena that promote splashing.
6.2 Recommendations for future work The findings of this study can be used as a basis for future work. The followings are suggestions that would prove beneficial to the advancement of scientific research in the field of thermal spray coatings. • Profile of axial variation of velocity, and particle deceleration rate, can be used to calculate gas velocities, which can be used to verify numerical modeling of fluid flow in the gun and spray. • Profile of axial variation of temperature, and particle cooling rates due to convection and radiation, can be used to calculate rate of oxidation of the particles. This can be verified by measuring the oxide content of substrates placed at different distances from the gun. • Shear stresses on the wire-tips can be used in a two-fluid CFD code to model shape and size of primary detachments.
124
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Appendix A: Metal Properties
Table 6.1. Properties of Copper, Aluminum and Aluminum Oxide (Al2O3) [6, 27, 49, 68] Stainless Steel
Copper
Aluminum
Aluminum Oxide
Melting Point (oC)
1536
1083
660
2015
Boiling Point (oC)
2861
2567
2494
2980
385
900
1637
Specific Heat (J/kg/K) @ 30 oC Density (kg/m3) @ 30 oC
7015
8960
2700
3970
Latent Heat of Fusion (kJ/kg)
246.6
205
388
1100
Latent Heat of evaporation (kJ/kg)
10800
Thermal Conductivity @30oC (W/m/K) Surface Tension (N/m) Viscosity in liquid form (Pa.s.)
1.872 6.0×10
-3
393
273
1.3
0.91
36
1.3×10-3
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Appendix B: Transport Properties of Air
Table 6.2. Transport properties of air at atmospheric pressure [12] Temperature (K) 50 100 200 300 400 500 600 700 800 900 1000 1500 2000 2500 3000 3500 4000 4500 5000 6000 7000 8000 9000 10000 11000 12000 13000 14000
Viscosity (kg/m/s) 3.479E-06 7.048E-06 1.302E-05 1.801E-05 2.240E-05 2.639E-05 3.008E-05 3.355E-05 3.685E-05 4.001E-05 4.304E-05 5.694E-05 6.949E-05 8.153E-05 9.501E-05 1.117E-04 1.291E-04 1.436E-04 1.566E-04 1.855E-04 2.153E-04 2.338E-04 2.509E-04 2.614E-04 2.540E-04 2.219E-04 1.748E-04 1.253E-04
Thermal Conductivity (W/m/K) 5.085E-03 1.031E-02 1.906E-02 2.642E-02 3.312E-02 3.961E-02 4.607E-02 5.252E-02 5.893E-02 6.527E-02 7.152E-02 0.1035 0.1382 0.2264 0.5232 0.7599 0.5507 0.5548 0.781 2.665E+00 4.267E+00 2.179E+00 1.262E+00 1.377E+00 1.775E+00 2.335E+00 2.948E+00 3.462E+00
Electric Specific Conductivity Enthalpy Entropy Heat Density (S/m) (cal/g) (cal/g/K) (cal/g/K) (g/m3) 0 121.77 1.2467 0.2419 7018.1 0 133.87 1.3984 0.2419 3509 0 158.06 1.5579 0.2421 1754.5 0 182.28 1.6533 0.2428 1169.6 0 206.62 1.7219 0.2449 877.22 0 231.27 1.776 0.2487 701.75 0 256.37 1.8212 0.2538 584.77 0 282.03 1.8603 0.2596 501.21 0 308.28 1.895 0.2654 438.53 2.443E-23 335.11 1.9263 0.2711 389.77 2.882E-20 362.5 1.955 0.2746 350.76 5.593E-07 502.9 2.0702 0.2955 233.83 8.832E-07 663.38 2.1705 0.3479 175.79 1.120E-02 848.62 2.274 0.4079 140.58 1.986E-02 1099.3 2.4205 0.64 113.7 0.4896 1508.1 2.6709 0.9428 91.276 2.162E+00 1954.3 2.9104 0.7661 76.625 7.197E+00 2281.9 3.0255 0.5964 66.395 2.273E+01 2597.4 3.1122 0.7156 58.223 9.857E+01 3804.7 3.5402 1.9643 44.181 3.277E+02 6692.6 4.5879 3.4157 30.852 1.060E+03 9448.3 5.3614 1.8803 23.213 2.146E+03 10785 5.5171 1.0318 19.659 3.264E+03 11812 5.5557 1.1142 17.23 4.372E+03 13148 5.6688 1.6212 15.113 5.478E+03 15185 5.9293 2.5217 13.083 6.535E+03 18304 6.3853 3.75 11.101 7.536E+03 22651 7.026 4.8648 9.2751
133
15000 16000 17000 18000 19000 20000 22000 24000 26000 28000 30000
8.617E-05 5.724E-05 4.003E-05 2.929E-05 2.418E-05 2.110E-05 1.955E-05 1.945E-05 1.804E-05 1.475E-05 1.125E-05
3.665E+00 3.531E+00 3.317E+00 3.143E+00 3.142E+00 3.225E+00 3.650E+00 4.264E+00 5.000E+00 5.779E+00 6.494E+00
8.418E+03 9.205E+03 9.886E+03 1.052E+04 1.111E+04 1.168E+04 1.277E+04 1.365E+04 1.405E+04 1.402E+04 1.399E+04
27767 32708 36741 39735 41937 43663 46658 50274 56186 66273 80033
7.733 8.3343 8.7321 8.9404 9.0234 9.0409 9.0283 9.0949 9.384 10.021 10.905
5.1913 4.5586 3.4915 2.5437 1.9157 1.5704 1.5337 2.2194 3.8729 6.2045 7.1159
7.7689 6.6522 5.868 5.3119 4.8967 4.5673 4.0505 3.6281 3.228 2.8072 2.4137
134