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Scrap melting in a continuous process rotary melting furnace Zhang, Yanjun 2007

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SCRAP M E L T I N G IN A CONTINUOUS PROCESS R O T A R Y M E L T I N G F U R N A C E by Yanjun Zhang B . Eng., Northeastern University, 1995 M . A . S c . , University of British Columbia, 2003 A THESIS S U B M I T T E D I N P A R T I A L F U L F I L L M E N T OF T H E R E Q U I R E M E N T S F O R T H E D E G R E E OF D O C T O R OF P H I L O S O P H Y in T H E F A C U L T Y OF G R A D U A T E S T U D I E S (Materials Engineering) T H E U N I V E R S I T Y OF B R I T I S H C O L U M B I A Apr i l 2007 © Yanjun Zhang, 2007 A B S T R A C T Based on the preliminary modeling study, an improved heat-transfer model has been developed in this study to further examine the viability of the oxy-fuel-fired continuous process rotary melting furnace ( C P R M F ) as a replacement of the electric arc furnace (EAF) in minimil l steelmaking. The model treats the furnace as three domains: the freeboard space, the liquid metal bath and slag, and the refractory structure. Based on certain physical correct assumptions for the gas flow and combustion patterns, radiative exchange within the freeboard is solved by the zone method in combination with a clear-plus-3-gray emissivity/absorptivity model for the gas phase thus the model allows axial temperature variations in the gas phase and the refractory hot-face. Assuming an isothermal metal bath condition, heat transfer to the exposed bath is simplified by a specified temperature difference between the slag/freeboard and slag/metal interfaces, while regenerative heat transfer to the covered bath is calculated using the local refractory temperature and the local heat-transfer coefficients. The refractory structure is solved by 1-D transient conduction in the radial direction. The three domains are linked by shared boundary conditions and the requirement that the furnace itself operates at steady-state. The model was partially validated using experimental results from copper melting trials on a bench-scale C P R M F , which was designed and constructed as a part of work in this study. The trials explored two operating variables, i.e., oxygen and slag. Both experimental and model results indicate an increase in furnace thermal efficiency with increasing oxygen enrichment in the combustion air and a decrease in the efficiency with increasing slag thickness. The partially validated model was then employed to evaluate the commercial viability o f the C P R M F . According to the model predictions, a melting rate in the order of 400 ton h"1 can be achieved b y a 4 m I D x 1 6 m furnace with a natural gas firing rate of 6000 N m 3 h"1. Under the baseline conditions, the furnace thermal efficiency is 66%. Without scrap preheating, this configuration consumes less direct energy at 619 k W h f 1 than the typical E A F (662 k W h f ) and can save at-source energy by about 45%. ii TABLE OF CONTENTS Abstract i i Table of Contents i i i List of Tables v List of Figures v i List of Symbols ix Acknowledgements xiv Chapter 1 - Introduction 1 Chapter 2 - Literature Review 5 2.1 Introduction to Electric Arc Furnace 5 2.2 General Characteristics of Rotary Melting Furnace 8 2.3 Combustion Aerodynamic Phenomena in Rotary Melt ing Furnaces 10 2.4 Combustion of Natural Gas at High Temperatures 14 2.5 Heat Transfer Processes in Rotary Melt ing Furnaces 16 2.6 Kinetics of Scrap Melting in Liquid Steel 24 2.7 Closely Related Furnaces - Rotary Kilns 27 2.8 Summary 31 Chapter 3 - Scope and Objectives 32 Chapter 4 - Methodology 33 4.1 Design and Configuration of the Bench-Scale C P R M F 33 4.2 Experimental Procedure 40 4.3 Gas Temperature Calculation and the Furnace Energy Balance 45 4.4 The Mathematical Model 50 4.5 Summary 62 Chapter 5 - Results and Discussion 64 5.1 Experimental Results (Steady-State Furnace Operation) 64 5.2 Partial Validation of the Model 68 5.3 Scale-up and Model Predictions for Industrial-Scale Furnaces 74 5.4 Summary 87 Chapter 6 - Conclusions 89 i i i C h a p t e r 7 - R e c o m m e n d a t i o n s on F u t u r e W o r k 92 References 93 A p p e n d i c e s 105 Appendix A : Evaluation of the Temperature-Independent Direct Exchange Areas ..: 105 Appendix B : Evaluation of the Temperature-Independent Total Exchange Areas 109 iv L I S T O F T A B L E S Table 1.1 Comparison of energy consumption by the E A F (from operating data) and the equivalent oxy-fuel C P R M F (model predictions) 4 Table 4.1 Properties of the refractory used in the bench-scale R M F 36 Table 4.2 The errors in the gas flow measurements 38 Table 4.3 Natural gas properties 41 Table 4.4 Properties of the copper scrap 42 Table 4.5 Compositions of the modified slag and zinc-fiiming slag 43 Table 4.6 The firing rates during the melting period 44 Table 4.7 Parameters used in the model to calculate the energy losses at the furnace ends 55 Table 5.1 Average temperatures during the thermal steady-state phase 65 Table 5.2 The energy balance in each trial 66 Table 5.3 Validation against terms in the furnace heat balance 71 Table 5.4 Summary of baseline design and operating conditions assumed for the industrial-scale furnace 75 Table 5.5 Properties of steel scrap 75 Table 5.6 Performance and energy dispositions in the 4 m ID x 16 m furnace at a firing rate of 6000 N m 3 h"1 under the baseline conditions 78 Table 5.7 Furnace performance versus length under the baseline conditions 82 v L I S T O F F I G U R E S Figure 1.1 Schematic of the proposed C P R M F process with scrap preheater 2 Figure 2.1 Schematic diagram of the E A F 6 Figure 2.2 Schematic diagram of a tilting rotary melting furnace 8 Figure 2.3 Schematic diagram of gas flow resulting from a single burner with a primary jet and secondary air 11 Figure 2.4 Schematic diagram of gas flow resulting from double concentric jets ... 12 Figure 2.5 Schematic diagram of gas flow resulting from multiple burner arrangement 12 Figure 2.6 The equilibrium products of C H 4 combustion as functions of flame temperature 15 Figure 2.7 Effective heat of C H 4 combustion as a function of flame temperature 16 Figure 2.8 Heat transfer in the transverse plane of the R M F 17 Figure 2.9 Directional variation in surface emissivities for some electrical nonconductors 19 Figure 2.10 Schematic diagram of an interior node (cylindrical coordinate) 23 Figure 2.11 Schematic diagram of the temperature profile 25 Figure 4.1 Overall layout of the bench-scale C P R M F 34 Figure 4.2 Positioning of thermocouples for measuring refractory temperatures .. . . 35 Figure 4.3 The initial burner design without cooling 37 Figure 4.4 The modified burner design including air-cooling 37 Figure 4.5 Schematic diagram of the suction pyrometer showing gas meter and suction pump 38 Figure 4.6 Schematic diagram of the crucible and the steel box 39 Figure 4.7 Schematic diagram showing the measurement of slag thickness 40 Figure 4.8 Enthalpy of copper versus temperature 42 Figure 4.9 Experimental schedule 44 Figure 4.10 Gas temperature correction versus gas velocity over the thermocouple .. 46 v i Figure 4.11 Schematic diagram showing the treatment of the furnace back-end in the experimental calculations 49 Figure 4.12 Schematic diagram of the freeboard space containing the gas mixture ... 51 Figure 4.13 Schematic diagram showing energy balance on gas volume zone V ; 53 Figure 4.14 Schematic diagram showing the treatment of the furnace back-end in the model calculations 55 Figure 4.15 Schematic diagram of the liquid metal bath and slag 57 Figure 4.16 The local regenerative heat-transfer coefficients 58 Figure 4.17 Schematic diagram showing 1-D transient condition within the refractory 59 Figure 4.18 The solution procedure linking the three models 60 Figure 5.1 Metal bath temperatures during the melting period with tapping/charging at 30-minute intervals, 65 Figure 5.2 Thermal efficiency versus oxygen level in the combustion air 67 Figure 5.3 Thermal efficiency versus slag thickness 68 Figure 5.4 Validation against refractory temperatures (Trial 2-repeat) 69 Figure 5.5 Validation against gas and refractory hot-face temperatures (Trial 2-repeat) 70 Figure 5.6 Batch-scale furnace thermal efficiency versus oxygen enrichment (Trials 1, 2, and 3, no slag) 73 Figure 5.7 The influence of the slag on bench-scale furnace thermal efficiency (Trials 2, 4, and 5 with a constant oxygen level of 53%) 74 Figure 5.8 Enthalpy of Fe versus temperature 76 Figure 5.9 Ax ia l temperature profiles in the 4 m ID x 16 m furnace (baseline conditions) 77 Figure 5.10 Circumferential hot-face temperature profile at the axial position of 1.6 m 78 Figure 5.11 Energy input to the bath by source 79 Figure 5.12 The effect of fuel/oxygen mixing-length (recirculation zone) on refractory hot-face temperature at constant furnace length and firing rate 80 vi i Figure 5.13 The effect of fuel/oxygen mixing-length on the heat transfer rates to the bath at constant furnace length and firing rate 81 Figure 5.14 The effect of rotation rate on refractory temperature 83 Figure 5.15 The effect of rotation rate on heat transfer rates to the bath 83 Figure 5.16 Melting rate and furnace efficiency versus firing rate for baseline conditions 85 Figure 5.17 The effect of firing rate on refractory temperatures 85 Figure 5.18 The effect of A T s i a g on the heat transfer rates to the bath 86 Figure 5.19 The effect of A T s i a g on the refractory temperatures 87 Figure A . 1 Schematic diagram of the view factor between dAj and dAj 106 Figure A .2 Schematic diagram of the direct gas-surface exchange area 107 Figure B . 1 Schematic diagram of leaving flux density 110 vni LIST OF SYMBOLS a e , n (T g ) emissivity weighted coefficient a a , n ( T s > T g ) absorptivity weighted coefficient A area (m 2), or surface zone C P heat capacity (kj k g 1 °C"1 or k j kmol" 1 0 C"' ) Ct Craya-Curtet number d A infinitesimal surface element (m 2) dF view factor between two infinitesimal surface elements d V infinitesimal volume element (m 3) D diameter (m or cm) E b black body emissive power (W m"2) F view factor between two finite surfaces Fr firing rate (Nm 3 h"1) gg gas-gas direct exchange area (m2) gs gas-surface direct exchange area (m 2) G irradiation (W m"2) G G temperature-independent gas-gas total exchange area (m 2) G G temperature-dependent gas-gas total exchange area (m 2) GS temperature-independent gas-surface total exchange area (m 2) GS temperature-dependent gas-surface total exchange area (m 2) h heat-transfer coefficient (W m"2 °C _ 1 ) f,298°K formation heat (kJ kmol" 1) H m summation of fusion heat plus sensible heat at liquidus (kJ kg" H v heating value (kJ Nm" 3) I radiative intensity (W m"2 sr"1) k thermal conductivity (W m"1 °C"') K extinction coefficient (nf 1 atnf 1), or velocity shape factor L distance or length (m or cm) IX L m b mean beam length (m) m Craya-Curtet similarity parameter, or the total number of surface zones m mass flow rate (kg s"1) M melting rate (kg h"1 or ton h"1) n the total number of volume zones N reaction rate, generation rate, or mole flow rate (kmol s"1) P partial pressure (atm) q v volumetric emissive power (W m"3) q heat flux (W m"2) Q heat or energy, (J, kJ or MJ) Q m energy needed to melt unit weight of scrap and reach the bath temperature (J kg"1 or J ton"1) Q heat-transfer rate, or heat release rate from combustion (W, k W or M W ) r radius (m) r^  equivalent nozzle radius for a non-isothermal jet (m) r^  equivalent nozzle radius for non-isothermal double concentric jets (m) R excess discharge ratio sg surface-gas direct exchange area (m 2) ss surface -surface direct exchange area (m 2) S G temperature-independent surface -gas total exchange area (m 2) S G temperature-dependent surface -gas total exchange area (m 2) SS temperature-independent surface -surface total exchange area (m 2) SS temperature-dependent surface -surface total exchange area (m 2) t time (s) T temperature (°C or K ) V volume (m 3), or gas volume zone W leaving flux density (W m"2) x axial distance to burner nozzle (m) x p axial distance between burner nozzle and point P (m) x A H s difference in sensible heat of gas mixture entering and leaving (W) A L thickness (m) Ar radial nodal spacing (m) At time step (s) A T temperature difference or thermal cycling of the refractory (°C) A9 circumferential nodal spacing cpi Thring-Newby similarity parameter for single primary jet surrounded by secondary fluid cp2 Thring-Newby similarity parameter for double concentric jets r| furnace thermal efficiency 8* displacement thickness of boundary layer (m) a absorptivity s emissivity x transmissivity p density (kg m"3), or reflectivity v kinematics viscosity (m 2 s"1) a Stefan-Boltzmann constant, 5.67x 10"8 W m"2 K " 4 Dimensionless Group Gr Grashof number N u Nusselt number Pe Peclet number Pr Prandtl number Re Reynolds number Subscripts bath bulk metal bath c convection cb covered bath comb combustion x i cw covered wall cyl cylindrical refractory Cu copper D diameter eb exposed bath eff effective end end-wall refractory ew exposed wall exh exhaust pipe F furnace Fe iron or steel g gas hf refractory hot-face i the i ' th enclosure zone, the i 'th node, or the i ' th species j the j ' th enclo sure zone k the k ' th surface zone loss energy loss L liquid m melting point, or the m'th volume zone M a x maximum n the n'th gray gas component, or the n'th surface zone Nsec number of axial subdivisions in the furnace freeboard o nozzle orifice offgas gas mixture leaving the furnace opening opening on the back-end wall Pt platinum p primary flow r radiation rec recirculation s surface, secondary flow, or solid shell furnace shell xn slag slag layer, or make-up slag tc thermocouple tube alumina tube x local circumferential position oo ambient © rotation speed Superscripts + forward - backward n current time step n+1 next time step xin A C K N O W L E D G E M E N T S I offer my enduring gratitude to the faculty, staff and students at the U B C , who have inspired me to continue my work in this field. Particular thanks are owed to my supervisors, Professor Ray Meadowcroft and Professor Peter Barr, who offered me the opportunity to work with them. I really enjoyed the moment when we discussed technical problems in the cafeteria, where they bought me coffee in turn. Their wonderful ideas and suggestions are really helpful. I learnt a lot from them. The influence they have had in my life w i l l always be valued. Assistance with the experimental work provided by Mr . M i l a i m Dervishaj, Research Technician, is really appreciated. After each successful experiment, we had a glass of beer in the bar and spent an enjoyable moment. Special thinks are also due to my families for their loving support. xiv C H A P T E R 1 - I N T R O D U C T I O N The late 20 century saw the proliferation of low-cost, scrap-based steelmaking operations built around the electric arc furnace (EAF) . These small 'mimimil ls ' proved very successful in serving local markets for structural shapes and pipe. In the formative years, both scrap-melting and metallurgical adjustments were performed within the E A F . However, in the last two decades, the metallurgical functions have largely shifted downstream to a separate refining station (generally a ladle furnace). Thus the E A F has become focused on scrap-melting and furnace development has been aimed at reducing tap-to-tap time with no real metallurgical function other than melting. This has been accomplished largely by hydrocarbon addition, both through oxy-fuel burners and as carbon into the bath to generate C O which is subsequently combusted to CO2 in the freeboard space by oxygen injection. Since the cost of electricity is rising rapidly and nuclear power is controversial, the combustion energy from cheaper hydrocarbon fuels w i l l be the main energy source for melting in the future. This change has begun to expose limitations in the basic design of the E A F , particularly in terms of its ability to efficiently utilize the energy from hydrocarbon additions during melting. This encourages people to explore alternatives to replace the E A F for steel scarp melting in the mimimills. A potential alternative is the rotary melting furnace (RMF) . Because of advantages of low capital cost, ease of control and low environmental impact, oxy/fuel R M F ' s are common and competitive in the iron foundry industry. However, these furnaces (typically < 30 ton capacity) do not have sufficient melting capability to supplant the E A F in minimill steelmaking (where at least 100 ton h"1 melting capability would be needed) and, being batch operations, present the same control issues as the E A F ; i.e. highly variable conditions for heat transfer. In order to maintain uniform conditions for heat transfer; i.e. stable bath temperature as well as near-constant bath volume and surface area, Barr and Meadowcroft 1 proposed a continuous process rotary melting furnace ( C P R M F ) process shown in Figure 1.1. The unit consists of an oxy-fuel R M F and an optional scrap preheater. Although scrap charging would be semi-continuous, tapping of hot metal would be discontinuous to match the batch nature of the ladle furnace. B y employing a bath weight much greater than that of - 1 -the metal tapped, fluctuations in bath volume and temperature (and hence conditions for heat transfer) are minimized and, overall, the R M F approaches a continuous process in terms of furnace control. As an example, at a melting rate of 100 ton h"1 tapping might be 50 tons of hot metal at 30-minute intervals. Assuming an average bath weight of 200 tons, a 50-ton tap means that the actual bath weight would fluctuate between 175 and 225 tons. F i g u r e 1.1: S c h e m a t i c o f the p roposed C P R M F process w i t h sc rap p rehea te r Relative to the E A F , the potential advantages of the C P R M F would include: • The area for heat transfer to the bath is essentially doubled by the regenerative action of the rotating refractory. • Because only a thin, non-foamed, slag layer is required to protect the bath surface, the thermal resistance of slag is minimized as is the dust loss associated with foamy-slag practice. • The large freeboard volume ensures a long residence time for the gas. • Cooling of the refractory when submerged under the bath eliminates the need for auxiliary cooling. • The refractory-slag interaction is distributed uniformly over the entire refractory surface. • Improved process control. - 2 -• L o w noise levels and low dust carry-over. • Improved product quality; e.g. low nitrogen and sulphur pickup. • Simplicity and low capital cost. Potential difficulties identified were: • Spalling at the refractory hot-face due to thermal cycling. • Although much reduced relative to the E A F , the thermal resistance of the slag might still constrain the achievable melting rate. Results from the mathematical model developed by Barr and Meadowcroft 1 for the C P R M F process (termed 'the previous model' in this thesis) indicated that with scrap preheating, a melting rate of 100 ton h"1 would require a 3 m inner diameter (ID) by 12.5 m C P R M F operating at flame temperature of 2210 °C. Omission of the scrap preheater would increase the length to about 20 m. Energy consumption by the C P R M F without and with scrap preheating were compared with those by the E A F . The data on the E A F was determined based on 9 modern electric arc furnaces with oxy-fuel burners (started after 1995),2 as well as the energy balance of a shaft furnace ( E A F with scrap preheating) presented by Haissig et al . 3 As seen in Table 1.1, without scrap preheating, the C P R M F requires more direct energy than the E A F . However, considering an overall efficiency of 40% for electricity generation and transmission, 4 ' 5 the C P R M F can save at-source energy by 30%. With scrap preheating, the C P R M F consumes less direct energy and can save at-source energy by about 50%. Table 1.1: Comparison of energy consumption by the EAF (from operating data) and the equivalent oxy-fuel CPRMF (model predictions) Without Scrap Preheating With Scrap Preheating Typical EAF* Electrical energy (kWh t"1) 380 285 Bath reaction/post combustion (kWh t'1) 190 190 Burner energy (kWh t"1) 80 50 Scrap preheating (kWh t"1) N A 55 Sub total (kWh t' 1) 650 580 Oxygen (Nm 3 t" 1 ) 33 33 Electricity for 0 2 (kWh t"1) 12 12 Total direct energy (kWh t"1) 662 592 At-source energy (kWh t"1) 1250 1038 Proposed Oxy-Fuel CPRMF** Hydrocarbon fuel (kWh t"1) 737 456 Oxygen (Nm 31" 1) 149 92 Electricity for 0 2 (kWh t"1) 54 33 Total direct energy (kWh t"1) 791 489 At-source energy (kWh t"1) 872 539 Saving of at-source energy by the CPRMF 30% 48% * Typical Operating Da ta 2 ' 3 ** Model Predictions 1 Although promising, the results from the previous model were not validated against experimental data and the model itself was relatively simplistic in certain key assumptions. The present study investigates the C P R M F process farther by developing an improved heat transfer model to include the effects of axial temperature gradients within the gas phase. The model was partially validated against experimental results from a bench-scale R M F , which was designed and constructed as a part of the work in this study. The model was then used to evaluate the commercial viability of the C P R M F process. - 4 -CHAPTER 2 - LITERATURE REVIEW In this chapter, the evolution on E A F energy input is described briefly and the limitations of the E A F for the utilization of hydrocarbon energy inputs is discussed. Then a brief description of the rotary melting furnaces is presented, followed by a review of literature on the important phenomena involved in the C P R M F such as combustion aerodynamics and thermodynamics, heat transfer processes, and scrap melting kinetics. Finally, mathematical models developed for rotary kilns and closely related furnaces, are reviewed. 2.1 Introduction to Electric Arc Furnace A s shown in Figure 2.1, the E A F is a refractory lined vessel with water-cooled panels for the sidewalls. Three graphite electrodes, connected to a transformer by copper bus lines, project through the roof. Water-cooled oxy-fuel burners are fixed into the roof and/or the sidewalls. Oxygen and fuel lances can be inserted into the furnace through the slag gate or the sidewalls by a lance manipulator. Several bottom designs are in common use including the 'conventional' spout taphole, eccentric bottom tapping (EBT, shown in the figure) and offset bottom tapping (OBT). Figure 2.1: Schematic diagram of the E A F Direct Evacuat ion System Furnace Shel l Rocker Ti l t Cyl inder Water C o o l e d R o o f W o r k i n g Platform Power Conduct ing A r m s Graphite Electrodes M o l t e n Steel E B T Tapping Teeming Ladle R o o f Suspension B e a m Water Coo led Cable The E A F is a classic 'batch' process with all of the control issues associated with unsteady-state operation. The tap-to-tap cycle (from scrap charging to emptying the furnace of liquid slag and liquid steel) involves initial melting of lighter scrap with oxy-fuel burners in combination with radiant heat transfer from the arcs struck from the electrodes to the scrap. As melting progresses the electrodes are lowered (the bore-in period) to approach the liquid metal bath forming within the hearth. Once a significant bath level is achieved, oxygen and carbon are lanced into the metal bath to generate C O (the carbon boil) to generate a 'foamy' slag which, by submerging the electrodes, minimizes radiative heat transfer from the arcs and allows ramp-up to full electrical power. Because they generate less noise (both audible and into the electrical grid), from the mid 1990's D C furnaces have been favored over earlier A C designs. Once C O generation becomes significant, oxygen is injected into the freeboard space above the slag to provide additional heat release by combustion of C O to CO2 (termed post-combustion). Secondary exothermic reactions within the bath (e.g. - 6 -oxidation of Si) also provide small amounts of energy. The metallic oxides wi l l report to the slag. As the Tight' component of the scrap charge becomes fully melted the furnace approaches the flat bath condition where only 'heavy' scrap submerged within the bath remains to be melted. Normally it takes over 80% of tap-to-tap time to achieve the flat bath. Once the desired bath composition and temperature are achieved, the hot metal is tapped into a ladle and transported to the ladle furnace station for refining. Tap-to-tap time is typically - 3 5 minutes and the total energy input (electrical and hydrocarbon) wi l l be in the 560 to 680 k W h f 1 range.2 Although the split between electrical and hydrocarbon energy varies widely within the industry, typically about 60% of the energy is via the electrodes but may fall below 50% for some operators.2 Over the last 40 years the industry focus has been to reduce tap-to-tap time while shifting away from relatively expensive electricity to cheaper hydrocarbon fue l s . 6 ' 7 ' 8 ' 9 As a result, the tap-to-tap time has been shortened from 3 hours to less than one hour. 1 0 Also, the electricity consumption has been reduced to 50-60% of the total energy input while hydrocarbon fuels contributing 35% or more. 3 ' 1 1 This trend w i l l be continued because of the limited hydroelectricity generation and the environmental issues associated with the nuclear power plants. Therefore, with relatively small impact on the environment, combustion energy from cheaper hydrocarbon fuels w i l l contribute a progressively larger portion of the total energy input for melting at high temperatures in the future. Heat transfer to the bath from the E A F freeboard combustion is constrained by the high thermal resistance of the foamed slag (a combination of low conductivity and significant thickness). Particularly during flat bath conditions, there is limited surface area for heat transfer. The short residence time of the hot gas within the furnace also limits the opportunity for extraction of sensible heat (and also contributes to the substantial dust loss from the furnace). Heat transfer efficiency has been determined to be 60%~70% during scrap melting but only 20%~40% during flat bath conditions due to the foaming slag operation and the small bath surface area (compared with that of the scrap) for heat t ransfer . 1 2 ' 1 3 ' 1 4 ' 1 5 Although very efficient in terms of capturing electrical energy, the combination of operating practice (foamy slag) and furnace shape (which limits the area for - 7 -heat transfer) means that the E A F is perhaps not ideal for utilizing hydrocarbon energy inputs. 2.2 General Characteristics of Rotary Melting Furnace Rotary melting furnaces have been widely used for batch melting o f iron, copper, aluminum and lead. As shown in Figure 2.2, a typical batch rotary melting furnace is a refractory lined cylinder with conical ends. At the front end a burner projects into the furnace. Furnace rotation is by an electric motor drive to the support rollers. For charging and discharging the furnace is tilted forward or backward by hydraulic rams. Charging takes place at the back end of the furnace via a shaking conveyor located above the furnace when the furnace is tilted forward. Hot metal is tapped through the two tapping holes in the front cone. Slag can be poured out through the front or back furnace opening. Figure 2.2: Schematic diagram of a tilting rotary melting furnace Charging device Burner end: Exhaust end Early R M F ' s were generally oil-fired (to obtain a long, luminous flame) using preheated air to increase combustion temperatures and improve heat transfer. A survey of early type - 8 -furnaces (design features, application, operating costs and product quality) was presented by Sochor, 1 6 while other data 1 7 ' 1 8 supports the high specific fuel consumption (in the range of 1,190 kWh f 1 to 2,550 kWh f 1 for iron foundries) but it should be noted that the higher figure includes heating of the furnace from ambient. Although the air/fuel R M F has advantages such as low grit and dust emission, low noise, and low capital cos t , 1 9 ' 2 0 it very nearly disappeared in the iron foundry industry due to the low melting rates achievable as well as difficulties in controlling iron temperature and quality. In 1986 this situation was reversed when the oxy/fuel fired R M F was developed by Sider Progetti, an Italian furnace manufacturer. In comparative testing with 8000 lbs of ductile iron, Lepoutre et a l 2 1 reported a 62% increase in melting rate and a 46% decrease in specific fuel consumption for oxy-gas firing relative to air/oil firing (the energy for oxygen generation was not included in the latter figure). Due to the much lower freeboard gas velocities, oxy-gas firing resulted in only 190 mg m"3 particulate loading (before the baghouse). N O x was an acceptable 70 ppm in the flue gases and furnace noise was reported as low. At present the oxy/fuel R M F ' s are common in the iron foundry industry. A typical foundry charge might be 10-40%) steel scrap, 10-50% pig iron and 20-70% returns or cast iron scrap. The thermal efficiency is more than 60%. For the furnaces with 20-ton capacity, the specific fuel consumption for melting from a hot furnace is about 535 k W h f a n d for holding is 160 k W h t" 1 . 2 1 , 2 2 Timings are roughly 20 minutes for loading, 90-120 minutes for melting, and 10-75 minutes for tapping, the latter depending on the casting speed. 2 2 Levert 2 3 compared the oxy-fuel R M F ' s to cupola furnaces and medium-frequency induction furnaces, and concluded that the former had advantages such as attractive operating features, low energy costs, low investment, and high product quality. Although competitive in terms of specific fuel consumption (535 k W h f 1 for scrap melting), current R M F ' s have a relatively small capacity (typically < 30 tons) and operate in batch mode. In order to replace the E A F in minimill steelmaking, modifications must be made to convert the batch melting mode into a continuous melting process to achieve a - 9 -melting rate > 100 ton h"1. A continuous-type process also improves operational conditions, for example a relatively constant condition for heat transfer, stable working condition for the various sensors, and longer refractory life. Therefore, Barr and Meadowcroft 1 proposed the continuous process rotary melting furnace described previously. 2.3 Combustion Aerodynamic Phenomena in Rotary Melting Furnaces For the development of a heat-transfer model for the C P R M F , it is useful to first understand and predict combustion aerodynamic phenomena within the R M F . Combustion aerodynamics influences not only fuel/oxygen mixing patterns (hence the heat release rate from combustion) but also heat transfer within the gas phase. Because of the similar geometry and burner arrangement, aerodynamic phenomena in the R M F might be expected to be similar to those in rotary kilns. However, it should be noted that processing conditions in kilns are favoured by slowing the combustion process in order to extend heat release over a considerable distance along the kiln. The C P R M F is envisioned as a relatively short furnace and the design of the burner system would focus more on maximizing heat transfer. Many studies have been made on turbulent diffusion flames in rotary kilns. These efforts include the early acid/alkali modeling and the later three-dimensional computational flow dynamics (CFD) simulation. Based on experimental observations, Ruhland 2 4 developed an empirical flame length model to simulate fuel (pulverized coal) and air mixing in cement rotary kilns. In the experiments a mixture of caustic soda, water and thymolphthalein (as the visual indicator) was employed as the primary jet while a dilute solution of hydrochloric acid was used as the secondary stream. Interaction of the two streams represented the mixing of the fuel and air. Assuming that "mixed-is-burnt", the well-mixed region was considered the flame. Based on the laboratory and plant measurement, a general equation for flame length in a rotary kiln was developed. Although useful, the correlation is limited by a non-swirling jet of fuel from a smooth tubular nozzle. Combustion aerodynamics in rotary kilns (or R M F ' s ) is more complex due to various designs and arrangements of the burner (or burners) as well as operation conditions. - 10 -As shown in Figure 2.3, combustion aerodynamics in rotary kilns involves a confined primary jet (fuel plus primary air) entraining secondary air. Ricou et a l 2 5 measured the entrainment capability of a confined jet by surrounding a jet with a porous-walled cylindrical chamber then injecting air through the wall until no pressure gradient was detected. The measured flow rate of injected air was assumed to be equal to that a free jet would entrain. Recirculation may or may not occur depending on the primary to secondary momentum ratio. When the supply of secondary air is less than the jet is capable of entraining, a recirculating flow is set up downstream o f the point (point P in Figure 2.3) where all the secondary air has been entrained. When the fuel and air are introduced through double concentric jets, a longer recirculation zone would be produced as shown in Figure 2.4. Multiple burners distributed over the available area would produce only a short recirculation zone near the top of the furnace (Figure 2.5). 2 6 Figure 2.3: Schematic diagram of gas flow resulting from a single burner with a primary jet and secondary air I i i I i( Secondary f lu id i ~~--^ ____t= Pr imary jet ^ .—______ L i q u i d bath -11 -Figure 2.4: Schematic diagram of gas flow resulting from double concentric jets Recirculation zone ! p Double concentric _ i jets L i q u i d bath Figure 2.5: Schematic diagram of gas flow resulting from multiple burner arrangement Recircula t ion zone f« * ! ! P Multiple burners L i q u i d bath Several attempts have been made to obtain suitable similarity parameters for modelling the confined jets. The Thring-Newby 2 7 similarity criterion assumes that the primary jet behaves as a free jet until it reaches the wall at the axial distance x p = 4.5rF . Using Hinze's 28 formula for entrainment rate versus axial distance x, the mass flow rate at which the secondary flow exactly satisfies the entrainment requirement as the primary flow spreads to the wall can be evaluated by replacing x w i t h x p . A similarity parameter is proposed in this unique situation: - 1 2 -9 , = m p + m s r 0 m p r F (2-1) where rh p and rh s are the mass flow rates of the primary and secondary flows respectively, r 0 is the nozzle radius for the primary jet, and r F is the ki ln radius. When cpi<0.9, recirculation wi l l occur. This similarity parameter is only applicable to constant-density system. For a non-isothermal burning jet, the similarity parameter can be modified by replacing r 0 with an equivalent radius r'0 = r 0 ( p p / p s ) ° 5 where p p and p s are the densities of the primary and secondary flows respectively. When the fuel and air are introduced through double concentric jets (Figure 2.4), the two jets can be represented by a single burning jet of an equivalent radius (r0") and an equivalent density. Based on the modified Ricou's equation 2 5 for a non-isothermal jet and a jet angle of 9.7° ( x p = 5.85r F), a new similarity parameter is introduced: Again, q)2<0.9 means that recirculation w i l l occur. The Thring-Newby similarity parameters should only be applied to systems with a small nozzle diameter in a large mixing chamber A n alternative method to model the confined jets is the Craya-Curtet ' similarity criterion, in which a dimensionless parameter r\ was derived by solving the Navier-Stokes and continuity equations for a single constant-density incompressible fluid. The parameter m represents the thrust term (sum of momentum flux and pressure force) and is a function of the excess discharge ratio R (the ratio of excess volumetric flow rate of primary discharge to total volumetric flow rate): Here K is the momentum coefficient accounting for the shape of the excess velocity profile in the jet. For an axi-symmetric jet it is equal to 0.579 (cosine curve) or 0.5 (Gauss curve). r p and rs are the radius of the primary and secondary flows respectively. The Craya-Curtet (2-2) (— < 0.02). They do not apply to typical rotary kilns (or R M F ' s ) w i t h - ^ > 0.05. r F r F m = R - 1 . 5 R 2 + K ( r s / r p ) 2 R 2 (2-3) - 1 3 -parameter is also identified as Craya-Curtet number: Ct = - L (2-4) vm When Ct<0.8 (or m>1.5), recirculation wi l l occur. Using cold flow modeling techniques with operating conditions corresponding to typical recirculation intensity (0.4<Ct<0.8) in rotary kilns, Moles et a l 3 1 fund that Ct number is a useful indicators of recirculation levels. Many multi-dimensional C F D models have been developed for the hot gas flow within the freeboard of rotary kilns. These models w i l l be described later in the section "Closely Related Furnace - Rotary Ki lns" . In this study, C F D simulation is not employed because the data from the bench-scale trials was inadequate for meaningful validation, for example, the gas temperature was measured at only one position. The C P R M F in this study would almost certainly use a very high intensity burner and the key issue wi l l be recirculation induced by the confined gas-fuel jet. One effect of the recirculation is to increase the fuel/oxygen mixing-length (hence decrease the heat release intensity from combustion) because the entrainment of recirculated oxygen-deficient combustion products into the fuel jet delays the fuel/oxygen mixing by diluting the available oxygen in the flame. Another effect of the recirculation is to promote axially wel l -mixed conditions over the recirculation zone due to heat and mass transfers induced by the recirculated flow. The length of the recirculation zone can be controlled by the number and placement of the burners as well as the swirl effect induced by burner design. The intent of the current modeling work is to determine the burner characteristics suitable to the process so considerable latitude is desirable in the range of specifiable combustion variables. The recirculation length is treated as an independent variable for the furnace model, i.e., the model can assign axially isothermal gas conditions over any fraction of the furnace length (in discrete increments set by the number of volume zones used in the radiation model). 2.4 C o m b u s t i o n o f N a t u r a l G a s at H i g h T e m p e r a t u r e s The viability o f the oxy-fuel C P R M F depends on achieving combustion temperatures in the -14-order of 2200 °C. 1 A t these temperature levels both CO2 and H 2 0 wi l l be partially decomposed via the reactions: 2 C 0 2 = 2CO + 0 2 2H 2 0 = 2H 2 + 0 2 Thus the combustion process w i l l not be completed and the effective heat release w i l l be less than the theoretical (full conversion to C 0 2 and H 2 0 ) because the dissociation of H 2 0 and C 0 2 absorbs some of the combustion energy. Although not a significant factor in the bench scale trials, where gas temperatures were < 1700°C, the thermodynamics of these reactions w i l l become significant in the commercial-scale process. Using the commercial H S C 3 2 software, equilibrium compositions for methane combustion at different temperatures can be evaluated and the results are shown in Figure 2.6. Based on the equilibrium product compositions, the effective heat of combustion can be determined as a function of temperature; i.e. f \ Y H - V H Z _ I f,298°K /—i f,298°K ^products reactants J Q comb These results are shown in Figure 2.7 (2-5) Figure 2.6: The equilibrium products of C E U combustion as functions of flame temperature 70 11 60 — •g 50 --O <D 40 --a* Ji 30 " 0 20 — 10 — 0 1500 1650 1800 1950 2100 2250 2400 2550 2700 2850 3000 Flame temperature, °C -15-Figure 2.7: Effective heat of CH 4 combustion as a function of flame temperature - 36000 ! | 34000 -3 32000 -f 30000 -g 28000 -H 26000 -| 24000 -° 22000 -' f 1 1 1 1 1 I 1 i 1 1 1 1 1 1 1 1 L i I i i \ . i i L i 1 i ' s \ 1 i J - 1 1 1 " ^ J . i I l 1500 1650 1800 1950 2100 2250 2400 2550 2700 2850 3000 Flame temperature, °C 2.5 Heat Transfer Processes in Rotary Melting Furnaces A s shown in Figure 2.8, heat transfer in the rotary melting furnace involves three distinct domains; i.e. the freeboard volume, the metal/slag bath and the refractory, all linked by shared boundary conditions. Within the freeboard volume, energy is transferred by both radiation and convection from the hot freeboard gas to the exposed refractory and bath surfaces ( Q g _ e w and Q g _ e b ) . Radiative exchange also occurs between the refractory and bath surfaces ( Q e w _ e b ) . A n important feature of the R M F is regenerative heat transfer from the refractory to the bottom surface of the bath; i.e. due to furnace rotation, a portion of the energy absorbed by the refractory during exposure to the hot freeboard passes into the bath during the period in contact with the liquid metal ( Q c w _ c b ) with the remainder being lost through the refractory by conduction ( Q s h e l l ) . Thus the entire surface area of the bath is available for heat transfer. Regeneration provides a cooling mechanism for the refractory hot-face but also induces thermal cycling of the refractory which could impact on service life. Although a temperature gradient wi l l be developed between the slag/freeboard and slag/metal interfaces due to the small conductivity of the slag layer, the high conductivity of the metal bath (about 40 W m"1 °C _ 1 for steel), combined with rotation-induced stirring along with the tumbling motion of the solid scrap component within the bath, promotes an -16-isothermal metal bath in the transverse plane and, provided the furnace is kept 'short' (length/diameter <5) should also maintain relatively uniform metal bath temperature in the axial direction. F i g u r e 2.8: H e a t t r ans fe r i n the t ransverse p l ane of the R M F For industrial oxy-fuel-fired R M F ' s operating at >1600 °C thermal radiation is the dominant mechanism for heat transfer within the freeboard space with convection from the gas-phase playing only a minor role. According to Watkinson et a l , 3 3 for a 0.406m ID x 5.5m long kiln (heat transfer processes within the kiln freeboard are similar to those in the R M F freeboard) operating at low gas temperatures from 600 K to 1100 K , the convective heat transfer accounted for less than 15% of the total gas-to-wall heat flow. With increasing gas temperature, the increase in the total heat flow was mainly contributed by radiation and the convective coefficient was almost temperature-independent. Barr et a l 3 4 developed a cross-section model for the same kiln and reported that the gas/wall radiative coefficient (the partial pressure of emitting gases was 0.33 atm) increased from 30 W m"2 K" 1 to 60 W -17 -m"2 K" 1 as the gas temperature increased from 1000 K to 1800 K . In addition, scale-up by one order of magnitude (0.4 m to 4 m ID) resulted in a threefold increase in radiative heat transfer from the gas. In another study Tscheng and Watkinson 3 5 reported that the gas/wall convective coefficient decreased from 15 W m"2 K " 1 to 1.5 W m"2 K " 1 when the inner diameter of a ki ln increased from 0.2 m to 2 m. Therefore, for a 4 m ID oxy-fuel fired R M F convective heat transfer is unlikely to make any significant contribution to total heat transfer. Radiative Exchanee within the Furnace Freeboard In terms of radiative heat transfer, the furnace freeboard is an enclosure of several opaque walls (and end openings) containing the emitting/absorbing gas mixture resulting from combustion. The radiative characteristics of the walls can be described by the simple model of gray and diffuse emission, absorption and reflection. Although gray bodies do not exist in practice, radiation calculations based on the gray assumption can give satisfactory accuracy. 3 6 If an actual surface has large variations in the monochromatic properties, the total properties can be approximated by dividing the electromagnetic spectrum into segments over which the properties can be assumed constant. A diffuse surface is one for which the monochromatic radiative intensity is constant in all directions within a hemisphere over the surface. Actually no real surface can be a diffuse emitter. As seen in Figure 2 .9 , 3 7 for surfaces of electrical nonconductors directional emissivity (averaged over the entire spectrum) varies little over a large range of polar angles but decreases rapidly at grazing angles until a value of zero is reached at 0=71/2. Since little energy is emitted into the grazing directions, a surface of electrical nonconductor can be considered a diffuse emitter. In addition, refractory surfaces generally have larger roughness than optically smooth surfaces so that the diffuse reflection is an acceptable assumption. -18-Figure 2.9: Directional variation in surface emissivities for some electrical nonconductors 1.0 O.S 0.6 0,4 0.2 0.2 0.4 0.6 0.8 1.0 a wet ice b wood c glass d paper e clay / copper oxide g aluminum oxide The radiative properties of diatomic gases such as co2 and h2o vary so strongly and rapidly across the spectrum that the assumption of a gray gas cannot offer a good accuracy. Several techniques can be used for the treatment of nongray extinction coefficients such as the semigray approximation, the stepwise-gray model, the wide band model for isothermal media, and the weighted-sum-of-gray-gases model. The last method (also called clear-plus-N-gray-gas model) can be expressed by the equation 3 8 ^ - t ^ n ( T g ) ( l - e - K " P I - ) (2-6) n=0 where s g is total emissivity of the gas mixture, a r n ( T g ) is coefficient for the weighted summation (a function of gas temperature), K n is extinction coefficient, P is partial pressure of the emitting/absorbing gases, and L m b is mean beam length. In effect the radiative characteristics of the gas mixture are simulated by a weighted summation of several gray gases. In order to account for the wavelengths which are not absorbed by the actual gas, one of the gray gas components in the equation is assigned an extinction coefficient of zero. -19-Analytical solutions"*9 have been studied for simple problems such as thermal radiations in one-dimensional plane-parallel, spherical, and cylindrical gray mediums which are either at radiative equilibrium or whose temperature fields are known. These solutions can give qualitative indications for more difficult solutions and can be employed to test more general solution methods. Even for the simplest case the exact solutions can only be cast implicitly in the form of an integral equation. This leads to the development of approximate solution techniques, 4 0 some of which are applicable for limiting conditions (cold medium approximation, optically thin and thick approximations) and others are used to make approximations for directional distribution of intensity (two-flux approximation, P N -approximation, SN-approximation). Applications of these numerous approximations are limited by simple medium conditions (gray media or on a spectral basis). The zone method combined with a clear-plus-multiple-gray emissivity/absorptivity model for the gas phase is commonly employed to solve the radiative problem within an enclosure. This method was developed originally by Hottel and Cohen 4 1 in 1958 for an absorbing, emitting, nonscattering gray gas with constant absorption. Later it was extended to deal with isotropically scattering media with nonconstant and nongray absorption coefficients. 4 2 In this method the enclosure is subdivided into a finite number of gas volume and surface area zones. The surface zones are assumed to be small enough so that their radiosities do not vary appreciably across them. Also, each zone is assumed to be isothermal i.e. characterized by a single zone temperature. Once the enclosure is subdivided into n surface zones and m gas volume zones, the next step is to calculate the temperature-independent direct exchange areas (shown in Appendix A ) for each extinction coefficient, which are then solved for the temperature-independent total exchange areas (Appendix B) in order to account for surface reflection. Temperature-dependence can be brought in via energy balance in which one set of directed total exchange areas ( S ; S j , S ; G j , GjSj and G ; G j ) is evaluated using the temperature-independent total exchange areas for each extinction coefficient and the corresponding temperature-dependent emissivity/absorptivity weighted coefficients. -20 -H a v i n g the temperature-dependent total exchange areas, the energy balance can be performed for each enclosure zone. The net radiative heat transfer rate to surface zone Aj can be g i v e n by: Q A l =E(sX E bs, J - s ^ E b s J + j r ( o X E b & j - s ~ _ X , ) (2-7) j=i j=i Equa t ion (2-7) is the radiative component o f the surface zone heat balance w h i c h w i l l also include conduct ion through the w a l l plus convect ive heat transfer to the surface i f this is significant. S imi l a r ly , net radiation from vo lume zone V ; to other enclosure zones is Qvi = S f e b , , - W J + Z vWb61 - G ^ X J (2-8) j=l j=l F o r problems i n v o l v i n g combust ion and gas f l ow w i t h i n a furnace freeboard space, Q v i is balanced by the combust ion energy release and the change o f sensible enthalpy for the flow i n and out o f V i . T h e energy balance results i n a set o f simultaneous equations. B y so lv ing this system w i t h iteration technique, temperature o f each enclosure zone (as w e l l as the radiative exchange between zones) can be determined. The accuracy o f the zone method may be improved i n t w o ways: (1) increasing the number o f zones, and (2) increasing the accuracy o f the numer ica l quadrature used to determine ind iv idua l direct exchange areas. In case o f many zones, a l l direct exchange areas but one may be calculated by evaluating the integrand between zonal centers, mul t ip l i ed by the applicable zona l areas and/or volumes. The error made for the closest zones is then offset by app ly ing Equat ions ( A - 1 3 ) and ( A - 1 4 ) ( in A p p e n d i x A ) for the last one ( g ; g ; for vo lume-vo lume areas, common-face g ; s j for volume-surface areas, and common-boundary s ; Sj for a corner zone). I f the zone number is relat ively small , i nd iv idua l direct exchange areas may be evaluated by subdiv id ing each zone into many inf in i tes imal surface or vo lume elements as shown i n A p p e n d i x A . Problems i n thermal radiat ion can also be solved by the M o n t e Car lo me thod , 4 3 ' 4 4 w h i c h treats mathematical problems w i t h an appropriate statistical sampl ing technique. In general, -21 -the Monte Carlo methodology wi l l have advantages when dealing with convoluted enclosure geometries. However, for more regular geometries, the zone method has the advantage in terms of ease of implementation. Transient Conduction Within the Refractory In general the conduction problem is well defined internally, regardless o f whether it is carried over 1, 2 or 3 spatial dimensions. The difficulty comes in establishing the boundary conditions driving conduction. Because in rotary melting furnaces (including rotary kilns in this family) thermal gradients within the refractory in the radial direction are typically 1 to 2 orders of magnitude greater than in either the circumferential or axial furnace directions, the refractory problem has usually been treated as 1-D transient conduction in the radial direction. Vai l lant 4 5 reported that, for rotary kilns, the error introduced by neglecting conduction in both the longitudinal and circumferential directions was < 2%. Thus, at any axial position along a rotary melting furnace, the refractory problem is reduced to solving the 1-D transient conduction equation I A ( r 3 I ) = SPST r dr <9r k dt subject to realistic boundary conditions. Although analytical solutions 4 6 are available for 1-D transient conduction (including cylindrical coordinates), the boundary conditions and/or time constraints for these infinite and semi-infinite wall solutions are not usually applicable to rotary melting furnaces and virtually all rotary melting furnace models have resorted to numerical solutions of Equation (2-9). In terms of numerical solutions for conduction, finite difference (F-D) methods are commonly employed for problems having relatively simple geometries. Due to stability issues, explicit F -D schemes are not commonly chosen even for simple 1-D systems. Instead either fully implicit or semi-implicit (Crank-Nicholson) methods are favored. In implicit F -D form for the general interior node shown in Figure 2.10, Equation (2-9) becomes (uniform nodal spacing) -22 -kAr _ n + I {cppV, + k A ^ + k A + . k A : _ + 1 S p V , Ar At Ar; Ar; y T n + 1 Tn+1 = p j _ i _ T n j Ar 1 + 1 At 1 r + r r + r where A r = 1 '"' A8 and A ^ = 1 1 + 1 A8 (unit length in axial furnace direction) are backward and forward nodal areas respectively, and the superscript n refers to the current time step (i.e. the temperature is known) while n+1 refers to the temperature at the next time step (unknown). Because the adjacent nodes are also involved, Equation (2-10) is just one of a system o f similar linear equations for the nodal structure which must be solved simultaneously. Although implicit methods are numerically stable for any combination of time step and nodal spacing, the accuracy is improved by using smaller time steps and nodal spacing. Thus an organized approach combining sensitivity analysis and validation against analytical solutions (using appropriate boundary conditions) is required for any finite-difference numerical model. Figure 2.10: Schematic diagram of an interior node (cylindrical coordinate) The Crank-Nicholson method combines explicit and implicit steps with equal weighting of each. In general, for a given grid structure and time step, the Crank-Nicholson method is accepted to improve accuracy relative to the fully implicit formulation. However, the method is not unconditionally stable. For 1-D problems, the coefficient matrix for the simultaneous F-D equations resulting from the implicit formulation is tridiagonal; i.e. the only nonzero terms occur as 3 diagonal - 2 3 -'bands'. Although 2 and 3-dimensional F -D problems require iterative techniques for solution (for example Jacobi relaxation and Gauss-Seidel relaxation 4 7), tridiagonal systems can be efficiently solved using substitution methods such as Gauss elimination. 4 8 Finite Element Method ( F E M ) is another numerical approach for the transient conduction problems. This approach is based on the continuum view of nature in which natural phenomena can be described in terms of field variables. The F E M solution to the partial differential equations (PDE) is based on weighted residual method (Galerkin's method), a general technique for deriving approximate solution to linear and non-linear P D E . The technique involves two steps: (1) assume a general functional behaving of the field variable, and (2) substitute the approximate solution into the P D E and require the error or residual to be minimized. The advantage of the F E M solution is that it can solve both linear and non-linear problems while the finite-difference method is based on the assumption of linear temperature gradients. However, for geometrically simple problems, the complexity of the F E M formulation can outweigh the advantages. 2.6 K i n e t i c s o f S c r a p M e l t i n g i n L i q u i d Steel Scrap melting is a dissolution phenomenon involving both heat and mass transfer between liquid and solid phases. The melting process may be controlled by heat transfer, mass transfer or coupled heat and mass transfer depending on chemical composition of the solid and liquid phases. For steel scrap melting, the most important solute is carbon. When the carbon content of liquid steel is similar to that of solid steel scrap, mass transfer does not have significant effect on the melting process and the melting rate is controlled by heat transfer. When a piece of solid scrap is immersed into liquid steel, a temperature profile w i l l be developed as shown in Figure 2.11. At the liquid side, heat flow from the liquid to solid is controlled by the thickness and characteristics of the thermal boundary layer (the distance between the interface to the point where the temperature is 99% of T_). Inside the solid, heat is transferred from the exterior to interior sections by conduction. In the early stage of -24-melting, the temperature gradient at the solid side of the interface is large enough so that the heat flux within the solid is larger than that supplied by the liquid. Thus a solidified shell w i l l form around the scrap. The temperature gradient at the solid side decreases with time, while heat flux supplied by the liquid dose not change appreciably. When the heat flux dissipated in the solid is equal to that supplied by the liquid, the solidified shell reaches its maximum thickness. After that the heat flux dissipated in the solid is smaller than that supplied by the liquid thus the solidified shell re-melts. Because there is an interfacial gap between the original scrap and the solidified shell, the heat flux inside the solid phase is not constant, but time-dependent. Thermal resistance of the gap is critical for melting kinetics. However, it is poorly understood and needs to be studied further. F i g u r e 2.11: S c h e m a t i c d i a g r a m o f the t e m p e r a t u r e p ro f i l e I Thermal boundary B y immersing Type 1018 steel bars with different size, shapes and initial temperatures into a 70 kg liquid steel bath at 1650 °C, L i et a l 4 9 investigated the kinetics involved in steel scrap melting. According to the experimental results, the total melting time of a cylindrical bar without preheating increased almost linearly from about 38 seconds to 75 seconds with increasing the diameter from 25.4 mm to 38.1 mm. With preheating, the total melting time of the 25.4 mm (diameter) steel bar decreased approximately linearly from 38 seconds to 22 seconds with increasing the initial temperature from 25 °C to 800 °C. In case of a square bar, the total melting time versus size (edge length) followed the same trend. The difference -25 -was that when the solidified shell disappeared and the initial bar began to melt, the corners melted faster because the ratio of surface area to volume was larger. The angles disappeared gradually and the bar became round until it melted completely. Oxidized samples melted slightly faster than the polished samples, but the effect of the oxidation layer was very small. The maximum thickness of the solidified shell was a little larger for the oxidized samples because in the early stage of melting the heat flux supplied by the liquid steel was reduced by the release of bubbles from the samples. However, as the bubble density decreased at late time, the solidified shell re-melted faster due to an improved heat flux supply resulting from the stirring effect of the bubbles. Besides the experimental work, L i et a l 4 9 also developed a 2-D phase-field model to simulate the melting process and good agreement was obtained with experimental data for single pieces of scrap. In case of melting multiple pieces scrap, the formation of a solidified shell may result in an agglomeration of scrap pieces, which can have a significant effect on the melting process. 5 0 Although efforts are being made to simulate more complex multi-piece melting with fluid f low, 4 9 the results are not yet available. Applying this analysis to the scrap melting furnace indicate about 7 minutes w i l l be required to melt a single piece of steel bar with a diameter of 0.2 m. Considering an industrial-scale C P R M F process with a melting rate of 100 ton h"1, i f 50 tons of steel scrap is charged into a liquid steel bath of 200 tons (average) within 20 minutes during each 30-minute interval of tapping, the solid/liquid coexisting period wi l l account for 90% of the operating cycle while no scrap is present when tapping (agglomeration of the scrap pieces is not considered). The tumbling motion of the solid scrap component within the bath (induced by furnace rotation) wi l l improve a well-mixed bath condition. In addition, the amount of liquid metal is at least 12 times greater than that of the coexisting scrap during each operating cycle, meaning a relatively constant bath temperature and quasi-steady-state melting conditions. -26-2.7 C l o s e l y R e l a t e d F u r n a c e s - R o t a r y K i l n s Rotary kilns, which are employed widely for thermally processing solid granular materials, are functionally similar to the R M F , the chief difference being the much larger ratio of length to diameter (typically 50:1) and a slight slope to move the material axially by gravity. Most industrial kilns operate in countercurrent flow; i.e. solids and gas flowing in opposite directions. Typically the solids bed passes through a drying zone in which free moisture is removed, followed by a heating zone where the material is heated to reaction temperature and a reaction zone where chemical reactions occur. The hot discharged material is frequently used to preheat the combustion air via a grate cooler. Common fuels include pulverized coal, heavy oil and natural gas. A n important difference between the rotary kiln and oxy/fuel R M F is that the former contains granular solids while the later involves a bath of liquid metal and slag. The heat transfer process within the solid bed is affected by transverse bed motion and is quite different from that within the bath. The regenerative heat transfer coefficient in the wall/solid bed case should be much smaller than that in the wall/liquid bath case. The properties of the bed material and the heat transfer conditions vary along the ki ln axis. The bath in the short R M F , however, is assumed to be well mixed with uniform temperature and thermal properties. O n e - D i m e n s i o n a l M o d e l i n e Except that the bath is replaced by a bed of granular solids, rotary kilns involve the same domains (the freeboard and refractory) allowing some of the methodology developed for ki ln models to be applied to the C P R M F . Starting with the freeboard, early ki ln models simplified radiation within the freeboard by a variety of assumptions; e.g. well-stirred conditions, radiatively gray gas emissivity, estimated heat transfer coefficients, simplified geometries, e t c . 5 1 ' 5 2 ' 5 3 Applying the ray-tracing methods, 5 4 Gorog et al showed that although the gray-gas assumption w i l l incur > 20% error in heat-transfer calculations, neglecting axial temperature gradients would incur only minor error; i.e. the 'long furnace' - 27 -assumption. Because of its flexibility and relative ease of implementation, the zone method previously described has been applied to k i l n s , 5 6 ' 5 7 usually in combination with a clear-plus-multiple-gray emissivity/absorptivity model for the gas phase. For energy balance on the gas volume zones, the combustion terms are generally evaluated by prescribing the fraction of the fuel burnt in each volume zone, while the sensible enthalpy terms are evaluated by assuming a plug flow of combustion products. The radiant energy to each surface zone is normally balanced by conduction through the wall. Convective heat transfer can be accounted when it contributes a significant amount of energy to the surfaces. Early models of this type are generally one-dimensional, i.e., the gas temperature and composition are assumed to vary only along the kiln length. Because thermal gradients in the radial direction are 1 to 2 orders of magnitude greater than in the circumferential and axial furnace directions, most ki ln models have assumed heat transfer through the refractory to be transient, one-dimensional conduction in the radial direction, solutions being obtained using numerical finite difference (F-D) or finite element ( F E M ) methods. The chief difference among refractory models is the determination of the boundary conditions. In the earliest invest igat ions 5 8 ' 5 9 ' 6 0 the wall with infinite or finite thermal conductivity was insulated on one side while alternately heated and cooled by a hot gas and a well-mixed charge respectively on the other side to simulate ki ln wall conditions. Vai l lant 6 1 went on to simulate a rotating wall with finite thermal conductivity by including shell losses and wall radiation to the solids surface. Wachters et a l 6 2 applied penetration theory to simulate the period during which the refractory hot-face is beneath the charge and Lehmberg et a l 6 3 improved on this by including a gas film and associated heat-transfer coefficient at the interface to better reproduce experimental data. Cross et a l 6 4 were the first to apply numerical methods to predict the thermal cycling of the hot-face, followed by Gorog et a l 6 5 and Barr et a l 3 4 who extended the conduction domain into the 'plug-flow' region of the charge, again applying a heat-transfer coefficient at the interface. M u l t i - D i m e n s i o n a l M o d e l i n g Jenkins and M o l e s 6 6 were one of the first to develop an axi-symmetric model for the hot -28-gas flow in a cement kiln, using the zone method for radiation and the entrainment rate of Ricou and Spalding 2 5 for gas flow pattern. Heat release from flame was evaluated by the generation rates of combustion products. Although the measured data supported the axi-symmetric temperature profile resulting from the model, the effects of rotating wall and bed were not included. Neglecting the effect of the bed, Alyaser 6 7 developed an axi-symmetric C F D model for combustion aerodynamics and heat transfer in rotary kilns. The turbulent, chemically reacting gas flow was governed by the physical laws of heat transfer (first law of thermodynamics), momentum (Newton's second law) and mass transfer (mass conservation). Using CH4 combustion and heat transfer rates by turbulent diffusion and radiation as the source term, a thermal energy balance was formulated for an incompressible flow in terms of enthalpy (a function of temperature) under an assumption of steady state. In the absence of buoyancy, the momentum equation was solved with the normal stress (pressure) and the viscous force due to shear as the driving forces. For mass conservation, the rate of species consumption or generation in the fluid is governed by the rate of mass transfer (diffusion driven by turbulence) and the rate of combustion reaction. Ignoring buoyancy and rotation, the standard K - S m o d e l 6 8 ' 6 9 was employed to simulate the turbulent diffusivities of heat, mass and momentum using effective viscosity, thermal conductivity and mass diffusivity, each of which was related to the turbulent viscosity. A two-step combustion model for CH4 was adopted. The combustion process was controlled by the mixing of fuel and combustion air. Reaction rates of CH4 and C O were determined 70 from Magnussen's Eddy-Dissipation Model . Radiative heat transfer was solved using the Pi-approximation. 4 0 Using a commercial finite element C F D package (FIDAP) , the equations were treated by Galerkin finite element method 7 1 to obtain a system of linear algebraic equations for each degree of freedom. To obtain a steady state solution, an initial guess for all of the degrees of freedom was given. Convergence was achieved when the relative error for each degree of freedom reached 1 x l O 4 . Mastorakos et a l 7 2 simulated 2-D axi-symmetric gas flow in coal-fired rotary cement kilns then coupled the solution with 1-D models for the rotating wall and bed. The Favre--29 -averaged equations of gas momentum, species concentrations, and energy were solved by an axi-symmetric commercially available C F D code (FLOW-3D) in conjunction with a radiation module ( R A D - 3 D ) in which radiative heat transfer was solved by the Monte-Carlo method. 4 3 ' 4 4 The kiln was divided in non-uniform zones, in each of which the radiation intensity was assumed uniform and the effects of local gas composition and temperature were not considered. The output of the R A D - 3 D module was interfaced internally to the F L O W - 3 D module for fluid calculation, and externally to the codes for the walls and clinker. The authors claimed that the results from the comprehensive model for rotary cement kiln operation were reasonable and reproduced experimentally observed trends. 73 More recently, Georgallis simulated 3-dimensional gas flow and combustion within the freeboard of lime kilns using an existing C F D solver. 7 4 The gas flow model was based on the finite volume method and used block-structured body-fitted coordinates with domain segmentation. The gas was treated as incompressible throughout the domain except for the region near the burner exit where Mach number was high (-0.6) and buoyancy effects were considered by including both the pressure and gravitational forces as the driving forces for momentum transfer. Turbulence was simulated with the standard K - S model of Launder and Spalding together with the wall function approximation. 7 5 Combustion process was simulated by a 1-step model. Combustion rate was limited by the mixing of turbulent eddies and was described using a turbulent time scale K / S in conjunction with the 1-step combustion reaction. Radiation intensity was solved by the ray-tracing technique (Discrete Ordinate Me thod 7 6 ' 7 7 ) , which was carried out for a non-luminous hydrocarbon flame (CO2 and H2O) where only absorption and emission were considered while scattering was neglected. The gray-band model with 5 intervals for each species was used to integrate the spectral intensity. Although a transient solution of the hot gas flow alone was presented, the 3-D gas flow model was coupled with a 3-D bed model and a 3-D refractory model based on an assumption of steady state. Although the zone method has been applied to the radiation calculation with C F D models by using a relative coarse radiative zone grid superimposed over the much finer fluid-flow -30-calculation grid, its application to C F D solutions has been limited by difficulties with coupling the radiation model to fluid flow and combustion models along with the lengthy computation time required in calculating the direct exchange areas. 2.8 Summary The C P R M F process involves phenomena such as combustion aerodynamics and thermodynamics, fluid dynamics, heat transfer processes, and scrap melting kinetics. To rigorously account for all o f these would require a complex and computationally demanding mathematical model. In order to bring the task within reasonable limits, the literature relating to each was used to form physically correct but relatively simplistic assumptions to be used within a heat-transfer model of the C P R M F . Because the geometry is not complicated, the model was built around the zone method for simulating radiative heat transfer. With emphasis determining the overall thermal performance of the C P R M F process, the gas flow pattern was specified rather than calculated. Although computational fluid dynamics allows multi-dimensional simulation for the hot gas flow, this was rejected because the experimental data from the bench-scale trials was inadequate for meaningful validation. In addition, any C F D simulation would require detailed specification of the burner design and arrangement but the intent of the modeling work was to determine the burner characteristics most suitable to the process; i.e. long or short flame, single or multiple burners, etc. rather than precise details. -31 -C H A P T E R 3 - S C O P E A N D O B J E C T I V E S M i n i m i l l steelmaking remains tied to the E A F . However, it is appropriate to consider alternatives due to the E A F ' s not entirely satisfactory transition to the current role of melting scrap at the highest possible rate with high levels of hydrocarbon energy addition. One alternative is the oxy-fiiel-fired continuous-process rotary melting furnace. Although a preliminary modeling study1 has indicated this to be a viable alternative to the E A F , the process has not been demonstrated at any scale and the model itself was relatively simplistic in certain key assumptions, for example, the bath and freeboard gas are each assumed to be well-mixed in both the radial and axial directions which renders the model essentially O-dimensional. The overall objective of this study is to further examine the viability of the oxy-fuel-fired C P R M F as a replacement for E A F ' s in minimill steelmaking. In detail, the tasks include: • The design and construction of a bench-scale C P R M F capable of melting up to 25 kg h"1 followed by a campaign of experimental trials to explore aspects of furnace operation such as oxygen enrichment and slag thickness. • Development of an improved heat-transfer model for the C P R M F , particularly to allow for axial variations in gas temperature over the furnace length. • Partial validation of the model using the results from the bench-scale trials. • Application of the partially validated model for scale-up of results in order to evaluate the commercial viability of the C P R M F process. -32 -C H A P T E R 4 - M E T H O D O L O G Y In this chapter, configuration of the bench-scale C P R M F is presented first, followed by a description of the experimental procedure. Then an attempt was made to evaluate the true gas temperature based on the readings obtained from a suction pyrometer. Finally, development of the heat-transfer model involving three calculation domains (the furnace freeboard, the liquid metal and slag bath, and the refractory structure) is described in detail. 4.1 Design and Configuration of the Bench-Scale C P R M F As shown in Figure 4.1, the bench-scale C P R M F constructed for the campaign consists of a refractory lined 51 cm diameter steel shell and a natural gas burner at one end with provision for scrap charging and tapping at the other end. The furnace is rotated by an electric motor with variable speed gearbox and a chain drive to the furnace. For discharging the liquid metal, a hydraulic jack located at the burner end tilts the entire unit about the pivot located near the discharge-end. Type-S (Pt-PtRh) thermocouples were placed at various depths and axial locations (Figure 4.2) within the furnace refractory structure in order to measure refractory temperatures and thus calculate radial temperature gradient and heat transfer through the wall. A thermocouple (protected by a steel tube) was also placed into the exhaust pipe and its readings were employed to estimate the offgas temperature. A portable gas analyzer (PG-250) 7 9 was employed to continuously monitor O2, C O , CO2, SO2 and N O x in the offgas. After exiting the furnace, air is introduced into the exhaust gas to complete the combustion process before releasing it into the building fume collection system. Although steel scrap would be the material of choice, all trials were performed using copper. Practical considerations limited the shell diameter to 51 cm (20") which, in order to allow a reasonable 25 cm diameter working volume, limited the total refractory thickness to about 12 cm including a 2.5 cm working lining. Wi th around 10 cm of insulating refractory, the shell temperature placed constraints on the maximum bath temperature allowable for the trials. Although the melting temperature of copper scrap is <1100 °C, for the trials the bath temperature was maintained at about 1250 °C (based on the shell temperature constraint) in order to at least approach that for steel scrap melting, about - 3 3 -1600 °C. Because some trials were to be performed with no protective slag layer, thus exposing the bath surface to oxidizing conditions, copper, being relatively noble (at least compared to iron), was deemed the safer material. Figure 4.1: Overal l layout of the bench-scale C P R M F -34-Figure 4.2: Positioning of thermocouples for measuring refractory temperatures 1,2 Thermocouple # 1,2 3 ,4 5 ,6 7 ,8 Shell Distance from hot face, cm 2.5 5.1 10.2 12.0 12.7 A s shown in Figure 4.2, the working volume consists of a cylindrical central section (25.4 cm ID by 40 cm long) with 15 cm long conical dams forming the ends. The relatively 'short' length to ID ratio (< 3:1) was selected in order to encourage a well-mixed (isothermal) bath condition. At the maximum fil l level of 20%, the capacity of the furnace is about 50 kg of liquid copper (8930 kg m"3). Again based on physical constraints, the furnace was designed to a maximum melting rate of 25 kg h"1. For the trials, the bath weight was maintained at about 47 kg except during the tapping/charging process (carried out at 30-minute intervals) during which -10 kg (depending on the melting rate) of liquid copper was tapped and a corresponding amount of solid scrap charged. The furnace design was based on a two-layer refractory structure, the thermal resistance of the denser working lining just being sufficient to avoid liquid copper penetration into the backing insulating refractory layer. N A R M A G - F G castable, which composition and properties are shown in Table 4 .1 , 8 0 was selected for the working lining. This magnesia--35 -chromite refractory has a very good resistance to corrosion by basic slags involved in steelmaking and copper melting. The insulating layer is P L I C A S T LWI-24R, also a castable with a low thermal conductivity and a low density (Table 4.1). With the fixed total refractory thickness of 12 cm, refractory compromises between the insulating and working layers were examined using the previous model. 1 The results indicated that a working layer of 2.5 cm combined with an insulating layer of 9.5 cm resulted in an interface temperature of 1240 °C and a shell temperature of 174 °C. Heat loss through the wall was about 15% of the total combustion heat. This was the best compromise to minimize the shell temperature and heat loss with a necessary thickness of the working lining to prevent penetration of the liquid metal. Although a thinner working layer (1.3 cm) with a thicker insulating layer (10.7 cm) could offer a lower shell temperature (158 °C) and a smaller heat loss (14%), the liquid metal and slag might penetrate through the cracks (resulting from thermal shock) in the working layer and reach the insulating layer. On the other hand, a thicker working layer (3.8 cm) with a thinner insulating layer (8.2 cm) was safer for corrosion and penetration of the liquid bath. However, it resulted in a higher shell temperature (192 °C) and a larger heat loss (17%). T a b l e 4 . 1 : P r o p e r t i e s o f the r e f r ac to ry used i n the bench-sca le R M F Composition (wt%) Conductivity (W nf 1 ° C _ 1 ) Density (kg m"3) Max. T CC) S i 0 2 A 1 2 0 3 CaO M g O C r 2 0 3 F e 2 0 3 N A R M A G -F G castable 1.0 5.6 0.9 62.4 18.8 11.3 3.0 3030 1870 P L I C A S T LWI-24R 47.6 37.5 9.3 - - - 0.5 1360 1371 Two burner designs were employed for the trials. For the initial trials carried out using air with low levels of oxygen (<55%), the burner (Figure 4.3) did not include an auxiliary cooling circuit. As shown in the figure the natural gas is supplied centrally to the nozzle with the combustion air flowing in the annulus. The natural gas jetted at an angle of about 15 deg to the furnace axis into the surrounding combustion air. The gas flows were measured by individual rotameters. Calibration of the rotameters was against a positive -36-displacement diaphragm-type gas meter (0.028 m 3 per round). Correction factors were applied to convert the readings to those under standard conditions so the error in the measurements mainly came from the readable error. Assuming a readable error of 25% of the increments, the errors were <0.2 N m 3 h"1 in the natural gas and oxygen measurements 3 1 and <0.4 N m h" in the air flow measurements (Table 4.2). These errors account for 5-10% of the corresponding readings in the experiments. For the trials carried out at high levels of oxygen enrichment, the burner design was modified to incorporate an air-cooling circuit (Figure 4.4) in order to control the temperature and oxidation rate of the nozzle head. Figure 4.3: The initial burner design without cooling Outer tubing Inner tubing 02 Figure 4.4: The modified burner design including air-cooling CH4 Air IJ-4 -Thermocouple Outlet for cooling air . " i n = t \ Q2 Inlet for cooling air -37-Table 4.2: The errors in the gas flow measurements Rotameter Readings in the experiments (Nm 3 h"1) Increment (Nm 3 h' 1) Error (Nm 3 h' 1) Error/Readings Natural gas Single 1.95-2.60 0.65 ±0.16 6.2%~8.2% Oxygen Single 2.93-4.04 0.73 ±0.18 4.5%~6.1% A i r #1 4.85-11.48 1.62 ±0.40 3.5%~8.2% #2 1.34 0.30 ±0.07 5.2% Measurement of the gas temperature within the furnace freeboard was by the suction pyrometer shown in Figure 4.5 which consists of a Type-S (Pt-PtRh) thermocouple within an alumina tube connected to a vacuum pump by flexible tubing. Suction from the pump produced a reasonable gas velocity (around 75 m s"1) at the thermocouple junction. The velocity was determined roughly using the gas flow rate measured by the positive displacement diaphragm-type gas meter and was checked by the pressure drop through the tubing measured by a pressure gauge with a full scale of 400 kPa and an increment of 10 kPa. A filter containing silica gel was employed to remove the dust and moisture in the gas sample. The procedure of gas temperature measurement is shown later in this chapter. Figure 4.5: Schematic diagram of the suction pyrometer showing gas meter and suction pump Thermocouple A l u m i n a tube Flex ib le tubing Suct ion pump Gas meter Fi l ter - 38 -The portable gas analyzer can measure the concentrations of five species O2, CO2, C O , SO2 and N O x in the offgas with measurement ranges of 0-25 vo l%, 0-20 vo l%, 0-5000 ppm, 0-3000 ppm and 0-2500 ppm respectively and accuracies within ± 2% of the full scales. With emphasis on combustion control, i.e., minimize both C O concentration (typically <2000 ppm) and 0 2 concentrations (typically <3%) in the offgas, calibration was conducted for oxygen only using argon (containing 2 ppm O2) for the zero point and air for the span point. The C O sensor was not calibrated because the C O concentration can be controlled to a very low level by the excess oxygen. The gas analyzer was connected to a computer data logger so that the readings can be recorded automatically at a specified interval. Again, a filter containing silicon gel was employed to remove the dust and moisture in the gas sample. A clay-graphite crucible (Figure 4.6) with a maximum service temperature of 1450 °C was employed for each tapping of liquid copper. Composition of the crucible includes 20-25% S i 0 2 , 12-14% AI2O3, 20-25% SiC and >38% free carbon. According to the predetermined volume of tapped copper, the same volume of water was put into the crucible and a mark was made at the "water line" on the inner crucible wall so that the amount of tapped copper can be controlled. After being dried, the crucible was placed in a steel box lined with firebricks. The box containing the crucible was moved to the tap position for tapping and was pulled away from the position after tapping. F i g u r e 4.6: S c h e m a t i c d i a g r a m o f the c r u c i b l e a n d the steel b o x Clay-graphite Crucible Mark -39-A simple device shown in Figure 4.7 was used to measure the slag thickness. It was made using a piece of copper rod with a diameter of 4 mm. The slag thickness is measured by immersing the copper rod into the liquid copper bath through the slag layer for 2 or 3 seconds then taking it out of the bath. In the early stage of the immersing period, both a solid slag shell and a solid copper shell w i l l form around the rod at different parts. The solid copper shell as well as the corresponding part of the rod wi l l be melted completely in 2 to 3 seconds, while the slag shell keeps in solid due to its larger heat capacity and the larger thermal resistance of the surrounding liquid slag. Thus the slag thickness can be measured. Figure 4.7: Schematic diagram showing the measurement of slag thickness 4.2 Experimental Procedure A l l trials were performed using copper scrap using the standardized procedure to be described. Each trial consisted of a warm-up phase requiring several hours followed by a steady-state operation (fluctuations in the bath temperature was <20 °C). Although the temperatures were monitored during the warm-up, all data reported is for the steady-state operation. Based on the previous modeling work the key variables to the furnace operation C o p p e r r o d T h e s l ag s h e l l keeps i n s o l i d T h e co p p e r she l l a n d the part o f the r o d are m e l t e d -40 -would be the combustion temperature achieved and the thermal resistance of the slag. Thus the variables for the trials were: (1) Oxygen content of the combustion air; i.e. 37.1%, 53.0%, and 80.3% oxygen. During these trials there was no slag present layer. The trial with 53.0% oxygen was repeated to check the repeatability. (2) Thickness of slag; i.e. 1.3 and 2.5 cm of slag. For all trials the furnace rotation was 1 rpm and the fill set at 20%. It should be noted that this 20% fill included the slag when present. The furnace was fired with natural gas and air with levels of oxygen enrichment up to 80%. Table 4.3 shows the composition of the natural gas provided by the vendor Terasen Gas. Based on a product temperature of 150 °C, low heating values of the'individual combustibles were determined using H S C software and then were used to calculate low heating value of the natural gas according to the composition. The result indicated that the low heating value of the natural gas is about 35,570 kj Nm" . Table 4.3: Natura l gas properties Composition (mol%) L o w heating value (kJ Nm" 3) C H 4 C2H6 C3H8 C4H10 C5H12 C 0 2 N 2 Remainder 96.4 1.6 0.42 0.15 0.04 0.53 0.8 0.06 35,570 The copper scrap was electrical grade copper (> 99.9% Cu) and the relevant thermophysical properties are summarized in Table 4 .4 . 8 1 ' 8 2 The thermal properties were 32 evaluated from Figure 4.8, which was obtained by H S C software. The heat content at liquidus is the summation of the fusion heat plus the sensible heat of solid scrap at the melting point. -41 -Table 4.4: Properties of the copper scrap Liquidus (°C) Heat content at liquidus (kJ k g 1 ) C p , C u , L ( k J k g 1 °C _ 1 ) Conductivity (W nf 1 "C^1) Density (kg m"3) Viscosity (V s"1) 1085 675.2 0.494 391 8940 3.36xl0" 7 Figure 4.8: Enthalpy of copper versus temperature iiHil 900 800 700 600 500 400 A 300 : ; ; . ! f l ; ; ; iiMl 200 100 0 SI! II ;;;;;; ' 1 1 liiipi;! U 1 I i-i!:!;:.;:.. ililii 1 1 il!)!!!!!! lip!!! i : : : : : ! : : : : : : „•.•„•„• ,-,.w,----• B #1§ _p " X -•••••• pi if ^ - ' i .::::: j,. :.:::. liii ! If §1 0 200 40Q 600 S0Q 1000 1200 1400 T e m p e r a t u r e , ° C For the trials performed with a slag layer two factors were considered; i.e. the melting temperature should be < 1250 °C (the bath temperature) and the composition should be basic to ensure fluidity and minimal interaction with the refractory lining. For this purpose slag from Teck-Cominco's zinc-fuming furnace was used as a starting point but modified by CaO, M g O and SiC>2 addition to the composition shown in Table 4.5 which is within the 83 low temperature liquidus region of the Si02-CaO-FeO system with a melting point of about 1220 °C. Using the conventional V ratio 8 4 wt%CaO + w t % M g O V wt%SiO, (4-1) the basicity is about 1.0 which should be compatible with the refractory at temperatures lower than 1500 °C. The M g O addition (7.3%) was to reduce viscosity without significantly increasing the melting temperature 85, 86 -42 -Table 4 . 5 : Compositions of the modified slag and zinc-fuming slag S i 0 2 (wt%) CaO (wt%) FeO (wt%) F e 2 0 3 (wt%) M g O (wt%) A 1 2 0 3 (wt%) ZnO (wt%) Remainder (wt%) Modified slag 29.7 23.0 29.1 2.5 7.3 3.5 2.8 2.1 Zinc-fuming slag 29.8 17.2 37.0 3.2 1.2 4.5 3.6 3.5 Each trial consisted of a warm-up phase followed by a steady-state operation. As shown in Figure 4.9, to begin each experiment the empty furnace was slowly heated to about 1200 °C (hot-face temperature) using low firing rates and low oxygen enrichments in the combustion air. Then the flow rates of natural gas, oxygen and air were set to the predetermined levels for each trial (Table 4.6) and held at these levels for the duration of the trial. After setting the firing rate, copper scrap was charged into the furnace and was melted at a hot face temperature of 1200-1250 °C to form a full bath (about 47 kg of liquid copper). Once the copper was fully melted and a bath temperature of 1250 °C reached the tapping/charging process (previously described) was commenced at 30-minute intervals. A l l conditions were then maintained constant (with tapping/charging every 30 minutes) until all furnace temperatures stabilized. This indicated steady-state which was then continued for one hour during which time all available operating data were recorded. A l l of the experimental results reported are based on the measured data during the steady-state phase. In the trials with slag, the slag thickness was measured after each tapping using the method described previously. A n approximately constant slag thickness was maintained by adding make-up slag as required to cover any slag loss during tapping (make-up slag was included in the energy balance described later in this chapter). - 4 3 -Figure 4.9: Experimental schedule Room temperature T hf=1200 °C T b a t h = 1 2 5 0 ° C L o w firing rate and oxygen enrichment V Start target firing conditions; melt 47 k g o f C u scrap and reach 1250 °C ^Commence target tapping and charging process ^ Beginning of thermal steady state Start k-Heat furnace up Make a full bath •*h-Melt C u scrap with tapping/charging •U -5 hours 2-3 hours 1 hour 1 hour Table 4.6: The firing rates during the melting period Trial Slag (cm) Natural gas ( N m 3 If 1) Oxygen (Nm 3 h"1) A i r (Nm 3 h"1) Total (Nm 3 h"1) O2 level (%) Excess O2 (%) 1 N / A 2.60 2.93 11.48 17.01 37.1 3.0 2 N / A 1.95 3.30 4.85 10.10 53.0 10.9 3 N / A 1.95 4.04 1.34 7.32 80.3 10.8 4 1.3 1.95 3.30 4.85 10.10 53.0 10.9 5 2.5 1.95 3.30 4.85 10.10 53.0 10.9 Once the tapping/charging process was commenced, the temperatures of the bulk metal bath (Tbath), exposed bath surface (Teb), exposed refractory hot-face (T e w ) and freeboard gas (T g ) were measured at 60-minute intervals so that the process was not interrupted too frequently as acquiring these temperatures required stopping furnace rotation. The bulk bath temperature was measured by immersing an alumina-sheathed thermocouple into the liquid copper to a depth of about 3 cm. The temperatures of the exposed bath surface and refractory hot-face were measured both by the thermocouple (inserted through the back-end -44-and brought into contact with each surface) and a dual colour optical pyrometer. Although the thermocouple has an accuracy of ±2 °C, the errors in the measurements of Tbath, T eb and T e w were estimated to be <20 °C because the thermocouple junction was sheathed with an alumina tube thus there was a temperature difference between the tube outer surface and the thermocouple junction. Data for determining the freeboard gas temperature were obtained with the suction pyrometer positioned on the furnace centreline about 18 cm into the furnace from the back-end (the same axial position as that of #2 thermocouple in Figure 4.2). In performing this measurement, a stable thermocouple reading was first obtained with the suction pump off, which was assumed to be the temperature of the alumina tube (Ttube) enclosing the thermocouple junction. The vacuum system was then started and maintained until the indicated temperature stabilized (T t c ). The gas temperature T g was calculated based on Ttube and T t c as shown later in this chapter. Also, the offgas temperature Toffgas was estimated according to the readings of the thermocouple placed into the exhaust pipe. During each trial the shell temperature (Tsheii) and refractory temperatures were recorded on a continuous basis, both for assessing when steady-sate had been achieved and for use in the heat balance calculation. The errors in the temperature measurements for the refractory and shell were estimated to be ±10 °C because of the minor difference of refractory thickness in different radial directions as well as the small error in thermocouple positioning. To monitor the combustion process, concentrations of O2, C O , CO2, S02 and N O x in the offgas were measured continually by the gas analyzer and were recorded automatically at 1-minute intervals with the computer data logger. 4.3 Gas Temperature Calculation and the Furnace Energy Balance In determining the gas temperature from the suction pyrometer data the heat balance for the thermocouple junction was used as the starting point: h c ( T g - T t c ) = h r ( T t c - T t u b e ) (4-2) In Equation (4-2) the convection heat-transfer coefficient was evaluated using the correlation for forced convection over a sphere: 8 7 -45 -N u = h c x D t c = 0.37 x Re£ 6 17<ReD<70000 (4-3) k s The radiative heat-transfer coefficient was evaluated using the expression for a small gray body within a large enclosure 8 8 h _ S P t ° ( T t c ~ T t u b e ) ^ _ 4 ^ where s p t is the normal emissivity of the thermocouple junction. Although the 89 hemispherical emissivity of polished platinum is around 0.18 at 1500 K , was assumed to be 0.5 because of the higher freeboard gas temperature and minor oxidation of the thermocouple junction. The applicable temperature correction T g - T t c as a function of gas velocity over the thermocouple is shown in Figure 4.10. Based on the gas velocity of 75 m s"1 as estimated from the procedure described previously, the thermocouple readings with the vacuum pump in operation can be seen to be about 100 °C below the true gas temperature. Figure 4.10: Gas temperature correction versus gas velocity over the thermocouple 550 i • 1 • 500 - L _i _i 450 - \ i 1 1 1 ~\ ~^ r "1 400 - \ j L J i L o o 350 - V 1 1 i 1 i o 300 - \ 1 1 1 ; \ ; 1 ; on H 250 -200 -•[ j" I 1 150 - ---'< — i ; 100 -i 1 1 i * — - < i I 1 i * • * • — * ~ — , 50 - - - - - - [ - - - - _ _ ; — i i j . 0 - j ] i i ..-0 10 20 30 40 50 60 70 80 90 100 Gas velocity, m s"1 -46-The temperature correction shown in Figure 4.10 can also be employed to estimate the true offgas temperature T 0ff g a s . In the trial with baseline conditions (53% 0 2 , no slag), the readings o f the thermocouple placed into the exhaust pipe was around 750 °C. Because the thermocouple was protected by a steel tube and no suction was applied for this measurement, gas velocity at the thermocouple junction was very small. Assuming a gas velocity of 5 m s"1, the true offgas temperature was about 1250 °C according to the temperature correction (500 °C). As shown later by both the experimental T g value and the model prediction on the trial, T0ffgas is about 250 °C lower than T g . For convenience T 0 ff g a s is determined to be T g - 2 5 0 °C in all experimental calculations. For steady-state conditions the furnace heat balance is: Qcomb ~ Qbath + Qshell + Qopening + Qofi'gas (4*5) The rate of energy input by combustion was calculated using the low heating value of the natural gas fuel (Hv = 35,570 kJ N m - 3 ) and the measured gas flow. H v x Fr ^ comb ~> r r\r\ (4-6) 3600 For the trials performed without slag, the rate of energy input bath was calculated from the melting rate and the measured bulk bath temperature: Qbath = T ^ A A [^m,Cu ~*~ C p , C u , L (^bath — Tm ,Cu )] (4"7) J O U U where H m C u is the heat content of liquid copper at the melting point T m C u and c p C u L is the heat capacity of liquid copper (temperature-independent). For the trials performed with slag present, a correction was applied to account for heat absorbed by the slag thus the rate of energy input bath becomes: Qbath = 3600 ^ n % C u + C P . C u . L ( ^ b a t h ~ ^m,Cu )]+ ^600 ^ m S ' a g + CP,slag,L (^bath _ ^ s l a g )] (4~8) Because the bath temperature was approximately constant, only the make-up slag (added to compensate for the small slag loss during tapping) was considered. Thermodynamic data for the slag was obtained using the H S C software assuming 2 F e O S i 0 2 for the composition. Calculation results indicated that the correction is 6-8% of the energy consumed by the -47-copper scrap. The heat loss at furnace shell is given as: Q s h e „ = Q c y , + 2 Q e „ d ( 4 - 9 ) The heat loss by conduction through the cylindrical refractory was calculated using the measured refractory temperatures on the basis of steady-state heat transfer through a cylindrical w a l l : 9 0 Q^JI3L (4-IO) 27zkLF where T i and T 2 are the measured refractory temperatures at radius ri and r 2. Referring to Figure 4 . 2 , thermocouple pairs for this calculation were located at two axial x two radial locations, allowing four values of Q c y l to be calculated. Due to factors such as variations in refractory thickness and radial positioning of the thermocouples, as well as any axial gradients in furnace temperature, the four values of typically differed by < 1 0 % and an average value of the four Q c y ] was employed in the energy balance calculation. B y simplifying the geometry as shown in Figure 4 . 1 1 , the heat loss by conduction through the refractory forming each furnace end was determined by : 9 1 Q e n d = A T T B A ' H ~ T T H 1 C 4 - 1 1 ) end _| * 1c A h' A ^ e n d e n d 1 1 to ^ end The bath temperature was used at the hot-face while the exhaust pipe temperature (Texh-500 °C) was used at the cold face because the hot-face contacted the bath while the cold face was enclosed by the exhaust pipe. The average refractory thickness was estimated to be 1 0 cm while the thermal conductivity was assumed to be 2 . 0 W m"1 ° C . The refractory area A e n d did not include the opening area Awning- Calculation results indicated that Q c y l is about 6 0 % of Q s h e l l and Q e n d accounts for 2 0 % . - 4 8 -F i g u r e 4.11: S c h e m a t i c d i a g r a m s h o w i n g the t r ea tment o f the fu rnace b a c k - e n d i n the e x p e r i m e n t a l c a l c u l a t i o n s T 7 ew • exh T T . 1 offgas \ \ . opening • Q e n d Bath T b a t h Besides the heat loss by conduction through the refractory ( Q e n d ) , at the furnace back-end energy is also lost by radiation through the opening as shown in Figure 4.11. Assuming a small black surface within a large enclosure at T e x h, the rate of heat loss by radiation was estimated from: ^ opening opening ^ leb T Aew ~ 1 offgas Lexh (4-12) - opening where T O ffgas-T g -250 °C as discussed previously. Calculation results indicated that Q c is about 32% of Q s h e l l . Because of its large thermal resistance (and small exposed area) no allowance was made for heat loss via the burner tile, i.e., there was no energy loss through the opening on the front-end wall. The rate of energy loss as sensible heat in the offgas was calculated from the integrated specific heat expressions and mole flows, N s , for each component: 1 offgas Qoffgas = _ _ N , K m o l e ^ T (4-13) 298 "K where the summation is made over the species H2O, CO2, C O , H2, O2, and N 2 . The mole flow for each species was determined from equilibrium products of methane combustion at Toffgas (evaluated by the H S C software as shown in Figure 2.6). The calculated mole flow of -49 -C 0 2 by H S C was checked by the measured concentration from the gas analyzer. The difference is typically 2% of the measured data. In assessing furnace performance, the thermal efficiency rjwas calculated on the basis of: ^ = 100 -2==- (4-14) Qcomb 4.4 The Mathematical Model A s noted previously in Charter 1, the previous model 1 was relatively simplistic in certain key assumptions, i.e., the well-mixed conditions within the gas phase and the bath. In terms of modeling, the objective of the current work was to develop an improved heat transfer model to include the effects of axial temperature gradients within the gas phase. It wi l l be shown that, within the bath the well-mixed assumption is adequate and was therefore retained. The current model treats the furnace as three calculation domains; i.e. the freeboard space, the liquid metal bath and slag, and the refractory wall structure. The Freeboard Model A s shown in Figure 4.12, the freeboard space is treated as an enclosure formed by the exposed bath and refractory surfaces containing an emitting/absorbing gas mixture resulting from C H 4 combustion. Radiative exchange within the enclosure is solved using the zone method. The main assumptions for this calculation domain are as follows: • The surfaces are assumed to be radiatively opaque, diffuse and gray. The opaque assumption applies to metallurgical slags with significant FeO at thickness > 5 92 mm. • Convective heat transfer to the surfaces is neglected. • Radiative characteristics of the gas phase are simulated using a clear-plus-3-gray-38 gas model with a uniform partial pressure of the emitting/absorbing gases over the entire freeboard space. No allowance is made for flame luminosity. • In terms of gas flow, the freeboard is divided into two regions: (i) a recirculation -50 -region where the flow is dominated by the recirculatory flow induced by the confined jet burner system and (ii) a plug-flow region downstream of where the expanding burner jet system impinges on the bath and refractory surfaces. • Fuel/oxygen mixing is assumed to occur within the recirculation region (where "mixed-is-burnt") where recirculation is assumed sufficient to approach well-mixed conditions both radially and axially. • In the plug-flow region, the gas is assumed well-mixed only in the radial direction and further combustion is under thermodynamic control. • The uniform temperature of the recirculation-region was determined by performing an overall energy balance on this region, while the gas temperature in the plug-flow region was calculated by performing an energy balance on each gas volume zone. F i g u r e 4.12: S c h e m a t i c d i a g r a m o f the f r eeboa rd space c o n t a i n i n g the gas m i x t u r e Back-end surface zone normal to the axis Following the standard zone-method, the freeboard is subdivided into isothermal gas volume zones and surface zones as shown schematically in Figure 4.12. Based on sensitivity analysis, 20 axial subdivisions were employed for the industrial-scale simulations. Being less sensitive to the number of zones, 10 subdivisions were used in the bench-scale simulations. Each conical end-cap (including the opening) is treated as an -51 -individual surface zone normal to the furnace axis. For the radiative calculations, the freeboard gas was taken to be a 2:1 mixture (by volume) of CO2 and H 2 0 (typical for natural gas combustion) and minor components such as C O were neglected. According to the clear-plus-3-gray-gas model, gas emissivity and absorptivity are given as: eg=EMTg)(l-e-K"p L) (4-15) n=0 a g=Z a.n(T s,T g)(l-e-K" p L) (4-16) n=0 The extinction coefficients and emissivity/absorptivity weighting coefficients were taken from Smith et a l . 9 3 Following the standard methodology, the temperature-independent direct exchange areas are determined for each extinction coefficient and then converted to total exchange areas to account for surface reflection. In solving the freeboard problem, temperatures of the bath and refractory (excluding the end caps) surface zones are assumed to be known. The unknown gas-zone and end-cap temperatures are then determined by simultaneous solution of the energy balance equations; e.g. for volume zone V ; (Figure 4.13) in the plug-flow region: Q c 0 m b , , = I v W b 6 . -GTGTEOJ+IIG^X, - S ~ G 7 E B S J + ( A H s ) i (4-17) j=i j=i where Q c o m b , is the effective combustion energy release rate within V i , G ; G j , G j G , , GjSj and SjGj are the temperature-dependent directed total exchange areas, m and n are the number of volume and surface zones respectively, and (AH,.); is the difference in sensible heat between species entering and exiting V i . Combustion process within the plug-flow region is thermodynamically controlled thus the heat release rate by combustion: - comb,i Y N H - Y N H (4-18) \^ products reactants J j was determined from Figure 2.7 by the gradient of local gas temperature; i.e. the change in equilibrium composition (Figure 2.6) between the entering and exiting gas temperatures. -52-Therefore, some of the lost heat induced by the uncompleted combustion within the high-temperature recirculation region (to be described) is recovered by the recombination of H 2 0 and C 0 2 in the plug-flow region with low gas temperatures. F i g u r e 4 .13: S c h e m a t i c d i a g r a m s h o w i n g energy ba lance on gas v o l u m e zone V i Gas mixture leaving V ; Net radiation from V ; to other enclosure zones: Z ( G 1 s J E b g , 1 - s J G , E b J 1=1 Gas mixture Gas volume entering ¥= z o n e V i The length of the recirculation region is controllable via the number and placement of the burners thus is treated as an independent variable for the model. Assuming a jet angle of 9.7 0 , 9 4 the recirculation region for a single, central burner (Figure 2.4) would extend -12 m into a 4 m ID furnace. Multiple burners distributed over the available area would produce only a short recirculation zone (Figure 2.5) near the top of the furnace. Recirculation promotes axially well-mixed conditions. The uniform temperature of the recirculation region is determined from the overall energy balance; i.e. =t E v W * * - G ^ E b J + £ f e E b f c l - S ^ X j + ( A H s ) r e c (4-19) 1=1 [j=i j=i where I is the number of discrete gas volume zones forming the recirculation region. Because 100% of the fuel is mixed with the oxygen within the isothermal recirculation region, the overall heat release rate from combustion in this region, Q c o m b r e c , is determined from Figure 2.7 by the uniform gas temperature rather than the fuel/oxygen mixing rate. Combustion process in the recirculation region can not be completed due to decomposition of H 2 0 and C 0 2 at the high temperature (>2000 °C). However, some o f the heat loss - 5 3 -induced by the uncompleted combustion is recovered in the low-temperature plug-flow region as described previously. The temperature of each end-cap surface zone is obtained from the energy balance: J(G~SX &J - S ^ X , ) + £ (S~SXS J - S ^ * E b s , ) - Q l o s v = 0 (4-20) J=I j=i At the furnace back-end, Q l o s s i includes both the heat loss by conduction through the refractory ( Q e n d ) and that by radiation through the opening ( Q o p e n m g ) . Similar to the calculation procedure for the bench-scale trials, Q e n d is determined by the simplified geometry shown in Figure 4.14: ^end T - T A s ,2Nsec+2 ^ A L e n d 1 k A h A K end ^ end " c o ^ e n d where T s 2 N s e c + 2 is the temperature of the surface zone forming the back-end. Again, assuming a small black surface within a large enclosure with a temperature of T e x h , Q o p enin g is calculated using Qopening A o p e n j n g O" f T + T + T 1 g,Nsec s.Nsec s,2Nsec ^ T 4 1 exh (4-22) where T g N s e c , T s N s e c and T s 2 N s e c are the temperatures of the neighboring volume zone, bath surface zone and cylindrical refractory surface zone respectively. Values of the parameters in determining Q e n d and Q o p e m n g for both model and experimental calculations are summarized in Table 4.7. Because there is no physical opening, only the conduction loss Q e n d is employed to balance the radiant energy to the surface zone at the furnace front-end. -54-F i g u r e 4.14: S c h e m a t i c d i a g r a m s h o w i n g the t r ea tment o f the fu rnace b a c k - e n d i n the m o d e l c a l cu l a t i ons T a b l e 4.7: P a r a m e t e r s used i n the m o d e l to ca lcu la te the energy losses at the fu rnace ends Too f C ) Texh (°c) End wall refractory Opening Thickness (m) Conductivity (W nf 1 "C" 1) Diameter (m) Bench scale* 500 500 0.1 2.0 0.1 Industrial scale** 25 1200 0.5 0.5 1.5 * Measured data or equivalent values estimated according to measurements ** Assumed The system of simultaneous equations is solved by Jacobi relaxation with assigned temperatures of the bath surface zones. Although the temperatures of the refractory surface zones are assumed to be known, an iterative procedure (to be described) is necessary to ensure that the refractory temperatures produce closure of the refractory energy balance. -55-The Ba th M o d e l The following assumptions are applied to the liquid metal bath and slag: • The metal bath is assumed to be well-mixed in both the transverse and axial directions, the justification being a combination of good thermal conductivity (about 40 W nf 1 °CA for steel) and rotation-induced stirring along with the tumbling motion of the solid scrap component within the bath. A s shown in the section "Kinetics of Scrap Melting in Liquid Steel", the solid scrap w i l l likely be present for about 90% of the time between taps. It is recognized that the axially isothermal assumption wi l l only apply to short furnaces (length/diameter <5).' • The slag is assumed to have a temperature difference A T s i a g (specified) between the slag-freeboard and slag-metal interfaces. Heat transfer in the axial direction is neglected. • Both the metal bath and slag are assumed to be at steady state, i.e., scrap melting occurs at a constant metal bath temperature Tbath (which is specified) with a constant AT s i a g over the entire melting period. The justifications are the large liquid metal to solid scrap weight ratio (as shown in C H A P T E R 1). In addition, because heat transfer to the exposed bath surface is by radiation, even a small decrease in the bath temperature induced by scrap addition w i l l result in a significant increase in heat transfer to the exposed bath due to the 4 t h power dependence on temperature. As shown in Figure 4.15, heat transfer to the metal bath is to both the top (exposed) and bottom surfaces. The thermal resistance of the slag layer w i l l depend on both the conductivity (which is low relative to the metal bath) and the stirring conditions induced by furnace rotation. 9 5 As the latter is difficult to quantify, the temperature difference through the slag, AT si ag, was assigned and its role in furnace performance assessed. The slag layer itself is assumed to be at steady-state so the total radiant energy to the slag top surface (determined based on the surface temperature T eb=Tbath+AT si a g) is transferred to the bulk metal bath by the assigned A T s i a g ; i.e. k A T - ^ - ^ = Veb + qew-eb (4-23) A L s l a g -56-Because both T b a t h and A T s i a g (hence T e b) are specified, evaluation of the effective thermal conductivity of the slag, k e f f , is avoided. F i g u r e 4 .15: S c h e m a t i c d i a g r a m of the l i q u i d me ta l b a t h a n d s lag V e l o c i t y b o u n d a r y l a y e r Heat flux on the liquid side of the bath-refractory interface is calculated according to: Qcw - cb.x ~ h cw-cb.x (TCW,X ~ T F E A T H ) (4-24) where T_._ is the local refractory surface temperature as determined by the refractory sub-model and T b a t h is the specified metal bath temperature (which is constant at steady state). The local heat-transfer coefficient h c w _ c b x was evaluated by assuming developing flow of liquid metal along the contact length. Although the velocity boundary layer may involve multiple regimes (laminar, transition and turbulent) bath agitation by solid scrap is likely to suppress the laminar and transition regions. The correlation for turbulent flow developing along a flat plate was employed: 9 6 N u = 0.032 4/5 Re P r 2 3 (4-25) [l + (0.0468/Pr) 2 / 3 f where R e x is the local Reynolds number and Pr is the Prandtl number (ratio of momentum to thermal diffusion). The local heat-transfer coefficients evaluated for the bench-scale furnace melting copper and the industrial-scale furnace melting steel (under the baseline conditions) are summarized in Figure 4.16. With the fixed rotation rate of 1 rpm, the local -57-Reynolds number increases by 112 times when the furnace inner diameter increases from 0.25 m to 4.0 m. That is the main reason why the local coefficients for the industrial-scale furnace are much larger than those in case of the bench-scale furnace. Calculation results indicated that the local heat-transfer coefficients have a very small effect on the predicted melting rate, but a relatively large effect on the predicted thermal cycling of the refractory. If the local coefficients for the industrial-scale furnace are reduced by 75% (the coefficients evaluated from Equation (4-25) time 0.25), under the baseline conditions the predicted melting rate decreases by only 0.7%. Although the predicted maximum temperature of the refractory hot-face increases by only 1.1%, the predicted maximum thermal cycling decreases by a large value of 16.5%. Figure 4.16: The local regenerative heat-transfer coefficients 11000 10000 o ° 9000 \ 8000 £ 7000 | 6000 3 5000 g 4000 •a 3 0 0 0 8 2000 J 1000 o 1 1 \ 1 J L 1 J 1 1 1 l l l L 1 J 1 1 1 1 1 Industrial-scale i • — — i 1 i 1 1 1 1 1 1 1 1 1 1 1 1 1 1 , I 1 I 1 i i i 1 ! 1 t 1 • "j" 1 T 1 r T i t i i L 1 J r T ~i i i i L 1 J i i i i i i T "I 1 1 I- T 1 ~ R£»nr*Vi_er*al£> 1 t- F m m t 1 1 1 1 1 1 1 0 10 20 30 40 50 60 70 80 90 100 110 120 130 Circumferential position, degree The Refractory Model As noted earlier, conduction within the refractory is assumed to be transient, 1-dimensional in the radial direction. The nodal structure used for the finite-difference numerical solution for the conduction equation is shown in Figure 4.17. Although not clear in the figure, the -58-finite difference solution is in cylindrical coordinates and allowance is made for composite refractory systems. As noted previously, for rotary kilns the error introduced by neglecting conduction in both the longitudinal and circumferential directions is < 2%. 4 5 Figure 4 . 1 7 : Schematic diagram showing 1 - D transient condition within the refractory The nodal structure employed for the conduction model is aligned to the refractory surface zone system used for the freeboard model. A fully-implicit finite-difference formulation is used. At the hot-face the boundary condition is the net radiative flux to that surface zone: 2 (GXE b & J -sXEBJ+Z(sXEbs j - W O (4-26) The shell-side boundary condition considered both radiant and combined free and forced convection 3 4 hshell = (r h shell +c hshell )(Tshell ~ T » ) ( 4 " 2 7 ) r h s h e l l = s s h e l l a ^ ^ (4-28) 1 shell ^00 N u s h e l l = 0.1 l[(o.5Re* + Gr)Pr ] 0 3 5 (4-29) where Gr is the Grashof number; i.e. a ratio of buoyancy to viscous forces. -59 -Solution Procedure The three domains (freeboard, refractory and bath) are linked by shared boundary conditions and the requirement that the furnace itself operates at steady-state. As shown in Figure 4.18, in the freeboard model the net radiative flux ( q ; ) to each surface zone is calculated using its temperature ( T s i ) as determined by the refractory model. This radiant flux is shared as a boundary condition by both the refractory and the bath models. Using these heat flux fresh T s ; values are then calculated by the refractory model which are returned to the freeboard model; etc. Figure 4.18: The solution procedure linking the three models Initial data i i Freeboard M o d e l Calculate unknown temperatures by iteration L _ J Abased on T s i N e w T s 4 Qcw-cb,x Refractory M o d e l l Reach steady-state by iteration The steady-state condition can be viewed in either of two ways, i.e. 1. A t any circumferential position the temperature is constant over time 2. The refractory as a whole is neither gaining nor losing energy over time. Clearly both requirements must be satisfied but in obtaining a solution it was found to more -60-computationally efficient to utilize the first condition, i.e. at a certain circumferential position temperatures of the refractory elements (Figure 4.17) converge to constant values. Energy Balance and Melting Rate A l l o f the individual components of the furnace heat balance are calculated using different procedures as those in the experimental calculation. The total effective heat release rate from combustion within the furnace is the summation of that in the recirculation region plus those in the plug-flow region, i.e.: Q - Q + V Q (4-30) ^comb ^comb.rec / . ^comb.i ^ ' i=l where I is the number of the gas zones forming the plug-flow region. The total heat transfer rate to the metal bath is Qbatb = Q e b + Q c w - c b (4-31) where Q e b = A e b ( q g _ e b + q e w _ e b ) is the total radiative heat transfer rate to the exposed bath surface zones (determined in the freeboard model based on Teb) and Q c w _ c b is the total regenerative heat transfer rate to the covered bath. Although Q s h e l l , Q o p e n i n g m ^ Q offgas a r e determined using the similar procedures as those in the experimental calculations, the measured temperatures Tbath, T e b , T e w and T0ffgas are replaced by the model-predicted surface-zone and gas-zone temperatures. Also, furnace thermal efficiency is defined by the same expression as that in the experimental calculation but the model-predicted Q b a t h and Qcomb a r e u s e d rather than those based on the measured data. A s noted previously, the melting rate of scrap is controlled by heat transfer and the effect of mass transfer can be neglected because the scrap has a similar composition to the liquid bath. At steady state Tbath is constant so the total heat transfer rate to the liquid metal bath ( Q b a t h ) * s e c l u a l to the rate of energy supply for scrap melting. The energy needed to melt unit weight of scrap and to reach the specified Tbath can be given as: Q m = H m + c p , L ( T b a t h - T m ) (4-32) - 6 1 -where H m is the heat content in the liquid metal (unit weight) at the melting point T m and c p L is the temperature-independent heat capacity of the liquid metal. Thus the model-predicted melting rate is M = _ _ i _ _ ( 4 . 33 ) 4.5 Summary A bench-scale C P R F M was constructed with a capacity of about 50 kg of liquid copper and a designed melting rate of 25 kg h"1. Two groups of trials were conducted on the bench-scale furnace. The fist explored the effect of oxygen levels (37.1%, 53.0% and 80.3) in the combustion air on furnace thermal performance with no slag in the furnace. The second group investigated the influence of slag thickness (1.3 cm and 2.5 cm) on the furnace performance with a fixed oxygen level of 53.0% in the combustion air. Although useful to demonstrate the C P R F M process, the experimental results are mainly employed to validate the mathematical model subsequently developed in this study. The heat-transfer model treats the furnace as three domains; the freeboard space, the liquid bath and the refractory. Based on certain physically correct assumptions for the gas flow and combustion patterns, radiative exchange within the freeboard is solved by the zone method in combination with a clear-plus-3-gray emissivity/absorptivity model for the gas phase. Heat transfer to the exposed bath is simplified by a specified temperature difference across the slag layer at steady state, while the regenerative heat transfer is calculated using the local refractory temperature resulting from the refractory model and the local heat-transfer coefficients evaluated by assuming developing flow of liquid metal along the contact length. Conduction within the refractory is assumed to be in the radial direction only and solved using standard implicit finite-difference methodology. Composite refractory systems are allowed. The three domains are linked by shared boundary conditions and the requirement that the furnace operates at steady-state. The main differences between the current model and the previous model include: -62 -(1) The zone method was employed in this study to solve the radiation problem within the freeboard space thus the current model allows axial temperature variations in the freeboard gas and the refractory hot-face, while in the previous model the freeboard gas and the hot-face were each assumed to be isothermal and the radiation problem was solved by assuming two gray surfaces (infinite in length) forming an enclosure containing an emitting/absorbing gas mixture. (2) In the current study the liquid metal bath was modeled in detail. The regenerative heat transfer to the covered bath was calculated using the local coefficients evaluated as described previously, while in the previous model an average heat-transfer coefficient was assigned. Also, melting kinetics of steel scrap in a liquid steel bath was checked in this study to confirm that the melting rate is controlled by heat transfer, but not mass transfer. In addition, the solid/liquid coexisting period during each operating cycle was estimated according to the melting kinetics, indicating that the stirring effect of the solid scrap is significant and the assumption of isothermal bath condition is reasonable. (3) In this study the heat-transfer coefficient between the furnace shell and the environment was evaluated by considering both radiation and combined free and forced convection, while that in the previous model was assigned. - 6 3 -C H A P T E R 5 - RESULTS AND DISCUSSION In this chapter the experimental results from the bench-scale trials are presented. The model results are compared with the experimental results in terms of both temperature and heat transfer rates. Finally, model predictions for an industrial-scale C P R F M are presented and the effects of several operating variables on furnace performance are discussed. 5.1 Experimental Results (Steady-State Furnace Operation) If it is to have any chance of supplanting the electric arc furnace for melting of steel scrap, the C P R M F must be capable of melting rates of at least 100 ton h ' 1 . Because the process would operate in quasi-steady state (with only small fluctuations in bath weight) the experimental data from the bench-scale trials is only reported for the steady-state portion of the trials; i.e. stable bath and refractory temperatures. Because the liquid metal bath has a large thermal conductivity and is most sensitive to a change of melting condition, its temperature was employed as an indicator of steady-state conditions, i.e., a steady-state condition was reached when fluctuations in the metal bath temperature were < 20 °C. As summarized in Figure 5.1, in each trial the metal bath temperature was relatively constant during the thermal steady-state phase. Although some drift in bath temperature can be observed (the maximum is 10 °C), this is mainly attributable to small fluctuations in the amounts tapped and charged at each 30-minute interval. Temperature data averaged over the steady-state phase are summarized in Table 5.1. A l l temperatures are those recorded by the thermocouples. The temperatures of the exposed bath surface (T eb) and the exposed refractory hot-face ( T e w ) were also checked by an optical pyrometer. Difference between the pyrometer readings and the thermocouple data were within ±10 °C. Note that the gas temperatures (T g ) have been corrected according to the procedure described previously. In most trials T g is about 250 °C higher than the offgas temperature T 0ff gaS (about 1250 °C under the baseline firing conditions as discussed previously). -64-Figure 5.1: Metal bath temperatures during the melting period with tapping/charging at 30-minute intervals ^ 1225 E-1200 1175 1150 Thermal steady-state phase Trial 1:37.1% 02, no slag Trial 2: 53.0% 02, no slag -o- Trial 2: repeat A Trial 3: 80.3% 02, no slag Trial 4: 53.0% 02, 1.3 cm slag -e-Trial 5: 53.0% 02, 2.5 cm slag 0.5 1 1.5 2 Melting period with tapping/charging, hours Table 5.1: Average temperatures during the thermal steady-state phase Trial Slag (cm) Oxygen (%) Tg CC) Tbath CC) T eb CC) Tew Tshell CC) 1 N / A 37.1 1615 • 1246 . N / A .1305 171 2 N / A 53.0 1632 1264 N / A 1303 178 2-repeat N / A 53.0 1464 1248 N / A 1294 188 3 N / A 80.3 1480 1238 N / A 1316 190 4 1.3 53.0 1438 1251 1307 1295 192 5 2.5 53.0 1493 1270 1327 1305 191 A s previously described, the data were used to calculate energy disposition within the furnace and these results are summarized in Table 5.2. It should be noted that, in calculating the sensible enthalpy loss with the offgas ( Q o t 5 g a s ) and the radiation loss through the opening at the back-end wall ( Q o p e n i n g ) , the offgas temperature T 0 ff g a s was employed rather than T g shown in Table 5.1 because T g was calculated based on the suction - 6 5 -pyrometer readings measured at the axial position of 0.2 m into the furnace from the back-end wall. As noted previously, T 0 f f g a s was determined to be T g -250 °C in all experimental calculations. This treatment has no effect on the other individual heat transfer rates because they are independent of the gas temperature. For the bench-scale trials Q o p e n m g is about 32% of Q s h e n . In Table 5.2 it is included i n Q o f f g a s . The error is defined as _ , Qcomb ""Qbath ~ Qshell ~ Q offgas , Error = J = L x l 0 0 (5-1) O ^comb Table 5.2: The energy balance in each trial Trial Slag o 2 M C u Q comb Qbath Qshell Q offgas Error (cm) (%) (kg h"1) (kW) (kW) (kW) (kW) (%) (%) 1 N A 37.1 20 25.7 4.2 7.8 13.4 16.3 1.2 2 N A 53.0 20 19.3 4.3 7.8 9.4 22.3 11.4 2-repeat N A 53.0 20 19.3 4.2 8.0 8.0 21.8 4.7 3 N A 80.3 25 19.3 5.2 7.9 6.9 26.9 3.6 4 1.3 53.0 15 19.3 3.4 7.9 8.0 17.6 0.0 5 2.5 53.0 10 19.3 2.3 7.8 8.5 11.9 3.6 A s can be seen in Table 5.2, closure of the energy balance is generally good with error<5%. The error in Trial 2 is larger at 11.4%. As shown in Table 5.1, T g in Trial 2 is higher than that in the repeat trial by 168 °C, resulting in a higher T 0 ff g a s value ( T 0 f f g a s = T g -250 °C), hence a larger sensible enthalpy loss with the offgas and a larger radiation loss through the opening on the back-end wall . Therefore, the large error might be attributable to the error in the T g measurement, which might be resulted by placing the suction pyrometer at an axial position closer to the burner. The possible reason for the error of zero in Trial 4 is that the positive errors in some components just offset those in the remainders. In terms of most individual heat transfer rates, the repeat trial is in good agreement with Trial 2, indicating repeatability under identical operating conditions. -66-A s shown in Figure 5.2, when operating without slag, the thermal efficiency is significantly improved by moving to higher levels of oxygen enrichment for the combustion air and, extrapolating the results, would be around 30% for full oxy-fuel firing. Relatively low thermal efficiencies were anticipated for the bench-scale furnace. This is attributable to a combination of the limited refractory thickness and the small volume of the freeboard gas space which translates into a mean-beam-lengths for radiative heat transfer of only about 15 cm. For rotary kilns, scale-up by one order of magnitude (0.4 m to 4 m ID) results in a threefold increase in radiative heat transfer from the gas. 3 5 Therefore, for an industrial oxy-fuel fired C P R M F , a thermal efficiency of more than 60% might be expected. F i g u r e 5.2: T h e r m a l eff ic iency versus oxygen leve l i n the c o m b u s t i o n a i r UH 28 26 24 22 2 0 18 16 14 12 10 J L J 1 « 0 Q-a a T r i a l 1 o T r i a l 2 T r i a l 2-repeat o T r i a l 3 1 > 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 L J L _ • r i L 1 > 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 L J 1 > 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 L J 1 > 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 L J i i i i i i i i i 1 1 1 1 ^ 1 30 35 4 0 45 50 55 60 65 7 0 75 80 85 O x y g e n l e v e l , % The introduction of a protective slag layer for the metal bath (1.3 cm and 2.5 cm for Trials 4 and 5 respectively) significantly lowers the thermal efficiency relative to Trial 2 (and its repeat run) which employ the same firing conditions (Figure 5.3). A t the same time the sustainable melting rate drops from 20 kg h"1 (no slag) to 15 kg h"1 (1.3 cm slag) and finally 10 kg h"1 (2.5 cm slag). A slag layer introduces a thermal resistance for heat transfer between the freeboard volume and the metal bath so the results follow the general trend to be expected. However, the issue is complicated by the fact that the fill level could not be increased for Trials 4 and 5 so the depth of the metal component of the bath was decreased -67-by the same amount as the slag thickness. This has significant implications in terms of the area for regenerative heat transfer from the refractory to the liquid metal. As shown in Table 5.2, the Q b a t h with no slag (Trial 2 and its repeat run) was reduced by 0.8 k W when 1.3 cm of slag was applied then decreased by a larger value, 1.1 kW, with increasing the slag thickness from 1.3 to 2.5 cm. The temperature difference across the slag was almost same when the thermal resistance of slag was decoupled. Therefore, a decrease in the regenerative heat transfer occurred with increasing the slag thickness. However, for industrial R M F ' s where the slag thickness accounts for a small fraction of the bath depth, a thick slag layer might increase the regenerative heat transfer rate by increasing the temperature difference across the refractory/metal interface. Figure 5.3: Thermal efficiency versus slag thickness 24 22 2 0 18 16 § 14 12 10 8 6 4 2 0 ^5 ' o 1 i i i - i i i a ' i i T -1 i i i T 1 i o T r i a l 2 A T r i a l 2-repeat • T r i a l 4 o T r i a l 5 V 1 1 1 1 | 1 1 i i i i i i 1 0.0 0.5 1.0 1.5 2.0 Slag thickness, cm 2.5 3.0 5.2 Partial Validation of the Model Using the operating conditions in the trials, such as the measured Tbath, T eb and gas flow rates as well as the observed recirculation-region length, the model was used to simulate the bench-scale furnace. For the simulations the emissivity of the refractory, the liquid copper and the high iron slag were assumed to be 0.7, 0.14 and 0.9 respectively. 9 7 , 9 8 ' 9 9 The model predictions and the experimental results were compared in terms of both temperature values -68-and the energy balance. The focus for the temperature validation was the repeat run of Trial 2 operating under baseline conditions (53.0% O2, no slag) because the error in the gas temperature measurement in Trial 2 is relatively large as discussed previously. As shown in Figure 5.4, the model predictions for the refractory temperatures at the axial position of 0.53 m (the center of the 8 t h axial subdivision in the freeboard) are in good agreement with the data measured at the same axial position. F i g u r e 5.4: V a l i d a t i o n aga ins t r e f r ac to ry t empera tu re s ( T r i a l 2-repeat) 1400 o o e 1 I 1000 800 600 400 200 0 0 1 1 1 1 1 1 1 1 1 — Model • Measured at beginning of the steady-state phase A Measured at end of the steady-state phase l_ ^ 5 6 7 8 Wall thickness, cm 10 11 12 13 Although the model develops the axial temperature profile for the gas phase (and refractory hot-face), the gas temperature was measured at only one axial position; i.e. 18 cm into the furnace from the back-end. The temperature of the exposed refractory hot-face (T e w ) was measured at the same axial position. However, the hot-face temperature was also back-calculated at the two axial positions of the thermocouples placed within the refractory (shown in Figure 4.2) using the measured internal temperatures to calculate the rate of heat transfer which could then be used to calculate the hot-face temperature via Equation (4-10). A s shown in Figure 5.5, the model predictions are reasonably good for the hot-face temperatures but high on the gas temperature by about 80 °C. Note that, based on the model predictions, the gas temperature drops by about 250 °C between the point where the measurement was made and the exit from the furnace ( T o f f g a s = T g - 2 5 0 °C). The figure also -69-indicates good agreement between the measured and back-calculated hot-face temperatures. F i g u r e 5.5: V a l i d a t i o n aga ins t gas a n d r e f r ac to ry hot-face t empera tu re s ( T r i a l 2-repeat) 1800 1700 u 1600 » 1500 a g 1400 a 1300 s H 1200 T g : Mode l T g : Measured : • CT T e w : Back-calculated 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 A x i a l distance, m 0.8 Validation of the model was also made against the furnace heat balance as summarized in Table 5.3. As described previously, in the model all o f the individual components of the heat balance were calculated using different procedures as those in the experimental calculations. The model-predicted melting rates were also compared with the measured data in the experiments. Although the make-up slag was not included in the measured melting rates, its energy consumption was accounted in the measured heat transfer rate to the bath ( Q b a t h ) . It can be seen that all of the model-predicted heat transfer rates, except for those in Trial 5, are in good agreement with the experimental values with the largest error being about 16%. This occurs between the measured and model-predicted Q o f f g a s in Trial 2. The Q o f f g a s in Table 5.3 includes both the sensible heat loss with the offgas and the radiation loss through the opening at the furnace back-end, both of which are a function of T 0 f f gas (hence T g ) . As discussed previously, in Trial 2 the error in T g measurement is relatively large, resulting in a large error in the experimental Q o f f g a s . In Trial 5, the make-up slag -70-addition was relatively large but it was not included in the measured melting rate. That explains why the large difference (36% of the measured data) occurs between the measured and model-predicted melting rates. Although the energy consumed by the make-up slag was accounted, the error in the measured Q b a t h was large when a thick slag layer was applied (as discussed later). The large error combined with the small Q b a t h value results in a large drift (26.1% of the measured Q b a t h ) between the measured and model-predicted data. Table 5.3: Validation against terms in the furnace heat balance Trial M (kg h"1) Q comb (kW) Qbath (kW) Q shell (kW) Q offgas (kW) (%) From Data 20 25.7' 4.2 7.8 13.4 16.3 1 Model 22.8 25.7 4.8 7.9 13.4 18.7 Error < 14.3% of the measured data From Data 20 19.3 4.3 7.8 9.4 22.3 2 Model 17.7 19.3 3.8 7.8 7.9 19.7 Error <16.0% From Data 20 19.3 4.2 8.0 8.0 21.8 2-repeat Model 19.4 19.3 4.1 7.8 7.8 21.2 Error <3.0% From Data 25 19.3 5.2 7.9 6.9 26.9 3 Model 26.8 19.3 5.6 8.0 6.3 29.0 Error <8.7% From Data 15 19.3 3.4 7.9 8.0 17.6 4 Model 15.6 19.3 3.3 7.8 7.8 17.1 Error <4.0% From Data 10 19.3 2.3 7.8 8.5 11.9 5 Model 13.6 19.3 2.9 7.8 8.1 15.0 Error <36.0% -71 -For a fixed firing rate, an increase of oxygen enrichment in the combustion air wi l l reduce not only the mass flow of nitrogen (a radiatively clear gas) but also the total mass flow of combustion products because nitrogen accounts for 79% of air. Therefore, the thermal burden imposed by nitrogen is lowered while the temperature of combustion products is increased. This improves the radiative heat transfer from the gas because of the increased th gas emissivity and the 4 power dependence on the gas temperature. As shown in Figure 5.6, the furnace thermal efficiency improves with increasing levels of oxygen enrichment so the results agree with what might be expected. The accuracy of the experimental thermal efficiency ( n = 100 ^ b a t h ) is influenced by error in the measurement o f the various Qcomb parameters used in the calculation. For example, Q c o m b is a function of both the measured firing rate (Fr) and the low heating value of the natural gas (Hv). As shown in Table 4.2, the error in the natural gas flow measurements was +0.16 N m 3 h"1. For the repeat run of Trial 2 with baseline conditions (53% O2, no slag), Q c o m b increases from 19.3 k W to 20.8 k W with increasing Fr from 1.95 N m 3 h"1 to 2.11 N m 3 h ' 1 . For the fixed Q b a t h (4.2 kW) the increase in Q c o m b results in a decrease of 1.6% in the thermal efficiency (from 21.8%) to 20.2%). In addition, Q b a t h is a function of the measured melting rate ( M C u ) , the measured bulk bath temperature (Tbath), and the thermal properties of the scrap. A s discussed previously, the error in Tbath measurements was estimated to be ±20 °C. When Tbath is decreased from 1248 °C to 1228°C, Q b a t h decreases from 4.20 k W to 4.15 kW. If Q c o m b is fixed to 19.3 kW, the decrease in Q b a l h would result in a decrease of 0.3% in the thermal efficiency. The error resulted from other factors, such as H v (determined based on the natural gas composition), M C u and the scrap thermal properties, was estimated to be 0.2%. Therefore, the overall accuracy of the experimental efficiency was ±2 .0% which is shown by the error bars in Figure 5.6. In general, the model predictions for thermal efficiency are in reasonable agreement with the experimental results. -72 -Figure 5.6: Bench-scale furnace thermal efficiency versus oxygen enrichment (Trials 1, 2, and 3, no slag) O c 30 28 26 24 22 20 18 16 14 12 10 n i r i r i [ r i f i — Model • Experimental ; i i i i i 1 1 1 1 i 30 35 40 45 50 55 60 65 Oxygen level, % 70 75 80 85 When a slag layer is introduced, the slag reduces the heat transfer rates to both the exposed and covered bath surfaces because of the high thermal resistance of the slag as well as the reduced metal/refractory contact area (as discussed previously). As shown in Figure 5.7, the model predictions indicate a decrease in the thermal efficiency with increasing slag thickness. Again, the results follow the general trend to be expected. In the experiments slag loss occurred during the discharges of liquid metal. Although make-up slag was added, the amount was only estimated from visual evidence so that the slag thickness was not necessarily maintained constant. This would influence the accuracy of efficiency because thermal resistance of the slag is an important factor in determining the heat transfer rate to the exposed bath. The estimated error band for the experimental values is ± 2 . 5 % and again this is indicated in the figure. Based on Figure 5.7, the model predictions are in reasonable agreement with the experimental results. - 7 3 -Figure 5 .7: The influence of the slag on bench-scale furnace thermal efficiency (Trials 2, 4, and 5 with a constant oxygen level of 53%) 26 24 22 20 18 16 14 12 10 8 6 4 2 0 : 1 1 1 1 1 l . ... i . _i _L "*****"'—"—.. , i i L _l ~~ —i . 1 1 t 1 1 1 1 1 1 1 1 i i TJ i i r ~r — Model • Experimental I ~r ~r 1 j i i i_ j 1 1 1 0 s O 0.5 1.5 Slag thickness, cm 2.5 5.3 Scale-up and Model Predictions for Industrial-Scale Furnaces Although the experimental data were insufficient for full validation, the next task was to use the partially validated model to address scale-up to industrial C P R M F operations for steel scrap melting. Table 5.4 summarizes the baseline design and operating conditions assumed for the industrial furnace. The furnace inner diameter is increased to 4.0 m while the length is increased to 16.0 m. The length/diameter ratio is 4:1, which meets the requirement of'short furnaces' (length/diameter ratio < 5:1).1 The emissivities of the refractory and the slag are assumed to be same as those in the bench-scale furnace. The industrial furnace is assumed to be fired with 100% oxygen. The partial pressure (P) of CO2+H2O in the freeboard gas was determined by H S C 3 2 calculation on CFLVC^ combustion at 2000 °C. The properties assumed for the steel scrap and liquid steel bath are given in Table 5 . 5 . 1 0 0 ' 1 0 1 The thermal properties were evaluated from Figure 5.8, which was obtained from the H S C software 3 2 for pure iron. A s described previously, for convenience the heat content of liquid metal (unit weight) at liquidus was used to replace the fusion heat and the heat capacity of solid scrap because the later is a function of -74-102 temperature. The melting point was estimated from Fe-Fe3C phase diagram. The assumed bath temperature of 1600 °C allows for 100 °C superheat on discharge from the furnace. Table 5.4: Summary of baseline design and operating conditions assumed for the industrial-scale furnace ID (m) L F (m) F i l l (%) Fuel Lrec (m) Rotation (rpm) Tbath TO Teb CC) P (atm) 4.0 16.0 20 CFL, 4.8 1.0 1600 1650 0.85 Emissivities Wal l Slag 0.7 0.9 Refractory Specifications Working layer Intermediate Backup Thickness (m) 0.20 0.15 0.15 Conductivity (W m"1 °C _ 1 ) 5.0 1.25 0.75 Density (kg m"3) 3400 1500 1000 Specific heat (kJ kg"1 °C"') 1.1 1.0 0.95 Table 5 . 5 : Properties of steel scrap Liquidus (°c) Heat content at liquidus (kJ k g 1 ) C p , F e , L ( k J k g 1 "a') Conductivity (W nf 1 °C-') Density (kg m"3) Viscosity (m 2 s"1) 1500 1298.3 0.824 43 7800 7.43xl0" 7 -75 -Figure 5.8: Enthalpy of Fe versus temperature 1800 Temperature, °C Temperature Profiles and The Furnace Heat Balance Based on the assumed design and operating conditions (the 4 m ID x 16 m furnace operating at a firing rate of 6,000 N m 3 h' 1), the predicted melting rate isl03 ton h"1. Figure 5.9 shows the axial temperature profiles for the gas and the exposed refractory hot-face (averaged in the circumferential direction). The constant gas temperature within the recirculation zone is due to the assumption of axially well-mixed conditions. Once moving into the plug-flow region, the gas temperature starts to decline due to heat transfer from the gas to the exposed refractory and bath. The axial temperature profile in the exposed refractory hot-face follows the same trend because the radiative flux to each refractory surface zone was employed as the driving force (boundary condition) for conduction through the refractory associated with the surface. -76 -Figure 5.9: Axial temperature profiles in the 4 m ID x 16 m furnace (baseline conditions) 2600 1600 i r ~ i i i i i i i i i i i i i i i i i i i i i i i i i i i i 1500 -I 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Axia l distance, m Figure 5.10 shows the circumferential hot-face temperature profile at 1.6 m into the furnace from the burner end which, under these operating conditions, is the location for the maximum refractory hot-face temperatures, T u M a x , and also the maximum thermal cycling of the hot-face, A T U - M a x . When rotated under the bath, the hot-face quickly cools to approach the bath temperature. Once re-exposed to the freeboard, the temperature increases to peak at about 2021 °C, meaning thermal cycling of about 393 °C. The maximum temperature is pushing the limit for conventional refractories in terms of TKMax and the high level of thermal cycling might well lead to thermally induced spalling. However, the circumferential temperature profile was obtained by neglecting the conduction within the refractory in this direction (which would reduce the thermal cycling) thus it indicates the worst condition. In practice, the thermal cycling can be reduced by using a refractory with a large thermal conductivity for the working lining. -77-Figure 5.10: Circumferential hot-face temperature profile at the axial position of 1.6m As shown in Table 5.6, the specific fuel consumption (SFC) is 577 k W h f U s i n g the calculation procedure described previously in Chapter 1, this configuration consumes less direct energy (619 k W h f i n c l u d i n g the electricity for oxygen generation) than the E A F without scrap preheating (662 kWh f 1 ) which translates into an at-source energy saving of 45%. Again, the radiation loss through the opening at the furnace back-end (about 56% of Qsheii) i s included in Q o f f g a s . The furnace thermal efficiency is about 66%>. A s shown in Figure 5.11, of the total energy transferred to the bath (39 M W ) , about 63% is from the exposed bath by radiation and 37% from the covered bath by the regenerative action of the refractory. The radiant energy is contributed mainly by the hot freeboard gas (16 M W , 66%) followed by the exposed refractory hot-face (7 M W , 29%) and the end walls (1.2 M W , 5%). Table 5.6: Performance and energy dispositions in the 4 m ID x 16 m furnace at a firing rate of 6,000 Nm3 h 1 under the baseline conditions Q comb ( M W ) Qbath ( M W ) Q shell ( M W ) Q offgas ( M W ) 4 (%) M (ton h"1) S F C (kWh t"1) S O C (NmV) 59.2 39.1 1.6 18.5 66.1 103 577 117 -78-F i g u r e 5.11: E n e r g y i n p u t to the ba th by source Regenerative heat transfer 14.6 M W , 37% Radiation from gas 16.2 M W , 42% Radiation from walls 8.3 M W , 2 1 % Effects o f D e s i g n a n d O p e r a t i o n V a r i a b l e s A n important improvement of this model is to allow axial temperature variations in the gas phase. For a constant firing rate of 6,000 N m 3 h"1, the model predictions show that increasing the length of the recirculation region (fuel/02 mixing-length) reduces the average gas temperature over the recirculation zone by extending a reduced heat release rate over a greater distance. This is beneficial in that it reduces the maximum temperature experienced by the refractory hot-face ( T M - M a x in Figure 5.12) and the thermal cycling ( A T t f M a x ) of the refractory, both of which should improve the refractory service life. However, the reduction of gas temperature results in a reduction in radiative heat transfer from the gas to both the exposed bath and refractory since these involve T g 4 . Lowering the refractory hot-face temperature reduces not only heat transfer directly from the exposed refractory but also regenerative heat transfer from the covered refractory ( Q c w _ c b in Figure 5.13) because the temperature difference at the refractory/liquid metal interface is smaller. A s shown in Figure 5.13, the model predictions indicate a decrease of 5.7 M W in Q b a t h when the fiael/02 mixing-length is increased from 10% to 90% of the furnace length, dropping the melting rate from 104 ton h"1 to 89 ton h" . However, in terms of refractory temperatures, T U M a x drops from 2157 °C to 1844 °C while A T U M a x goes from > 500 °C to -79-about 228 °C. Therefore, for a fixed firing rate and a fixed furnace length, the burner design and configuration can be used to balance working conditions for the refractory and the energy loss with the offgas. Figure 5.12: The effect of fuel/oxygen mixing-length (recirculation zone) on refractory hot-face temperature at constant furnace length and firing rate 2200 j 2150 2100 --u o 2050 -i 2 2000 -r i 1950 --1900 --1850 --1800 -1.6 3.2 4.8 6.4 8.0 9.6 11.2 Fuel/02 mixing-length, m 12.8 14.4 -80-Figure 5.13: The effect of fuel/oxygen mixing-length on the heat transfer rates to the bath at constant furnace length and firing rate 45 - , 1 1 1 1 - i 1 i I 0 -\ 1 1 r 1 1 i i I 1.6 3.2 4.8 6.4 8.0 9.6 11.2 12.8 14.4 Fuel/02 mixing-length, m Assuming the firing rate is fixed, the furnace length also plays a role in setting furnace performance. As shown in Table 5.7, with the firing rate of 6,000 N m 3 h"1 and the fixed fuel/oxygen mixing-length of 4.8 m, a 25% increase of furnace length (from 16 m to 20 m) is not helpful in terms of either melting rate or thermal efficiency. This is because at the back-end of the 16 m furnace the temperatures of both the gas and the refractory hot-face are close to that of the bath (Figure 5.9) so energy extraction from the gas is close to the maximum possible. Conversely, the melting rate decreases significantly by 8.5 ton h"1 when the furnace length is reduced by 25% (16 m to 12 m). This is because the surface area for heat transfer has reduced to the extent that energy extraction from the gas within the furnace is far from complete. This results in a higher offgas temperature (temperature of the last gas volume zone), hence an increased sensible empathy loss from 17.6 M W to 19.4 M W and an enlarged residual combustible loss (compared with CH4/O2 combustion at 1600 °C) from 0.6 M W to 1.5 M W . Therefore, for the specified firing rate and mixing length, 16 m is a close to the optimal furnace length. -81 -Table 5.7: Furnace performance versus length under the baseline conditions ED (m) L F (m) M (ton h"1) SFC (kWh t"1) soc (Nm 31" 1) (%) Toffgas C Q 4 12 94.1 620 128 60.5 1928 4 16 102.6 577 117 66.1 1773 4 20 103.2 576 116 66.2 1685 Furnace rotation rate is another factor in furnace performance in that it establishes the balance between direct and regenerative heat transfer to the bath. Increasing rotation rate wi l l result in large local Reynolds numbers, hence large local regenerative heat-transfer coefficients since the local Nusselt numbers are a function of R e x / 5 . Although refractory/ bath contact time is reduced during each furnace revolution, the local coefficients are large enough (also due to the liquid metal properties) so that the refractory hot-face temperature quickly approaches that of the liquid bath (Figure 5.10). In addition, the exposure period of the refractory is also shortened, resulting in a relatively low temperature of the hot-face before entering the bath. Therefore, not only T ^ - ^ but also A T U . M a x decreases with increasing the rotation rate as shown in Figure 5.14. As expected, increasing rotation rate improves regenerative heat transfer (Figure 5.15). However, the increase in Q c w _ c b is offset by the decrease in the radiant energy to the exposed bath ( Q e b ) because more radiant energy is transferred from the gas to the exposed refractory with decreased T e w while less energy is distributed to the exposed bath with the constant T e b (specified). Also, radiative heat transfer from the exposed refractory to the exposed bath is reduced due to the decrease in T e w . As a result, Q b a t h increases by only 1.1 M W by increasing the rotating speed from 0.5 rpm to 2 rpm (around the practical maximum for furnace operation), resulting in a minor increase of 3 ton h"1 in the melting rate. - 8 2 -Figure 5.14: The effect of rotation rate on refractory temperature 2100 2075 2050 o 2025 o 1 2000 H 1975 1950 1925 1900 0.5 1 1.5 Rotation rate, rpm CO CD 0.5 Q eb Q bath Figure 5.15: The effect of rotation rate on heat transfer rates to the bath 45 40 I 35 30 25 20 15 10 5 1 1.5 Rotation rate, rpm For a given furnace size and configuration firing rate is the remaining factor to be considered in assessing furnace performance. A s shown in Figure 5.16, under the baseline conditions the melting rate increases from 70 ton h _ 1 to 150 ton h _ 1 with increasing the firing - 8 3 -rate from 4,000 N m 3 h"1 to 9,500 N m 3 h"1. Beyond 5,000 N m 3 h"1 the furnace thermal efficiency starts to drop off but the decrease is very small and the efficiency is still a reasonable 62% at 9,500 N m 3 h"1. Therefore, the furnace has a large potential melting capability with an acceptable thermal efficiency. The melting rate of 150 ton h"1 achieved at a firing rate of 9,500 N m 3 h"l means that 75 tons of scrap is charged in each 30-minute interval of tapping. The bath volume of the 4 m ID x 16 m furnace with 20% fil l is about 40 m 3 . Assuming a liquid steel density of 7,800 kg nf 3 , the bath weight is 312 tons, about 4 times greater than that of the charged scrap. Thus fluctuation in the bath temperature would be small and the scrap is melted at relatively steady state which is one of the assumptions for the model. However, with the fixed fuel/oxygen mixing-length of 4.8 m, energy release intensity from combustion within the mixing-region increases with increasing the firing rate, resulting in an increased peak value of the gas temperature. As a result, both TKMm and A T y ^ increase with increasing the firing rate (Figure 5.17) because of the increased local radiative heat transfer to the exposed refractory. This degrades working conditions for the refractory in the high-temperature mixing-region. Although this problem can be solved to some extent by producing a longer fuel/oxygen mixing-region to reduce the energy release intensity from combustion, this would increase the energy loss with the offgas. Thus the furnace thermal efficiency would be reduced. -84-Figure 5.16: Melting rate and furnace efficiency versus firing rate for baseline conditions Discussion of the Results The model predictions are based on the specified metal bath temperature (Tbath=1600 °C) and the specified temperature difference ( A T s i a g = 5 0 °C) between the slag-freeboard and -85 -slag-metal interfaces. A l t h o u g h the temperature o f the metal bath can be control led by adjusting the mel t ing rate at a fixed firing rate, it is more diff icul t to just i fy the assumption o f 50 °C for AT s iag. Because the thermal conduct iv i ty o f the slag is inherently l o w (0.4 W m' 2 ° r j - ' ^ 1 0 3 thermal resistance o f the slag layer w i l l largely depend o n the stirring condit ions induced by furnace rotation and sol id scrap wi th in the bath, w h i c h is diff icult to quantify. Therefore, it is useful to analyze sensit ivi ty o f the mode l predictions to this parameter. A s shown in F igure 5.18, for the fixed Tbath o f 1600 °C the radiative heat transfer to the exposed bath decreases w i t h increasing A T s i a g because o f an increased temperature o f the slag top surface ( T e b = T b a l h + A T s l a g ) . A l t h o u g h the regenerative heat-transfer rate Q c w _ c b increases due to an increase o f the temperature difference across the refractory/metal interface (resulting from the increased temperature o f the exposed refractory), the overal l effect o f a setting A T s i a g to 200 °C is to reduce Q b a t h by 1.9 M W , resulting i n a decrease o f 5.1 ton h" 1 in the mel t ing rate. A s shown i n F igure 5.19, because radiative heat transfer f rom the gas to the exposed refractory increases w i t h increasing A T s i a g (and hence T e b ) , both TM-Mlix and A T K M a x are increased. Figure 5.18: The effect of AT s i a g on the heat transfer rates to the bath 45 -, . : — i : 1 • . 1 • — | 40 -k 5 + 0 -I 1 1 1 1 1 1 50 75 100 125 150 175 200 Specified A T s l a g , °C - 8 6 -F i g u r e 5.19: T h e effect o f A T s i a g on the r e f r ac to ry t empera tu re s 2100 j 2090 --2080 --2070 --o o 2060 --& 2 2050 --2040 --2030 --2020 - : 2010 --2000 - : j 490 - 480 -- 470 - 460 ' - 450 u o -- 440 & S -- 430 - 420 < -- 410 - 400 ~ 390 50 75 100 125 150 175 200 Specified A T s l a g , °C Since the effect of a large A T s i a g is to reduce the melting rate while increase both the refractory hot-face temperature and the thermal shock on the refractory, it is worthwhile to investigate how to minimize A T s i a g . The model predictions indicate that i f there is no slag present ( A T s i a g =0), the melting rate decreases by a larger value (6.4 ton h _ 1)than that (5.1 ton h"1) with AT s i a g =200 °C due to the smaller emissivity (0.28) of liquid steel. 1 0 4 Also, both T M - M a x and A T W . M a x are increased, to 2200 °C and 558 °C respectively. Therefore, a slag layer with a high emissivity and minimum A T s i a g is helpful to improve the furnace performance. When no slag is added during the melting process, some slag would.be produced due to oxidation of the iron and other elements in the scrap such as silicon and manganese. The amount of slag generated can, to some extent, be controlled by adding carbon to the bath, which suppresses formation of FeO, so that a very thin slag film might be achieved. Alternative might be to inject finer carbon particles onto the bath surface, recognizing that some of this would instead be combusted within the freeboard. 5.4 S u m m a r y The heat-transfer model was partially validated using the experimental data from the bench-scale trials. Both experimental results and model predictions indicate that the furnace -87-thermal efficiency increases with increasing oxygen enrichment in the combustion air and decreases with increasing thickness of a slag layer. Model predictions shows that a melting rate in order of 100 ton h"1 can be achieved b y a 4 m I D x 16m long furnace at a firing rate of 6000 N m 3 h"1. The effects of several design and operating variables on furnace performance are investigated and the sensitivity of the model predictions to some of the input parameters is assessed. -88-C H A P T E R 6 - C O N C L U S I O N S In order to further investigate the viability of the continuous process rotary melting furnace ( C P R M F ) as a replacement of the E A F in minimill steel operations, a bench-scale furnace was designed and constructed. In a campaign of trials melting copper, the effect of oxygen enrichment level and slag thickness was assessed. In conjunction with experimental campaign an improved thermal model was developed in order to examine the effects of axial temperature variations and to allow scale-up to industrial furnace operations. The model was partially validated against the bench-scale results. In general the results support the viability of the proposed C P R M F and indicate that a 4 m ID x 16 m furnace with oxy-fuel firing could achieve a melting rate of > 100 ton h"1 with a thermal efficiency of about 66%. The modeling work indicates that acceptable refractory life might be achieved by proper design of the burner system in order to extend the heat release by combustion over a significant fraction of the furnace length. Based on the experimental results, the following conclusions can be made: (1) For melting copper the bench-scale C P R M F achieved the design melting rate of 25 kg per hour. In a limited campaign the furnace proved easily controllable and experienced no refractory problems. (2) The melting rate and thermal efficiency improved significantly in moving from 37% to 80%) oxygen in the combustion air. Extrapolating the results to full oxy-fuel firing suggests 30% thermal efficiency which is close to the expected level given the very limited working volume of the furnace. (3) The introduction of a slag layer into the bench-scale furnace resulted in significantly lower thermal efficiency and melting rate. However, the effect of the slag thermal resistance could not be isolated from the effect of the reduction in the depth and surface area of the liquid metal component of the bath. Predictions from modelling the industrial-scale C P R M F lead to a number of significant conclusions: -89-(1) A melting rate in order of 100 ton h"1 can be achieved b y a 4 m I D x 16m furnace operating at a natural gas firing rate of 6000 N m 3 per hour. Under the baseline conditions, the furnace thermal efficiency is around 66%. Without scrap preheating, the direct energy consumption is 619 k W h f 1 (including the energy for oxygen generation), which is less than the 662 k W h f ' o f a typical electric arc furnace and represents a saving of about 45% in terms of at-source energy. (2) Refractory life wi l l be an issue in the C P R M F . Under the baseline conditions, the maximum temperature predicted for the refractory hot-face is 2021 °C in combination with 393 °C thermal cycling over each furnace revolution. (3) For a fixed firing rate, a longer fuel/oxygen mixing-region can significantly reduce both maximum hot-face temperature and thermal cycling. B y extending the fuel/oxygen mixing-region to 90% of the furnace length the maximum hot-face temperature was reduced to 1844 °C in conjunction with 228 °C in thermal cycling. (4) For a given furnace with a constant fuel/oxygen mixing-length, increasing the melting rate by increasing the firing rate wi l l result in higher refractory temperature and increased thermal cycling. For the 4 m ID x 16 m furnace, increasing the firing rate by 58%, i.e., from 6000 to 9500 N m 3 h"1, increased the melting rate from 103 to 150 ton h"1 but also raised maximum refractory hot-face temperature by 89 °C and thermal cycling by 83 °C. (5) Operating at the maximum practical rotation rate wi l l minimize the refractory hot-face temperature and thermal cycling. Under the baseline conditions, increasing the rotation rate from 0.5 to 2 rpm reduced maximum hot-face temperature by about 124 °C and thermal cycling by 105 °C. This was accompanied a small (3%) increase in melting rate. Rotation rate influences the balance between direct and regenerative heat transfer to the bath but has relatively little impact on total heat transfer to the bath. (6) The furnace should be operated with minimal slag on the bath surface. Increasing the slag present within the furnace has relatively little influence on the net rate of heat transfer to the bath, the decrease in direct input via the top surface o f the bath being offset by an increase in the regenerative input. However, the thermal resistance of a slag layer wi l l result in higher refractory temperatures and increased -90-thermal cycling. Relative to operating with no slag, a thin slag layer improves heat transfer to the bath due to the high emissivity of the slag relative to the liquid metal. -91 -C H A P T E R 7 - R E C O M M E N D A T I O N S ON F U T U R E W O R K The future works might include following items: (1) The current model provides important information for burner design, i.e., what is furnace performance in case of a long fuel/oxygen mixing region and what would happen when using a short mixing region. Once the burner system is determined, multi-dimensional gas flow pattern can be investigated using C F D simulation. Also, multi-dimensional temperature distribution within the gas phase can be determined. (2) The effective thermal conductivity of the slag should be determined so that the temperature of the exposed slag top surface (also the temperature difference across the slag) w i l l be determined by energy balance, but not specified. (3) Although the local regenerative heat-transfer coefficients have a minor effect on the predicted melting rate, their influence on the predicted thermal cycling of the refractory is relatively large. Therefore, they should be measured experimentally. - 9 2 -R E F E R E N C E S 1 P. V . Barr and T. R. Meadowcroft, "Scrap Melting in an Oxy-fuel Fired Rotary Furnace", 2001 Electric Furnace Conference Proceedings, pp.451-463 2 Annual E A F Roundup of the Iron & Steel Society, Iron & Steelmaker. Vol.27, No. 5, Apr i l 2000, pp.31-54 3 M . Haissig, G. 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Paschkis, Drehrohrofen als Warmeaustauscher, Vol .4 , 1960, pp. 183-197 6 0 H . S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids, Oxford University Press, London, 1947 6 1 A . Vaillant, P h D Thesis, Faculty of Mechanical Engineering, Columbia University, 1965 6 2 L . H . J. Wachters and H . Kramers, "The Calcining of Sodium Bicarbonate in Rotary K i l n " Proc. 3 r d European Symp. Chem. Reaction Eng., Amsterdam, 1964, pp.77-85 6 3 J. Lehmberg, M . Hehl and K . Schugerl, "Transverse M i x i n g and Heat Transfer in Horizontal Rotary Drum Reactors", Presented by K . Schugerl at the International Conference SPIRE in Arad, Israel, November 30-December 5, 1975, Powder Technology (1977), Vol.18, pp. 149-163 6 4 M . Cross and R. W. Young, "Mathematical Model of Rotary Ki lns Used in the Production of Iron Ore Pellets", Ironmaking and Steelmaking, 1976, No.3, pp. 129-137 6 5 J. P. Gorog, T. N . Adams and J. K . Brimacombe, "Regenerate Heat Transfer in Rotary K i l n " , Metallurgical Transactions B . V o l . l 3 B , June 1982, pp. 153-163 6 6 B . G. Jenkins and F. D. Moles, "Modeling of Heat Transfer from a Large Enclosed Flame in a Rotary K i l n " , Trans. Inst. Chem. Eng.. Vol.59, 1981, pp. 17-25 -99-A . H . Alyaser, Fluid Flow and Combustion in Rotary Kilns , PhD Thesis, Department of Metals and Materials Engineering, University of British Columbia, 1998 68 F . H . Harlow and P. Nakayama, "Transport of Turbulence Energy Decay Rate", Report LA-3854, Los Alamos Science Lab, University of California, 1968 6 9 M . Nallasamy, " A Critical Evaluation of Various Turbulence Models as Applied to Internal Fluid Flows", N A S A Technical Paper 2474. 1985 7 0 B .F . Magnussen and B . W . Hjertager, "On Mathematical Modeling of Turbulent Combustion with Special Emphasis on Soot Formation and Combustion", Sixteenth Symposium (International) on Combustion, The Combustion Institute, 1976, pp.719-729 7 1 A . J . Baker, Finite Element Computational Fluid Mechanics, McGraw-Hi l l , 1983 7 2 E . Mastorakos, A . Massias, C. D. Tsakiroglou, D. A . Goussis, V . N . Burganos and A . C. Payatakes, " C F D Predictions for Cement Ki lns Including Flame Modeling, Heat Transfer and Clinker Chemistry", Submitted to Applied Mathematical Modeling in 1997 7 3 M . Georgallis, Mathematical Modell ing of Lime Kilns, PhD Thesis, Department of Mechanical Engineering, University of British Columbia, 2004 7 4 P. He, M . Salcudean, L S . Gartshore and P. Nowak, "Multigrid Calculation of the Fluid Flows in Complex 3D Geometries Using Curvilinear Grids", Computers and Fluids. Vol.25, No.4, 1996, pp.395-419 7 5 B . E . Launder and D . B . 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Post, "Modell ing of Gas-Fired Glass Furnace's", Proc. 1 s t European Conference on Industrial Furnaces and Boilers, Lisbon, March 1988 ' PG-250 portable gas analyzer is manufactured by H O R I B A I N S T R U M E N T S I N C O R P O R A T E D , 17671 Armstrong Irvine Industrial Complex, Irvine, California 92614, U S A , Telephone: 949-250-4811, Fax number: 949-250-0924 } Refractory data sheet and private communication with Brad Price, R H I Canada Inc., Langley, B . C . , Canada, June 4 t h , 2004 1 Data from MatWeb, a searchable database of material data sheets, http://www.matweb.com/search/SpecificMaterial.asp?bassnum=MC102J 1 Carl L . Yaws, Handbook of Viscosity: Volume 4 - Inorganic Compounds and Elements. Gu l f Publishing Company, Houston, Texas, 1994, pp.94 ' C. Diaz, "The Thermodynamic Properties of Copper-Slag System", Incra Monograph III: The Metallurgy of Copper, International Copper Research Association, Inc., 1974, pp.105 % E . T. Turkdogan, Fundamentals of Steelmaking, The Institute of Materials, London, U K , 1976, pp.140 ' J. F. Elliott, M . Gleiser and V . Ramakrishna, Thermochemistry for Steelmaking: -101-Thermodynamic and Transport Properties. Addison-Wesley Publishing Company, Inc., 1963, pp.673 A . Muan and E . F. Osborn, Phase Equilibria Among Oxides in Steelmaking. Addison-Wesley Publishing Company, Inc., 1965, pp.154 8 7 F. Kreith and W. Z . Black, Basic Heat Transfer, Harper & Row, Publishers, Inc., New York, 1980, pp.275 8 8 M . F. Modest, Radiative Heat Transfer, M c G r a w - H i l l Series in Mechanical Engineering, M c G r a w - H i l l , Inc., New York, 1993, pp.206 8 9 F. P. Incropera and D. P. DeWitt, Fundamentals of Heat and Mass Transfer, Second Edition, John Wiley & Sons, Inc., New York, 1985, pp.779 9 0 F. Kreith and W. Z. Black, Basic Heat Transfer, Harper & Row, Publishers, Inc., New York, 1980, pp.55 9 1 F. Kreith and W. Z . Black, Basic Heat Transfer, Harper & Row, Publishers, Inc., New York, 1980, pp. 53 9 2 M . Susa and K . C. Mi l l s , Slag Atlas (Second Edition), Chapter 16 - Optical Properties of Slags: Data for Refractive Indices and Absorption Coefficients, Woodhead Publishing Limited, Abington, Cambridge, England, 1995, pp.602-616 9 3 Smith, T. F., Shen, Z . F., and Friedman, J. N . , "Evaluation of Coefficients for the Weighted Sum of Gray Gases Model" , Transactions of the A S M E , Vol.104, November 1982, pp.602-608 9 4 J. M . Rhine and R. J. Tucker, Modell ing of Gas-Fired Furnaces and Boilers. British Gas, -102-M c G r a w - H i l l Book Company, London arid New York, 1991, pp.39 A . Mitchell and J. F. Wadier, "Some Observations on the Radiative Properties of E S R Slads", Canadian Metallurgical Quarterly. Vol.20, No.4, 1981, pp.373-386 3 S. W . Churchill, " A Comprehensive Correlating Equation for Forced Convection from Flat Plates", A I C h E Journal. Vol.22, No.2, March 1976, pp.264-268 7 Charles E . Baukal, Jr., Heat Transfer in Industrial Combustion. Chapter 3 - Heat Transfer Modes. Table 3.2 - Normal Total Emissivities of Refractories as a Function of Temperature. C R C Press L L C , New York, 2000, U B C Library E-book Charles E . Baukal, Jr., Heat Transfer in Industrial Combustion. Chapter 3 - Heat Transfer Modes. Table 3.1 - Normal Total Emissivities of Various Surfaces as a Function of Temperature. C R C Press L L C , New York, 2000, U B C Library E-book 3 J. R. Markham, P. E. Best, P. R. Solomon and Z . Z . Y u , "Measurement of Radiative Properties of Ash and Slag by FT- IR Emission and Reflection Spectroscopy", Journal of Heat Transfer. Vol.114, May 1992, pp.458-464 } 0 F. Kreith and W. Z . Black, Basic Heat Transfer. Harper & Row, Publishers, Inc., New York, 1980, pp.511 n Carl L . Yaws, Handbook of Viscosity: Volume 4 - Inorganic Compounds and Elements. Gu l f Publishing Company, Houston, Texas, 1994, pp.105 ) 2http://www.sv.vt.edu/classes/MSE2094_NoteBook/96ClassProj/examples/kimcon.html ) 3 1. E. Powell, J. W. Bryant and K . C. Mi l l s , "The Thermal Conductivity o f Liquids at High Temperature", Symp. Transp. Prop, of Fluids, Glasgow, N P L report, 1979 -103 -E . A . Brandes and G. B . Brook, editors, Smithells Metals Reference Book, seventh edition, Butterworth-Heinemann, 1992, Chapter 17, pp. 17-10, U B C Library E-book. -104-APPENDICES Appendix A: Evaluation of the Temperature-Independent Direct Exchange Areas The direct surface-surface exchange areas can be evaluated using view factors. The view factor between infinitesimal surface elements dA; and dAj on two isothermal, black and diffuse surfaces A ; and Aj, as shown in Figure A . 1, is defined as the portion of total energy leaving dAithat is directly toward and intercepted by dAj. Radiative heat transfer rate from dAj to dAj is given as cos9;COS0, QdAi->dAj = I, • dA, • cose, • dfl. = I, ! r _ i - d A i d A J ( A - l ) where I, is radiative intensity from A ; (the radiative energy per unit time, per unit solid angle, and per unit area normal to the rays). It is constant in all directions for diffuse surfaces. Total energy emitted from dA; into all direction within a hemisphere over dA; is E b s , r d A i = jjl, dAj-cosG, dOj = I ; - T i - d A , (A-2) hemisphere where E b s l is black body emissive power from A;. Therefore, the view factor from dAj to dAj is Q n A i ^ d A i COS0-COS8: - f f - A i - d * = ir*rt= —^dA; (A~3) Thus the view factor between two diffuse finite surfaces A ; and Aj can be given by the equation 1 f r COS0.COS0. F - = A - U ^ < ^ D A ' ,A-" and the direct surface-surface exchange area from Aj to Aj is defined as r r cosG-cosO-V , = A , F A , _ A l = J J A j — ^ > A , d A , (A-5) If there is a participating medium between A ; and Aj, transmissivity of the medium must be considered and the direct surface-surface exchange area becomes - 105 -Figure A . l : Schematic diagram of the view factor between dAj and dAj Radiation from gases is a volume phenomenon and emissive power wi l l be per volume (W m"3). The volumetric emissive power is given by where K g is extinction coefficient, a is Stefan-Boltzmann constant (5.67xl0" 8 W m" 2 K" 4 ) , and T g is absolute gas temperature. A l l energy emitted by a differential volume dVi in Figure A .2 must pass through the sphere centered on dVj and this emission wi l l be uniformly distributed over 4n steradians. Therefore radiative heat transfer rate from dV; to a differential surface element dAj is q v = 4 (K g P)o7; 4 (A-7) 4 ( K g P ) , E dA ,cos0 Q dVi->dAj (A-8) = E ( K g P ) 1 c o s 9 J t , . ,dA.dV. where E b g ; = c T 4 . Thus radiative heat transfer rate from a finite isothermal gas volume V i to a finite surface Aj is given by - 106-, , (K 2 P) ,cos9 , Q v ~ A j = ^UAi £ \ K ^ d V , = g , S j E b & 1 (A-9) , r ( K PVcosO, where g l S j = f f % d A , d V , (A-10) 1 JVI J A J 7tr is the direct gas-surface exchange area. Similarly, radiative heat transfer rate from Vj to another finite gas volume Vj is ( K g P ) i ( K g P ) j 'Vi->Vj E, f f ^>^*y\. d V d V = g ~ g E b ( A - l l ) where ^ = g ^g ^ ^ d V , (A-12) / i JVj ^ is the direct gas-gas exchange area. Obviously, the direct exchange areas have following relationships: sisJ = 8 ^ , = Sjg, and g,gj =gigi Figure A.2: Schematic diagram o f the direct gas-surface exchange area Since the direct exchange areas wi l l be evaluated by approximate methods (subdivision in finite areas and volumes), the question of accuracy must be addressed. For individual values there is no real check. However, for an enclosure consisting of n surface zones and - 107-m gas volume zones, the overall accuracy is easily determined by the equations: n m E s i s j + Z s i 8 j = A i (A-13) j = i j = i n m S 8 i s j + Z 8 i g j = 4 ( K B P ) i V i (A-14) j=i j=i - 108 -Appendix B : Evaluation of the Temperature-Independent Total Exchange Areas If the direct exchange areas are used to perform energy balances for the surface and gas volume zones, the process leads to a set of simultaneous equations for the unknown temperatures or heat fluxes. The unknown heat fluxes at the surfaces may be determined by matrix inversion i f all zone temperatures are known. If the zone temperatures are not known, but must be determined iteratively by considering conduction and/or convection as well, one matrix inversion must be performed for every iteration. To avoid such unnecessary matrix inversions (since the direct exchange areas do not depend on temperature), a more general technique involving total exchange areas is introduced. To evaluate the total exchange areas, leaving flux densities from the surface zones have to be determined. Considering surface zone A ; (Figure B . 1) in an enclosure consisting of n surface zones and m gas volume zones, the following equation can be written: n m A . W , = A , £ l E b v + A . P . G , = A . B . E ^ , + P l ( _ _ s j s i W J + _ _ g j S l E b & j ) ( B - l ) j=i j=i Rearranging to place all known quantities on right hand side: n A A P E m __ (s j S , - 8^ ^ = - - L U S L - £ g j S i E b g J (B-2) H P i P i H where: 5: ; = 0 for j ^ i 5i,j =1 for j = i Eq.(B-2) can be written for each enclosure surface zone, resulting in a set of n simultaneous linear equations in n values of leaving flux density. In matrix form this system of equations becomes: - 109-r s l S l - • SjS 2 S 2Sj A , S 2 S 2 s n s 2 S l S n S 2 S n w 2 s „ s „ - — J n n Pn r A i £ i E bs , l - § l S l E b & l ••• - g m S l E A , s 2 2 E - a s E ^bs,2 & l s 2 i j b g , l g m s 2 E 'J2J^bg,m (B-3) A n s r P n E bs,n § l S n E b g , l ••• § m S n E bgm J This system can be solved using standard methods (e.g. matrix inversion for relatively small systems or Gauss-Seidel iteration for larger systems) to obtain the leaving flux densities Wj, which account for all emitted, absorbed and reflected radiant energy within the enclosure. Figure B.l: Schematic diagram of leaving flux density Leaving flux density W, Surface A ; - 110-The total exchange areas are achieved by setting the black body emissive power of all zones to zero except for zone i , for which the emissive power is set to unity. When surface zone A; (Ebs,i = 1) is the only source of radiative energy within the enclosure, radiative flux from Aj per unite black body emissive power for A ; is given as: Ai = - ( E b l l j - i W j ) = ( B -4 ) P, P J where EbSj = 0 and ;Wj is the leaving flux density from Aj when A ; (Ebs,i = 1) is the sole emitting zone. If we remove the minus sign " - " to get radiative flux to (rather than from) Aj, multiply by Aj to convert W m"2 to W, and remove the restriction EbS,i = 1 to simply EbS,i, we obtain "one-way" radiative heat transfer rate from A i to Aj (including all reflections) A J £ J — Q A 1 ^ A J = (• J J , W ; ) E h s , = S ^ E ^ (B-5) A ; 6 : where = - ^ , W , (B -6) P, is the total exchange area from Aj to Aj. The only thing not yet considered is the energy emitted by A ; which ultimately gets reabsorbed by A;. For this case the following equations can be written: Q A ^ A i = A i - a l Y G 1 = A 1 . s i - 1 G 1 (B-7) 1 W 1 = £ i - E b s i + p 1 - 1 G 1 = 8 1 + p 1 - 1 G 1 (B-8) where EbS,i = 1. Therefore: W - s ( B - 9 ) Pi Substituting E q . ( B - 9 ) in the expression for QAl_,Ai and remove the restriction Ebs,i = 1, QAJ-AI becomes Q A I ->A, - e ^ = p~E b v (B-10) Pi where S~S~ = ^ - ( j W ; - s,) ( B - l l ) Pi is the total exchange area from A; to itself. - I l l In deriving the surface-surface total exchange areas we assumed the sole emitter to be a surface zone (unite black body emissive power). However, we can apply same technique for a gas volume zone V ; ( E D g , i = 1, E b g j =0, i , E b s ^ O ) . For this case all terms in the excitation vector are zero except for s,g; , s 2 g, ... s n g ; . Again we can solve the system to obtain n leaving flux densities ; W k where i refers to the emitting volume zone V i and k=-l~n refers to the surface zones. In exactly the same manner as before we can obtain radiative heat transfer rate from V ; to Ak Q v i - .Ak = — = G A E b & , (B-12) Pk where G~s7 = ^ i L 1 W k (B-13) Pk is the gas-surface total exchange area. Similarly, radiative heat transfer rate from V; to another gas volume zone Vj is Qvi-vj = ( g ^ + E s S-. W k ) E b 6 . = G ~ G ~ E b 6 i (B-14) k=l where = g ^ + £ s ^ T - W k (B-15) k=l is the gas-gas total exchange area. Unlike the direct exchange areas, the total exchange areas account for reflection in all directions. Also, they completely account for the enclosure geometry and are temperature-independent (in case of a gray gas) so that they need to be calculated only once. For systems where all temperatures are known the total exchange areas do not supply any additional information. These problems can be solved using the direct exchange areas. However, the total exchange areas allow the solution of the general enclosure problem where neither zone temperatures nor surface heat flux are known. Similarly to the direct exchange areas, the accuracy of the total exchange areas can be checked by the equations: - 112-_ _ S i S j + Z S i G i = A i e i (B-16) j=i j=i S G i S j + S G j G ^ ^ P X X (B-17) J=I j=i Also, for an enclosure containing a gray gas, the total exchange areas have following relationships: SiSi = SjSj , G,Sj =S J G 1 and G ^ = GjG, - 113 -

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