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Modeling of aluminum evaporation during electron beam cold hearth melting of titanium alloy ingots Shuster, Riley Evan 2013

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MODELING OF ALUMINUM EVAPORATION DURING ELECTRON BEAM COLD HEARTH MELTING OF TITANIUM ALLOY INGOTS by  RILEY EVAN SHUSTER B.A.Sc., The University of British Columbia, 2007  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in  THE FACULTY OF GRADUATE STUDIES (Materials Engineering)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)  June 2013 © Riley Evan Shuster, 2013  Abstract  Electron beam cold heart melting (EBCHM) is a consolidation and refining process capable of consolidating titanium scrap and sponge material into high quality titanium alloy ingots. Unlike other consolidation processes for titanium, EBCHM is efficient in removing both high and low density inclusions. During the final stage of casting in EBCHM, operators must balance the potential to form large shrinkage voids, caused by turning off the electron beam heating, against the tendency to evaporate alloying additions, which occurs if the top surface remains molten. To this end, a comprehensive understanding of the evaporation and fluid flow conditions occurring during the final stage of EBCHM is required in order to optimize ingot production. This research focused on developing a coupled thermal, fluid flow and composition model, capable of predicting the temperature, fluid flow and composition fields within an EBCHM cast, Ti-6Al-4V ingot. The physical phenomena of thermal and compositional buoyancy, mushy zone flow attenuation and aluminum evaporation were incorporated in the model formulation. Industrial scale experiments were carried out at the production facilities of a leading industrial producer of titanium to provide data and measurements used for model verification. The model has been used to study the effects of variation of electron beam power input and hot top time duration on the evaporative losses and position of solidification voids. Model predictions for liquid pool profile, last liquid to solidify and composition fields are in good agreement with the industrially measured results. Sensitivity analysis ii  was performed by varying electron beam power and hot top duration independently and observing the effect on the composition fields and last liquid to solidify. For the cases examined, there was a strong correlation between electron beam power and alloying element losses, while hot top duration variation results indicated a stronger dependence on last liquid to solidify than on alloying element losses. Therefore a classic optimization problem arises between balancing hot top duration with alloying element losses.  iii  Preface  The material in this dissertation is an unpublished, original, intellectual product of the author, R. E. Shuster. Dr. D.M. Maijer and Dr. S.L. Cockcroft provided input on research direction, experimental planning and analysis and editorial support throughout the duration of the project. Industrial trials were conducted with the cooperation of the engineering and technical staff of a leading titanium producer. Characterization of the material produced during the industrial trials was carried out by R.E. Shuster with consultation and supervision of the technical staff at the research facility of the industrial partner.  iv  Table of Contents  Abstract ..................................................................................................................................................................... ii Preface ...................................................................................................................................................................... iv Table of Contents .................................................................................................................................................. v List of Figures ..................................................................................................................................................... viii Acknowledgements ............................................................................................................................................. xi Chapter 1. Introduction ...................................................................................................................................... 1 1.1. Titanium Alloys and Relevant Applications................................................................................... 1 1.2. Melt Related Defects ............................................................................................................................... 2 1.3. Consolidation Processes........................................................................................................................ 3 1.3.1.  Vacuum Arc Remelting ............................................................................................................ 4  1.3.2. Cold Hearth Melting ........................................................................................................................ 5 1.3.3. The Casting Process Associated with Electron Beam Cold Hearth Melting .............. 6 Chapter 2. Literature Review ........................................................................................................................... 9 2.1. Refining Hearth Research .................................................................................................................. 10 2.2. Ingot Casting Research ....................................................................................................................... 12 2.2.1. Thermal and Coupled Thermal-Fluid Models.................................................................... 13  v  2.2.2. Composition Models .................................................................................................................... 15 Chapter 3. Scope and Objectives .................................................................................................................. 19 Chapter 4. Industrial Measurements .......................................................................................................... 21 4.1. Plant Trial................................................................................................................................................. 21 4.1.1. Melt Pool Additions...................................................................................................................... 22 4.1.2. Heat Parameters ........................................................................................................................... 22 4.1.3. Temperature Data Acquisition ................................................................................................ 24 4.2. Characterization of Ingots ................................................................................................................. 25 4.2.1. Sample Preparation ..................................................................................................................... 25 4.2.2. Chemical Etching .......................................................................................................................... 26 4.2.3. Composition Testing.................................................................................................................... 26 4.3. Data and Observations ........................................................................................................................ 27 Chapter 5. Mathematical Model Development ....................................................................................... 39 5.1. Governing Equations ........................................................................................................................... 40 5.1.1. Conservation Equations ............................................................................................................. 40 5.1.2. Buoyancy Source Term .............................................................................................................. 42 5.1.3. Solution Frame of Reference and Single Phase Model implementation ................. 42 5.1.4. Evolution of Latent Heat ............................................................................................................ 44 5.2. Domain ...................................................................................................................................................... 44 5.3. Material Properties .............................................................................................................................. 45 vi  5.4. Initial Conditions ................................................................................................................................... 46 5.5. Boundary Conditions ........................................................................................................................... 47 5.6. Model Verification Examples ............................................................................................................ 54 5.6.1. Verification of Semi-infinite Slab Analytical Solution .................................................... 54 5.6.2. Buoyancy Subroutine Verification ......................................................................................... 55 Chapter 6. Results and Discussion............................................................................................................... 64 6.1. Steady State Results ............................................................................................................................. 64 6.1.1. Pool Shape ....................................................................................................................................... 66 6.2. Final Transient Stage Results ........................................................................................................... 67 6.2.1. Liquid Pool Profile and Composition Evolution with Time.......................................... 67 6.2.1. Comparison of Composition Variation with Height ........................................................ 70 6.2.2. Shrinkage Void Analysis............................................................................................................. 71 6.3. Sensitivity Analysis .............................................................................................................................. 73 6.3.1. Electron Beam Power ................................................................................................................. 73 6.3.2. Hot Top Duration .......................................................................................................................... 75 Chapter 7. Conclusions and Recommendations ..................................................................................... 97 7.1. Summary and Conclusions ................................................................................................................ 97 7.2. Recommendations for Future Work .............................................................................................. 98 Bibliography....................................................................................................................................................... 100 Appendix ............................................................................................................................................................. 104 vii  List of Figures  Figure 1.1 - Vacuum arc remelting furnace example layout ................................................................ 8 Figure 1.2 – Electron beam cold hearth melting furnace example layout ...................................... 8 Figure 4.1– Copper turnings .......................................................................................................................... 30 Figure 4.2 - Tungsten markers...................................................................................................................... 30 Figure 4.3 – Cooled ingots in the as-cast Condition .............................................................................. 31 Figure 4.4 – Pour lip feature (highlighted in dashed region) ........................................................... 31 Figure 4.5 - 8" Disc section ............................................................................................................................. 32 Figure 4.6 - Slice from CN5271 (saw blade marks visible as horizontal lines) ......................... 32 Figure 4.7 - Slice after surface facing (CN5271) .................................................................................... 33 Figure 4.8 - 35% HNO3 - 5% HF etched slice (CN5273) ..................................................................... 33 Figure 4.9 - Top four slices from CN5272 after lactic acid etch ....................................................... 34 Figure 4.10 - Chemical sampling plan for heat CN5272 (dashed lines represent approximate liquid pool size) ......................................................................................................... 35 Figure 4.11 – Centerline copper and aluminum composition data ................................................ 36 Figure 4.12 – Thermal arrest before and after data scaling .............................................................. 37 Figure 4.13 – Thermocouple data ................................................................................................................ 37 Figure 4.14 – Pyrometer data ........................................................................................................................ 38 Figure 5.1 – Computation domain (length not to scale) ..................................................................... 57 Figure 5.2 – Density variation with aluminium composition ........................................................... 57 Figure 5.3 - Specific heat capacity data ..................................................................................................... 58 Figure 5.4 – Thermal conductivity data .................................................................................................... 58 Figure 5.5 – Specific heat modification of the / phase change.................................................... 59 Figure 5.6 – Specific heat modification of the solid/liquid phase change.................................... 59 Figure 5.7 – Top down schematic of an example beam pattern ...................................................... 60 Figure 5.8 – 3D representation of electron beam heat flux ............................................................... 60 Figure 5.9 – Vapor pressure of pure aluminum ..................................................................................... 61 Figure 5.10 – Heat transfer coefficient graph ......................................................................................... 61 viii  Figure 5.11 – Analytical solution of a semi-infinite slab ..................................................................... 62 Figure 5.12 – Comparison of analytical solution to simple case using CFX ................................. 62 Figure 5.13 – Comparison of CFX buoyancy module with user subroutine for temperature driven buoyancy forces ..................................................................................................................... 63 Figure 5.14 – Comparison of user subroutine for composition and temperature driven buoyancy forces.................................................................................................................................... 63 Figure 6.1 – Steady state temperature contours on the symmetry plane and top faces of the model. Vectors representing the direction and magnitude of the fluid flow are overlaid on the symmetry plane result. ...................................................................................... 77 Figure 6.2 – Comparison of top 0.82m of the model and real ingot sump profile .................... 78 Figure 6.3 – Model sump profile overlaid onto real ingot .................................................................. 78 Figure 6.4 – Temperature profiles at various time steps for heat CN5272 ................................. 79 Figure 6.5 – Temperature profiles at various time steps for heat CN5272 ................................. 80 Figure 6.6 – Temperature profiles at various time steps for heat CN5272 ................................. 81 Figure 6.7 – Temperature profiles at various time steps for heat CN5272 ................................. 82 Figure 6.8 – Composition profiles at various time steps for heat CN5272 .................................. 83 Figure 6.9 – Composition profiles at various time steps for heat CN5272 .................................. 84 Figure 6.10 – Composition profiles at various time steps for heat CN5272 ............................... 85 Figure 6.11 – Composition profiles at various time steps for heat CN5272 ............................... 86 Figure 6.12 – Composition profile results for CN5271, centerline of the ingot ......................... 87 Figure 6.13 - Composition profile results for CN5272, centerline of the ingot. ......................... 87 Figure 6.14 - Composition profile results for CN5273, centerline of the ingot.......................... 88 Figure 6.15 – Top 0.20m of each heat for the model (left) and experiment (right). Lines within the model result represent the solidus isotherms at the start of hot topping, oval shaped lines represent the last region to solidify.......................................................... 89 Figure 6.16 – Beam power sensitivity results halfway through hot topping ............................. 90 Figure 6.17 – Beam power sensitivity at the end of hot topping..................................................... 91 Figure 6.18 – Beam power sensitivity at the point of last liquid ..................................................... 92 Figure 6.19 – Beam power sensitivity final Al composition .............................................................. 93 Figure 6.20 – Hot top duration sensitivity at end of hot topping .................................................... 94 Figure 6.21 – Hot top duration sensitivity at the point of last liquid............................................. 95 ix  Figure 6.22 – Hot top duration sensitivity final Al composition...................................................... 96  x  Acknowledgements  I would like to thank Dr. Daan Maijer and Dr. Steven Cockcroft for their guidance, expertise, encouragement and extreme patience in what has proved to be a lengthy, but rewarding process. I appreciated the opportunities to travel to conferences and make site visits over the course of the project. Regrettably, I am unable to thank members of the research engineering and technical staff of the industrial partner by name. They provided technical expertise during the characterization of the industrial trials, extensive knowledge of the titanium production process and generously opened their homes to me during numerous visits to the production and research facilities. Many thanks to my colleagues: Dr. Lu Yao, Dr. Carl Reilly, Dr. Denis Favez, Mr. Boran Xue, Mr. Tao Meng, Mr. Jun Lu and Mr. Jun Ou for the discussion and support in developing and executing the numerical model. Thank you to my friend and officemate Dr. Jason Mitchell for the encouragement and support through the years. My thanks to my family for the unwavering love, support and encouragement during what has proven to be the most challenging period of my life. Finally, thank you to Elim for believing in me when I did not, and staying beside me through the hard times.  xi  Chapter 1. Introduction  Titanium makes up 0.6% of the earth’s crust making it the ninth most prevalent element and the fourth most abundant structural metal behind only aluminum, iron and magnesium [1]. It is most commonly found in nature as ilmenite (FeTiO3) and rutile (TiO2). Titanium and its alloys are approximately 60% of the density of iron or nickel alloys, yet their tensile strengths are comparable. They also have excellent corrosion resistance in a variety of environments. The major issue limiting more widespread use of titanium and its alloys is the high cost associated with production.  1.1. Titanium Alloys and Relevant Applications In 1950, it was discovered that aluminum additions to titanium provided significant strengthening and ultimately led to advances in titanium alloy development. Four years later marked the appearance of the Ti-6Al-4V (6% aluminum and 4% vanadium in weight percent) alloy, which, as recently as 1998, accounted for over fifty percent of the titanium market in the USA [2]. The largest application for titanium alloys continues to be the aerospace industry due to their high specific strength. Ti-6Al-4V is used for the production of low temperature rotating jet-engine components such as compressor fan blades and disks and for other applications such as airframe and landing gear [3]. As production methods have improved over the years, titanium and its alloys have found use in the luxury sporting goods industries to produce such items as bicycles and golf 1  clubs. The high strength and low density of titanium allowed golf club manufacturers to produce larger club heads that makes striking the ball easier without increasing the weight to a point where the club is too difficult to swing. The biocompatibility of titanium alloys also makes them excellent candidates for use in the biomedical industry for implants in the human body. Finally, titanium alloys have been used for many years in the high performance car racing industry where weight savings are a high priority. Due to their relatively high cost, titanium alloys have not become widely utilized to realize weight savings in the mass-produced consumer automobile industry.  1.2. Melt Related Defects There are a number of defects that can be traced back to the liquid metal processing steps employed to produce products from titanium and its alloys. High interstitial defects (HID), referred to as Type I defects, can form when titanium is exposed to oxygen and/or nitrogen at elevated temperatures. Sources include burnt sponge, scrap and vacuum leaks during liquid metal processing or welding. High density inclusions (HDI) include tungsten carbide tool bits or tungsten from welding electrodes that are incorporated into the melt via the scrap metal feedstock. Both of these defects are hard and brittle and will significantly degrade the fatigue performance of the material and can also limit the ability of the material to be deformed. In titanium alloys containing aluminum, Al-rich defects called Type II defects are relatively soft and weak compared to the surrounding material and serve as crack initiation sites during fatigue cycles. These defects form in association with shrinkage voids that can 2  form at the end of casting due to the encapsulation. As the material within the encapsulated region solidifies and shrinks, the pressure drops to the point where an aluminum vapor bubble forms. Further cooling results in the condensation of the aluminum vapor on the inside of the void leading to an area locally enriched in aluminum that can lead to additional Type II defects during downstream processing steps.  1.3. Consolidation Processes Due to its high reactivity with oxygen and nitrogen a viable purification process to produce titanium metal was not developed until the early 1900’s, more than 100 years after its discovery in 1791. This process, called the Kroll process is still the only commercially viable purification process used by titanium producers. It was developed in the 1930’s in Germany and uses magnesium to reduce a titanium tetrachloride solution and produce titanium metal [1]. The titanium metal produced by the Kroll process is formed in the solid state resulting in a porous solid referred to as titanium sponge. Once titanium sponge has been isolated it must be consolidated into primary ingots to allow for further downstream processing operations. Due to the high cost of sponge production, scrap or recycled titanium from carefully controlled sources is generally used to offset the amount of titanium sponge used to help lower primary production costs. The two consolidation processes currently in use are vacuum arc remelting (VAR) or cold hearth melting (CHM). The CHM processes include both Electron Beam Cold Hearth Melting (EBCHM) and Plasma Arc Remelting (PAM). The CHM processes have the advantage that they are better able to  3  process scrap in the feedstock in comparison to VAR since the melting and refining process is physically decoupled from the casting process.  1.3.1. Vacuum Arc Remelting Vacuum arc remelting (VAR) was the first commercial process for consolidating titanium and titanium alloys for the production of primary ingot. The feedstock for the VAR process is a combination of titanium sponge and alloying elements which are mechanically compacted at room temperature into blocks. The blocks are welded together in inert environments to form a melt electrode often referred to as a “stick”. The stick is then melted in an upright position in a VAR furnace (shown in Figure 1.1) to produce a first melt electrode which is then inverted and melted again. In the case of rotating grade materials for aerospace applications, the original specification requires all VAR products to be triple melted. Carefully controlled additions of titanium scrap can be added to the electrodes prior to VAR processing. However, for rotating grade materials the use of titanium scrap is limited due to the inability of the VAR process to remove high density inclusions which can be present in scrap materials. Moreover, the limited residence time the material spends in the liquid pool also limits the ability to treat TiN inclusions, which typically have a melting point that exceeds normal liquid metal processing temperatures. Despite the limited capacity for scrap additions, the resulting VAR ingots have excellent chemical homogeneity and microstructure. [2].  4  1.3.2. Cold Hearth Melting Cold hearth melting (CHM) is a newer consolidation method compared to VAR that came into widespread commercial use following the Sioux City Iowa crash of a DC-10. The crash was as a result of the failure of a Ti-6Al-4V compressor disc in the number-two engine, which was linked to a TiN defect in the material. As previously described there are two variants of CHM technology PAM and EBCHM. In both processes the feedstock is first melted in a melting hearth and then flows some distance over a refining hearth before entering the mold where it is solidified into an ingot. Plasma arc furnaces operate with near ambient pressure of an inert gas (typically helium for titanium processing) and one or more torches are physically directed towards the melting and refining hearths and mold. The torches possess some limited ability to be directed and hence may be routinely in motion during the process in order to vary the location where the thermal energy is being applied. The rate of motion of the torches is relatively slow leading to large transients in surface temperature when in motion. In contrast electron beam furnaces operate under vacuum and the electron beams are directed towards the surface using electromagnetic deflection coils allowing a high degree of flexibility and speed in where the energy may be directed. As a result of this increased flexibility to direct heat provided by the electron beams, EBCHM has dominated in the commercial production of premium quality titanium alloys. The production specification for rotating quality titanium (the highest quality designation) now requires single EBCHM melting followed by VAR melting for most of the leading engine  5  manufactures including GE, Pratt and Whitney and Rolls Royce. Note: a double VAR process  is still specified to provide good chemical homogenization.  1.3.3. The Casting Process Associated with Electron Beam Cold Hearth Melting A schematic of an EBCHM furnace is shown in Figure 1.2. The associated casting process, which is the subject of this research project, possesses three stages with respect to operation of the casting processes – initial start-up, steady state operation and hot topping. During initial start-up, raw material is introduced into the melting hearth, from a supply hopper at a prescribed rate, where it is melted by electron beam guns. The liquid titanium flows through the refining hearth and into the water cooled mold area which is fitted with a starter block initially. Once the mold is filled, the starter block is extracted downwards and the process transitions to steady state. During steady state operation, the casting rate is controlled by the amount of raw material being melted in the melting hearth. The ingot continues to be extracted downwards at a rate designed to keep up with the rate of metal entering the ingot. A steady state liquid metal pool develops, with the shape dependent on the various processing parameters (example pool shown in Figure 1.2). During steady state operation electron beam guns are continually tracing prescribed beam patterns across the surface of the refining hearth and the ingot top surface. Once the ingot has reached the desired length, melting of material in the melting hearth is stopped and the final transient of the process begins. For material that will not be processed further via VAR, the first stage of the final transient includes a hot topping phase where the electron beam guns continue to trace the top surface of the ingot to keep it molten while the liquid pool begins to solidify from the bottom up. Following the hot topping phase, the electron beam guns are turned off 6  and the remaining liquid in the ingot solidifies. After the ingot has solidified and cooled, a portion of the top of the ingot is cropped in order to ensure that any solidification voids (potential sites for Type II defects described in section 1.2) are removed. The main function of the hot topping stage is to reduce the depth of the solidification void in the solidified ingot. While on the one-hand hot topping may reduce void on the other it can lead to excessive aluminum loss due to evaporation. Conversely too little hot topping yields excessively deep voids that necessitate cropping of a large section of the ingot. Therefore a balance must be achieved between the reduction of shrinkage voids and control of the aluminum concentration, which is a classic optimization problem. The EBCHM furnace studied in this research is located at the production facility of a leading titanium producer. The strategy at this facility is to use a combination of hot topping and ingot cropping. In order to optimize the process a better understanding of the hot topping step is required. A mathematical model has been developed to describe the thermal, fluid flow and evaporative processes taking place during hot topping and validated using industrially derived empirical data. Once complete the model can be used to simulate different hot topping strategies in order to optimize alloy element concentration and shrinkage void location.  7  Figure 1.1 - Vacuum arc remelting furnace example layout  Figure 1.2 – Electron beam cold hearth melting furnace example layout  8  Chapter 2. Literature Review  There are many advantages to using the EBCHM process for high-quality titanium ingot production [2], and the technology continues to improve through various research efforts. One of the challenges in conducting research on this process is the difficulty in making direct measurements. Lesnoy and Demechenko [4] attributed this difficulty to the relatively high operating temperature, vacuum environment, non-transparency of the alloy, high solubility of many metals in titanium and the depth of the liquid metal pool. Using computational models is a convenient method that can provide insight and improve our understanding of the process, reducing the need for trial and error experiments. To augment this approach, specific experiments designed to validate and fine tune the model can be carried out which can be more cost effective in terms of raw material usage and reduced production time. For modeling purposes, the process is often treated as a number of separate chemical reactors connected together in series. In this analogy, the melting hearth provides sufficient heat to melt the feedstock and controls the flow rate of material into the process, the refining hearth removes inclusions and the mold/casting process removes heat and solidifies the ingot. Based on the literature reviewed, research tends to focus primarily on either the refining hearth or ingot solidification.  9  2.1. Refining Hearth Research Studies on the refining hearth generally focus on either the removal or entrapment of inclusions (both LDI and HDI), or on quantifying the chemical composition variations caused by differences in the rate of evaporation of the different alloy constituents when processing certain alloys such as Ti-6Al-4V. Entrekin [5] introduced tungsten carbide tool bits (HDI’s) directly into a refining hearth and showed through ultrasonic and radiographic inspection that nearly all of the inclusions became trapped in the solid skull. Further investigation [6] showed that HDI’s ranging in size from 0.2 mm to 13 mm were consistently removed in the refining hearth. Jarrett carried out experiments on a small scale EBCHM furnace and developed a model to characterize the effectiveness of both HDI and LDI removal [7]. Mitchell studied the ability of different technologies (including EBCHM) to remove inclusions and melt related defects from materials produced for the aerospace industry [8, 9]. He concluded that EBCHM is the most effective process for producing high quality titanium alloys when recycled material is used in the feed stock [9]. In 1992, Isawa et al [10] studied Al evaporation from various titanium alloys using a 250 kW EBCHM furnace. The five possible locations where Al evaporation was thought to occur in the process were as follows: 1) Feedstock, 2) Metal drops falling from the feedstock, 3) Hearth pool, 4) Metal drops from the hearth, and 5) Ingot casting. A combination of electron probe micro-analysis (EPMA) and scanning electron microscope energy-dispersive X-ray spectroscopy (SEM/EDX) measurement techniques were used to quantify the aluminum evaporation in the feedstock material. Sections taken from the 10  hearth and ingot were etched and analyzed using inductively coupled plasma atomic emission spectrometry (ICP). Aluminum concentration throughout the feedstock was found to be nearly identical, suggesting that evaporation did not take place. Metal drops were estimated to take approximately 0.1 seconds to fall into the hearth and based on the reaction time for the feedstock of approximately one second, it was assumed that appreciable evaporation would not occur. The aluminum concentration in the ingot and the hearth were found to be almost the same, leading to the conclusion that evaporation did not take place in the mold. This was attributed to the EB power being kept at a level where the melt temperature was just above the melting temperature. They found that the hearth pool was the most significant site for evaporation due to the combination of the large surface area exposed to the vacuum environment and the long residence times relative to the other locations [10]. The most significant finding was that increasing the casting rate resulted in a reduction in Al evaporation. This result was consistent with previous findings by Mitchell et al [11] and Tripp et al [12]. The effect of beam oscillation rate on evaporation of Al and Ti from the refining hearth in Ti-6Al-4V was investigated by Nakamura et al [13] using a 30 kW furnace setup. They proposed an optimal beam oscillation rate range of 1.0-10Hz to minimize evaporation rates. Bellot et al [14] developed a 3-D finite volume model capable of predicting the fluid velocity, temperature, turbulence and composition of the refining hearth in a 250kW pilot scale EBCHM. A number of physical phenomena were accounted for in the model, including thermal and compositional buoyancy, thermal Marangoni force, Darcy mushy zone flow resistance, and a Gaussian distribution describing the electron beam scanning pattern. The model was used to study the effectiveness of inclusion removal, and to characterize the 11  effect different electron beam scanning frequencies had on aluminum evaporation rates. They reported three significant findings: 1) Liquid metal flow occurs in only the top 15 to 20% of the total depth (liquid) of the hearth. 2) Increasing the electron beam scanning frequency from 0.5Hz to 10Hz resulted in a 10% decrease in the aluminum evaporation rate for Ti-6Al-4V (increasing further beyond 10Hz did not show additional reduction in rate). 3) Hard-alpha type particles with densities that differ by more than ±3% from the density of the liquid melt either settle to the bottom or rise to the surface of the refining hearth, while particles which have similar densities to that of the liquid melt remain in the liquid stream.  2.2. Ingot Casting Research The EBCHM process is complex, requiring an understanding of the thermal, fluid flow and compositional phenomena that occur in order to accurately model the process. Early work was comprised of thermal-only models, which only approximated the contributions of fluid flow. Coupled thermal-fluid models were then developed which were capable of predicting both the temperature and fluid flow fields. Composition models were limited to diffusion models which assumed a uniform composition in the bulk liquid where advection dominates and used a mass-transfer coefficient in the boundary layer where diffusion dominates.  12  2.2.1. Thermal and Coupled Thermal-Fluid Models Most of the early work [15-18] related to modeling the EBCHM process used a modified-parameter approach where fluid flow was approximated by artificially increasing the thermal conductivity in the liquid to account for advective heat transport. The increase in thermal conductivity was determined through trial and error comparisons to experimental data. The modified-parameter approach has a number of limitations, including an inability to accurately describe the geometry and effect of liquid entering the domain, an inability to calculate the contribution of buoyancy forces on the fluid flow and difficulty in predicting the evaporation rate accurately due to the absence of fluid flow. The desire to accurately capture these additional phenomena led to the development of coupled-thermal fluid models. Despite the fact that electromagnetic forces are present in the VAR process (they are absent in the EBCHM casting process) certain aspects of the thermal, fluid flow and composition behavior in the VAR process may be expected to be similar to those observed in EBCHM casting. In 1990, Jardy et al [19] developed a coupled thermal-fluid model of a VAR ingot with a fixed liquid pool. Their approach required that the shape of the liquid metal pool be predefined and therefore, was limited in its ability to explore the potential effects of modifying process parameters. Further collaborations [20, 21] resulted in the development of the SOLAR (SOLidification during Arc Remelting) software, a finite element model capable of numerically solving the coupled transient heat transfer, momentum and solute transport equations (including turbulence). The SOLAR software proved to be capable of accurately predicting the position of the final shrinkage void and macro-  13  segregation of solute in the final ingot, leading to a better understanding of the effects of each operating parameter on ingot quality. In terms of the EBCHM casting process, Shyy et al [22, 23] studied the effect of including turbulent flow in an EBCHM model of Ti-6Al-4V ingot production. A finite volume model was developed based on the Navier-Stokes equations, including a low Reynolds number modified k-ε turbulence formulation, with modifications to account for Darcy flow resistance, thermal buoyancy, and Marangoni flow. Two simulations with different casting rates of -2 x 10-4 m/s and -4 x 10-4 m/s were carried out and compared with an experimental ingot cast at -1.8 x 10-4 m/s. Their results suggest that for high casting rates, inclusion of a modified k-ε turbulence model can increase the accuracy of models by increasing the accuracy of predicted mushy zone thickness. However, their model was unable to predict the observed asymmetry of the melt pool resulting from metal pouring into only one side of the domain [23]. Zhao [24] developed a three-dimensional thermal-fluid model of the EBCHM process for production of Ti-6Al-4V slabs. His model included two components, a portion simulating the steady state casting operation and a transient hot top portion simulating the solidification of the ingot. The analysis performed with these models focused primarily on predicting the location of the shrinkage voids in the final solidified ingot and an optimization strategy was presented for minimizing the prevalence of shrinkage voids. Despite the quality of the work, it did not include a method for quantifying the evaporation of aluminum from the melt.  14  2.2.2. Composition Models In 1913, Irving Langmuir [25] studied the relationship between vapor pressure of liquid metals and the evaporation rate in a vacuum environment. This work has formed the basis for many of the research efforts related to modeling aluminum evaporation in the Ti6Al-4V system. The Langmuir equation assumes that the kinetics are interface reactioncontrolled and that reflection of the evaporating atoms back to the surface due to collisions in the surrounding atmosphere do not occur because of the vacuum environment. Ritchie et al [26-28] studied the feasibility of using SEM/EDX technology to quantify the composition of stainless steel during EBCHM casting using a combined experimental and computational approach. The experiments were carried out on a laboratory scale electron beam furnace at UBC, fitted with a 30kW EB gun, an EDX detector and a near infrared (NIR) pyrometer. Two different molds were used for the experiments in order to compare the effect of surface tension driven flow on evaporation. A finite volume model was developed, incorporating heat transfer, fluid flow, surface tension, electromagnetism and evaporation. The model results compared well with the experimental measurements for pool shape, velocities and temperatures and bulk composition. Langmuir evaporation was found to be the rate controlling step and was dominated by surface temperature. They concluded that real-time monitoring was possible on a laboratory scale, but that a number of design challenges would need to be overcome in order to utilize the technology in an industrial setting. Fukumoto et al [29] confirmed that the Langmuir equation was capable of estimating the evaporation of aluminum from Ti-6Al-4V under EBCHM conditions. Powell et al [30, 31] studied the effect of different beam scanning frequencies on  15  composition change in CP Ti and Ti-6Al-4V. They found that increasing the beam scanning frequency resulted in a reduction of localized high temperature regions around the beam spot, resulting in lower overall evaporation rates. Akhonin et al [32] developed a model describing the kinetics of aluminum evaporation during EBCHM casting of various titanium alloys. Their analysis accounted for the diffusion of aluminum to the surface of the melt, the physical reaction at the surface and subsequent evaporation of aluminum. Instead of calculating fluid flow conditions throughout the domain, the assumption was made that the bulk liquid pool would be sufficiently mixed with advection dominating diffusion even at low fluid velocities. A thin boundary layer was defined adjacent to the surface of the melt where diffusion was assumed to be the dominant mass transfer mechanism. Evaporation of aluminum was modeled based on the Langmuir equation and an overall mass transfer coefficient was developed by combining the contributions of each phenomenon. Ivanchenko et al [33] took a more theoretical approach where more rigorous thermodynamic theory was used to calculate the activity coefficients of the alloying elements in Ti-6Al-4V. The activity coefficients were used to calculate an ideal evaporation rate based on the Langmuir equation. Aluminum evaporation rates were found to agree well with the work of Ahkonin et al [32] and the evaporation ratio of aluminum to titanium was found to quantitatively agree with experimental results presented by Powell [31]. Semiatin, Ivanchenko, Akhonin and Ivasishin [34] combined efforts to provide a theoretical foundation for the use of diffusion models to predict melt losses in EBCHM casting of titanium alloys. They developed finite and semi-infinite domain diffusion models and compared the resulting concentration gradients with previous work [31, 32]. They concluded that diffusion models 16  are able to provide a good estimate of the overall alloying element losses during EBCHM of Ti-6Al-4V and therefore, can be used to select the appropriate composition of the feed stock in order to achieve the desired final alloy composition. Zhang et al [35] developed a mathematical model of the evaporation mechanism of aluminum during EBCHM of Ti-6Al-4V. They divided the process into three steps as follows: 1) The diffusion of the aluminum from the bulk liquid metal to the liquid/gas interface aided by advection in the liquid metal pool. 2) The evaporation reaction at the liquid/gas interface, modeled using the Langmuir equation. 3) The transportation of the gas phase from the liquid metal surface into the vacuum chamber. Similar to previously reviewed research [31-33], a diffusion model approach was employed where the bulk liquid was assumed to be uniformly mixed and diffusion is the dominant mass transport phenomenon in the boundary layer adjacent to the surface of the liquid metal pool. A validation experiment was carried out on a pilot scale EBCHM furnace with a feedstock aluminum content of 7.3 wt% and a final ingot composition of 6.2 wt%. The calculated overall evaporation rate was on the same order of magnitude as the model result and they concluded that that the process was double controlled, with both diffusion and evaporation being rate limiting steps [35]. Based on the literature reviewed, the thermal, fluid flow and compositional phenomena are well understood for the refining hearth. Research focusing on developing 17  models for ingot casting has not been as comprehensive as that for the hearth, choosing to focus on a deeper understanding of either fluid flow factors or compositional effects, but not both. In the research that has combined all three phenomena, models have been carried out on small laboratory scale furnaces. As a result, there is a strong need for the development of a fully-coupled 3D, industrial scale model capable of predicting the thermal, fluid flow and composition conditions of an ingot produced in the EBCHM process.  18  Chapter 3. Scope and Objectives  The objective of this study is to develop a mathematical model capable of predicting the thermal, fluid flow, and chemical composition phenomena in Ti-6Al-4V alloy ingots during the EBCHM casting process. A collaborative research and development program between the Department of Materials Engineering at UBC and a leading producer of titanium has been ongoing since 2005. Previous research under this agreement has focused on the development of a coupled thermal-fluid model capable of predicting the temperature and fluid flow conditions in the ingot casting process associated with EBCHM during both the steady state casting operation and during the final transient stage (hottop) at the end of the casting process. This study builds upon the previous work by including the ability to track compositional changes in the ingot caused by evaporation of volatile elements in the vacuum environment and the effect of compositionally induced density gradients in the melt on fluid flow and heat transport. The commercial computational fluid dynamics software package ANSYS CFX v.11 was used to develop the mathematical model. The governing equations for mass, momentum and energy have been solved to predict the evolution of the thermal-fluid flow conditions present during both the steady state casting and hot topping periods of the process. In addition, the mass transport equation is solved to predict aluminum composition throughout the ingot during the hot topping portion of the casting. The steady state casting portion of the model provides an initial thermal-fluid flow condition for the transient hot topping portion of the model. Thermal boundary conditions are applied to 19  describe the power supplied by the electron beams bombarding the top surface as well as the loss of heat from the various surfaces bounding the domain. Boundary conditions are also provided for the boundaries of the domain related to solution of the momentum and mass conservation equations including evaporation of aluminum from the top surface of the domain exposed to the vacuum environment, which has been quantified using the Langmuir equation. Within the bulk of the liquid, thermal and compositional buoyancy momentum source terms have been developed and applied to assess the impact of buoyancy on the flow and thermal fields in the liquid sump. In addition, a Darcy momentum source term has been developed and applied to account for the attenuation in flow associated with the developing solid structure in the mushy zone during solidification. To validate the model, industrial measurements have been carried out on a set of ingots produced by varying the electron beam power and the hot top duration at the sponsoring company’s industrial facility. Both the liquid sump profile at the end of steady state casting and the variation in aluminum content with height and position in the solidified ingot has been obtained. The model was run under the same conditions and the results compared with the industrial empirical data to verify the model and assess its predictive capabilities under a range of process conditions.  20  Chapter 4. Industrial Measurements  A plant trial was performed at the production facilities of a leading titanium producer. There were two key measurements that were required: (1) Liquid pool (sump) profile data to validate the thermal-fluid results and (2) Compositional data to validate the concentration profile results. A series of experimental ingots were cast at the main EBCHM production facility of the sponsor company by the on-site operators and engineers. Following casting, the subsequent characterization operations and measurements were carried out at the technical labs of the sponsor company.  4.1. Plant Trial Three 0.432 m (17”) diameter, Ti-6Al-4V ingots, designated CN5271, CN5272 and CN5273, were cast as part of the experimental program for this work in order to explore a range of operating conditions suitable for validating the model. The ingots were initially cast to a desired length using the standard industrial procedure. The range in process conditions was obtained by varying the electron beam power input and the duration of power input during the hot top portion of the final transient stage of the casting process. All of the other production parameters were held constant during each test.  21  4.1.1. Melt Pool Additions Two strategies were used to mark the depth and shape of the sump at the end of steady state casting and during the hot top procedure. The first method involved the addition of copper turnings (Figure 4.1) into the liquid melt pool. Copper is soluble in liquid titanium, mixes readily due to fluid flow and serves as a chemical marker as the addition of relatively small amounts of copper facilitate a different response of the alloy to the application of an etchant. The slow diffusion rates of copper in solid titanium ensure that the copper will be predominantly present in areas of the ingot that were liquid when the copper turnings were introduced. After solidification, chemical sampling and macroetching can be used to determine the approximate shape of the sump or liquid pool at the time of addition. The second method used to identify the depth of the sump was the addition of tungsten markers (Figure 4.2) into the liquid melt pool. Due to their limited solubility and high density relative to titanium, the tungsten markers sink to the bottom of the sump and become trapped in the mushy zone acting as a physical marker. If the tungsten markers can be located and identified by sectioning after casting then it is possible to obtain a second estimate of the depth of the melt pool at the time of the addition.  4.1.2. Heat Parameters In all three heats, standard casting practice was employed during the start-up and throughout the steady state phase of casting. Once the ingots had reached the desired lengths, melt operations were terminated and the hot top procedures were performed. The 22  two process parameters, which were varied during the hot top period, were the electron beam power and the hot top duration. In the interest of protecting the intellectual property of the industrial partner, the exact process parameters cannot be divulged. Rather, the change to a given parameter is presented as a percent change relative to “normal” hot topping practice. The relative experimental conditions for each heat are as follows:  CN5271 Heat CN5271 was cast to a length of 1.52 m (60”) using the standard casting practice. During the hot top, the surface of the ingot was subjected to 120% of the standard electron beam power for the standard duration hot topping period. At the start of hot topping, 0.34 kg (0.75 lb) of copper turnings and a tungsten marker were added to the liquid pool. Two minutes before the electron beam power was shut off at the end of the hot top period a second tungsten marker was added to the liquid pool.  CN5272 Heat CN5272 was cast to a length of 1.52 m (60”) using the standard casting practice. During the hot top, the surface of the ingot was subjected to 120% of the standard electron beam power for a period of time 300% longer than standard practice. At the start of hot topping, 0.34 kg (0.75 lb) of copper turnings and a tungsten marker were added to the liquid pool. Two additional tungsten markers were added at equal time intervals during the hot top. Finally, two minutes before the electron beam power was shut off at the end of the hot top period, a fourth tungsten marker was added to the liquid pool.  CN5273 23  Heat CN5273 was cast using the standard industrial practice until all of the remaining raw materials were exhausted from the feed hopper. This resulted in an ingot length of 2.36 m (93”). The heat was subjected to a hot top with the standard electron beam power for a standard duration. At the start of hot topping, 0.34 kg (0.75 lb) of copper turnings and a tungsten marker were added to the liquid pool. Immediately before the electron beam power was shut off at the end of the hot top period, a second tungsten marker was added to the liquid pool. At the conclusion of hot topping period for each heat, the electron beam power was shut off and the ingots were allowed to cool before being removed from the casting chamber. The cooled ingots were labelled and shipped to the technical lab facility for subsequent processing and characterization. Figure 4.3 shows the cooled ingots in the ascast condition.  4.1.3. Temperature Data Acquisition Temperature measurements were made using both a thermocouple (contact method) and optical pyrometer (non-contact method). For heats CN5271 and CN5272, a single type-C thermocouple was inserted into the top surface of the ingot through a vacuum-sealed apparatus (normally used for chemical sampling) after the additions were made to the liquid pool of the ingots. The thermocouple was frozen into the top surface of the ingot once the top surface solidified. A view port on the furnace vacuum chamber located above the top surface of the liquid metal pool was fitted with a near infrared (NIR) camera connected to an optical pyrometer to measure temperature data for all three heats.  24  4.2. Characterization of Ingots One of the challenges associated with ingot characterization was manipulating the ingots which weighed between 900 kg and 1450 kg. To make samples easier to handle and etch, the ingots were sectioned into smaller sized pieces (~0.216 m tall x 0.432 m wide x 0.0254 m thick) which allowed for easier manipulation.  4.2.1. Sample Preparation The layout of the furnace at the production facility is such that the molten metal enters the mould at one location on the outer diameter referred to as the pour lip. As a result of the sensible heat input at the circumferential location coinciding with the pour lip, the surface of the ingot has different surface morphology, which allows identification of the as-cast orientation of the ingot. This surface “feature” is highlighted in Figure 4.4. Each ingot was cut into 0.216 m (8”) tall discs (refer to Figure 4.5) starting from the top and working downwards Then, 0.0254 m (1”) wide slices were cut through the middle of each disc perpendicular to the pour lip feature (refer to Figure 4.4). The surface quality of the resulting slices was not adequate for further etching operations due to the coarse pattern caused by the saw blade (visible as vertical lines in Figure 4.6). To prepare the surface for etching each slice was mounted in a milling machine and approximately 5 to 10 mm of material was removed from the face of the slices using a carbide tool bit. The resulting surface quality of each slice, shown in Figure 4.7, was adequate for etching.  25  4.2.2. Chemical Etching Once a uniform surface quality had been achieved, each slice was submerged into an etching tank containing a solution of 35% HNO3 – 5% HF (Figure 4.8). This etching solution is a common solution used to reveal the microstructure of titanium alloys. A second etching solution consisting of 0.5% HF – 5% lactic acid was used on the same slices after the results of the first round of etching were photographed (Figure 4.9). This etching solution provides an increased sensitivity to differences in chemical composition which is important in characterizing the melt pool profile.  4.2.3. Composition Testing Once the melt pool had been identified a plan was developed to determine the spatial variation of composition in the cast ingots. The sampling plan for heat CN5272 can be seen in Figure 4.10. A series of sample locations were selected down the vertical centerline in 0.102 m intervals (Locations 1-15 in Figure 4.10). In addition one sample location per slice was selected near the edge of the liquid pool (Locations 16-22 in Figure 4.10). Finally, two sample locations were selected in areas that were solid at the time of hot topping (locations 23 and 24 in Figure 4.10). At each sample location, a drill bit was used to collect a core sample and a small quantity of shavings which were sent to the chemical testing lab of the industrial partner. The samples were analysed by the sponsor company’s lab technicians using the direct-coupled plasma method. The results for all chemical testing have been normalized to protect the intellectual property of the sponsor company. The  26  variation of aluminum and copper concentrations as a function of depth along the centerline of each heat is shown in Figure 4.11.  4.3. Data and Observations An example of the microstructure revealed by the 35% HNO3 – 5% HF etch is shown in Figure 4.8. In previous work described by Zhao [24], copper additions made to the liquid pool of a slab ingot delineated what was the liquid pool after etching. Despite the visibility of the microstructure in the slices following the first etching procedure in this work, there was no definitive visible indication of the pool profile. It is likely that less copper was added, resulting in only limited differentiation in the response to etching. In an attempt to better resolve the pool profile, the slices were etched again using the 0.5% HF – 5% lactic acid solution. Figure 4.9 shows the top four slices from heat CN5272 after etching with the 0.5% HF – 5% lactic acid solution. The image shows a lighter region consistent with where the liquid pool may be expected allowing liquid pool profile or liquid sump to be delineated at the start of the hot top. It is unclear whether the contrast observed from application of the etchant containing lactic acid is due solely to the copper concentration differences as there was also a significant difference in the aluminum composition due to evaporation. None of the tungsten markers added to the castings were identified in any of the slices, which was likely due to their incorporation into the solid at locations off-centerline. There was no visible evidence of un-dissolved copper shavings in any of the exposed areas of the three ingots. The dark area near the centerline in Figure 4.9 on the sectioned surface was from an addition unrelated to this work. Copper concentration analysis was included 27  as part of the chemical testing carried out on the ingot (described in 4.2.3) and results for each of the three heats are shown in Figure 4.11. As expected, in all three heats copper was present in regions of the ingot that were liquid at the time of addition. In all three cases the drop off in copper content occurs between a depth of 44” and 52” from the top surface of the ingot, indicating a liquid pool depth in that range. Discussion on the aluminum composition measurements will be presented in Chapter 6. A number of inconsistencies were noted after reviewing the original temperature data measured via the thermocouples embedded in the top surface for heats CN5271 and CN5272. The thermocouple data from heat CN5271 was found to be approximately 150°C lower than the expected values for molten Ti-6Al-4V. A ground fault loop was identified as the most likely cause of the temperature mischaracterization. Several grounding schemes were tested during thermocouple measurements on heat CN5272, however none proved to be effective in clearing up the ground fault loop issue. As a result of these issues which were noted during the plant trial, the technical staff decided not to use a thermocouple to collect data for heat CN5273. Following the plant trial, the thermocouple data from the two heats was scaled using correction factors applied to each set of data individually. The correction factor was applied such that the thermal arrest coincided with the liquidus temperature of 1625°C. Data presented in Figure 4.12 illustrates the magnitude of the shift in temperature between the raw and scaled data from heat CN5271 for the first minute of measurement. The temperature curves for the two heats (results shown in Figure 4.13) are in good agreement for the first five minutes after the beam power is shut off, at which point the temperature of CN5272 begins to drop more quickly than CN5271. Due to the uncertainty in these temperature measurements, it is not clear if the temperature 28  differences are related to differences in the process parameters used during the trial or if they are caused by the data manipulation. The raw voltage data collected using the optical pyrometer and NIR camera can be converted into temperature data using a modified form of Plank’s Law: (  )  (  )  273.15  (4.1)  where A and B are fitting constants, ε and τ are the emissivity and transmissivity of the optical apparatus, respectively, and V is the measured voltage. The methodology used to obtain correct values for the A and B fit parameters by the industrial sponsor and is considered proprietary. The resulting temperature profiles for the three heats are shown in Figure 4.14. The large dip in the data for heat CN5271 relative to the other two heats is attributed to an adjustment made to the collection system approximately one minute after data acquisition had begun. The resulting temperature profiles are consistent in terms of liquidus and solidus temperatures and the variation of temperature with time compared to the process parameters.  29  Figure 4.1– Copper turnings  Figure 4.2 - Tungsten markers 30  Figure 4.3 – Cooled ingots in the as-cast Condition  Figure 4.4 – Pour lip feature (highlighted in dashed region)  31  Figure 4.5 - 8" Disc section  Figure 4.6 - Slice from CN5271 (saw blade marks visible as horizontal lines)  32  Figure 4.7 - Slice after surface facing (CN5271)  Figure 4.8 - 35% HNO3 - 5% HF etched slice (CN5273)  33  Figure 4.9 - Top four slices from CN5272 after lactic acid etch  34  Figure 4.10 - Chemical sampling plan for heat CN5272 (dashed lines represent approximate liquid pool size)  35  Figure 4.11 – Centerline copper and aluminum composition data (a) CN5271 (b) CN5272 (c) CN5273 36  Figure 4.12 – Thermal arrest before and after data scaling  Figure 4.13 – Thermocouple data  37  Figure 4.14 – Pyrometer data  38  Chapter 5. Mathematical Model Development  The goal of this research is to develop and validate a mathematical model that is capable of predicting the evolution of temperature, fluid flow and aluminum composition during the hot topping portion of Ti-6Al-4V ingot production associated with the EBCHM process. The model should be capable of predicting the depth, shape, and composition of the liquid metal pool at steady state and during the final transient when the ingot fully solidifies, including the portion were power is applied (the hot top). A commercial computational fluid dynamics software package, ANSYS CFX v.11, was selected as the development platform for the model since it is capable of solving the coupled thermal-fluid flow problem while tracking the composition variation through the use of various user defined functions and subroutines. A quick analysis of the range of Reynolds numbers expected in the process suggests that Laminar flow conditions dominate within the liquid metal pool other than in direct proximity to the inlet. Thus, a laminar flow model has been used. Furthermore, in spite of the dominance of thermal diffusion over mass diffusion in liquid metal alloys, including titanium, both means of transport are considered along with advective transport owing to the range of conditions occurring in the process.  39  5.1. Governing Equations To predict the conditions within the ingot during the final transient stage of the casting process, including during hot topping, the model must first be able to predict the liquid pool profile during steady state casting conditions. The steady conditions then serve as the initial conditions for the final transient stage of the casting process. To solve for the liquid pool profile the equations of conservation of mass, momentum and energy are solved in a fully coupled form. As the spatial variation in aluminum composition within the computational domain is also sought, an additional variable describing the mass fraction of aluminum is introduced within CFX.  5.1.1. Conservation Equations Continuity The equation for the conservation of mass in vector form is as follows: (  )  0  (5.1)  where ρ is the density (kg/m3), t (s) is the time and U (m/s) is the velocity vector.  Momentum The equation describing the conservation of momentum in vector form is as follows: (  )  (  )  (5.2)  40  where P is the static pressure (Pa),  is the dynamic viscosity (Pa∙s) and SM is a momentum  source term (kg/m2·s2), which in this application is comprised of two terms that are defined in sections 5.1.2 and 5.1.3.  Energy The equation for the conservation of energy in vector form is as follows: (  (  )  )  (5.3)  where Cp is the specific heat (J/kg·K), T is the temperature (K) and k is the thermal conductivity (W/m∙K).  Composition As one of the objectives in the current work was to develop a method to predict the changing Al concentration in the liquid pool during the final transient stage of the casting process it was necessary to introduce an additional variable, ϕ, defined as the mass fraction of aluminum. The mass conservation equation for the additional variable ϕ is then solved to predict the variation of ϕ as a function of location and time. The general form of the equation is: (  )  (  )  (  )  (5.4)  where ρ is density of the mixture,  is the conserved quantity defined as the mass fraction of Al in the melt (kg of Al/kg melt) D is diffusivity of the conserved quantity (m2/s) and Sϕ is a volumetric source term (kg/m3·s), which is set to zero in the current problem.  41  During steady state casting, evaporation of aluminum is ignored as liquid metal with an approximately constant Al content is being added to the liquid pool overwhelming the loss associated with evaporation.  5.1.2. Buoyancy Source Term During EBCHM, the density of Ti-6Al-4V varies due to both temperature and composition differences throughout the domain, the latter associated with the preferential evaporation of Al from the melt surface. The density variations lead to buoyancy forces that induce flow in the liquid pool. In order to account for buoyancy driven flow, a source term is added to the momentum equation in 5.2 as follows:  ,  (  )  (5.5)  where ρ and ρref are the local and reference densities, respectively, and g is the acceleration due to gravity (m/s2). The CFX software package has a built-in buoyancy module which supports temperature dependence but does not support compositional dependence. In order to implement a compositionally dependant buoyancy force, a subroutine was created which calculates the density based on the current temperature and composition. The source code for the user-defined buoyancy subroutine can be found in the appendix.  5.1.3. Solution Frame of Reference and Single Phase Model implementation The default model formulation in CFX is a single-phase model that assumes the domain is filled with one phase. In addition an Eulerian frame of reference is adopted in  42  which material is advected or moved through the domain during steady state casting (ingot withdrawal). As the solid portion of the ingot is subject to solution of Equations 5.1 through 5.3 together with the fluid, a strategy must be adopted to gradually supress flow as the material transitions from liquid to solid. Two approaches are used. In the first, the dynamic viscosity is varied from 0.003 Pas for temperatures above the liquidus to 3000 Pas for temperatures below the solidus. Between the liquidus and solidus, the dynamic viscosity is scaled exponentially from 0.3 Pas to 3000 Pas [24]. The second approach involves the application of a momentum source term to suppress flow in the developing solid network. The approach used is based on Darcy’s Law, for flow through a porous medium [36]. This source term is also used to ensure that solid material is advected through the domain at the casting withdrawal rate uw (m/s) during the steady state portion of the casting process. The overall momentum source terms is evaluated as follows: (  ,  )  (5.6)  where µ (Pas )is the dynamic viscosity of the liquid, K is the permeability (m2). Note: uw is set to zero during hot topping. The permeability is calculated using the Kozeny-Carmen equation: (  )  (5.7)  where fs is the fraction solid, k is the Kozeny constant and s0 is the solid/liquid interfacial area per unit volume of solid (m-1). k is assigned a value of 5 and s0 a value 5.77x10-6, which have been shown to result in appropriate flow resistance for inter-dendritic flow [36]. 43  5.1.4. Evolution of Latent Heat There are two phase transformations that must be considered when modelling the solidification and subsequent cooling of Ti-6Al-4V: they are the liquid-to-solid transformation and the solid-state, -to- transformation. The latent heat evolved during the two phase changes is accounted for by replacing the specific heat in Equation 5.3 with an effective specific heat according to the following equation:  ,  (5.8)  where L is the value of the latent heat of the transformation (see section 5.3) and f is the fraction of the new phase which has formed [37].  5.2. Domain The domain used in the models describing both steady state casting and the final transient is a half cylinder, as shown in Figure 5.1. The radius was set equal to 0.216 m, based on the geometry of the ingots cast at the industrial partner to support the program. The length of the domain was set 2.21 m to ensure that at steady state the liquidus and solidus isotherms would be contained within the domain. The ingot was simplified to a half cylinder to reduce the computation time for the simulations. This simplification assumes that the heat transfer and flow conditions are symmetric about the vertical plane dividing the inlet along the centerline. The mesh of the domain was generated using ANSYS Workbench, a pre-processing program included with ANSYS CFX, and consists of 117882 nodes and 611594 tetrahedral elements. 44  5.3. Material Properties The thermo-physical properties for Ti-6Al-4V that were used in the model for this work were based on a combination of data from Mills [38], Shyy et al. [22, 23], and the PANDAT software [39] package (an integrated computational environment for simulation of phase diagrams and material properties based on the CALPHAD method). The fraction solid as a function of temperature for Ti-6Al-4V was calculated using the PANDAT software. Unfortunately, the predicted liquidus and solidus temperatures did not agree with the plant trial measurements. The solidus and liquidus temperatures of 1868 K and 1898 K, respectively, reported by Shyy et al, did. To compensate, the fraction solid data was scaled to fit across the liquidus and solidus temperatures reported by Shyy. The thermophysical property data for Ti-6Al-4V for the liquid and solid phases were based on the data reported by Mills [38]. In the mushy zone, an ideal mixture equation was used to calculate the properties based on the fraction solid at a given temperature. Density provided a unique challenge due to limitations of the ANSYS CFX software package. As described in section 5.1.2, ANSYS CFX is unable to calculate the density as a function of composition, which limits the buoyancy to thermal effects only. A user-defined density was calculated using a rule-of-mixtures approximation based on mass fraction according to: (1  )  (5.9)  where Al and Ti-4V are the densities of aluminum and Ti-4V, respectively. All values of density for temperatures below the solidus were held constant to account for the fact that 45  the volume of the domain does not change. A plot of the density variation for different compositions based on equation 5.9 is show in Figure 5.2. The diffusivity of Al in Ti-6Al-4V was calculated using the following equation: ((  ⁄ )(( ⁄  ) ( ⁄ )))  (5.10)  where Dliq is the diffusion coefficient at the liquidus (1x10-8 m2/s) and EA is the activation energy (250 kJ/mol) [34]. The specific heat capacity and thermal conductivity as a function of temperature are shown in Figure 5.3 and Figure 5.4, respectively [38]. Latent heat values of 48 kJ/kg and 286 kJ/kg were used for the α/β and solid/liquid phase changes, respectively. Graphs showing the modification of specific heat based on these latent heat values are presented in Figure 5.5 and Figure 5.6.  5.4. Initial Conditions The steady state and transient models use the same set of governing equations described previously and require an initial condition for the solution procedure. For the model of steady state casting, the velocity and pressure of the Ti-6Al-4V in the domain are initially set to zero, while the temperature is set to the temperature of the liquid metal entering through the inlet. The model is then solved and checked after every time step (1s) to see if steady state conditions have been reached. For this work, a residuals target of 1x10-5 for each equation set (refer to equations 5.1 – 5.3) was sought to represent the  46  steady state solution. Note: as previously described, for the steady state casting model, the  composition variation was not calculated. The predicted temperature and velocity vectors from the steady state casting model solution are used as initial conditions for the model of the final transient stage. The final transient stage model is used to predict the variation of temperature, fluid flow, and composition as a function of time for the hot top and subsequent cool down, through to the completion of solidification. The measured aluminum composition representing the steady state casting composition (refer to section 4.2.3) obtained during the industrial trials was used as the initial condition for the composition variable in the transient stage models of the three heats. The steady state casting composition was calculated as the average of the measurements from areas of the ingots that were known to be solidified at the end of steady state casting.  5.5. Boundary Conditions The five distinct surfaces of the calculation domain that require boundary conditions for the model are: 1) the inlet, 2) top surface, 3) side wall, 4) bottom surface and 5) symmetry plane. The surfaces together with the assigned numbers are shown in Figure 5.1. Thermal and fluid flow boundary conditions were applied to each of these surfaces in the steady state casting and final transient stage models. Additionally, a compositional boundary condition was also applied to the top surface for the hot topping model to account for the evaporative loss of Al.  47  Inlet In the industrial process, the casting rate is affected by the amount of raw material that is being melted in the melting hearth. For the purposes of the current work, an average ingot withdrawal velocity has been calculated and applied throughout the steady state simulation based on the total ingot length and the duration of the casting process (the casting rate is considered proprietary and therefore the value will not be reported). The inlet region on the top surface of the domain (a 0.076 m x 0.038 m rectangle on the corner of the top surface) was estimated based on examination of the surfaces of the solidified ingots and considering the geometry of the pour notch. The temperature of the material entering the domain is set at 2028 K, which assumes a superheat of 130 degrees based on discussions with the technical staff and previous work by Zhao [24]. In the final transient stage model, the inlet boundary condition is removed from the model.  Top Surface The remaining area of the top surface has thermal, fluid flow and mass flux boundary conditions applied to it. The fluid flow conditions at this wall are assumed to be free-slip, since the top of the ingot is open to the vacuum atmosphere of the furnace. Specification of a free-slip condition means the movement of the fluid is unconstrained in directions parallel to the surface and the shear stress is fixed at zero [40]. From the standpoint of heat transfer, the loss of heat due to radiation and the input of heat from the electron beam pattern need to be accounted for. The top surface of the  48  ingot is assumed to behave as a small grey body within a large grey enclosure and the heat loss from the top surface can be described using the following radiation equation: (  )  (5.10)  where σ is the Stefan-Boltzmann constant, ε is the emissivity (0.4 below the solidus, 0.6 above the liquidus, and linear variation based on temperature between [41]), Ts is the temperature of the ingot surface at the point of interest and Tf is the temperature of the interior furnace surfaces [24]. As described previously, electron beam guns bombard the top surface of the ingot with electrons in order to keep it molten throughout the casting process. The computer controlled electron beam guns trace a pattern across the top surface of the ingot. While tracing each shape in the pattern, the electron beam pauses for a short time period at a series of points. The guns trace each individual shape before moving on to the next one until the entire pattern has been completed. It takes approximately one second to trace a complete beam pattern. The pattern from each gun is repeated continuously throughout the casting campaign. Due to the short dwell time at each point and relatively high frequencies used to draw the pattern, a time averaged approach has been used to describe the thermal energy input. Using the operational parameters of the electron beam, the details of the pattern being traced, and assuming a Gaussian heat distribution about each point where the beam pauses, the time averaged heat flux is calculated at each surface integration point i(xi,yi) on the top surface. The boundary condition is described by the following equation:  49  √  ∑  (  )  (  )  (5.11)  where fABS is the fraction of gun power absorbed on the surface, PEB is the power of the electron beam gun, s is the standard deviation, ti is the time spent at a given point i, and t is the total time required to complete the entire pattern. For this work, a fABS value of 0.7 is used which takes into account the energy lost from converting kinetic energy into thermal energy, the backscattering of electrons, and the heat lost due to evaporation [24, 42]. The exact configuration of the electron beam pattern varies depending on the size and shape of the ingot being produced and is considered proprietary information. A representative example of an electron beam pattern has been generated using fictional parameters. Figure 5.7 shows a top down view of the example electron beam path defined by two overlapping circles. Figure 5.8 shows the resulting heat flux distribution with normalized axes. Two industrial electron beam patterns supplied by the industrial partner have been used in the models of the plant trial heats in this work; one for the steady state casting process and one for the hot topping duration. Once the hot topping time has elapsed, the electron beam gun is shut off while the ingot fully solidifies. The top surface of the cast ingot is unique in that it is the only boundary which is exposed to the vacuum environment of the furnace while being held at temperatures above the liquidus. Combined, these factors result in substantial evaporative losses. As outlined in Chapter 2, the evaporation of atoms from the liquid metal surface into the vacuum environment has been found to be the rate-limiting step. The Langmuir equation which has  50  been used to describe the evaporation of aluminum (kg/m2·s) from molten titanium is as follows:  √  (5.12)  where XAl is the mole fraction, γAl is the activity coefficient,  (Pa)is the vapor pressure of  pure aluminum, MAl is the molar mass, R (J/mol∙K) is the gas constant and T is the temperature of the liquid metal at the point of interest [25, 33]. Although aluminum is not the only element evaporating in the EBCHM process when processing Ti-6Al-4V, the rate of aluminum evaporation is much higher relative to the other elements because it’s vapor pressure is two to three orders of magnitude higher than both titanium and vanadium in the range of temperatures where Ti-6Al-4V is molten. The vapor pressure of an element i can be estimated using an adaptation of the Clausius-Clapeyron equation: 133 ∙ 10(  )  ∙  (5.13)  where A, B and C are fit parameters based on measured values and T is the temperature [26, 33]. A graph showing the vapor pressure of aluminum over the relevant temperature range can be seen in Figure 5.9.  Side wall The upper portion of cast ingot is surrounded by a water-cooled copper mold. Below the mould, the cast ingot is withdrawn into a large diameter metal tube (referred to as the can) which is not temperature controlled. A positionally dependent boundary condition  51  was developed to describe the varying heat transfer conditions experienced by the side of the cast ingot. In the can, radiation conditions similar to the top surface are assumed to prevail and can be described by the following equation: (  )  (5.14)  where the temperature, Tcan, is the average temperature of the can based on measurements carried out by Zhao [24] on a similar EBCHM furnace run by the same industrial partner. The heat transfer between the cast ingot and the water-cooled copper mold will vary between interfacial contact conduction and radiation as solidification shrinkage proceeds. The variation in heat transfer conditions in this region has been described using an effective heat transfer coefficient to calculate the heat flux: (  )  (5.15)  where he is the effective heat transfer coefficient and Tmold is the temperature of the water chilled copper mold [24]. When the casting surface temperature is above the liquidus, direct contact between the liquid metal and the mold wall is assumed and he is set to 1500 W/m2K. During solidification, shrinkage occurs and the contact between the mold and the ingot degrades until the surfaces separate. In order to reflect this transition, he is decreased linearly from 1500 W/m2K to 1000 W/m2K for surface temperatures between the liquidus and solidus. As solidification proceeds, a gap forms between the mold and the ingot and radiation becomes the dominant form of heat transfer. To model this, he is reduced linearly from 1000 W/m2K at the solidus to an equivalent radiation heat transfer coefficient at 30 K 52  below the solidus temperature. The equivalent radiation heat transfer coefficient is calculated using equation 5.16. (  )(  )  (5.16)  Figure 5.10 shows the evolution of he through the relevant temperature range. The mold temperature measurement used in the development of the side wall thermal boundary condition was obtained using inverse heat conduction analysis by Zhao [24].  Bottom Surface The boundary conditions of the bottom face are different for the steady state casting and hot topping models. In the steady state casting model, the bottom face is modelled as an outlet boundary where metal is withdrawn at a velocity set to match the amount of material entering through the inlet. Previous work reported by Zhao indicated that the heat loss due to the advection of material out of the domain is dominant under these conditions, and heat lost due conduction can be considered negligible. For the hot topping model, the material is no longer being extracted through the bottom of the domain and the assumption of negligible heat loss due to conduction no longer applies. The surface is modelled as a noslip (velocities on the boundary fixed at zero) boundary and the heat losses due to conduction are approximated by applying a heat flux equal to: (5.17)  where k is the thermal conductivity of Ti-6Al-4V and  is the temperature gradient  normal to the bottom surface. This assumes additional ingot material below the bottom  53  surface of the domain, which would be the case for most of the steady state regime of casting behaviour.  Symmetry On the plane generated by cutting the domain down the centerline, a symmetry boundary condition is applied where the boundary acts as a mirror that reflects the simulation conditions where the other half of the domain would normally be.  5.6. Model Verification Examples The ability of CFX to accurately predict the thermal and fluid flow conditions in a slab ingot produced by a similar process was verified in previous work by Zhao [24]. However, aluminum composition and effects related to its variation were not considered. Two example problems have been solved to verify the additional variable formulation used in the current work.  5.6.1. Verification of Semi-infinite Slab Analytical Solution The mass transfer conditions for diffusion in a semi-infinite slab are shown schematically in Figure 5.11 [43]. The analytical solution for this problem allows the mass transfer rate nx at any time t to be calculated based on the following equation:  |  (  ) (  )  (5.18)  54  where Ax is the area, DAB is the diffusivity, Ci is the initial uniform concentration of the slab and C0 represents the concentration of the boundary that is instantaneously changed to induce the mass flow. A high diffusion coefficient (not representative of titanium) was used to achieve significant diffusive transport in a short period of time. A rectangular model was developed using CFX with geometry designed to mimic a semi-infinite slab (0.25m x 0.25m x 2m). An initial concentration of 0.05 kg/m3 was applied throughout the domain and the time dependent mass transfer rate in equation 5.18 was applied as a boundary condition on one face of the model. The simulation was run for 100 seconds with a 0.25s time-step. The concentration profiles calculated with the analytical solution and predicted by CFX are compared in Figure 5.12. The model results are in excellent agreement with the analytical solution and suggest that the additional variable formulation within CFX is capable of accurately predicting diffusive mass transport.  5.6.2. Buoyancy Subroutine Verification Due to the method used to vary density as a function of composition in CFX, it is not possible to directly verify that the subroutine is producing the correct buoyancy force. In order to get around this issue, a two part comparison was carried out to incrementally verify the implementation of a thermally-based buoyancy source term and the extension to compositionally-based buoyancy. First, a thin slice model (10m x 10m x 0.25m) was developed with free-slip boundary conditions and an initial temperature distribution which varies only in the x-direction (linearly between 1923 K and 2123 K). The fluid flow in the domain was calculated while the solution of the heat transfer equations was disabled, in order to maintain the temperature distribution. This model was run with the 55  built in CFX buoyancy model for a set period of simulation time. The resulting velocity profile is influenced solely by buoyancy. A second model with identical domain, initial and boundary conditions was run with the only difference being that the CFX buoyancy model was disabled and replaced with the user developed buoyancy subroutine. This model was run for the same simulation time period as the first model. A comparison showing the velocity profile through the centerline of the model is shown in Figure 5.13. The results are in good agreement, providing confidence that the subroutine is capable of reproducing thermal-buoyancy related results consistent with the CFX buoyancy model. In order to test the compositional-based buoyancy feature of the subroutine a third model was developed, again with the same domain, and boundary conditions as the previous models. The temperature profile from the first two models was used to calculate the resulting buoyancy force for each location within the domain. The compositional variation necessary to produce the density distribution that would result in the equivalent buoyancy force as existed in the two previous models was then calculated and applied to the model in the form of a linear composition distribution. A uniform temperature distribution was also applied to ensure that thermal buoyancy did not have any influence on the solution. The resulting velocity profile after the same simulation time exhibits excellent agreement with the results of the example prediction using the user subroutine for temperature driven buoyancy (Figure 5.14). Verification of the thermal and compositional components of buoyancy driven flow individually gives confidence that the combined influences can be modeled accurately by the user buoyancy subroutine.  56  Figure 5.1 – Computation domain (length not to scale)  Figure 5.2 – Density variation with aluminium composition  57  Figure 5.3 - Specific heat capacity data  Figure 5.4 – Thermal conductivity data  58  Figure 5.5 – Specific heat modification of the / phase change  Figure 5.6 – Specific heat modification of the solid/liquid phase change  59  Figure 5.7 – Top down schematic of an example beam pattern  Figure 5.8 – 3D representation of electron beam heat flux  60  Figure 5.9 – Vapor pressure of pure aluminum  Figure 5.10 – Heat transfer coefficient graph  61  Figure 5.11 – Analytical solution of a semi-infinite slab  Figure 5.12 – Comparison of analytical solution to simple case using CFX  62  Figure 5.13 – Comparison of CFX buoyancy module with user subroutine for temperature driven buoyancy forces  Figure 5.14 – Comparison of user subroutine for composition and temperature driven buoyancy forces  63  Chapter 6. Results and Discussion  The model results and comparison to the experimental data will be presented in two parts. First, the results of the steady state model are presented, which has been used to define the initial thermal, velocity and pressure fields for the transient-stage model. The steady state results are validated by comparing the model predictions with the experimental results for sump depth and width as delineated from the macrostructure images of the sectioned ingot and from the liquid pool depth estimate from the copper chemistry analysis. Second, the transient model composition results are validated against the aluminum composition data and the solidification voids are compared with the last point of liquid to solidify predicted by the model. It should be noted that the majority of the model results are presented with normalized axes in order to protect the intellectual property of the industrial partner.  6.1. Steady State Results The model was used to predict the temperature, pressure field and fluid velocities in the ingot at steady state. Figure 6.1 shows the predicted temperature distributions on the symmetry plane and on the top surface. Fluid flow vectors have been overlaid on the symmetry plane to show the direction and magnitude of flow in the liquid region and the solidus isotherm has also been overlaid as a solid black line on the symmetry plane cross section. The aluminum composition has been held constant during the steady state analysis  64  because the rate of metal input was assumed to be sufficient to offset any evaporative loss of aluminum and the development of an aluminum concentration gradient at the surface. Thus, the main drivers for fluid flow are thermal buoyancy, related to temperature differences, and the momentum of the metal inlet stream. As can be seen, the pool shape exhibits an asymmetry due to the sensible heat and momentum of the metal inlet. The asymmetry can be observed most clearly where the solidus line approaches the top surface. On average the solidus line is 0.005m closer to the inlet side and the bottom of the pool is slightly off-center. The temperature variation visible on the top surface cross section is a result of the combination of the proprietary electron beam gun pattern and the fluid flow near the top surface of the liquid pool. The largest velocities (as indicated by the length of the vectors) appear adjacent to the inlet and the flow appears to be driven both downward and along the top surface toward the opposite side of the ingot by the momentum of the inlet stream. It is interesting to note that the downward flow associated with the metal inlet appears to be quickly reflected back upward resulting in most of the flow from the inlet stream being directed across the ingot. It is believed that this is a result of buoyancy forces - i.e. the hot fluid pushed below the surface finds itself in cooler denser liquid where it is buoyant. Another observation that can be made from the flow vectors is that there is fluid flow approximately normal to the solidus isotherm along the entire length of the isotherm. This flow is believed to be associated with mass feeding – i.e. there is liquid drawn into the mushy zone to feed the volume change associated with the liquid to solid transformation.  65  6.1.1. Pool Shape Evidence of the liquid metal pool is most visible in the macrographs of heat CN5272 allowing a comparison to be made with the predicted steady state melt pool profile. Figure 6.2 shows a comparison of the top four sections (approximately 0.8m) from CN5272 after etching with an identical section from the steady state model showing the shape of the solidus isotherm. The model result has been overlaid on the macrostructure image in Figure 6.3. It is not clear whether the melt pool shape evident following application of the etchant is caused by the addition of copper or the difference in aluminum composition following the hot top. Visually, it is evident that the model result and the experimental result are in good agreement over the section of the ingot examined. It is noteworthy that the experimental result validates the asymmetry in the melt pool predicted with the model. The copper concentration data, introduced in Section 4.3, has been used to estimate the depth of the sump pool at the time of copper addition (end of steady state casting). The region of elevated copper concentration in Figure 4.14 (a) is assumed to be indicative of the areas of the ingot that were liquid at the time of copper addition (the start of hot topping) in heat CN5272. Unfortunately, the resolution in this data limits the accuracy of determining the pool depth to the scale of the distance between data points. As the data points are approximately 0.1m apart, the results indicate that the bottom of the liquid pool would have been somewhere between 1.12 and 1.32 m from the top surface at the end of steady state casting. For comparison, the depth of the liquidus and solidus isotherms predicted by the model are 1.18 and 1.47 m, respectively. As it is anticipated that the  66  copper would penetrate some distance into the mushy region but not all of the way to solidus, these results are consistent and provide additional verification of the model.  6.2. Final Transient Stage Results The transient version of the model was used to examine the three hot top conditions employed during the industrial trials (refer to section 4.1 for the hot top conditions). To start, the results predicted by the model for temperature and composition are presented qualitatively in a series of contour plots for heat CN5272 to get a sense of the behavior of the liquid pool and the variation in composition within it during the final transient stage of the casting process. As a reminder, ingot CN5272 was subject to a hot topping regime that included 120% of the standard amount of power applied for a period 300% longer than standard practice, and as expected, experienced the most dramatic drop in Al content due the extended period of evaporation. The results for compositional comparison in all three ingots are then presented in a more quantitative form using traditional x-y plots. Finally, a qualitative comparison is made between the last material to solidify predicted by the model and the location of shrinkage void.  6.2.1. Liquid Pool Profile and Composition Evolution with Time Figures 6.4 through 6.7 show a series of contour plots of temperature on the symmetry plane at various times in the final transient stage of the casting process predicted by the model for CN5272. These images may be used to illustrate the evolution of the liquid pool profile with time predicted by the model as demarked by the black solidus 67  isotherm appearing on each image. Vectors indicating the direction and magnitude (proportional to length) of the fluid flow have been overlaid on the temperature contours. Figures 6.8 through 6.11 show a series of contour plots of Al composition on the symmetry plane at various times predicted by the model. The solidus isotherms have been overlaid on these images and thus they serve to illustrate the evolution in Al concentration within the liquid pool and solidified ingot predicted by the model with time. All of the aluminum composition plots have had the values normalized so that the composition values fall between 0 and 1, at the request of the industrial partner. The duration of elapsed time between the images is equal, (X minutes) but the exact value has not been presented, also at the request of the industrial partner. Time t = 0, for Figure 6.4 (a), corresponds to the end of steady state casting or 0 s elapsed time into the final transient stage of the casting process. The pouring has just been stopped, but the impact of the pour stream momentum remains evident by the large flow velocities adjacent to the pour notch in the top left-hand corner of the image. The sequence of Figures 6.4 (b) through to 6.7 (a), at times t = 1x – 9x, shows that the liquid pool gradually shrinks from the bottom up. Considering the image for t = 9x, the top surface remains relatively hot and above the solidus temperature as a result of the application of electron beam power to the top surface – referred to as hot topping. For times t > 9x (Figure 6.7a), the electron beam is shut off and hot topping is complete. The top surface of the liquid pool freezes over soon after the electron beam power is shut off due to the high rate of heat loss associated with radiation from the top surface, encapsulating liquid below the surface. Figure 6.7 (c), at time t = 10x, shows a small amount of liquid encapsulated  68  below the top surface. Based on the location of the last material to solidify, once the application of EB power to the top surface is suspended, solidification proceeds from the top down and from the bottom up. Turning to fluid flow, the large flows associated with the inlet have dissipated by Figure 6.4 (b). Also in Figure 6.4 (b), there are no significant flows present within the bulk of the liquid pool suggesting a stable condition within the fluid, resulting from hot, less dense, material present on the top surface. Note that in contrast in Figures 6.4 (c) through 6.5 (b), times t = 2x through 4x, there is some increased flow observed below the surface possibly indicating the formation of a convective cell centered approximately 1/3-1/2 of the distance to the bottom of the liquid sump. This indicates the development of some driving force for flow despite the presence of hotter, less dense material, in proximity to the top surface. By Figure 6.5 (c), time t = 5x, the convective cell seems to have dissipated and the pool remains relatively quiescent for the balance of the hot topping phase of the process (t = 6x – 9x). The evolution of the composition in the liquid pool is presented in Figures 6.8 through 6.11. The results show a gradual depletion in Al adjacent to the top surface associated with the evaporative loss of aluminum as would be expected. It is interesting to note that the generation of convective cells in the bulk corresponds with the downward transport of the liquid depleted in aluminum, which suggests a density inversion associated with evaporation of the lighter Al alloy constituent on the top surface of the melt. Presumably, as the material on the top surface becomes denser due to the compositional change, eventually a point is reached where the compositional increase in density  69  overcomes the thermal decrease in density (associated with the EB heating of the top surface) leading to a net downward buoyancy force. In the series of images Figure 6.9 (a) – (c), the downward compositional transport and mixing associated with this can be clearly seen. Figure 6.10 (a) - (c), continues to show this trend and in addition, shows the profile of depleted material in the solidified ingot as a result of this process – e.g. the gradual decease in the concentration of Al left in the wake of the solidus isotherm as it moves upward toward the top of the ingot. Again, hot topping and therefore the evaporation of Al from the top surface continues until time t = 9X corresponding to image 6.11 (a). The final compositional map in the top of the ingot is shown in Figure 6.11 (c).  6.2.1. Comparison of Composition Variation with Height In a more quantitative comparison, graphs comparing the measured aluminum composition profile down the centerline of the ingot to the model results are presented in Figures 6.12 through 6.14 for the three experimental ingots CN5271, CN5272 and CN5273, respectively. All three sets of data have been normalized so that the compositional range falls between 0 and 1 as was the case for the compositional contour images presented in the previous section. The most striking difference between the three ingots is the comparatively large region (depth) of aluminum depletion in CN5272. A review of the operational parameters (outlined in section 4.1) indicates that heat CN5272 was subject to an extended hot top duration, while the other two heats were run for the standard hot top duration, but with different EB power levels. Comparison of profiles for heats CN5271 (120% beam power) and CN5273 (100% beam power) suggests that the effect of beam power on aluminum depletion is much less than hot top duration, within the range 70  examined. The good agreement between the model predictions and the experimental measurements in Figures 6.12 through 6.14, reveals the model is capable of predicting the aluminum concentration profile down the centerline of the top of the ingot correctly, suggesting that the model accurately accounts for both Al evaporation from the surface and the redistribution the depleted liquid within the liquid pool due to buoyancy driven flows.  6.2.2. Shrinkage Void Analysis As this research program was centered on the development of a computation tool for hot top optimization it is necessary to predict both the compositional variation in the top of the ingot and the location of shrinkage void as function of the casting and hottopping parameters. Shrinkage voids form as a result of the encapsulation of liquid occurring when the top surface of the ingot solidifies and there is still liquid present below. As solidification proceeds, the volumetric shrinkage associated with solidification causes the pressure to drop in the encapsulated liquid to the point where the vapor pressure of aluminum in equilibrium with the aluminum in solution in the alloy is exceeded. At this point a vapor bubble of aluminum can form, which after solidification is complete, results in a void or voids. The total volume of the void(s) is generally related to the volume of encapsulated liquid. In the context of the current model formulation, which does not consider the formation of a second phase (Al-vapor), the model is capable of predicting only the lowest point in the ingot that a bubble will form, which is based on the location of the last material to solidify. It is likely that if bubbles form while there is still significant liquid present then they float upwards under buoyancy forces until they impact on the top surface of the encapsulated liquid. As a result they would not be expected to occur below 71  the location of the last liquid to solidify, but may well be present above it. From a hot-top optimization standpoint this is a conservative estimate – e.g. the model prediction will maximize the depth of an ingot crop - and therefore in the context of avoidance of Alstringers is the desired result. Figure 6.15 shows a series of images of the model predictions for each of the three ingots cast in the program together with photographs of the corresponding top 0.20 m of the ingot containing the shrinkage void. The model results show the solidus line plotted at two different times in final transient stage of the casting process: one, representing the shape of the liquid pool at the point when the electron beam power was shut off; and the other smaller enclosed area, which represents the final area of liquid to solidify in the model. Turning to interpretation of the results, there are a number of observations that can be made based on a comparison between model predictions with the empirical data. In the case of the results for heat CN5272 there is good agreement between the location of the void and the last region predicted to solidify in the ingot. Again, this is the ingot produced with a 300% longer hot-top duration than was the case for the other two heats. The good agreement likely stems from the fact that the liquid pool is high up and shallow at the end of hot topping and as a result the pressure drop would occur in a relatively small volume of encapsulated liquid. In this shallow pool the critical pressure for the Al-vapor bubble would be reached in close proximity to the last liquid predicted to solidify in the model. Moreover, once formed it would be less likely that the void would rise upward significantly.  72  In the other two ingots – heats CN5271 and CN5273 - the pool size at the end of hot topping is substantially larger due to the reduced hot top time resulting in the encapsulation of a comparatively large volume of liquid. Thus the voids in heats CN5271 and CN5273 are larger in both size and number than observed in CN5272 and are located above the last material predicted to solidify by the model. This result is consistent with the belief that the vapor bubbles will rise to the top of the liquid pool when formed within a large encapsulated volume of liquid.  6.3. Sensitivity Analysis Additional transient model simulations were performed to determine the effect of electron beam power and hot top duration on the aluminum composition of the solidified ingot and the shape of the melt pool at the end of hot topping. These parameters were selected because they can be easily varied in the industrial process based on industrial partner’s recommendations. Conditions consistent with industrial heat CN5273 were used as the base case for the sensitivity analysis. The electron beam power was varied from 50% to 200% of the standard hot top power and the hot top duration was varied from 50% to 200% of the standard hot top duration.  6.3.1. Electron Beam Power Figure 6.16 compares the predicted temperature distributions at a time exactly halfway through the hot topping process in the three cases in which the electron beam power was varied. As can be seen, a large portion of the top surface has solidified in the 73  50% beam power case except for a small circular area at approximately the ¼ radius position. In the 200% beam power case, it is clear that the temperature on the top surface is much higher (between 50 and 100°C) than the base case as would expected due to the increased power input. The width of the liquid metal pool near the top of the ingot is also wider than in the base case. Figure 6.17 shows the temperature distribution at the end of hot topping. At this time, the entire top surface of the pool has solidified in the 50% beam power case while the width of the liquid metal pool has continued to grow in the 200% beam power case. Comparison of the sump depth at the end of hot topping shows a trend to increasing depth with beam power, but does not appear to be strongly dependent on beam power for the hot top time examined. Figure 6.18 shows the position of the last liquid to solidify in the three cases examined. The depth of the last liquid to solidify is nearly identical for the base and 200% beam power cases and is slightly deeper in the 50% power case. This suggests a greater degree of solidification from the top surface downward in the 50% power case and may suggest that a minimum power is necessary to effectively move the void toward the top surface for the hot top time examined. The aluminum composition comparison, presented in Figure 6.19, shows little or no evaporation loss in the 50% beam power case, a relatively small amount in the base case condition and a significant amount in the 200% beam power case. The high aluminum depletion in the 200% case relative to the base case can be attributed to the exponential  74  dependence of the vapor pressure of aluminum (Figure 5.9) on temperature and therefore evaporation rate predicted by the Langmuir equation. Overall these results indicate that there is little advantage to increasing the beam power above that necessary to keep the top surface liquid from the standpoint of minimizing the depth of void formation and a significant penalty from the standpoint of compositional control. Thus there is clearly an optimum from the standpoint of beam power.  6.3.2. Hot Top Duration In terms of the effect of hot top duration, the model was used to assess the effect of decreasing the hot top duration by 50% and increasing it by 200% relative to the base-case condition. The comparison has been made on the basis of the depth of melt pool at the end of hot topping (Figure 6.20) and the point of last liquid to solidify (Figure 6.21). The electron beam power was held constant for the three cases examined. From a comparison of the results it is clear that an increase or decrease in the hot top duration has a significant effect on the depth of the liquid metal pool at the time when the electron beam power is cut off. The position of the last liquid to solidify also seems strongly dependent on hot top duration showing a trend to decreasing depth with increasing hot top time. As previously discussed, the location of the last liquid to solidify is likely to correlate well with the deepest location of void, whereas the total volume of liquid encapsulated (not shown), should correlate with the volume of void.  75  The aluminum composition of the three cases is shown in Figure 6.22. The reduced hot top duration (50% case) resulted in very little aluminum depletion relative to the base case since there was little time for evaporation to occur. The 200% duration case showed a relatively large area of Al depletion in comparison to the base case. It is interesting to note that the 200% beam power case, Figure 6.19(c), is predicted to have a much larger and more depleted region at the top of the ingot than the 200% hot top duration case. Overall these results suggest that it may be possible to increase hot top duration without incurring too much alloy loss, particularly when applied in combination with beam power optimization.  76  Figure 6.1 – Steady state temperature contours on the symmetry plane and top faces of the model. Vectors representing the direction and magnitude of the fluid flow are overlaid on the symmetry plane result.  77  Figure 6.2 – Comparison of top 0.82m of the model and real ingot sump profile  Figure 6.3 – Model sump profile overlaid onto real ingot 78  (a)  (b)  (c)  Figure 6.4 – Temperature profiles at various time steps for heat CN5272 a) t=0 b) t=1x c) t=2x  79  (a)  (b)  (c)  Figure 6.5 – Temperature profiles at various time steps for heat CN5272 a) t=3x b) t=4x c) t=5x  80  (a)  (b)  (c)  Figure 6.6 – Temperature profiles at various time steps for heat CN5272 a) t=6x b) t=7x c) t=8x  81  (a)  (b)  (c)  Figure 6.7 – Temperature profiles at various time steps for heat CN5272 a) t=9x b) t=10x c) t=11x  82  (a)  (b)  (c)  Figure 6.8 – Composition profiles at various time steps for heat CN5272 a) t=0 b) t=1x c) t=2x  83  (a)  (b)  (c)  Figure 6.9 – Composition profiles at various time steps for heat CN5272 a) t=3x b) t=4x c) t=5x  84  (a)  (b)  (c)  Figure 6.10 – Composition profiles at various time steps for heat CN5272 a) t=6x b) t=7x c) t=8x  85  (a)  (b)  (c)  Figure 6.11 – Composition profiles at various time steps for heat CN5272 a) t=9x b) t=10x c) t=11x  86  Figure 6.12 – Composition profile results for CN5271, centerline of the ingot  Figure 6.13 - Composition profile results for CN5272, centerline of the ingot.  87  Figure 6.14 - Composition profile results for CN5273, centerline of the ingot  88  CN5271  CN5272  CN5273  Figure 6.15 – Top 0.20m of each heat for the model (left) and experiment (right). Lines within the model result represent the solidus isotherms at the start of hot topping, oval shaped lines represent the last region to solidify.  89  (a)  (b)  (c)  Figure 6.16 – Beam power sensitivity results halfway through hot topping a) 50% b) 100% c) 200%  90  (a)  (b)  (c)  Figure 6.17 – Beam power sensitivity at the end of hot topping a) 50% b) 100% c) 200%  91  (a)  (b)  (c)  Figure 6.18 – Beam power sensitivity at the point of last liquid a) 50% b) 100% c) 200%  92  (a)  (b)  (c)  Figure 6.19 – Beam power sensitivity final Al composition a) 50% b) 100% c) 200%  93  (a)  (b)  (c)  Figure 6.20 – Hot top duration sensitivity at end of hot topping a) 50% b) 100% c) 200%  94  (a)  (b)  (c)  Figure 6.21 – Hot top duration sensitivity at the point of last liquid a) 50% b) 100% c) 200%  95  (a)  (b)  (c)  Figure 6.22 – Hot top duration sensitivity final Al composition a) 50% b) 100% c) 200%  96  Chapter 7. Conclusions and Recommendations  7.1. Summary and Conclusions A coupled thermal, fluid flow and composition model has been developed to simulate the temperature, velocity and concentration profiles that develop during the final transient stage of electron beam cold hearth melted Ti-6Al-4V ingots. The contributions of flow resistance in the mushy zone (Darcy flow), compositional and thermal buoyancy on the fluid flow conditions were implemented in the model using source terms. Evaporative losses were accounted for in the model through application of the Langmuir equation as a boundary condition on the exposed liquid metal surface. Industrial scale experimental trials were carried out at the production facilities of a leading titanium producer to provide data for verification of various aspects of the model. Three industrial heats were cast during the experimental trial by varying electron beam power and hot top duration. Various strategies were employed during the production of the heats to characterize the size and shape of the liquid metal pool during casting. The model was developed in two parts: i) a model of the steady state ingot casting process, and ii) a final transient model including the hot topping portion of the process. The depth and asymmetry of the liquid metal pool predicted by the steady state model was verified by comparison with measurements taken from the industrial trials. Using the results from the steady state model as an initial condition, the model of the final transient stage of the process was used to predict the evolution of the liquid pool and aluminum 97  composition in the ingot for the plant trial conditions. Aluminum composition measurements from the plant trial ingots were used to verify the accuracy of the composition fields predicted by the transient stage model. Fluid flow from the inlet pour stream quickly dissipates after hot topping commences and the liquid pool appears to be stable due to thermal buoyancy. As aluminum evaporation begins to deplete the material at the top surface of the pool, compositional buoyancy effects increase, eventually reaching a point where they overcome the thermal buoyancy effects and a downwards flow occurs leading to a well-mixed liquid metal pool. A set of additional transient simulations were performed in order to determine the effect of electron beam power and hot top duration variation on the aluminum composition in the solidified ingot and the shape of the liquid metal pool. Findings confirm that reduction of the electron beam power can lead to solidification of the metal on the top surface of the ingot prior to the end of hot topping. In contrast, increasing beam power has a negative effect on compositional control, without having any significant positive effect on the position of solidification void formation. The results of the hot top duration variation simulations indicate that the position of the last liquid to solidify is strongly dependent on the hot top duration.  7.2. Recommendations for Future Work The main focus during development of the numerical model was incorporating the primary effects associated with tracking compositional changes and the resulting  98  compositional buoyancy forces. There could be some potential benefit in investigating the contribution that secondary compositional effects may have on additional material properties like the solidification range. Incorporating some of the laboratory scale work being carried in the department related, to thermal and compositional Marangoni effects into the industrial scale model could also be explored. Of note is the fact that the experiment ingots produced during the industrial trials never reached a true steady state. There is potential to develop a model capable of simulating the transient nature of the start-up stage of the process to provide further understanding of the temperature and fluid flow conditions during the EBCHM casting process.  99  Bibliography  [1]  Lutjering, G., & Williams, J.C. (2007). Titanium. New York: Springer.  [2]  Donachie, M.J. (2000). Titanium: A technical guide second edition. Ohio: ASM International.  [3]  Leyens, C., & Peters, M. (2003). Titanium and titanium alloys. Darmstadt: WileyVCH.  [4]  Lesnoj, A.B., & Demchenko, V.F. (2003). Modeling of hydrodynamics and mass exchange in electron beam remelting of titanium alloys. Electron Beam Processes, 3, 17-21.  [5]  Entrekin, C.H. (1985). Removal of high density inclusions by the hearth refining process. In Proceedings of the Conference on Electron Beam Melting and Refining – State of the Art 1985: Part One. Reno, Nevada: Bakish Materials Corp.  [6]  Entrekin, C.H., & Clarkson, D.S. (1986). EB refining promises super clean metal production. Metal Progress, 129, 35-39.  [7]  Jarrett, R.N. (1986). Removal of defects from titanium alloys with electron beam cold hearth refining. In Proceedings of the Conference on Electron Beam Melting and Refining – State of the Art 1986. Reno, Nevada: Bakish Materials Corp.  [8]  Mitchell, A. (1992). Clean melting and the removal of defects from aero-engine materials. In Simultaneous Convening of the 3rd International SAMPE Metals Conference and the 24th International SAMPE Technical Conference: Part Two. Toronto, Ontario: SAMPE.  [9]  Mitchell, A. (1999). Elimination of random defects in aerospace materials. Chinese Journal of Lasers, 26, 283-296.  [10]  Isawa, T., Nakamura, H., & Murakami, K. (1992). Aluminum evaporation from titanium alloys in EB hearth melting process. ISIJ International, 32, 607-615.  [11]  Mitchell, A., & Takagi, K. (1984). The evaporation problem in the electron-beam hearth-melting of superalloys. In Proceedings of the 1984 Vacuum Metallurgy Conference on Specialty Metals Melting and Processing. Pittsburgh, Pennsylvania: Iron & Steel Society.  100  [12]  Tripp, D.W., & Mitchell, A. (1985). Thermal regime in an EB hearth. In Proceedings  of the Conference on Electron Beam Melting and Refining – State of the Art 1985: Part Two. Reno, Nevada: Bakish Materials Corp. [13]  Nakamura, H., & Mitchell, A. (1992). Effect of beam oscillation rate on Al evaporation from a Ti-6Al-4V alloy in the electron beam melting process. ISIJ International, 32, 583-592.  [14]  Bellot, J.P., Hess, E., & Ablitzer, D. (2000). Aluminum volatilization and inclusion removal in the electron beam cold hearth melting of Ti alloys. Metallurgical and Materials Transactions B, 31B, 845-853.  [15]  Carvajal, F., & Geiger, G.E. (1971). Analysis of the temperature distribution and the location of the solidus, mushy, and liquid zones for binary alloys in remelting processes. Metallurgical Transactions, 2, 2087-2092.  [16]  Eisen, W.B., & Campagna, A.J. (1970). Computer simulation of consumable melted slabs. Metallurgical Transactions, 1, 849-856.  [17]  Mitchell, A., & Joshi, S. (1970). Thermal characteristics of the electroslag process. Metallurgical Transactions, 4, 631-642.  [18]  Pocklington, D.N., & Patrick, B. (1979). Heat flow in 3-phase ESR slab production. Metallurgical Transactions B, 10B, 359-366.  [19]  Jardy, A., & Ablitzer, D. (1990). Behavior of the liquid pool in VAR ingots. Memoires et Etudes Scientifiques Revue de Matallurgie, 87, 421-427.  [20]  Grandemange, D., Combres, Y., Champin, B., Jardy, A., Hans, S., & Ablitzer, D. (1997). The modeling of heat, momentum and solute transfers to optimize the melting parameters of VAR titanium ingots: an application to the “water” practice. In Proceedings of the 1997 Vacuum Metallurgy Conference. Sante Fe, New Mexico: American Vacuum Society.  [21]  Jardy, A., Ablitzer, D., Campin, B. Robbe, X. (1999). The use of a mathematical model to simulate a triple VAR processing route. In Proceedings of the 1999 Vacuum Metallurgy Conference. Sante Fe, New Mexico: American Vacuum Society.  [22]  Shyy, W., Pang, Y., Hunter, G.B., Wei, D.Y., & Chen, M.H. (1992). Modeling of turbulent transport and solidification during continuous ingot casting. International Journal of Heat and Mass Transfer, 35, 1229-1245.  101  [23]  Shyy, W., Pang, Y., Hunter, G.B., et al. (1993). Effect of turbulent heat transfer on continuous ingot solidification. Journal of Engineering Materials and Technology, 115, 8-16.  [24]  Zhao, X. (2006). 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Diffusion models for evaporation losses during electron-beam melting of alpha/beta-titanium alloys. Metallurgical and Materials Transactions B, 35B, 235-245. 102  [35]  Zhang, Y., Zhou, L., Sun, J., Han, M., & Zhao, Y. (2009). Evaporation mechanism of aluminum during electron beam cold hearth melting of Ti64 alloy. International Journal of Materials Research, 100, 248-253.  [36]  Brown, S.G.R., Spittle, J.A., Jarvis, D.J., & Walden-Bevan, R. (2002). Numerical determination of liquid flow permeabilities for equiaxed dendritic structures. Acta Materialia, 50, 1559-1569.  [37]  Ahn, K., Kim, D., Kim, B.S., & Sohn, C.H. (2004). Numerical investigation on the heat transfer characteristics of a liquid-metal pool subjected to partial solidification process. Progress in Nuclear Energy, 44, 227-304.  [38]  Mills, K.C. (2002) Recommended values of thermophysical properties for selected commercial alloys. Cambridge, England: Woodhead Publishing Ltd.  [39]  PANDAT (Software). (2012). 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USA: Addison-Wesley Publishing.  103  Appendix  Fortran source code for the user-subroutine used to calculate buoyancy forces. #include "cfx5ext.h" dllexport(user_buoyancy) SUBROUTINE USER_BUOYANCY ( & NLOC,NRET,NARG,RET,ARGS,CRESLT,CZ,DZ,IZ,LZ,RZ) C-------------------C Details C -------------------C ARGS(1:NLOC,1) holds INPUT parameters C RET(1:NLOC,1) will hold return result (Source) C -----------------------------C Preprocessor includes C -----------------------------#include "MMS.h" #include "stack_point.h" C -----------------------------C Argument list C -----------------------------INTEGER NLOC,NARG,NRET,CLOC CHARACTER CRESLT*(*) REAL ARGS(NLOC,NARG), RET(NLOC,NRET) INTEGER IZ(*) CHARACTER CZ(*)*(1) DOUBLE PRECISION DZ(*) LOGICAL LZ(*) REAL RZ(*) C -----------------------------C Local Variables CHARACTER*120 File_Name C -----------------------------C Stack pointers C -----------------------------C __stack_point__ pTEMP C --------------------------C Executable Statements C --------------------------C Initialise success flag. CRESLT = 'GOOD' 104  C Initialise RET to zero. CALL SET_A_0 ( RET, NLOC*NRET ) C C---- Calculate source expression in RET(1:NLOC,1) C DO CLOC = 1, NLOC RET(CLOC,1) = -9.81*(ARGS(CLOC,2)-ARGS(CLOC,1)) END DO C 999 CONTINUE C C Send any diagnostics or stop requests via master processor IF (CRESLT .NE. 'GOOD') THEN CALL MESAGE( 'BUFF', 'USER_BUOYANCY returned error:' ) CALL MESAGE( 'BUFF', CRESLT ) CALL MESAGE( 'BUFF-OUT', ' ' ) END IF C C=================================================== ==================== END  105  

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