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2014 18 Mauricio Yilmer Carmona García Numerical Analysis of Melting and Holding Furnaces in Secondary Aluminum Production Director/es Departamento Instituto Universitario de Investigación Mixto CIRCE Cortés Gracia, Cristóbal Director/es Tesis Doctoral Autor Repositorio de la Universidad de Zaragoza – Zaguan http://zaguan.unizar.es UNIVERSIDAD DE ZARAGOZA Departamento Director/es Autor Mauricio Yilmer Carmona García NUMERICAL ANALYSIS OF MELTING AND HOLDING FURNACES IN SECONDARY ALUMINUM PRODUCTION Instituto Universitario de Investigación Mixto CIRCE Director/es Cortés Gracia, Cristóbal Tesis Doctoral Repositorio de la Universidad de Zaragoza – Zaguan http://zaguan.unizar.es UNIVERSIDAD DE ZARAGOZA 2014 Departamento Director/es Director/es Tesis Doctoral Autor Repositorio de la Universidad de Zaragoza – Zaguan http://zaguan.unizar.es UNIVERSIDAD DE ZARAGOZA Ph.D. Thesis NUMERICAL ANALYSIS OF MELTING AND HOLDING FURNACES IN SECONDARY ALUMINUM PRODUCTION By Mauricio Yilmer Carmona García January 2014 Advisor: Cristóbal Cortés Gracia, Ph.D. Instituto CIRCE Escuela de Ingeniería y Arquitectura Universidad de Zaragoza i Numerical analysis of melting and holding furnaces in secondary aluminum production Mauricio Yilmer Carmona García Thesis submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy University of Zaragoza, Spain Abstract In this thesis, two different aluminum furnaces are analyzed numerically: 1) a new prototype of melting furnace; 2) a new prototype of holding furnace. These devices are a key factor in secondary aluminum production. Models used take into account heat conduction in solid parts, convection in air and molten aluminum, interactions between gas-liquid-solid zones, phase change of the load and radiation heat transfer. With the objective to develop a calculating tool to assist in the design and scaling-up of industrial furnaces, several calculation strategies are tested concerning their computational economy and their accuracy in computing different key parameters. Estimations of temperatures in furnaces are compared with experimental measurements taken in real prototypes in typical operation cycles. iii Análisis numérico de hornos de fundición y mantenimiento en producción de aluminio secundario Mauricio Yilmer Carmona García Tesis realizada para cumplir con los requisitos del grado de Doctor Universidad de Zaragoza, España Resumen En esta tesis, dos hornos de aluminio diferentes se analizan numéricamente: 1) un nuevo prototipo de horno de fundición; 2) un nuevo prototipo de horno de mantenimiento. Estos dispositivos son claves en la producción de aluminio secundario. Los modelos utilizados tienen en cuenta la conducción de calor en las partes sólidas, la convección en el aire y de aluminio fundido, las interacciones entre las zonas de gas-líquido-sólido, cambio de fase de la carga y la transferencia de calor por radiación. Con el objetivo de desarrollar una herramienta de cálculo para asistir en el diseño y escalado de hornos industriales, se evalúan diferentes estrategias de cálculo concernientes a la economía computacional y su precisión de cálculo de diferentes parámetros importantes. Las estimaciones de las temperaturas en los hornos se comparan con las mediciones experimentales realizadas en prototipos reales en ciclos de operación típicos. xi Contents 1. SCOPE, AIMS AND OUTLINE .............................................................................................................. 1 2. INTRODUCTION ................................................................................................................................ 3 2.1 ALUMINUM CHARACTERISTICS ............................................................................................................... 3 2.2 ALUMINUM PRODUCTION ..................................................................................................................... 4 2.3 ALUMINUM UTILIZATION ...................................................................................................................... 6 2.4 SECONDARY ALUMINUM PERSPECTIVES .................................................................................................... 9 2.4.1 Advantages ................................................................................................................................ 9 2.4.2 Production ............................................................................................................................... 10 2.4.3 Final products .......................................................................................................................... 15 2.4.4 Recycling plants in the world ................................................................................................... 16 2.4.5 Prospect ................................................................................................................................... 17 2.5 STAGES OF SECONDARY ALUMINUM PROCESS .......................................................................................... 18 2.6 FURNACES USED IN ALUMINUM SECONDARY PRODUCTION ......................................................................... 21 2.6.1 Melting furnaces ...................................................................................................................... 22 2.6.2 Holding furnaces ...................................................................................................................... 36 2.7 MOTIVATION ................................................................................................................................... 39 3. MODELS USED IN NUMERICAL SIMULATIONS OF INDUSTRIAL FURNACES ...................................... 43 3.1 LIQUID-SOLID PHASE CHANGE IN PURE SUBSTANCES AND MIXTURES ............................................................ 45 3.1.1 Phase diagrams for alloys ........................................................................................................ 46 3.1.2 Phase diagrams of alloys -towards modeling .......................................................................... 51 3.2 NUMERICAL MODELS FOR PHASE CHANGE PROBLEMS ............................................................................... 53 3.2.1 Analytical methods .................................................................................................................. 53 3.2.2 Variable-grid methods ............................................................................................................. 56 3.2.3 Fixed-grid methods .................................................................................................................. 60 3.3 GOVERNING EQUATIONS OF THE ENTHALPY METHOD ................................................................................ 62 3.4 SURFACE-TO-SURFACE RADIATION MODEL (S2S): NUMERICAL SIMULATION BY COMPUTING VIEW FACTORS ....... 65 CONTENTS xii 4. NUMERICAL SIMULATION OF AN ALUMINUM MELTING FURNACE ................................................. 69 4.1 STATE OF THE ART IN RELATED NUMERICAL SIMULATIONS .......................................................................... 69 4.1.1 Melting furnaces ...................................................................................................................... 69 4.1.2 Phase change problems ........................................................................................................... 76 4.1.3 Plasma torch ............................................................................................................................ 78 4.2 EXPERIMENTAL CONFIGURATION .......................................................................................................... 83 4.2.1 Principle of operation and test protocol................................................................................... 83 4.2.2 Measurement equipment......................................................................................................... 86 4.3 MODEL DESCRIPTION ......................................................................................................................... 91 4.3.1 General assumptions and boundary conditions ....................................................................... 91 4.3.2 Geometry and materials .......................................................................................................... 93 4.3.3 Simulation of gas cavity ........................................................................................................... 94 4.3.4 Numerical time step ................................................................................................................. 97 4.3.5 Meshing scheme ...................................................................................................................... 97 4.4 PREHEATING OF THE REFRACTORY LADLE ................................................................................................ 98 4.5 RESULTS AND DISCUSSION ................................................................................................................. 100 4.5.1 Melting time ........................................................................................................................... 100 4.5.2 Distribution of liquid fraction ................................................................................................. 101 4.5.3 Temperatures ......................................................................................................................... 103 4.5.4 Molten load movement .......................................................................................................... 107 4.5.5 Energy balance ....................................................................................................................... 109 4.5.6 Computational resources ....................................................................................................... 109 5. NUMERICAL SIMULATION OF AN ALUMINUM HOLDING FURNACE ............................................... 111 5.1 STATE OF THE ART IN NUMERICAL SIMULATIONS OF HOLDING FURNACES ..................................................... 112 5.2 EXPERIMENTAL CONFIGURATION ........................................................................................................ 114 5.2.1 Prototype description ............................................................................................................. 114 5.2.2 Dimensions and temperature measurements ........................................................................ 116 5.2.3 Test protocol .......................................................................................................................... 117 5.3 MODEL DESCRIPTION ................................................................................................................. 118 5.3.1 Assumptions and boundary conditions .................................................................................. 118 5.3.2 Geometry and materials ........................................................................................................ 120 5.3.3 Models.................................................................................................................................... 122 5.3.4 Meshing scheme .................................................................................................................... 123 5.3.5 Numerical time step ............................................................................................................... 124 5.4 RESULTS AND DISCUSSION ................................................................................................................. 124 5.4.1 Preheating stage .................................................................................................................... 124 5.4.2 Temperatures - holding process ............................................................................................. 125 5.4.3 Energy balance ....................................................................................................................... 127 5.4.4 Convection effects .................................................................................................................. 128 CONTENTS xiii 6. SUMMARY AND CONCLUSIONS .................................................................................................... 139 6.1 MELTING FURNACE.......................................................................................................................... 139 6.2 HOLDING FURNACE.......................................................................................................................... 141 6.3 PERSPECTIVES FOR FUTURE WORK ...................................................................................................... 142 7. RESUMEN Y CONCLUSIONES ......................................................................................................... 145 7.1 HORNO DE FUNDICIÓN ..................................................................................................................... 146 7.2 HORNO DE MANTENIMIENTO ............................................................................................................. 147 7.3 PERSPECTIVAS PARA TRABAJO FUTURO ................................................................................................ 149 REFERENCES .......................................................................................................................................... 151 xv List of Figures Figure 2.1. Scheme of the Bayer and Hall-Heroult processes (JBI, 2013) ........................................ 5 Figure 2.2. Global aluminum mass flow for the year 2011 (Tsesmelis, 2012) ................................. 7 Figure 2.3. Diagram of aluminum production and life cycle (Word-aluminium, 2013) .................. 8 Figure 2.4. Aluminum consumption (left) and total aluminum in use (right) by sectors – 2010 (Bayliss, 2012) .................................................................................................................................. 8 Figure 2.5. Global share of primary and recycled aluminum production-current day and estimated production until 2020 (Word-aluminium, 2013).......................................................... 11 Figure 2.6. Product lifetimes vs. recycling rates (Tsesmelis, 2012) ............................................... 12 Figure 2.7. Regional UBC recycling rates, 1995-2010 (Bayliss, 2012) ............................................ 14 Figure 2.8. Global UBC recycling rate and collection volume, 1995-2010 (Bayliss, 2012) ............. 14 Figure 2.9. UCB collection rate different countries: 2008 – Adapted from Word-aluminium (2013) ........................................................................................................................................................ 15 Figure 2.10. Number of recycling plants – 2008 (Word-aluminium, 2013) ................................... 17 Figure 2.11. Aluminum secondary stages ...................................................................................... 21 Figure 2.12. Large-scale rotary sweat furnace (Schlesinger, 2006) ............................................... 23 Figure 2.13. Generic reverberatory wet-hearth melting furnace (Schlesinger, 2006) .................. 24 Figure 2.14. Sketch of dry-hearth melting furnace-Adapted from StrikoMelter (2013) ................ 25 Figure 2.15. Sketch of stack melter (Schlesinger, 2006) ................................................................ 26 Figure 2.16. Sketch of sidewell furnace (Schlesinger, 2006) .......................................................... 27 Figure 2.17. Sketch of sidewell furnace with scrap submergence system and mechanical pump (StrikoMelter, 2013) ....................................................................................................................... 28 LIST OF FIGURES xvi Figure 2.18. Sketch of the rotary furnace (Zhou et al., 2006) ........................................................ 29 Figure 2.19. Schematic design of a gas-heated crucible-Adapted from Nabertherm (2013) ........ 30 Figure 2.20. Scheme of the eddy current effect (left) and coreless induction furnace (right)- Adapted from Schmitz (2006) ........................................................................................................ 31 Figure 2.21. Scheme of the channel induction furnace (Langejürgen et al., 2008) ....................... 33 Figure 2.22. Thermal plasmas: transferred-arc (left) and non-transferred-arc (right); adapted from Murphy (2001) ....................................................................................................................... 34 Figure 2.23. Schematic arrangement of transferred arc furnace; Adapted from Jones et al. (2001) ........................................................................................................................................................ 36 Figure 2.24. Reverberatory furnace heated by direct combustion flame (StrikoMelter, 2013) .... 37 Figure 2.25. Radiant tube in reverberatory furnace (Khanthal, 2011) ........................................... 37 Figure 2.26. Electrical holding furnaces: a) heated from lateral walls (Nabertherm, 2013) b) heated from the roof (SPX, 2013) .................................................................................................. 38 Figure 2.27. Electric immersion holding furnace (SPX, 2013) ........................................................ 39 Figure 2.28. 2D numerical simulation of a industrial holding furnace heated by radiant tubes (Khanthal, 2011) ............................................................................................................................. 41 Figure 3.1. Typical phase diagram in a binary alloy ....................................................................... 47 Figure 3.2. Close up of the region of liquid-solid phase change of the alloy with composition C1 (see Figure 3.1) ............................................................................................................................... 49 Figure 3.3. Region of liquid-solid phase change of the alloy with composition C2 (see Figure 3.1) ........................................................................................................................................................ 50 Figure 3.4. Liquid fraction evolution with temperature for a binary eutectic alloy ....................... 52 Figure 3.5. Solidification from a plane cold surface-Adapted from Poulikakos (1994) .................. 54 Figure 3.6. Application of the unstructured deforming grid method-Adapted from Mencinger (2004): streamlines (up); dimensionless temperature (center); deforming grid (down) .............. 57 Figure 3.7. Relationship between the physical and transformed grids-Adapted from Lacroix and Voller (1990) ................................................................................................................................... 58 Figure 4.1. Scheme of a common spectrometer (Sismanoglu et al., 2009) ................................... 82 LIST OF FIGURES xvii Figure 4.2. (a) Pilot melting furnace; (b) Sectional view (1. Crucible/ ladle; 2. Top of furnace; 3. Anode; 4. Cathode; 5. Exhaust gas pipe; 6. Cooling system of electrodes; 7. Inlet nitrogen pipe; 8. Transport hook; 9. Temperature measurement sensor; 10. Load) ................................................ 84 Figure 4.3. (a) Electric/hydraulic connections for the electricity supply and electrode refrigeration; (b) connection for the N2 supply ............................................................................. 85 Figure 4.4. Preheating process for the ladle with a gas burner ..................................................... 85 Figure 4.5. Appearance of the furnace in the melting process ...................................................... 86 Figure 4.6. Measurement of external temperatures of the furnace: (a) IR thermograph camera system; (b) furnace in melting process; (c) typical thermographic image ..................................... 88 Figure 4.7. Measurement of molten temperature......................................................................... 89 Figure 4.8. Measurement instruments: (a) digital scale; (b) water and N2 flowmeter; (c) control box and analogue instruments for power supply .......................................................................... 90 Figure 4.9. a) Main dimensions of melting furnace; b) Geometry for the numerical simulations 93 Figure 4.10. 2-D axisymmetric grid for the numerical simulation ................................................. 98 Figure 4.11. Temperature distribution [K] in the crucible at the end of the preheating stage ..... 99 Figure 4.12. Temperature along the thickness of the refractory wall at the end of the preheating process ......................................................................................................................................... 100 Figure 4.13. Liquid fraction in the load throughout simulation time for five study cases ........... 101 Figure 4.14. Liquid fraction at t =150 s: a) Case 1; b) Case 2; c) Case 3; d) Case 4; e) Case 5 ..... 102 Figure 4.15. Liquid fraction at t = 480 s: a) Case 1; b) Case 2; c) Case 3; d) Case 4; e) Case 5 .... 103 Figure 4.16.Temperature [K] at t = 150 s: a) Case 1; b) Case 2; c) Case 3; d) Case 4; e) Case 5 ... 104 Figure 4.17. Temperature [K] at t = 480 s: a) Case 1; b) Case 2; c) Case 3; d) Case 4; e) Case 5 .. 105 Figure 4.18. Thermal images of the outer crucible surface: a) t = 150 [s]; b) t = 480 [s] ............. 106 Figure 4.19. Evolution of measured temperatures of crucible wall and gases ............................ 106 Figure 4.20. Thermal image at the end of the test ...................................................................... 107 Figure 4.21. Velocity vectors [m/s] for the molten aluminum at the end of the melting process: a) Case 1; b) Case 2; c) Case 3; d) Case 4 .......................................................................................... 108 LIST OF FIGURES xviii Figure 5.1. Photographs of the aluminum holding furnace and sectional view (1-holding chamber, 2-heating chamber, 3-layer of refractory material A, 4layer of refractory material B, 5layer of refractory material C, 6aluminum load, 7electrical resistances) ................................ 115 Figure 5.2. Photograph of the electrical resistances array .......................................................... 116 Figure 5.3. Dimensions of aluminum holding furnace (mm) and measurements points for the temperature (A-D) at a height h = 150 mm.................................................................................. 117 Figure 5.4. Heat transfer scheme and thermal circuit in the lateral walls of the crucible ........... 119 Figure 5.5. Geometry for the numerical simulationsQuarter of domain and full domain (translucent view)......................................................................................................................... 121 Figure 5.6. Grid details-quarter of domain. a) General, b) Resistances, c) Air filling the resistances chamber ....................................................................................................................................... 123 Figure 5.7. Temperature for preheating stage [K]. Up: quarter of domain. Down: full domain.. 125 Figure 5.8. Temperature for holding stage [K]. Up: quarter of domain. Down: full domain ....... 126 Figure 5.9. Wall temperature profile ........................................................................................... 127 Figure 5.10. Vertical velocity profile [m/s] and velocity vector for the molten aluminum. Up: quarter of domain. Down: full domain ........................................................................................ 129 Figure 5.11. Iso-surfaces of vertical velocity for the molten aluminum. Up: quarter of domain. Down: full domain ........................................................................................................................ 130 Figure 5.12. Location of control points for the molten load ........................................................ 131 Figure 5.13. Z-velocities registered (m/s) in control points P1-P4. Left: quarter of domain. Right: full domain ................................................................................................................................... 132 Figure 5.14. Temperatures registered (K) in control points P1-P4. Left: quarter of domain. Right: full domain ................................................................................................................................... 133 Figure 5.15. FFT for Z-velocities registered in control points P1-P4. Left: quarter of domain. Right: full domain ................................................................................................................................... 134 Figure 5.16. FFT for Temperatures registered in control points P1-P4. Left: quarter of domain. Right: full domain ......................................................................................................................... 135 xix List of Tables Table 2.1. Main physical characteristics of aluminum (Totten and MacKenzie, 2003b) ................. 3 Table 2.2. Main mechanical properties of pure aluminum (Totten and MacKenzie, 2003b) .......... 4 Table 2.3. Generated new scrap by market sector (Schlesinger, 2006) ........................................ 12 Table 2.4. Main scrap types - European aluminum scrap standard (EN 13920) (Boin and Bertram, 2005) .............................................................................................................................................. 19 Table 4.1. Summary of the typical works developed in PCM simulations ..................................... 78 Table 4.2: Thermophysical properties of refractory (Carbosanluis, 2007) .................................... 94 Table 4.3: Thermophysical properties of aluminum load .............................................................. 94 Table 4.4: Terms of the energy balance (KJ) and time (s) for each computational case and experimental data ........................................................................................................................ 109 Table 4.5: Consumed computational resource for each computational case ............................. 110 Table 5.1: Thermal properties of solid parts ................................................................................ 122 Table 5.2: Thermophysical properties of aluminum load ............................................................ 122 3 2. Introduction 2.1 Aluminum characteristics Aluminum has become increasingly important in the production of automobiles and trucks, packing of food and beverages, buildings and construction, transmission of electricity, development of transportation infrastructures, production of defense and aerospace equipment, manufacture of machinery and tools, and production of durable consumer products. This tendency is due to the special properties of aluminum such as its light weight, high corrosion resistance, good formability and non-toxicity (Totten and MacKenzie, 2003a). The main physical properties of aluminum appear in Table 2.1, and their main mechanical properties are shown in Table 2.2. Table 2.1. Main physical characteristics of aluminum (Totten and MacKenzie, 2003b) Properties Crystalline structure fcc Atomic weight 26.98154 Specific mass at 20ºC (g/cm3) 2.69890 Solidification shrinkage (%) 6.5 Fusion temperature (ºC) 660.4 Ebullition temperature (ºC) 2494 Linear thermal dilation coefficient, from 20ºC up to 400ºC (ºC x 106) 26.4 Specific heat at 25ºC (J/kgºC) 900.0 Latent heat of fusion (kJ/kg) 397.0 Combustion heat (MJ/kg) 31.07 Volumetric electric conductivity (% IACS) 64.94 Thermal conductivity at 25 ºC (W/m ºC) 247 Numerical analysis of melting and holding furnaces in secondary aluminum production 4 Table 2.2. Main mechanical properties of pure aluminum (Totten and MacKenzie, 2003b) Property Annealed Hard-drawn (90%) Tensile strength (MPa) 40-50 120-140 Yield point (MPa) 15-20 100-120 Brinell hardness (kgf/mm 2 ) 12-16 27 Stretch 50-70 8-12 Despite that the tensile strength and the yield point of pure aluminum are fairly low, which reduces the applicability of this metal in structural uses, aluminum alloys can achieve tensile strengths over 600MPa after heat treatment. The specific weight of the aluminum is about one-third of the specific weight of iron or copper. Due to these general good properties, the aluminum is the second most used metal in the world. 2.2 Aluminum production Aluminum is the most abundant metal in the earth crust. Nevertheless, in nature, aluminum does not exist as a metal because of the high chemical affinity for oxygen. Chemical processing has always been necessary to extract pure alumina (aluminum oxide, Al2O3) from the other ingredients associated with it in the deposit. The primary natural ore for aluminum is bauxite, a mineral consisting primarily of hydrated aluminum oxides. Aluminum is recovered from bauxite by a selective leaching sequence known as the Bayer process, which dissolves most of the aluminum while leaving impurities behind. The aluminum is recovered from the leach solution by precipitating it as aluminum hydroxide. The hydroxide is then dried and calcined to generate purified alumina. The calcined alumina is fed to electrolytic cells containing a molten salt electrolyte based on cryolite (Na3AlF6). The alumina dissolves in the cryolite and is electrolyzed to generate molten aluminum metal and carbon dioxide gas. This process called the Hall-Heroult process has been the sole approach for producing primary aluminum metal since the late 1800s and will likely continue in this role for decades to come (Schlesinger, 2006, Totten and MacKenzie, 2003a). Figure 2.1 shows a diagram of the Bayer and Hall-Heroult processes. Chapter 2. Introduction 5 Figure 2.1. Scheme of the Bayer and Hall-Heroult processes (JBI, 2013) Numerical analysis of melting and holding furnaces in secondary aluminum production 6 Production of aluminum metal has previously focused on its recovery from naturally occurring raw materials. However, in recent decades an increasingly large fraction of the world’s aluminum supply has come from a different source. This is the aluminum scrap recovered from industrial waste and discarded postconsumer items. The treatment of this scrap to produce new aluminum metal and alloys is known as recycling, and metal produced this way is frequently named secondary (Schlesinger, 2006). 2.3 Aluminum utilization Around 54 million tonnes of aluminum, from primary and recycled sources, ended up in finished products in 2011. Three quarters of all the aluminum ever produced (since the 1880s) is still in productive use, in fact 90% of aluminum goes into products with long life times. About 32% is located in buildings in the form of facades, windows, doors etc., 28% as electrical cable and machinery and 28% within moving objects such as cars, commercial vehicles, trains and ships. In 2011 this stock had grown to about 727 million tonnes (approximately 1 billion tonnes today). The global stock of aluminum in productive use is growing every year, in 2011 by 40 million tones. More than a third of all the aluminum currently produced originates from recycled and two-thirds from primary metal; making the secondary production a key element of the aluminum market. Aluminum recycling is divided in two categories: (a) new scrap arises during the manufacturing of aluminum semi-fabricated and final products; (b) old scrap refers to those products collected after disposal by consumers. Old scrap is often more contaminated than new scrap. End-of-life vehicles, demolished buildings and constructions, discarded packaging material, home and office appliances, as well as machinery equipment are all potential sources of old aluminum scrap (Tsesmelis, 2012). A special mention receives the old scrap with low thickness and reduced contamination, which is called light-gauge scraps; typical examples are the used beverage cans (UBCs), aluminum chips or aluminum foils. Figure 2.2 shows the aluminum mass flow model presented by the international aluminium institute (IAI) for the year 2011. Chapter 2. Introduction 7 Values in millions of metric tonnes. Values might not add up due to rounding. *Change in stocks not shown. 1 Aluminium in skimmings; 2 Scrap generated by foundries, rolling mills and extruders. Most is internal scrap and not taken into account in statistics; 3 Such as deoxidation aluminium (metalproperty is lost); 4 Area of current research to identify final aluminium destination (reuse, recycling, recovery or disposal); 5 Calculated based on IAI LCI report - update 2010. Includes,depending on the ore, between 30% and 50% alumina; 6 Calculated. Includes on a global average 52% aluminium; 7 Scrap generated during the production of finished products from semis; 8 Either incinerated with/without energy recovery, material recovery or disposal; 9 Estimated stock decrease 440,000 tonnes Figure 2.2. Global aluminum mass flow for the year 2011 (Tsesmelis, 2012) Numerical analysis of melting and holding furnaces in secondary aluminum production 8 Figure 2.3 shows a diagram of the aluminum production and life cycle to illustrate the capacity of aluminum to reach the statistical data presented. Figure 2.3. Diagram of aluminum production and life cycle (Word-aluminium, 2013) The market for aluminum products is generally separated into seven segments: building and construction, transportation, consumer durables, electrical, machinery and equipment, packaging, and other. Figure 2.4 shows the aluminum consumption and the total aluminum in use by sectors for the year 2010. Figure 2.4. Aluminum consumption (left) and total aluminum in use (right) by sectors – 2010 (Bayliss, 2012) Chapter 2. Introduction 9 2.4 Secondary aluminum perspectives 2.4.1 Advantages The secondary metallurgy of aluminum allows an economy of raw materials and energy. The recycled aluminum production has a gain of 95% in energy compared with primary aluminum (Bayliss, 2012, Green, 2007, Schlesinger, 2006, Totten and MacKenzie, 2003b, Tsesmelis, 2012). Aluminum scrap has considerable market value because most of the energy required for the production of primary aluminum is embodied in obtain the metal itself, and consequently in the scrap. Therefore, the energy needed to melt aluminum scrap is only a fraction of that required for primary aluminum production. Another positive aspect of aluminum recycling is the environmental impact. Compared with the production of primary aluminum, recycling of aluminum products emits only 5% of the greenhouse gas so that recycling used aluminum products currently saves 100 million tonnes of CO2e (equivalent carbon dioxide) per year. On the other hand, primary aluminum production generates solid waste at every step in the process. The most significant of these is the red mud residue created during alumina purification; the production of one metric ton of primary aluminum requires about four metric tons of bauxite and it produces around two metric tons of red mud. With the generation of red mud, the production of primary aluminum also releases fluorides. The mining of bauxite is also an activity that causes problems to the environment, because this activity devastates forests and needs space to dispose of the wastes. While aluminum recycling generates solid wastes as well (primarily the dross and salt slag created during remelting), the volumes are much smaller (Schlesinger, 2006, Totten and MacKenzie, 2003b). Furthermore, primary aluminum production requires a mining operation, a Bayerprocess plant to produce purified alumina, and an electrolytic pot line to extract aluminum metal from the alumina. The equipment used for recycling is less complex and thus less expensive; also the process can be adjusted to the demand, sources of combustibles or electricity supply. Numerical analysis of melting and holding furnaces in secondary aluminum production 10 Finally, the aluminum has a great recycling potential. On the one hand, from a technical point of view, if scrap is pre-treated and/or sorted appropriately, the recycled aluminum can be utilized for almost all aluminum applications. Aluminum can be recycled over and over again without any loss of its inherent properties. Almost all the aluminum alloys can be recycled, either separately or in combination with others alloys (Schlesinger, 2006). These characteristics have enabled the high percentage of metal still in use of the total production, some having been through countless loops of its lifecycle. On the other hand, for most countries, there is a well-established market for recycled aluminum with firmly defined distribution chains. For all these advantages, the recycled rate of aluminum has been increased. Today secondary metallurgy is a major aspect of continued aluminum use and it is a growing industry. 2.4.2 Production The high intrinsic value of aluminum scrap has always been the main impetus for recycling, independent of any legislative or political initiatives. For some products, in addition to this obvious economic dimension, growing environmental concerns and heightened social responsibility, over the last decade in particular, have served to boost recycling activity in order to conserve resources and to avoid littering. In 1990 the total aluminum production was around 28 million tonnes and today the total is close to 69 million tonnes (with around 20 million tonnes recycled from scrap). By 2020 metal demand is projected to have increased to around 110 million tonnes (with around 35 million tonnes recycled from scrap). Figure 2.5 shows the global share of primary and recycled aluminum production from 1950 to the current day and the estimated production until 2020 (Word-aluminium, 2013). Chapter 2. Introduction 11 Figure 2.5. Global share of primary and recycled aluminum production-current day and estimated production until 2020 (Word-aluminium, 2013) The aluminum industry recycles all the aluminum scrap it can obtain. Primary aluminum producers and the producers of semi-fabricated and fabricated products generally collect and recycle all of the aluminum scrap they generate (new scrap) and therefore the success of a recycling system depends on the degree to which used products are collected at the end of their lives. Collection rates vary depending on the product in question, waste management systems in place and on society's understanding of the value of aluminum scrap and its compromise to conserve that value. Table 2.3 lists the average percent of the input aluminum turned into scrap by manufacturing operations in different industrial sectors (new scrap). Figure 2.6 shows a scheme of the product life and recycling rate for aluminum products in various sectors, which is associated to the availability of old scrap. Numerical analysis of melting and holding furnaces in secondary aluminum production 12 Table 2.3. Generated new scrap by market sector (Schlesinger, 2006) Market Scrap/input material (%) Building and construction 20 Transportation: aerospace 60 Transportation: auto and light truck 25 Transportation: trucks, buses and trailers 25 Transportation: rail 25 Transportation: other 25 Consumer durables 20 Electrical 10 Machinery and equipment 15 Containers and packaging: foil 10 Containers and packaging: other 25 Other 25 Figure 2.6. Product lifetimes vs. recycling rates (Tsesmelis, 2012) Globally, aluminum achieves among the highest material recycling rates for end of life products, with up to 90% for transport and construction applications. Only a few package products presents low recycling rate. The metal’s economic scrap value and Chapter 2. Introduction 19 Table 2.4. Main scrap types - European aluminum scrap standard (EN 13920) (Boin and Bertram, 2005) Part Scrap Description Aluminum Metala (%) Oxidesb (%) Foreign Materialb (%) 3 Wire and cable (new scrap) 98.7 1.3 — Wire and cable (old scrap) 97.7 1.8 0.5 4 One single wrought alloy 97.2 1 1.8 5 Two or more wrought alloys of the same series 97.2 0.8 2 6 Two or more wrought alloys 94 0.8 5.2 7 Castings 83.4 6.2 10.4 9 Shredded and density separated scrap 84.5 5.4 10.1 10 Used beverage cans 94 0.8 5.2 12 Turnings, one single alloy 95.3 3.7 1 13 Mixed turnings, two or more alloys 84 3.3 12.8 14 Packaging (coated) 71.5 3.8 24.7 15 Packaging (de-coated) 86.1 12.9 1 16 Dross 55.7 44.3 — a Based on empirical data. b According to the definitions of the different EN 139208 scrap categories and industry knowledge about scrap composition The load is charged into the melting furnaces. The melting of scraps is usually performed in rotary, reverberatory or crucibles furnaces. Molten salt fluxes are often used in the melting of scraps highly oxidized or light-gauge scraps. Even though the oxidation is low on light-gauge scraps, this phenomenon is only superficial; thus, the thickness of the raw materials to be melted influences the amount of oxide produced during the process, i.e., the thinner the raw material, the higher the oxide formation. This behavior occurs because the relation surface/volume becomes high when dealing with thin raw material. The oxidation process of aluminum alloys depends on the superficial condition of the sample, on the alloy composition and on the temperature. Typically, the proportion of the fluxes is not more than 2% by weight of the charge, but this fraction might be higher when the raw material is composed mainly of light-gauge scraps or contains organic coatings. The main function of the saline fluxes is to act as a barrier between the liquid aluminum and the oxygen of the atmosphere, diminishing the process of superficial oxidation of aluminum. Other function of the salts layer is to serve as a flux and remove impurities in the molten load (Totten and MacKenzie, 2003b). Numerical analysis of melting and holding furnaces in secondary aluminum production 20 Drosses are produced during the aluminum melting processes. Due to the high aluminum reactivity with oxygen, the formation of a superficial layer of oxide occurs. This layer becomes a physical barrier between the melt aluminum and the oxidant atmosphere, hence protecting the bath against oxidation. Turbulence generated by the handling of the liquid metal makes a new exposure of aluminum, which causes an increase in the oxide layer. At the end of the melting process, this oxide layer is removed. During the removal of the oxide layer, some amount of aluminum is dragged along with the oxide. The drosses are separated into three different classes (Totten and MacKenzie, 2003b): • White Dross: It is formed from the primary metallurgy of aluminum. The main characteristics that distinguish this class of dross from the others are the absence of salt fluxes and the fact that this dross is usually whitish or grayish or presents a light color. • Black Dross: It is produced in the secondary metallurgy of aluminum due to the use of salt fluxes. The produced dross presents dark colors. • Saltcake. It is the result of the aluminum recovered from white and black drosses. It is characterized by the high concentration of salt and by its darkish color. Schlesinger (2006) describes the choices available in dross treatment technology, and the factors determining whether one technology is favored over another. Totten and MacKenzie (2003b) describe the technology used to recover the aluminum content from each dross type. After melting, the molten metal is transferred to holding furnaces for further refining processes such as de-gassing, reduction of magnesium content (a process known as “demagging”) and for adding alloying elements. Also, its temperature is maintained or increased and its composition is adjusted for the casting process. Typically, the holding process is performed in reverberatory or crucible furnaces. From the holding furnaces, molten metal is either tapped to the casting unit to produce ingot or slabs, or into crucibles for liquid aluminum delivery. Figure 2.11 shows the aluminum secondary stages after scrap collecting. Chapter 2. Introduction 21 Figure 2.11. Aluminum secondary stages 2.6 Furnaces used in aluminum secondary production The key equipments for the metallurgical processing of aluminum scrap are furnaces. Remnant contaminations and foreign matter can be removed as soon as the metal reaches the liquid stage. Also, it is possible to adjust the composition and obtain the SCRAP MELTING HOLDING CASTING FINAL PRODUCT Numerical analysis of melting and holding furnaces in secondary aluminum production 22 desired alloy during the process (Schmitz, 2006). In this section, some details about melting and holding furnaces used in secondary aluminum are presented. This summary is organized based in the layouts of the works of Schlesinger (2006) and Schmitz (2006) and, where the data is partially gathered and more detailed information can be found about the topics involved. 2.6.1 Melting furnaces 2.6.1.1 Sweat furnace Some aluminum parts are so intricately attached to iron parts that they will not be separated by ordinary shredding. Examples include transmissions, cylinder heads, and manifolds. These items are known as high-irony scrap because of the extremely high levels of iron (50% or more at times). Scrap of this type has too much aluminum to be classified as ferrous scrap but too much iron to be remelted by secondary smelters. To separate these components, it is often used the sweat furnaces. Here, the high-irony scrap fed to the furnace is heated to a temperature just above the melting point of aluminum. At this temperature, the aluminum slowly melts away (hence the term sweating), leaving the higher-melting-point iron behind. The liquid aluminum drains from the bottom of the furnace and is cast in the form of sows or pigs. The product is often known as sweated pig and is sold to secondary smelters, where it is remelted and mixed with other scrap. Figure 2.12 shows large-scale rotary sweat furnace. Chapter 2. Introduction 23 Figure 2.12. Large-scale rotary sweat furnace (Schlesinger, 2006) 2.6.1.2 Wet-hearth The classic single chamber reverberatory furnace is called “wet-hearth”. In this, scrap is simply dumped or loaded into the melting chamber, the furnace opening is closed, and process begins. When the molten metal reaches the desired temperature, it is either pumped out or tapped from a hole in the bottom. Burners are mounted at the opposite end of the furnace from the charge well. A pool of molten metal in the furnace bottom after tapping is conserved to make melting easier of the next charge and to reduce damage to the bottom refractories from the shock of the scrap being dumped in. The most severe limitation of this furnace is the problem of charging through a relatively small opening, even though new furnace designs have incorporated wider doors, charging furnaces this way is slow. The most advanced design of wet-hearth furnace includes side burners and a removable top. Other limitations of wet-hearth furnaces are the poor thermal efficiency, poor heat transfer to the charge, low melting rates, high melt loss rates, especially for smaller scrap, difficulty in sealing the furnace and contamination from metallic impurities in the scrap. As a result, wet-hearth furnaces are best suited for melting good-quality scrap, such as sows from sweat furnaces, large Numerical analysis of melting and holding furnaces in secondary aluminum production 24 castings, and other bulky uncontaminated scrap. Figure 2.13 shows a generic scheme of reverberatory wet-hearth melting furnace. Figure 2.13. Generic reverberatory wet-hearth melting furnace (Schlesinger, 2006) 2.6.1.3 Dry-hearth Dry-hearth furnace features a sloping hearth, onto which solid scrap is placed for initial heating. As the metal melts, it drains down the hearth into the bath, leaving other metallic materials behind. Figure 2.14 shows a sketch of a typical dry-hearth furnace. The scrap also dries during the heating process, reducing the possibility of explosions and reducing the potential for melt loss from interaction between the metal and water vapor. Also, convective flames are used in the dry hearth area to maximize heat transfer to the solid scrap; flat luminous flames work better to heat the molten metal. Toploading dry-hearth furnaces are widely used to maximize capacity. As a result, dryhearth furnaces are the most popular approach for melting large or bulky scrap. Chapter 2. Introduction 25 Figure 2.14. Sketch of dry-hearth melting furnace-Adapted from StrikoMelter (2013) 2.6.1.4 Stack melter An improvement of the dry-hearth furnace is the stack melter shown in Figure 2.15. As the heated scrap descends to the sloping hearth, additional burners melt it, causing it to flow into the molten bath. This in turn allows more scrap to descend to the hearth, creating a semicontinuous melting operation. Flue stack Metal bath Dry hearth area Burner Level detector Numerical analysis of melting and holding furnaces in secondary aluminum production 26 Figure 2.15. Sketch of stack melter (Schlesinger, 2006) Stack melting has higher efficiency compared with traditional wetor dry-hearth melting. The high preheating of the scrap by the exhaust gas also reduces melting time on the hearth, improving furnace productivity. Stack melting is not suitable for very large scrap, but a stack can be combined with a dry hearth to accommodate a range of charge materials. These advantages often justify the additional investment required for a stack melter. The main disadvantage is controllability; scrap descends as quickly as it melts, which makes slowing down the melting rate difficult. 2.6.1.5 Tower melter The pressure of the scrap on the stack limits the depth to which it can be stacked, and this in turn limits the time that it can be preheated. The most advanced design of single chamber furnaces is the tower melter; the tower through which exhaust gas flows consists of several chambers separated by cast iron bars. Scrap is introduced into the top chamber while melting is completed in the furnace hearth below. When metal is tapped from the furnace, the bars on each chamber are sequentially released, and the scrap falls into the next chamber. The design allows a greater amount of scrap to be held in Chapter 2. Introduction 27 the column, improving heat recovery and ultimately furnace efficiency. However, tower melters have higher capital costs than other furnaces, and the number of moving parts is a potential maintenance problem. 2.6.1.6 Sidewell furnace The sidewell furnace avoids the direct interaction between combustion gases and solid scrap, which increased melt loss and dross generation. Instead, only the molten metal in the clean chamber is heated. The superheated molten metal flows underneath a baffle and contacts solid scrap charged to the side well, heating and ultimately melting it. When the charge is melted, the molten metal is then reheated to pouring temperature and tapped, and the process is repeated. Sidewell furnaces are an effective way to melt light scrap such as UBCs, but fuel efficiencies are poor due no preheating of scrap is provided, a bigger problem has been the slow kinetics of melting limited by the rate at which metal can flow under the baffle to contact the scrap in the well. Even though the sidewell furnace prevents direct exposure of the scrap to combustion flames, the finely divided material oxidizes sufficiently during heating to generate a significant amount of dross. Figure 2.16 shows a sketch of a simple sidewell furnace. Figure 2.16. Sketch of sidewell furnace (Schlesinger, 2006) Several methods have been developed to submerge the pieces of scrap in the molten metal in the sidewell while they melted, which would minimize oxidization of the scrap Numerical analysis of melting and holding furnaces in secondary aluminum production 28 and eliminate the need for fluxing. An example is that presented in Figure 2.17; here a mechanical pump is used to pump superheated molten metal into a vortex chamber. Figure 2.17. Sketch of sidewell furnace with scrap submergence system and mechanical pump (StrikoMelter, 2013) 2.6.1.7 Rotary furnace For highly oxidized scrap or with low thickness, the use of flux during melting is a requirement. Separating the resulting salt slag from the metal is difficult without sufficient agitation. The most used furnaces for this kind of applications are the rotary furnaces. They are longs sloping tubes, tilted back for charging and firing and tilted forward for slag and molten metal discharge. Typically, these furnaces have the capacity to process 1-10 metric tons of dross or scrap per cycle and burn fuel as the energy source. The salt fluxes that are composed of NaCl and KCl mixtures, should have the following characteristics: melting point below 720ºC; low viscosity; easily detachable from the liquid bath; must not react with the metal; must not add impurities into the metal; must not be hygroscopic; low vapor pressure; low cost; and low treatment cost (Totten and MacKenzie, 2003b, Zhou et al., 2006). When the contents have reached the desired temperature, the furnace is tilted and the metal and salt slag are poured off. Rotation of the furnace is slow during the early stages Chapter 2. Introduction 35 Non-transferred arc torches are typically used in applications that rely on the formation of a plasma jet with moderate to very high velocity and, its use as a heat source, hightemperature processing medium, or source of specific reactive species, such as plasma spraying and powder synthesis. Transferred arc torches are mostly used in applications that maximize the utilization of heat from the plasma, such as plasma cutting, welding, and metallurgy (Trelles et al., 2009). By this reasons, currently the melting furnaces heated by plasma torches are in transferred arc configurations. Recently, the European Union through the EDEFU project (EDEFU, 2010) of the seventh framework programme, has promoted the development of new prototypes of melting furnaces that can use thermal plasmas as a heating means. However, this technology is still developing and there are not widely used commercial devices. In plasma torch melting furnaces for aluminum, inert gas as argon or nitrogen must be employed in order to prevent the oxidation of the load. The main advantages of this process in comparison with conventional rotary furnace are that the final dross has no salt content, better heat transfer, low times of melting and less amount of generated gases. On the other hand, the main shortcomings are the use of electric energy, the process needs trained people to operate and maintain the system, and the large cooling requirements that can represent a considerable loss of energy. Figure 2.23 shows a scheme of a transferred arc furnace. Numerical analysis of melting and holding furnaces in secondary aluminum production 36 Figure 2.23. Schematic arrangement of transferred arc furnace; Adapted from Jones et al. (2001) 2.6.2 Holding furnaces In smaller melting facilities, molten metal tapped from a melting furnace is usually transferred to a ladle prior to casting. Larger facilities often employ a holding furnace, where the temperature and composition of the metal can be adjusted. This allows the melting furnace to be used mostly for its intended purpose of increasing productivity. The use of a holding furnace also makes it possible to operate the melting furnace under conditions that most favor heating of solid scrap (reducing condition, convective heat transfer), improving the efficiency and melting rate. 2.6.2.1 Reverberatory furnaces Many different holding furnaces are available; the most widely used are the reverberatory furnaces with both gas-fired and electric furnaces. Figure 2.24 shows a commonly used reverberatory furnace operating under luminous flame conditions. The main advantage is their low cost, but high oxidation and melt losses presented prevent the intensive use in secondary production. Chapter 2. Introduction 37 Figure 2.24. Reverberatory furnace heated by direct combustion flame (StrikoMelter, 2013) To prevent the direct contact of the combustion gases and the load, the radiant tube furnaces are widely used. Figure 2.25 presents a furnace using this principle. In this furnace the products of combustion are passed through ceramic tubes mounted in the furnace; as the tubes heat up, they radiate energy to the molten metal below. Electrical resistance elements mounted inside the radiant tubes have the same effect. Figure 2.25. Radiant tube in reverberatory furnace (Khanthal, 2011) 2.6.2.2 Crucible furnaces Crucible furnaces also are used for holding applications especially in small capacities. They are used as holding furnaces in sand or die casting plants; they are ideally suited for metal treatment. For operation, the crucible is filled with liquid metal followed by the Numerical analysis of melting and holding furnaces in secondary aluminum production 38 required metal treatment and temperature adjustment. After thorough metal treatment, an excellent metal quality is obtained. 2.6.2.3 Electrical furnaces Generally, the electrical furnaces are used in applications of smaller size than the crucible furnaces. Electric resistance furnaces feature a wire element looped throughout the sides of the furnace. The elements in most resistance furnaces are made of the nickel–chromium alloy nichrome or aluminum–chromium alloy aluchrom. The element is often installed as an open-coil element supported on high-purity ceramic tubes; elements can also be obtained semiembedded in refractory panels, which are simply swapped out when the element fails. Other option is to install the resistances in the roof. Figure 2.26 shows an electrical furnace heated from lateral walls and another heated from the roof. a) b) Figure 2.26. Electrical holding furnaces: a) heated from lateral walls (Nabertherm, 2013) b) heated from the roof (SPX, 2013) A special design is the immersed electric furnace; Figure 2.27 shows this kind of application where high efficiency is obtained. Chapter 2. Introduction 39 Figure 2.27. Electric immersion holding furnace (SPX, 2013) 2.6.2.4 Induction furnaces Induction furnaces are used also in the holding stage. Channel furnaces are used more often as holding furnaces, rather than as melting units, and typically for larger operations. In spite of some limitations, from the mechanical and operational point of view the channel induction furnace is the ideal holding furnace. There is no contact with combustion products nor with ambient air. The eddy currents in the inductors cause a through stirring effect which creates a good mixture of all alloying components with the result of a homogeneous melt. Also very good temperature distribution is obtained over the entire bath which is easy to maintain during casting. Their efficiency is typically 70 to 75%, compared with the 50 to 55% efficiencies of coreless furnaces. A second advantage is the reduced agitation in channel furnaces. However, channel furnaces are more expensive per unit melting capacity than coreless units (and much more expensive than fossil-fuel furnaces). 2.7 Motivation Aluminum is a metal used in a wide variety of applications through all sectors due to their good properties. The secondary aluminum production is a key factor in the global market of this metal. Long product lifetimes and growing markets mean that the future demand will continue to be met from both primary and recycled sources. Numerical analysis of melting and holding furnaces in secondary aluminum production 40 The transformation of scrap into recycled aluminum alloys requires approximately only 5% of the energy input needed to produce primary ingot from bauxite. In secondary aluminum production, energy is consumed throughout the refining process, but the key equipments for the metallurgical processing are furnaces. The aluminum secondary industry focuses its efforts in develop a method for recycling the metal that be economically competitive and satisfies the requirements of the market. Several furnace types are developed for the different applications and conditions. Nevertheless, traditional design of melting and holding furnaces has been based on semi-empirical methods due to the complexity of the phenomena involved, which has limited the use of computational techniques based on first principles physics. In addition, the inherent difficulty and shortcomings of experimental measurements do not allow a comprehensive description of the operation. Accordingly, a great deal of information has been missing in these kinds of devices. Some companies have developed some simplified numerical models of their units. As in the case of Kanthal; which simulate their holding furnace heated by radiant tubes in a simplified 2D domain (Figure 2.28). Chapter 2. Introduction 41 Figure 2.28. 2D numerical simulation of a industrial holding furnace heated by radiant tubes (Khanthal, 2011) Nevertheless, the use of numerical techniques is not a common practice in the development process of industrial furnaces. In scientific literature, only few works has been published concerning to numerical simulations in melting and holding furnaces. In Numerical analysis of melting and holding furnaces in secondary aluminum production 42 melting applications, most works about numerical simulations did not consider the molten load in the furnace and the interactions between heating space and load; others consider the solid–liquid region of the load as a conducting solid with constant thermal properties (i.e. the convection effects are not considered) and neglect the heat losses from the walls. In holding applications, the works that consider the interaction with the molten load have been developed under steady state assumption, others simulations also neglect the conjugated problem, the radiation losses, the three dimensional geometries or the convection effects. Descriptions of the current state of the simulations for melting and holding furnaces will be presented in detail in chapters 4 and 5, respectively; but according to the literature reviews of scientific papers and industrial devices, it is possible to point out that comprehensive simulations with realistic models are still undeveloped for these kinds of devices. 43 3. Models used in numerical simulations of industrial furnaces The operation of furnaces relies on the relationship between fluid flow and heat transfer. The laws governing these processes can be represented by a set of partial differential equations. Analytical solution for each particular problem is not available but it is possible to obtain numerical solutions that resemble the exact solutions with a good level of accuracy. Furthermore, numerical simulations often become the most economical and fastest approaches to provide a broad understanding of the practical processes. What a numerical calculation does is essentially to simultaneously solve the conservation equations of mass, momentum and energy in gases, liquids and solid phases. This is done numerically by (a) adopting an adequate discretization of the geometrical domain and (b) transforming the original partial differential equations into approximate, algebraic counterparts. For present modeling purposes, multi-phase modeling is required for including the interaction between the different domains in the furnaces, i.e. load (liquid-mushy-solid), refractories walls (solid) and the air in cavities (gas). This kind of numerical analysis can be accomplished by either finite volume method (FVM), finite element method (FVM) or boundary element method (BEM). The success of FEM and BEM lies in their ability to handle complex geometries, but their drawback is the high time consuming in terms of computing and programming. Because of their good performance solving thermal-fluid problems and their simplicity in formulation and programming, most commercial codes of computational fluid dynamics (CFD) implement their algorithms with the FVM. Values of thermal variables are Numerical analysis of melting and holding furnaces in secondary aluminum production 44 obtained at a large but finite number of discrete points, providing an adequate approximation to the corresponding fields and fluxes. Several commercial codes have been developed that solve numerically the constitutive equations using the finite difference approximation. In this thesis, the commercial CFD code, FLUENT software version 13.0.0 (ANSYS, 2012) has been used to simulate numerically the melting and holding furnaces. In the numerical simulations of the furnaces presented in this thesis, the main phenomena considered are the mass, momentum and energy conservation; flows induced by natural convection due to variation of density as function of temperature; conjugated problems and interactions between gas-liquid-solid zones; radiation heat transfer in cavities and phase change. The flow is governed by the Navier-Stokes equations, which describe the principle of mass and momentum conservation; an additional equation for energy conservation is solved in problems involving heat transfer. These basic equations are commonly presented in works of numerical modeling of flows (Pope, 2000, Ferziger and Perić, 2002). Variation of density with temperature increases the non-linearity of the equations. It may be possible to ignore the density variations in all terms other than body force in the vertical momentum equation. This method is called the Boussinesq approximation and it allows the equations to be solved by methods that are essentially identical to those used for incompressible flow, but this approach is valid if the density variations are small (Ferziger and Perić, 2002), which is not the present case; therefore, the Boussinesq approximation is not taken for this work. The sequential solution method for a density variable with temperature is accomplished in the same way as the energy equation; i.e. the fluid properties are calculated after each iteration and treated as known during the next iteration. The volume expansion of liquids in gases is typically solved with the method of "Volume of Fluid" (VOF), but this technique is difficult to implement in conjugated problems, so that most commercial CFD codes avoid it. Since the interaction between the refractory walls and the load is a major consideration for the melting and Chapter 3. Models used in numerical simulations of industrial furnaces 51 range of T2,L - T2,E. The results of the cooling process so far are grains of solid α (Cα,max % B, 100Cα,max % A) with patches of layered α + β . But even though the alloy is solid the process still hasn't finished. As the material cools to room temperature the solid α can hold on to less and less substance B, and the same process happens with the solid β . This is shown by the curved, dashed lines beneath the solidus line. The phase change presented for the left side of the eutectic point E (i.e. the solid α and mushy zone α + L) is also valid for the right side of E (i.e. the solid β and mushy zone β + L). Finally, a particular concentration of the alloy is the eutectic composition (CE), since the liquid cools down to the point marked E at a temperature TE and stays there. At some points in the liquid grains of solid α start to grow and at others, grains of solid β are created. The entire process happens at the fixed temperature TE. Once the alloy is fully solid the temperature can begin to drop again. 3.1.2 Phase diagrams of alloys -towards modeling Figure 3.4 shows the evolution of the liquid fraction with temperature for the binary eutectic alloy. On the one hand, isothermal curves represent the solid-liquid phase change of the two pure metals and the alloy of eutectic composition, where the latent heat is evolved at a unique temperature; Tmelt and TE are the melting and the eutectic temperatures of the material, respectively. On the other hand, the solid-liquid phase change process for alloys is performed in a temperature range, between the solidus temperature (TS) and liquidus temperature (TL), given by the solidus and liquidus lines, respectively. In this case, the liquid fraction is computed from the inverse lever rule presented in the previous section. This results in several relations between the liquid fraction and temperature. Voller and Swaminathan (1991), Swaminathan and Voller (1992) and Swaminathan and Voller (1993) have developed models to implement cases of potential relations and combinations of eutectic and linear relations, but in practical terms and with the purpose to reduce the computational cost, the relation between the liquid fraction and temperature for mixture substances is simplified typically as a linear Numerical analysis of melting and holding furnaces in secondary aluminum production 52 function (Hu and Argyropoulos, 1996). Currently, only this relation is included in commercial codes (ANSYS, 2012, CD-ADAPCO, 2004). Figure 3.4. Liquid fraction evolution with temperature for a binary eutectic alloy 100% A Composition 0% A 0% B 100% B Temperature Liquid fraction Temperature 0 1 T S T l Liquid fraction Temperature 0 1 T melt Liquid fraction Temperature 0 1 T melt Liquid fraction Temperature 0 1 T E Solid solution (SS): α + β Eutectic composition Solid β Solid α Liquid (L) Liquidus line Solidus line α + L β + L Liquid fraction Temperature 0 1 T S T l Real Simplified Real Simplified E Chapter 3. Models used in numerical simulations of industrial furnaces 53 3.2 Numerical models for phase change problems In the general case the phase change of the load material depends on time and space and originates a phase-separating boundary moving within the medium during the process. Transport properties vary considerably between phases, resulting in totally different rates of energy, mass and momentum transfer from one phase to the other. The position of this moving boundary cannot be identified in advance, but has to be determined as an essential constituent of the solution. The term “moving boundary problems” is associated with time-dependent boundary problems, where the position of the moving boundary must be determined as a function of time and space. Moving boundary problems are also referred to as Stefan problems (Hu and Argyropoulos, 1996). Phase change methods are divided into three main categories: analytical, variable grid and fixed grid methods. The last two approaches make use of numerical simulations. 3.2.1 Analytical methods The simplified analytical methods offer an exact solution and are mathematically elegant. However due to their limitations, analytical solutions are mainly used in 1D cases of an infinite or semi-infinite region, with simple boundary conditions and constant thermal properties. These evidently entail important simplifications, related to geometry and physical properties of the distinct phases, that prevent their use in almost all practical problems of solidification and melting, but the analytical solutions developed serve as a cornerstone of this discipline and are still used today as standard references to validate the numerical models. In order to appreciate the complexity of the fundamental physics and understand the method adopted in this work, the theory of liquid-solid phase change for unidirectional problems, in a pure substance without liquid movement is presented (Alexiades and Solomon, 1993, Hu and Argyropoulos, 1996, Poulikakos, 1994). Numerical analysis of melting and holding furnaces in secondary aluminum production 54 Focusing on the melting or freezing front, Figure 3.5 shows such a front separating a solid from a liquid region, the horizontal dashed lines represent an infinitely thin control volume surrounding this front. Figure 3.5. Solidification from a plane cold surface-Adapted from Poulikakos (1994) It is assumed that freezing takes place in the liquid because of the presence of cold boundary. The study of a melting process is analogous. As the freezing progresses, the interface moves upward (in the positive direction) n the stationary medium. It is easier to model the heat transfer in the foregoing freezing process if, instead, it is assumed that the interface and the control volume surrounding it are stationary and that the medium moves downward through the interface. To this end, liquid of density ρ L and velocity uL enters the upper side of the control volume and solid of density ρ S and velocity uS exists the lower side of the control volume (in this case assuming ρ S > ρ L). Mass conservation: 𝜌𝐿𝑢𝐿𝐴𝑉=𝜌𝑆𝑢𝑆𝐴𝑉 (3.1) where AV is the large area of each side of the control volume. Solid, TS(x), ρ s Interface x ∞ Cold boundary Velocity, us Velocity, uL Liquid, T L (x), ρ L ∞ "Fixed" control volume x SL Chapter 3. Models used in numerical simulations of industrial furnaces 55 An energy balance on the control volume yields: 𝑄𝑖𝑛,𝑐𝑜𝑛𝑑+𝑄𝑖𝑛 𝑐𝑜𝑛𝑣−𝑄𝑜𝑢𝑡,𝑐𝑜𝑛𝑑−𝑄𝑜𝑢𝑡 𝑐𝑜𝑛𝑣 = 0 (3.2) where Qin,cond is the heat transferred into the control volume by conduction, Qin,conv is the energy transferred into the control volume by convection (since the medium is moving through the control volume), and Qin,cond and Qin,conv are the analogous quantities exiting the control volume. Fourier's law accounting for the fact that heat diffuses in the negative x-direction states that: 𝑄𝑖𝑛,𝑐𝑜𝑛𝑑 =𝑘𝐿𝐴𝑉�𝜕𝑇𝐿 𝜕𝑥�𝑥=𝑥𝑆𝐿 (3.3) 𝑄𝑜𝑢𝑡,𝑐𝑜𝑛𝑑 =𝑘𝑆𝐴𝑉�𝜕𝑇𝑆 𝜕𝑥�𝑥=𝑥𝑆𝐿 (3.4) In addition, the energy convected In and out of the control volume is: 𝑄𝑖𝑛,𝑐𝑜𝑛𝑣 =𝜌𝐿𝑢𝐿𝐴𝑉ℎ𝐿 (3.5) 𝑄𝑜𝑢𝑡,𝑐𝑜𝑛𝑣 =𝜌𝑆𝑢𝑆𝐴𝑉ℎ𝑆 (3.6) where hL and hS are the specific enthalpies at the liquid and solid sides of the control volume. Combining equations (3.2) to (3.6) yields: 𝑘𝐿�𝜕𝑇𝐿 𝜕𝑥�𝑥=𝑥𝑆𝐿 −𝑘𝑆�𝜕𝑇𝑆 𝜕𝑥�𝑥=𝑥𝑆𝐿 +𝜌𝐿𝑢𝐿ℎ𝐿−𝜌𝑆𝑢𝑆ℎ𝑆= 0 (3.7) Reconizing that the latent heat of fusion (hSL) is given by hSL = hL - hS and making use of the equation (3.1), equation (3.7) yields: 𝑘𝐿�𝜕𝑇𝐿 𝜕𝑥�𝑥=𝑥𝑆𝐿 −𝑘𝑆�𝜕𝑇𝑆 𝜕𝑥�𝑥=𝑥𝑆𝐿 +𝜌𝑆𝑢𝑆ℎ𝑆𝐿 = 0 (3.8) or 𝑘𝐿�𝜕𝑇𝐿 𝜕𝑥�𝑥=𝑥𝑆𝐿 −𝑘𝑆�𝜕𝑇𝑆 𝜕𝑥�𝑥=𝑥𝑆𝐿 +𝜌𝑆ℎ𝑆𝐿𝑑𝑥𝑆𝐿 𝑑𝑡 = 0 (3.9) Numerical analysis of melting and holding furnaces in secondary aluminum production 56 Equation (3.9) is called the Stefan condition (Hu and Argyropoulos, 1996). It is a direct result of an energy balance at the solidification front and provides a needed matching condition for the solution of the temperature field in the system. It is worth noting that this formulation holds for the case of radial conduction in cylindrical spherical coordinates if the Cartesian coordinate, x, is simply replaced by the radial coordinate, r, of a cylindrical or spherical system of coordinates. Examples of the solution of equation (3.9), in one-dimensional transient phase change problems for Cartesian, cylindrical and spherical coordinates are presented by Hu and Argyropoulos (1996) and Poulikakos (1994). 3.2.2 Variable-grid methods Most widespread variable-grid methods use dynamical grids, where some nodes move with the phase change boundary and others are dynamically reconstructed at every time step. Therefore, the use of non-structured grid is mandatory. Transport equations are solved for each phase separately. This is the most direct approximation to the underlying physics, having the inherent shortcoming of a large computational expense related to grid calculations, which adds up to (and usually is larger than) the approximation and resolution of transport equations themselves. The fixed grid methods can be subdivided into the following subgroups: 3.2.2.1 Unstructured deforming grids In this method the initial grid (non-transformed) is deformed in a new unstructured one. The number of spatial intervals is kept constant but their shape is adjusted in such a manner that the moving boundary lies on a particular grid point. The position of the moving boundary is updated at each step by the Stefan condition on the moving boundary (Hu and Argyropoulos, 1996). Calculations at every time-step are performed as follows: first, a new phase change interface locations is evaluated from the Stefan conditions (quasi-stationary approach); secondly, a new grid is generated; and thirdly, the values of variables are interpolated on the new grid. An example of results from an implementation of this method in a typical problem of phase change is shown in Figure 3.6. Chapter 3. Models used in numerical simulations of industrial furnaces 57 t1 t2 Figure 3.6. Application of the unstructured deforming grid method-Adapted from Mencinger (2004): streamlines (up); dimensionless temperature (center); deforming grid (down) Numerical analysis of melting and holding furnaces in secondary aluminum production 58 Voller (1997) and Mencinger (2004) present details of the mathematical treatment for this method. 3.2.2.2 Domain transforming techniques This subgroup refers to the methods which are based on a transformation of the considered irregular physical domain into a rectangular one introducing new independent variables. The essential feature of this method is the fixing, in space and time, of the liquid-solid interface via a suitable choice of new space coordinates. The movement of the solid-liquid interface and of the mesh points in the original region appears only as changes in the x and y, at the corresponding fixed points at each time step. The nature of the relationship between the fixed and physical grids is illustrated in Figure 3.7. Figure 3.7. Relationship between the physical and transformed grids-Adapted from Lacroix and Voller (1990) REAL SPACE Phase front Grid line Time t2 Time t1 Time t3 TRANSFORMED SPACE Chapter 3. Models used in numerical simulations of industrial furnaces 59 The major advantage of this method is that the governing flow and energy equations are solved on a fixed rectangular and uniformly spaced computational grid, with no loss of accuracy in discretization near curved boundaries. The simplicity in the numerical grid, however, comes at the expense of more complex governing equations. The method uses the coordinate transformations to map the irregular physical domain to rectangular computational space. It calculates the new interface position and the corresponding coordinate transformation after achieving stationary state. However, this quasistationary assumption is limited to cases with relatively slow interface movement. Also, a stationary state may not exist even with fixed interface position (Mencinger, 2004). The key step in using this approach is the grid generation, that is, the relationship between the fixed and physical grids at any point in time. Although the same differential equations can be obtained in previous and current subgroup, the discretizations of these are different (Samarskii et al., 1993). The mathematical model for this method is explained in detail by Samarskii et al. (1993) and Lacroix and Voller (1990). 3.2.2.3 Local adaptation methods Finally, the last subgroup encompasses the local adaptation methods. Here, the phase change interface is determined explicitly and governing equations are accurately approximated near the interface points of a fixed grid. The essence of this approach is that smooth phase change interface is approximated by a polygonal line through the grid points (Samarskii et al., 1993). In this method the grid adapts to the solid–liquid interface, which is calculated from the heat flux balance and the grid quality is controlled with a local grid refinement method. This method becomes troublesome when the topology of the interface changes (merging or breaking), and the implementation in 3D problems is rather complicated. Also, the interface-tracking is not suitable for the cases where a phase change region appears (phase change in alloys) instead of a sharp interface characteristic of phase change of a pure metal (Mencinger, 2004). Numerical analysis of melting and holding furnaces in secondary aluminum production 60 3.2.2.4 Final comment about dynamical grid methods In phase change problems, since the phase front moves, the grid needs to be regenerated at every time step. There are a number of options for generating the grid, but this is a procedure that could prove to be expensive in computational terms. Particular emphasis must be placed on the fact that, in the general case, construction of the grid is a very important and complicated problem by itself. In fact, grid generation can require more computational resources than the solution of the transport equations themselves. 3.2.3 Fixed-grid methods In fixed-grid methods, a single equation is solved for the whole domain, made up of solid, mushy (for alloys) and liquid regions, instead of separated equations for each phase. The boundary is tracked implicitly over the entire region of a fixed domain. The most widely fixed grid methods used are the apparent capacity method, the source based method and the enthalpy method. Voller et al. (1990) review merits and demerits of these schemes, but a summary of each is presented in the next sections. 3.2.3.1 Apparent heat capacity methods In this method, the latent heat is accounted for by increasing the heat capacity of the material in the phase change temperature range. The major advantage of the method is that the final energy equation is similar in form to the standard heat conduction equation; therefore it can be easily discretized and numerically solved with welldeveloped algorithms. Hu and Argyropoulos (1996) and Voller and co-workers (Voller, 1997, Swaminathan and Voller, 1992, Swaminathan and Voller, 1993, Voller et al., 1990) present the procedure to calculate and discretize the apparent heat capacity method. The method has been extended to finite element formulation in a generally applicable approach to one and two dimensional problems, with both moving boundaries and temperature-dependent physical properties. Although the apparent heat capacity method is conceptually simple, the method does not perform well as compared with other methods (Hu and Argyropoulos, 1996, Voller et al., 1990). The reason for such a Chapter 3. Models used in numerical simulations of industrial furnaces 67 Thermal radiation is calculated by the so-called “surface-to-surface” (S2S) radiation model of FLUENT (ANSYS, 2012). This is a built-in implementation of the net radiation method (Mills, 1992) coupled to the diffusive term of surface energy balances. It relies on the numerical calculation of geometric view factors between pairs of surface elements, only dependent on discretization, and assumes diffuse-gray radiation, which is reasonable for the problem. Equations involved in the S2S model are presented in the theory guide of FLUENT (ANSYS, 2012). The basic theory is presented as follows: The net heat radiation of a surface k is computed from: 𝑞 𝑟𝑎𝑑,𝑘 =𝐴 𝑘 �𝐹 𝑘𝑗 �𝐽 𝑘 −𝐽 𝑗 � 𝑁 𝑗=1 (3.23) and 𝑞𝑟𝑎𝑑,𝑘=𝜀𝑘𝐴𝑘 1−𝜀𝑘(𝜎𝑇𝑘 4 −𝐽𝑘) (3.24) where εk is the emissivity of surface k, σ the Stefan-Boltzmann's constant, Ak is the area of surface k, Fkj is the view factor between surface k and surface j and J is the surface radiosity. In equations (3.23) and (3.24), the values of qrad,k, Tk and Jk are unknown. The net heat radiation is incorporated to the energy conservation in the surface, and it is taken into account for the balance with terms of conduction or convection for solid or fluid adjacent domains, respectively. These latest terms are solved numerically by the CFD code. Equations (3.23), (3.24) and energy conservation are solved simultaneously in an iterative procedure in order to obtain qrad,k, Tk and Jk. The method is also holds for transient state, since the mass of the surface is by definition very small, the radiation heat transfer is too fast and there is not accumulation. The view factor Fkj between two finite surfaces k and j is given by: Numerical analysis of melting and holding furnaces in secondary aluminum production 68 𝐹𝑘𝑗 =1 𝐴𝑘� � 𝑐𝑜𝑠𝜃 𝑘 𝑐𝑜𝑠𝜃 𝑗 𝜋𝑟2𝛿𝑘𝑗𝑑𝐴𝑘𝑑𝐴𝑗 𝐴𝑗 𝐴𝑘 (3.25) where δkj is determined by the visibility of dAj to dAk. δkj = 1 if dAj is visible to dAk and δkj = 0 otherwise. Rays are traced through the centers of every face to determine which surfaces are visible through that face. At each radiating face, rays are fired at discrete values of the polar and azimuthal angles. To cover the radiating hemisphere, polar angle is varied from to 0 to π /2 and azimuthal angle from 0 to 2 π . Each ray is then traced to determine the control volumes it intercepts as well as its length within each control volume. This information is then stored in the radiation file, which must be read in before the fluid flow calculations begin. The reciprocity relationship is also used: 𝐴𝑗𝐹𝑗𝑘 =𝐴𝑘𝐹𝑘𝑗 for 𝑗= 1,2,3, … , 𝑁 (3.26) The first step in the implementation of the S2S radiation model is to compute the view factors for the specific problem and grid. This process consumes high computational resources, but it is performed only once by each simulated domain. 69 4. Numerical simulation of an aluminum melting furnace In this chapter, simulations of a new aluminum melting furnace heated by a plasma torch are presented; these simulations reproduce an experimental test carried out in a real prototype. The aim is to calculate melting time, heat losses and temperature distributions in the aluminum load and refractory parts. Models used are 2D axisymmetric and take into account heat conduction in solid parts, convection in air and molten aluminum, interactions between gas-liquid-solid zones and radiation heat transfer. Several calculation strategies are tested concerning their computational economy and their accuracy in computing different key parameters. Results show that interactions gas-liquid-solid have an important effect. Firstly, a proper account of heat transfer and losses requires solving the conjugated problem comprising refractory walls and heated load. Secondly, thermal interaction with air cavities seems to determine the convective movement of the molten load and therefore inner-load temperature patterns and their time evolution. 4.1 State of the art in related numerical simulations 4.1.1 Melting furnaces In addition to phase change, several other complex physical phenomena occur in industrial furnaces that are difficult to model and couple within an unified simulation. Conjugate heat diffusion through solid and fluid volumes, movement of the molten load Numerical analysis of melting and holding furnaces in secondary aluminum production 70 and radiation heat transfer are some of them. Accordingly, works dealing with realistic, comprehensive simulations are rather scarce in the literature, so that a review is forcibly brief and encompasses very different applications and approximations. As direct antecedents of the work presented here, the following can be quoted: 4.1.1.1 Empirical studies of melting furnaces Furnace manufacturers test their devices in industrial conditions. But experimental data are often not available for public domain. In this sense, only a general perspective is known about the operation of furnaces in secondary aluminum production. The U.S. Department of Energy has sponsored an investigation to improve the energy efficiency in reverberatory furnaces for aluminum melting. As a result, an experimental reverberatory furnace has been constructed (Das, 2008, Das, 2007, King et al., 2005b); some general parameters have been obtained (King et al., 2005a, Belt et al., 2006, King et al., 2005b, Li et al., 2003, Golchert et al., 2005), e.g. the influence of power input, burner loading and combustion space volume on melting efficiency; scaling laws (Penmetsa et al., 2005) and simplified models based in thermodynamic procedures to estimate the performance (Li et al., 2006, Li et al., 2005). Concerning rotary furnaces, Zhang et al. (2008) present an experimental study on steel scrap melting in a continuous process furnace. They also developed a simplified thermal model to evaluate commercial viability of industrial-scale units. All these empirical works were developed for specific furnace types; in addition, the studies were based on combustion heating, which makes difficult the use of the results in the development of new technologies. 4.1.1.2 Aluminum melting furnaces Wang et al. (2013) present a numerical simulation to estimate the melting process of a regenerative aluminum melting furnace; the model consists in a combination of a selfdeveloped melting model and a CFD commercial code. Different burner factors such as the location, orientation and inlet conditions are investigated in order to estimate their effects on the melting process. Inside the furnace, the CFD solution of the combustion is coupled with the melting sub-model. The solid–liquid region (load) is treated as a Chapter 4. Numerical simulation of an aluminum melting furnace 71 conducting solid with constant thermal properties. In this simulation, the heat losses by the walls are neglected. Wang et al. (2012) present a study of the optimization of parameters for a regenerative aluminum melting furnace using the Taguchi approach. The effects of the burner location and operational conditions are analyzed through numerical CFD experiments in an orthogonal array. These simulations are the base for the work of Wang et al. (2013) presented above. Therefore, the same simplifications are taken. In this case, the main objectives are to reduce energy consumption and pollutant emission, instead of improve the melting performance. A similar approach is presented by Zhou et al. (2006), who simulate the melting of aluminum scrap in a rotary furnace under a salt layer. In this work, the combustion is also simulated with a commercial CFD code and the solution is coupled to a melting model, the treatment for the load is also as a conductive solid with constant thermal properties, averaged in this case with the total mass of scrap and salt flux. The main target of this study is to predict the melting rate and energy distribution and their relation with types and properties of the scrap. In this approach the conjugated problem is taken into account and the oxidation of the load is estimated with a self-developed sub-model. The rotation of the furnace is not included in the model. The main drawback is that the overall simulation must be adjusted to empirical data, that are difficult to obtain a priori. Wu and Lacroix (1995) applied a two-dimensional time-dependent heat transfer model for the melting of scrap metal in a circular furnace without considering radiation heat transfer. The phase change problem is treated with the enthalpy method in an assumed porosity domain. The model is limited to the prediction of the temperature distribution in the axial direction in a non conjugated domain. 4.1.1.3 Electric arc furnaces The electric arc furnaces (EAF) are typically used in secondary production of steel, but they share several features with the melting furnace analyzed in this thesis. The design of these devices, as in other furnaces types, is based in semi-empirical models as those presented by Logar and Škrjanc (2012a), that develop an industrial EAF simulator, based on semi-empirical correlations for the electrical and hydraulic model (Logar et al., 2011), heat and mass transfer (Logar et al., 2012a), thermo-chemistry (Logar et al., 2012b) and Numerical analysis of melting and holding furnaces in secondary aluminum production 72 radiative heat transfer (Logar and Škrjanc, 2012b). This kind of models can be used to estimate the general parameters of the furnace designed, but don't offer details of the thermal behavior for a specific device. Arzpeyma et al. (2013) simulate an eccentric bottom tapping EAF to investigate the influence of electromagnetic stirring on melting of a single piece of scrap. Only the load domain is considered in this study; other components like the electrical electrodes, furnace walls or air in cavity are considered indirectly through different boundary conditions. The piece of scrap is a little cube located on the bottom of the furnace and the remaining charge is considered in liquid state. The phase change process is modeled by the enthalpy method. The heat transfer and fluid flow in the melt for both conditions with and without electromagnetic stirring are studied. The results show that electromagnetic stirring leads to a considerable reduced melting time; this conclusion is justified by the increase of the convection inside the molten load, which is predicted for the same problem by ABB Metallurgy (Widlund et al., 2011) in an EAF without melting. González et al. (2010b) develop a Lagrangian model of melting particles to describe the melting kinetics of metallic particles in an industrial EAF. This model must be coupled to a CFD solution that predicts the fluid flow previously (González et al., 2010a). In these works, the Boussinesq approximation is invoked to model the convection effects, and again, only the load domain is considered. 4.1.1.4 Induction furnaces Simulations of induction furnaces have increased in the last years with the development of multi-physics codes. Even though this kind of simulations requires a coupling between the flow model and Maxwell equations, the induction furnaces present some advantages in computational terms compared with other used technologies: e.g. low temperatures in the whole furnace, the movement of the molten load is mainly driven by the Lorentz force and the geometries can be simplified to 2D axisymmetrical. Nevertheless, so far only a few works include an integration of the magnetohydrodynamic problem with the phase change energy balance and fluid flow. Bermudez and co-workers (Bermúdez et al., 2007b, Bermúdez et al., 2010, Bermúdez et al., 2009, Bermúdez et al., 2007a, Bermúdez et al., 2011) have developed one of the most comprehensive. The enthalpy method is Chapter 4. Numerical simulation of an aluminum melting furnace 73 used to consider the phase change of the load. The solutions have been implemented in 2D axisymmetrical domains with the finite element method (FEM) (Bermúdez et al., 2007b, Bermúdez et al., 2010) and with a combination between boundary element method (BEM) and FEM method (Bermúdez et al., 2009, Bermúdez et al., 2007a, Bermúdez et al., 2011). The latest methodology avoids the numerical solution of the air around the coils. 4.1.1.5 Electro slag remelting process Other melting process whose modeling involves the coupling of the Maxwell and flow equations is the electro-slag remelting (ESR) process. This is used in aluminum secondary production to produce large ingots of higher quality than the original material, by controlled solidification and chemical refinement. Usually, an ESR furnace consists of one electrode submerged in a poorly conducting mix, relatively conductive slag, and a highly conductive crucible. The passage of current through the electrode supplies electrical energy to the slag for metallurgical processes. At steady state the heat transfer mechanisms are a combination of thermal conduction together with forced and free convection. The body forces causing the motion are a combination of electromagnetic (dominant in this case) and thermal buoyancy (Ahn et al., 2009, Prasad and Rao, 2000). One of the main complications in the simulation of these processes, is that material properties are a strong function of temperature, which greatly influences the electrical, magnetic, temperature, and velocity fields. Furthermore, a major aim of the process is to separate the contaminants from the metal of high quality by density difference. Therefore, in many cases an additional multiphase model must be coupled. Simulations in this subject are performed with simplified geometries in 2D axisymmetric, without considering any external element to the load, like walls, electrodes or air in the cavity of the furnace (Kelkar et al., 2005, Patel and Kelkar, 2009, Rückert and Pfeifer, 2009, Rückert and Pfeifer, 2007, Weber et al., 2009, Chang and Li, 2008, Kharicha et al., 2005). Currently, three dimensional models are even more simplified cases; for instance, Xihai et al. (2011) and Li et al. (2012) implement 3D models of ESR processes for the heating of the load, but without considering the melting or the movement of the fused phase. Recently Kharicha et al. (2011) simulated the 3D movement of a molten load in an ESR Numerical analysis of melting and holding furnaces in secondary aluminum production 74 process and found three-dimensional flow effects for large geometries. Unfortunately the current computational resources force the use of 2D approaches in melting analysis. 4.1.1.6 Glass melting furnaces In the glass production, works of numerical simulations can be found for melting furnaces. This is a most complicated problem in terms of radiation calculation; because it is necessary take into account the volumetric radiation in a participating media, since in general, the surfaces are not opaque and the reflection is not diffusive. Choudhary et al. (2010) present a review of the principles and practices involved in mathematical modeling of batch melting, electric heating of glass melt, convection due to bubbling, combustion, turbulence, radiation, and viscoelasticity for the industrial-scale glass melting furnaces. Abbassi and Khoshmanesh (2008) undertake a three dimensional steady state study of a gas-fired, regenerative, side-port glass melting furnace. The melting process of the solid load (batch blanket), the natural convection of the resulting molten glass and the turbulence and chemical reactions of the combustion space are all simulated. The glass load and the combustion space are simulated separately. Despite the load reaches temperatures above 1073 K, this comprehensive approach doesn't consider the radiation in the molten bath and the conjugated problem, neglecting the heat losses through the walls of the furnace. Recently, Díaz et al. (2013) performed CFD calculations in steady state condition to define the effect of the burner configuration in a day tank glass furnace (tank glass melting furnace of periodic operation, is used when the daily demand may not be enough to use a continuous furnace). To represent the entire system, the combustion chamber and glass tank are modeled separately, but coupled through boundary conditions. Natural convection is represented by the Boussinesq approximation and radiation is simulated in both the combustion chamber and the glass tank whit a radiation model, but the density of the molten load inside the tank is considered constant and the melting process is not estimated. The authors also developed a simplified mathematical transient model to estimate the thermal behavior in the furnace considering radiation, combustion, convection, heat loss through walls and glass melting. Chapter 4. Numerical simulation of an aluminum melting furnace 75 4.1.1.7 Other numerical simulations in furnaces Most literature about numerical simulation of aluminum melting furnaces does not consider the molten aluminum in the furnace and the interaction between combustion space and aluminum bath. Below some simulations related with processes of melting furnaces are presented. Nieckele et al. (2011) and Nieckele et al. (2004) present numerical simulations of the combustion process inside industrial aluminum melting reverberatory furnaces. They analyze the flame patterns, species concentration distribution, temperatures and velocity fields with combinations of oxygen and air, natural gas and liquid oil, and different injection options. Hongjie et al. (2012) also performed simulations of the combustion process in a prototype of reverberatory furnace for copper recovery. A series of simulations was used to optimize the combustion performance varying the burner construction and installation location. Golchert et al. (2005) used a non commercial CFD code in order to simulate the combustion, heat transfer (including thermal radiation), gaseous product flow (mainly CO2 and H2O), and production/transport of pollutant species/greenhouse gases in an aluminum reverberatory furnace. Using this code, the surface heat fluxes are calculated and these data can be used in a melt code. The output from the code is compared and validated against in the furnace measurements carried out by King et al. (2005a). Cadavid et al. (2010) present a three dimensional numerical simulation of a gas-fired self-regenerative crucible furnace; different combustion models are used to assess their effects on the numerical results. Aerodynamics, temperature fields, species profiles and emissions are compared with experimental data. Mei et al. (2008) simulate the combustion space of an oil fired float glass furnace including the turbulence, radiation and the oil drop motion. Davies et al. (2013) analyze the energy flows within a rotary aluminum recycling furnace, using the global properties of its main components, i.e. the gas, metal and refractory walls. With this simplified model, different operations such as loading, heating and stirring are estimated. The furnace is broken up into its components and each is treated Numerical analysis of melting and holding furnaces in secondary aluminum production 76 differently within the model. A one-dimensional numerical model is used for each section neglecting any losses through the sides. Radiative exchange within the furnace, melting of the charge, and forced convection in the melt due to the rotation of the furnace are also considered. Khoei et al. (2003) carried out numerical simulations of a rotary furnace to estimate the evolution and distribution of temperatures in the furnace walls under different flame positions. In order to apply the heat generated at the flame position and heat transferred between the melted material and the internal surface of the furnace, the segments of the walls (elements in the FEM model) are modeled by different flux pulses applied successively to each segment to simulate the changes in thermal loading during rotation. Guo and Irons (2008) modeled the steel scrap movement into a device to understand the phenomenon and thus avoid operational problems in melting furnaces. Finally, several simulations have been done for the heating of solid pieces inside furnaces. Since these cases are more simplified than heating of liquid material or melting processes, the models used can be represented with 3D approaches, including interaction of the solid pieces with combustion products (DellaRocca et al., 2012, Han et al., 2009) or with turbulent flow in a conjugated problem (Hachem et al., 2013). 4.1.2 Phase change problems Bermúdez and Otero (2004) simulate a phase change problem of aluminum for a casting process with in a 3D domain. Solidification is considered with the enthalpy formulation taking into account the convection effects. Because of symmetry, only a quarter of the region occupied by the metal is simulated. The problem is considered as not conjugated, the cooling by the contact of the slab with either the bottom block or air or water, are represented by means of boundary conditions. Melting in metals with low fusion points in rectangular cavities have been simulated by different authors. 2D simulations in not conjugated problems, including convection and heating from the side with a fixed temperature boundary condition, are solved for gallium (Belhamadia et al., 2012) and tin (Hannoun et al., 2005). Recently, Ben-David et al. (2013) solve this same problem for melting of gallium using 2D and 3D approaches; Chapter 4. Numerical simulation of an aluminum melting furnace 83 Implementation and interpretation of OES is complicated and expensive, but careful analysis can yield quantitative information. Finally, in problems where the plasma torch is a part of a process (e.g. in this case is part of a melting process); the interaction of the torch with the processing material must be taken into account. Nevertheless, most of the works presented in numerical simulation of thermal plasmas, the resolution of the energy equation is carried out only in the plasma. The anode is assumed to be a simple surface at the domain boundary where a temperature profile or a heat flux condition is imposed as a boundary condition. Tanaka and Lowke (2007) and Wang et al. (2006) simulate plasma torches with phase change in the anode using the enthalpy method; while Tanaka and Lowke (2007) limit their experimental procedure to the measurement of the load temperature after switching off the arc with an IR pyrometer, Wang et al. (2006) omit any experimental validation. Lago et al. (2004) and Gonzalez et al. (2005) compare the estimated temperatures in the plasma torch and the heat flux to the anode with available measurements in literature; they simulate the thermal interaction between the plasma torch and the anode without considering the melting of the load, although the temperature predicted exceeds the melting point of the material. 4.2 Experimental configuration 4.2.1 Principle of operation and test protocol Under the general objective of developing an innovative type of secondary aluminum melting furnace, experiments were undertaken with a reduced-size prototype (ca. 50 kg max. load). Experimental facilities and tests were provided and accomplished by Corporación Tecnalia (Tecnalia/Inasmet facilities at Irun-San Sebastián) in the frame of the EDEFU project (EDEFU, 2010). The heating means is a transferred plasma torch that superficially heats the aluminum load, which acts as a conducting body. The load is confined within a crucible made of refractory material. Figure 4.2(a) is a photograph of the practical experimental rig, externally showing the main elements: graphite Numerical analysis of melting and holding furnaces in secondary aluminum production 84 electrodes, plasma gas (nitrogen) injection, cooling system of the electrodes and electrical and measurement equipment. For clarity, Figure 4.2(b) shows a sectional view of the furnace. Figure 4.2. (a) Pilot melting furnace; (b) Sectional view (1. Crucible/ ladle; 2. Top of furnace; 3. Anode; 4. Cathode; 5. Exhaust gas pipe; 6. Cooling system of electrodes; 7. Inlet nitrogen pipe; 8. Transport hook; 9. Temperature measurement sensor; 10. Load) The anode and cathode are graphite electrodes. The anode is a solid cylinder with a diameter of 5 cm and the cathode is a hollow cylinder with outer and inner diameter of 5 and 1 cm respectively. Refrigeration is provided by a system of water circulation and is used for cooling of the supports of the electrodes. Any other part of the global prototype is not cooled with this system. The input electricity is transmitted to the electrodes through a special wire that also is used as the water duct for the refrigeration. The plasma gas used is nitrogen (N2) that is provided from a storage tank. Figure 4.3 shows the electric/hydraulic connections for the electrode refrigeration and the connection for the N2 supply in the cathode. a) b) 3 2 1 10 4 Chapter 4. Numerical simulation of an aluminum melting furnace 85 Figure 4.3. (a) Electric/hydraulic connections for the electricity supply and electrode refrigeration; (b) connection for the N2 supply The first stage of the experimental test is preheating the crucible by a propane gas burner for two hours approximately, until it reaches the operation temperature. This is done to avoid damage due to cracking from thermal expansion; the lid is not heated. For the tests, the preheated crucible temperature was set at 658 ºC. Figure 4.4 shows the preheating process in the facility. Figure 4.4. Preheating process for the ladle with a gas burner a a b Numerical analysis of melting and holding furnaces in secondary aluminum production 86 The load of aluminum is weighted before the test and then it is placed inside the furnace. At the initial instant, both electrodes have to be in contact through the metallic load, so that the starting point is a short-circuit. The plasma gas is injected and the cathode is separated; at this moment the plasma torch starts and begins to heat the aluminum surface. In order to maintain a constant power input, the separation distance between the cathode and the load is frequently adjusted. After the theoretical time for melting, temperature is measured in the aluminum; once fusion of the material has been verified, it is poured into a mould. Figure 4.5 shows the appearance of the furnace during the melting process. Several tests were carried out for different configurations, type and amounts of load and power input. A single representative case is selected for the simulations. Figure 4.5. Appearance of the furnace in the melting process 4.2.2 Measurement equipment An infrared IR thermograph camera is used to produce a map of outer surface temperature of different components of the furnace. The maximum temperature that Chapter 4. Numerical simulation of an aluminum melting furnace 87 can be measured with this camera is 2000 ºC. Thermal images of the crucible are taken periodically by the camera. Since the emissivity of real objects depends, besides temperature and wavelength, on factors such as material composition, surface condition and viewing angle, the contact thermometer method was used to obtain the emissivity of the furnace wall. Temperature readings with a thermocouple provided an absolute datum to calculate the emissivity correction of the camera. Emissivity was fixed at 0.7. For the method used (narrow-band IR pyrometer), the way in which the error of the assumed emissivity is transmitted to the absolute temperature can be estimated according to (Doebelin, 1990): 𝑇 𝑎𝑐𝑡𝑢𝑎𝑙 𝑇𝑚𝑒𝑎𝑠𝑢𝑟𝑒 =�𝜀 𝑒𝑠𝑡𝑖𝑚𝑎𝑡𝑒𝑑 𝜀𝑎𝑐𝑡𝑢𝑎𝑙 �13 � (4.1) Since the relation of the emissivities is equal to the cubic relation of temperatures, the error on the measurement of temperatures is very low for large values of emissivities, typical of rough-finished surfaces (as in this case). Figure 4.6 shows the IR thermograph camera and a thermal image obtained for the process. Numerical analysis of melting and holding furnaces in secondary aluminum production 88 (a) (b) (c) Figure 4.6. Measurement of external temperatures of the furnace: (a) IR thermograph camera system; (b) furnace in melting process; (c) typical thermographic image An assembly made up of a thermocouple in a steel tube that the operator shoves in the molten metal is used to measure its temperature. Figure 4.7 shows the measurement of the load temperature after the melting process. Chapter 4. Numerical simulation of an aluminum melting furnace 89 Figure 4.7. Measurement of molten temperature Exhaust gas temperature, which is indicative of that of the inner atmosphere, is measured through a thermocouple probe installed in the pipe. Contact thermocouple probes are used to record temperature into the wall of the crucible; the measurement point (Pm) is located at a height of 245 mm from the bottom of the crucible and at the center of the wall thickness. The electrical system includes measurement of instantaneous power and accumulated energy input. Most of the measurements related to thermal magnitudes are taken under industrial conditions. Measurement of temperatures in solid parts and fused metal has an estimated accuracy of ± 2 ºC, whereas electric power supply is measured to within ± 0.1 kW. Load weights and times can be considered exact in practical terms. However, heat losses to ambient and initial preheat of the crucible are determined only indicatively, which is to be taken into account when comparing with numerical results. Different measurement instruments used in the test are shown in Figure 4.8. Numerical analysis of melting and holding furnaces in secondary aluminum production 90 (a) (b) (c) Figure 4.8. Measurement instruments: (a) digital scale; (b) water and N2 flowmeter; (c) control box and analogue instruments for power supply Chapter 4. Numerical simulation of an aluminum melting furnace 91 4.3 Model description 4.3.1 General assumptions and boundary conditions Numerical simulations is undertaken with the commercial CFD code FLUENT. Pressurevelocity coupling is implemented by the SIMPLE algorithm, with the standard scheme for pressure interpolation. A first-order upwind scheme is adopted for spatial discretization. The criterion of numerical convergence by time step is to achieve a decrease of 1x10-3 in the absolute residuals of the continuity and momentum equations, and a decrease 1x10-6 in the absolute residual of the energy equation. Details of the numerical techniques are given in the user’s manual (ANSYS, 2012). In order to reduce the computational cost, the real geometry is simplified to a 2-D axisymmetric model; details such as the anode and sections of gas outlet and temperature probes are thus ignored. The load consisting in 10 kg of metal is assumed to fill the ladle uniformly from the bottom up to a specific height. The whole domain is closed: gas inlet and outlets and air infiltrations are neglected. Heating from the plasma torch is represented by a small, circular heating area of equal diameter as the electrode, 50 mm, located at the centerline on the top surface of the load. Obviously, better models of the plasma torch can be incorporated under the same general scheme. However, as was presented before, due to the complexity of the phenomenon, there are no simple, reliable models of heat transfer from thermal plasmas. Moreover, the existing models must be calibrated with experimental measures not available for industrial applications. Given the absence of experimental observations regarding e.g., electrode and arc geometry or plasma temperature, the accuracy of any thermal model for the plasma torch is not warranted at this stage. By these reasons, an averaged power transferred to the load is used as the heat input of the simulations. Hur et al. (2001) measure the power transferred to the load in a similar application and Ünlü and Drouet (2002) present typical values for the transferred efficiency for these kind of furnaces. The authors coincide in that the fraction of energy transferred to the load ranges from 45 to 60 % depending on arc length. In this case, a value of 55% is adopted, Numerical analysis of melting and holding furnaces in secondary aluminum production 92 and a typical experimental measurement of 30 kW input electricity, input power to the load (Winput) is 16.3 kW. This is uniformly distributed on the assumed heating area and imposed as a boundary condition, the concentration of the energy is justified since the greatest part of the energy is given at the centre of the anode, where the total heat flux is 500 times larger than at the plasma edges (Lago et al., 2004). This simplification is often used in electric arc applications (Arzpeyma et al., 2013, González et al., 2010b, González et al., 2010a, Widlund et al., 2011). The assumption is intended as a rough approach to represent the heating means and focus the calculation on material fusion, temperatures and losses. Gas and molten aluminum move due to thermally induced density differences. Corresponding Rayleigh numbers can be estimated as 2x108 and 106, respectively. Although the first is relatively close to the critical value of 109 usually given for external flows in air (Mills, 1992), whereas turbulence transition for liquid metals heated from the top is not clear, laminar flow is considered for both sub-domains, which additionally simplifies the problem. Heat losses from the external surface of the crucible to the surroundings are approximated as follows. The bottom is considered perfectly insulated. In the remaining external walls, heat transfer by natural convection and radiation takes place. A constant, average heat transfer coefficient hav = hconv + hrad [W/(m2K)] is estimated according to elementary heat transfer calculations (Incropera and DeWitt, 1990). It should be noted that, since the major part of temperature decrease occurs in the refractory parts, not a precise value but only an indicative figure is needed here. For the convective coefficient hconv, an empirical correlation for the ideal geometry of a vertical cylinder is applied. Radiation is estimated through the formula giving the losses to a large (thus, black) radiative environment. Both coefficients depend on surface and ambient temperatures, assumed uniform and known. Values of 250 ºC and 18 ºC, respectively, are used, the former confirmed as representative of the typical average of numerical results for the surface temperature distribution. Total emissivity used is 0.7, estimated from the measurement of the superficial emissivity presented above. Calculation results in hconv ≈ 7.2 W/(m2K), hrad ≈ 11.7 W/(m2K), and thus hav ≈ 18 W/(m2K). Chapter 4. Numerical simulation of an aluminum melting furnace 99 simulated at this stage. Assuming that the temperature of the refractory material is increased 500 ºC in average for all the volume during a time interval of two hours, a heat flux of 15 000 W/m2 can be estimated. The preheating process starts from ambient temperature and lasts for 7 200 s. A large numerical time step of 5 s is used, adequate for simple heat conduction problems. Results and comparison with experimental measurements can be discussed as follows. Figure 4.11 shows the calculated final temperature distribution in the ladle material, as well as the position of the temperature measurement point Pm. Final temperature along the thickness of the crucible wall at the same height is shown in Figure 4.12. Temperatures numerically predicted are 1050, 775 and 625 K for the inner wall, measurement point and outer wall, respectively. These estimations agree reasonably with experimental observations, in which inner wall temperature ranges from 950 to 1180 K, temperature of the measurement point Pm is 750 K, and outer wall temperature ranges from 509 to 600 K. Figure 4.11. Temperature distribution [K] in the crucible at the end of the preheating stage Numerical analysis of melting and holding furnaces in secondary aluminum production 100 Figure 4.12. Temperature along the thickness of the refractory wall at the end of the preheating process The temperature distribution shown in Figure 4.11 is taken as the initial one in the refractory material for the transient simulation of aluminum melting. Top lid, air and load are added at ambient temperature to complete this initial state. 4.5 Results and discussion 4.5.1 Melting time An approximate melting time (tm) can be calculated by assuming heat is communicated to the load at a constant rate. Total heat needed for melting is: 𝑄=𝑚𝐶∆𝑇+𝑚𝐿 (4.2) Where ∆T = Tm – T0 is the increment from ambient to fusion temperatures. Thus, 𝑡𝑚=𝑄 𝑊𝑖𝑛𝑝𝑢𝑡 =560 𝑠 (4.3) Melting time predicted by the simulation is measured by a monitor of the melting fraction, defined as total amount of molten aluminum divided by the initial solid load. For cases 1-5, predicted melting times are 625, 603, 622, 614, 584 s, respectively. Experimental value is 671 s, although this includes some overheating of the fused Chapter 4. Numerical simulation of an aluminum melting furnace 101 aluminum. In conclusion, numerically predicted times agree reasonably, both with approximate guesses and with measurement. Figure 4.13 shows total liquid fraction in the load throughout the simulation time for the five cases studied. Behavior of the melting rate is roughly the same for the two models including radiation (cases 1 and 3), that correspondingly predict similar melting times. Compared with them, simulation without radiation (case 2) and without the whole gas cavity (case 4) exhibit a similar melting rate for, say, the initial five sixths of the process, but clearly accelerate during the last sixth. This is an indication that radiative losses logically predominate at latter stages, under increased load temperatures; the effect is more pronounced for case 4 than for case 2, which is also coherent. Finally, case 5 overpredicts load temperature and leads to a shorter melting time. Difference with case 4, and the lack of it between cases 2 and 4, clearly show that influence of heat convection inside the load surpasses that of losses through the gas cavity. Figure 4.13. Liquid fraction in the load throughout simulation time for five study cases 4.5.2 Distribution of liquid fraction Figure 4.14 and Figure 4.15 show liquid fraction distribution for cases 1-5 at times 150 and 480 s, respectively. The gas cavity sub-domain is not colored in these drawings. The shapes clearly suggest that melting is initially controlled by heat conduction, and at a certain time, effects of natural convection inside the load become important. In the last figure, differences between cases 1 and 2 on the one hand, and cases 3 and 4 on the Numerical analysis of melting and holding furnaces in secondary aluminum production 102 other pinpoint the effect air movement has on movement of the molten load. Input heat seems to extend superficially more, but to a lower depth, when surface is assumed free, not subjected to the shear stress needed to drag air along. Similarity between cases 3 and 4 indicates that this is unaffected by heat losses from the surface of the load. Finally, a pure heat conduction situation, for a very conductive material, is clearly observed for case 5. Figure 4.14. Liquid fraction at t =150 s: a) Case 1; b) Case 2; c) Case 3; d) Case 4; e) Case 5 Chapter 4. Numerical simulation of an aluminum melting furnace 103 Figure 4.15. Liquid fraction at t = 480 s: a) Case 1; b) Case 2; c) Case 3; d) Case 4; e) Case 5 4.5.3 Temperatures Figure 4.16 and Figure 4.17 show color maps of calculated domain temperature for cases 1-5 at times 150 and 480 s, respectively. For comparison purposes, Figure 4.18 shows thermal images of the outer surface taken during the experiment at times 150 and 480 [s], as well as the values estimated at Numerical analysis of melting and holding furnaces in secondary aluminum production 104 specific points on the ladle, lid and electrodes. Figure 4.19 shows the evolution of temperature of gas inside the cavity and wall of the crucible. Figure 4.16.Temperature [K] at t = 150 s: a) Case 1; b) Case 2; c) Case 3; d) Case 4; e) Case 5 Chapter 4. Numerical simulation of an aluminum melting furnace 105 Figure 4.17. Temperature [K] at t = 480 s: a) Case 1; b) Case 2; c) Case 3; d) Case 4; e) Case 5 Numerical analysis of melting and holding furnaces in secondary aluminum production 106 Figure 4.18. Thermal images of the outer crucible surface: a) t = 150 [s]; b) t = 480 [s] Figure 4.19. Evolution of measured temperatures of crucible wall and gases Outer surface temperatures predicted by the simulation, Figure 4.16 and Figure 4.17, range from 500 to 600 [K] for t = 150 [s] and 450 to 550 K for t = 480 [s]. These values agree reasonably with the thermal images presented in Figure 4.18, that show 483 to 517 [K] for t = 150 [s] and 478 to 512 [K] for t = 480 [s]. Temperature predicted in the measurement point Pm ranges from 750 to 850 [K] for t = 150 [s], and 700 to 800 [K] for t = 480 [s], which agrees with experimental values shown in Figure 4.19. It is interesting to note that the temperature of the crucible continuously decreases, which means that it supplies a part of the energy to the process, that it is subsequently distributed for load heating and losses to the environment. Gas cavity temperature predicted by the full Chapter 4. Numerical simulation of an aluminum melting furnace 107 model (case 1) ranges from 500 to 700 K, which is of the same order than the experimental value in Figure 4.19. Experimental measurements of the inner wall temperature are shown in Figure 4.20, as estimated by thermal images taken at the end of the test, when the top lid of the ladle is removed. Values range from 700 to 950 [K], which is also in agreement with numerical estimations. Figure 4.20. Thermal image at the end of the test Final load temperature predicted in case 1 ranges from 933 to 950 [K], with hot spots of 1200 K. This value corresponds to the time at which all the metal load is in liquid phase, t = 627 [s]. Load temperature at the end of the experimental test, for t = 671 [s] is 1030 K, which further shows that calculation and experiment agree reasonably. 4.5.4 Molten load movement Figure 4.21 shows velocity vectors in the liquid aluminum for cases 1-4 at the end of the melting process. It is observed that four concentric recirculation zones are predicted in cases 1 and 2, whereas only one is formed in cases 3 and 4. This is coherent with the differences observed in Figure 4.15, and points out the fact that a full model of air movement and coupling at the interface are needed to adequately predict natural circulation of the molten metal. It is important to note that industrial-scale hot melting Numerical analysis of melting and holding furnaces in secondary aluminum production 108 experiments are very expensive and complicated. Moreover, as known, until now there are no workable technical means for velocity measurements in high-temperature liquid metals (Ben-David et al., 2013). Therefore, a validation of the estimated flow is not possible with the current measurement techniques. Nevertheless, the flow patterns predicted in cases 1 and 2 agree with the roll cells expected for circular containers in convective problems. (Gebhart, 1988). Figure 4.21. Velocity vectors [m/s] for the molten aluminum at the end of the melting process: a) Case 1; b) Case 2; c) Case 3; d) Case 4 From preceding results, it is clear that differences in local temperature and liquid fraction are important, but not so overall figures, such as melting time and overall liquid fraction, Figure 4.13. Chapter 5. Numerical simulation of an aluminum holding furnace 115 Figure 5.1. Photographs of the aluminum holding furnace and sectional view (1-holding chamber, 2-heating chamber, 3-layer of refractory material A, 4layer of refractory material B, 5layer of refractory material C, 6aluminum load, 7electrical resistances) Additionally to the materials presented in Figure 5.1, two materials are located in the lateral walls of the furnace: a ceramic layer used as a supplementary insulation and a sheet of steel 1018 used as a protection for the refractory materials. Figure 5.2 shows the array of electrical resistances used as the heating means. Numerical analysis of melting and holding furnaces in secondary aluminum production 116 Figure 5.2. Photograph of the electrical resistances array Experimental facilities and tests were provided and accomplished by Giesserei Instandsetzung Service 2003 S.L. (GIS 2003-Vilanova i la Geltrú, Barcelona) in the frame of the EDEFU project (EDEFU, 2010). 5.2.2 Dimensions and temperature measurements The internal temperatures of the refractory walls have been measured through an array of thermocouples in four points at a height of 150 mm from the top of the furnace. An assembly made up of a thermocouple in a steel tube submerged in the molten metal is used to measure its temperature. The air temperatures inside the holding and heating cavities are measured through thermocouple probes installed in the respective chambers. The measurements of temperatures are taken under industrial conditions and have an estimated accuracy of ±2 ºC. Load weights and times can be considered exact in practical terms. Figure 5.3 shows the main dimensions of the furnace and the location of the temperature measurement points. Chapter 5. Numerical simulation of an aluminum holding furnace 117 Figure 5.3. Dimensions of aluminum holding furnace (mm) and measurements points for the temperature (A-D) at a height h = 150 mm 5.2.3 Test protocol The holding furnace is preheated by the electrical resistances until the refractory walls reach the operation temperature and the furnace becomes stable (12-15 days). The high temperatures of the refractory walls are used to maintaining the load above the melting point and avoid refractory damages due to cracking from thermal expansion. Molten aluminum is poured into the holding chamber and it is held for several hours. The power supply is a simple on-off control, which introduces a constant power until the resistances chamber reach a maximum operation temperature and then is turned off until a minimum operation temperature. This commutative power is employed in order to raise the refractory temperature and compensate the heat losses in the furnace. Numerical analysis of melting and holding furnaces in secondary aluminum production 118 5.3 MODEL DESCRIPTION 5.3.1 Assumptions and boundary conditions Numerical simulation is undertaken with the commercial CFD code FLUENT. Pressurevelocity coupling is implemented by the SIMPLE algorithm, with the standard scheme for pressure interpolation. A first-order upwind scheme is adopted for spatial discretization. The criterion of numerical convergence by time step is to achieve a decrease of 1 x 10-3 in the absolute residuals of the continuity and momentum equations, and a decrease 1 x 10-6 in the absolute residual of the energy equation. The load consisting in 250 kg of metal is assumed to fill the ladle uniformly from the bottom up to a specific height. The whole domain is closed: air infiltrations are neglected. Air and molten aluminum move due to thermally induced density differences in the holding chamber. Corresponding Rayleigh numbers can be estimated as 8 x 105 and 5 x 107, respectively. Since the first is relatively far to the critical value of 109 usually given for external flows in air (Mills, 1992), whereas turbulence transition for liquid aluminum in confined spaces heating from all walls is not clear, laminar flow is considered for both sub-domains, which additionally reduces the computational resources required. The treatment of the air in the resistances chamber is based in the purely diffusive transfer in the gas, with an augmented, effective thermal conductivity. Since details of the temperature distribution in the air of the resistances cavity are not relevant for the energy balance, this approach is used in order to save computational resources. The overall energy effect is suitably represented (see chapter 4-section 4.3.3.3). The fact that real heat transfer by convection and especially by radiation is more intense can be represented by an augmented thermal conductivity given by keff = hefftc. Considering the resistances chamber as a box with an array of cylinders that represent the resistances, with a height equal to the distance between the electrical resistances and the top of the heating chamber (in this case: tc = 61 mm), and uniform surface temperatures of 1200 ºC Chapter 5. Numerical simulation of an aluminum holding furnace 119 for the resistances and 800 ºC for the top and lateral walls of the resistance chamber, respectively, coefficients are estimated according to basic heat transfer calculations (Incropera and DeWitt, 1990). Results are hconv≈ 3.5 W/(m2K), hrad≈ 231.7 W/(m2K), heff = hconv + hrad ≈ 235.2 W/(m2K), so that air conductivity is taken as keff = 14.35 W/(mK). Heat losses from the external surface of the crucible to the surroundings are approximated as follows. The bottom is considered perfectly insulated. Lateral walls of the furnace are composed of two sheets of different materials: 1) A ceramic fiber layer, which is the final material in the refractory array. 2) A sheet of steel 1018. Both sheets have very small thickness in comparison with the other materials and thus would force an exaggerated grading of the mesh, which may lead to numerical convergence problems. In order to represent heat conduction in these small planar thicknesses without meshing the domains, a thin-wall model was used. In this model, a 1D heat conduction equation is solved to compute the thermal resistance imposed by the wall. The thermal resistance of the wall is ∆ x/k, where k is the conductivity of the wall material and ∆ x is the wall thickness. Heat transfer conditions and thermal circuit of the lateral walls are schematically represented in Figure 5.4. Figure 5.4. Heat transfer scheme and thermal circuit in the lateral walls of the crucible tC tCer tSteel material C Ceramic layer Steel 1018 Ambient (1) (2) (3) (4) Numerical analysis of melting and holding furnaces in secondary aluminum production 120 Solving the equivalent circuit, the equivalent thermal conductivity for the ceramic and steel sheets is keq = 0.26 W/(mK). On the other hand, heat transfer by natural convection and radiation takes place. A constant, average heat transfer coefficient hav = hconv + hrad [W/(m2K)] is estimated according to elementary heat transfer calculations (Incropera and DeWitt, 1990). For the convective coefficient hconv, an empirical correlation for the ideal geometry of vertical walls is applied. Radiation is estimated through the formula giving the losses to a large (thus, black) radiative environment. Both coefficients depend on surface and ambient temperatures, assumed uniform and known. Values of 250ºC and 18ºC, respectively, are used, the former confirmed as representative of the typical average of numerical results for the surface temperature distribution. Total emissivity used is a typical value of 0.7 for non-polished surfaces. Calculation results in hconv ≈ 7 W/(m2K), hrad ≈ 11 W/(m2K), and thus hav ≈ 18 W/(m2K). Finally, the electrical resistances supplies a total constant input power (Winput = 11 kW) until the heating chamber reaches a temperature of 1000 ºC, then these are turned off until the temperature in the heating chamber drops to 995 ºC. The resistances are simplified as an array of cylinders. Since the internal temperature of the resistances is not of interest for the present simulations, the heat generation is imposed as a boundary condition in the cylinders faces; which is in fact the power input in the furnace: w = Winput/NAres = 28356.08 [W/m2]. Where N is the number of resistances and Ares is the unitary volume. The on-off control condition has been imposed in the resistances area by means of a User Defined Function (UDF) in FLUENT. 5.3.2 Geometry and materials In order to reduce the computational cost and take advantage of the symmetry, only a quarter of the domain was simulated in a first approach. Since strong asymmetry was observed in the natural flow within the load, afterwards the full domain was simulated to compare the results obtained by both approaches. Figure 5.5 shows the geometries simulated for the cases of the quarter of domain and the full domain (translucent view), Chapter 5. Numerical simulation of an aluminum holding furnace 121 that reproduce the refractory array of the real furnace. The air in the resistances chambers and holding chamber is not shown for clarity. Figure 5.5. Geometry for the numerical simulationsQuarter of domain and full domain (translucent view) The resistances used in the furnace are wire elements of the typical material "aluchrom". Table 5.1 shows the thermal properties for the solid parts in the furnace, while the thermo-physical properties of the aluminum load are summarized in Table 5.2. Numerical analysis of melting and holding furnaces in secondary aluminum production 122 Table 5.1: Thermal properties of solid parts Material Density kg/m3 Specific heat (KJ/kg.K) Thermal conductivity (W/m.K) Refractory material A [a] 2563 0.690 8 Refractory material B [b,c] 1200 1.200 0.2 Refractory material C [b,d] 930 1.200 0.28 Ceramic layer [e] 160 1.088 0.143 Aluchrom[a,f] 7100 0.640 16 Steel 1018 [g] 7800 0.489 50 a Goodfellow (2012); b Skamol (2010); c Dupré (2008); d Christy (2004); e Rath (2012); f Outokumpu (2008); g MatWeb (2012) Table 5.2: Thermophysical properties of aluminum load Density (kg/m3)a 2700 -3.873T+5992 -0.3116T+2668 T < 873 K 873 K < T < 933.15 K T > 933.15 K Specific heat (kJ/kg.K) b 0.900 Thermal conductivity (W/m.K)b 237 Viscosity (kg/m.s) a 0.001 Latent heat of fusion (kJ/kg) b 397 Solidus Temperature (K)c 873 Liquidus Temperature (K) c 933.15 a Assael et al. (2006); b Brandt (1984); c Zeiger and Nielsen (2004) 5.3.3 Models For the convective motion of the molten load and air filling up the holding chamber, the Navier Stokes equations corresponding to a fluid of variable density are solved, which takes into account buoyancy. Non-slip, or velocity continuity, is imposed on all interfaces. Energy conservation is solved in full domain, which is equivalent to a problem of heat conduction in solids and heat convection in air and liquid aluminum. The method used enforces temperature continuity and conservation of heat flux through interfaces. Due to the solidification potential of the molten aluminum, the enthalpy method is used in the load domain in order to detect phase change points. Thermal radiation is calculated for the air cavity by the S2S radiation model. Chapter 5. Numerical simulation of an aluminum holding furnace 123 5.3.4 Meshing scheme Due to the diverse complex phenomena involved, the implementation of the numerical simulations is very expensive in computational terms. Therefore, currently it is not feasible to carry out a grid convergence study, only a single mesh of 531150 cells and a single mesh of 2124600 cells are used for the approaches of quarter and full domain respectively. The whole mesh is structured except by the heating chamber that presents a complex geometry. Figure 5.6 shows the general grid and details of the heating chamber for the case of the quarter of domain; this mesh is reproduced in each symmetry plane for the full domain approach. a) b) c) Figure 5.6. Grid details-quarter of domain. a) General, b) Resistances, c) Air filling the resistances chamber Numerical analysis of melting and holding furnaces in secondary aluminum production 124 5.3.5 Numerical time step In this work, iterative convergence at each time step is verified. Different values were tested, which resulted in that the required maximum value should be lower the complex the problem solved. The problem complexity increases by two factors: first, after the preheating process, a new material is added in the domain (molten load introduced after preheating process); second the on-off control prevents the use of a high value for the time step. Since in actual conditions the resistances are switched each 10 to 20 s approximately, the maximum time step used in the simulations is 3 s. 5.4 Results and discussion 5.4.1 Preheating stage The process doesn’t start from cold conditions but firstly the furnace is preheated by several days. In fact, this operation is the most important part of the process, since the high temperatures reached by the walls are used for the holding of molten aluminum. This imposes an initial internal energy content and a temperature distribution in the refractory material, and both should be taken into account. Therefore, firstly the preheating process is simulated, and its final state is taken as the initial one for the ensuing simulation of the holding of the molten load. The holding chamber is filled with air in this part of the simulation; it is simulated along with all the others domains. The heat losses in walls and the heat input from the electrical resistances are taken into account by the boundary conditions defined before. The preheating process is accomplished until the furnace temperature becomes stable. Figure 5.7 shows the temperature profile in the furnace estimated in the simulations of the quarter and full domain for the preheating stage.