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Measurement of primary region heat transfer in horizontal direct chill continuous casting of aluminum… Di Ciano, Massimo 2007

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MEASUREMENT OF PRIMARY REGION HEAT TRANSFER IN HORIZONTAL DIRECT CHILL CONTINUOUS CASTING OF ALUMINUM ALLOY RE-MELT INGOTS by MASSIMO Dl CIANO B.A.Sc, The University of Toronto, 2004 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES (Materials Engineering) THE UNIVERSITY OF BRITISH COLUMBIA March 2007 © Massimo Di Ciano, 2007 Abstract Thermal-fluid modeling of the Horizontal Direct Chill (HDC) casting process has been used to aid in process optimization and development of HDC casting of aluminum foundry alloy re-melt ingots. Characterization of the heat transfer conditions present in the process is essential to accurate model development. In this study, the heat transfer conditions in the primary cooling region of an HDC casting machine were characterized using mould temperature measurements taken during plant trials. Steady state mould heat flux distributions were determined for various casting conditions through inverse heat conduction modeling. The calculated heat fluxes are of comparable magnitude to values reported in DC casting literature. Mould heat fluxes were affected by casting speed but relatively insensitive to casting temperature and mould water flow rates. To compliment the plant trial approach, an apparatus was built to replicate primary cooling region heat transfer phenomenon. Mould temperatures taken from the casting simulator were used to determine mould heat fluxes during lab tests. Comparing lab results and plant trial results confirm the applicability of the lab tests to in-plant operating conditions. These preliminary lab results suggest that use of a casting simulator could suffice as a means for characterizing primary cooling heat transfer in HDC casting, thus avoiding the need for extensive plant trials. Table of Contents Abstract Table of Contents List of Tables List of Figures Acknowledgements 1 INTRODUCTION 1.1 Aluminum Production 1.2 DC Casting 1.3 HDC Casting 2 BACKGROUND INFORMATION AND LITERATURE REVIEW 2.1 Introduction 2.2 Primary Cooling Phenomenon in DC Casting 2.3 Experimental Methods for Determining Heat Fluxes during Casting 1 3 OBJECTIVE 4 EXPERIMENTAL METHODS AND MEASUREMENTS 4.1 Industrial HDC Casting Machine Plant Trial 4.1.1 Experimental Matrix 4.1.2 Mould Instrumentation 4.1.3 Results 4.2 Lab Scale Characterization of Primary Zone Heat Transfer 4.2.1 Casting Simulator Design iv 4.2.2 Initial Casting Trials: Operating Parameter Investigation 31 4.2.3 Scope of Experiments 36 4.2.4 Instrumentation of Copper Chill 38 4.2.5 Results 40 4.3 Chapter Summary 4 5 4.3.1 Plant Trial 45 4.3.2 Lab Experiments 46 5 INVERSE HEAT CONDUCTION ANALYSIS TECHNIQUE 47 5.1 Forward Heat Conduction Problems 47 5.1.1 The Heat Conduction Equation 47 5.1.2 Finite Element Method for Solving Heat Conduction Problems 49 5.2 The Inverse Heat Conduction Problem 49 5.2.1 Beck's Technique 50 5.3 IHC Model of an Industrial HDC Mould 54 5.3.1 Geometry and Mesh 55 5.3.2 Boundary Conditions 56 5.3.3 Thermophysical Properties 57 5.4 Casting Simulator Chill 58 5.4.1 Geometry and Mesh 58 5.4.2 Boundary Conditions 58 5.4.3 Thermophysical Properties 60 5.5 Validation 61 5.5.1 FE Validation 61 V 5.5.2 Steady State IHC Validation 63 5.5.3 Transient IHC Validation 66 5.6 Summary 69 6 RESULTS AND DISCUSSION 70 6.1 Industrial IHC Analysis 70 6.1.1 Industrial IHC Results 70 6.1.2 Model Sensitivity to Regularization Parameter 72 6.2 Casting Simulator IHC Analysis 74 6.2.1 Casting Simulator IHC Results 76 6.2.2 Sensitivity 81 6.3 Comparison of Results 83 6.4 Summary of Results 88 7 CONCLUSIONS AND FUTURE WORK RECOMMENDATIONS 90 7.1 Conclusions 90 7.2 Future Work Recommendations 91 REFERENCES 93 APPENDIX 1 - CALCULATION OF WATER COOLING HEAT TRANSFER CO-EFFICIENTS 98 VI List of Tables Table 1 -1 - 2006 worldwide sales of aluminum car parts (Ducker Worldwide, 2006) 3 Table 2-1 - Results from industrial characterization of primary zone heat fluxes in aluminum and magnesium DC casting systems 14 Table 4-1 - Test Matrix for the 2003 Dubuc plant trial 19 Table 4-2 - Locations of T/c placement in the industrial HDC casting mould 20 Table 4-3 - Summary of experimental troubles encountered with the casting simulator 32 Table 4-4 - Final eight experimental trials of casting simulator (increased metal head pressure). 38 Table 4-5- Locations of T/c placement in copper chill 39 Table 5-1 - Thermophysical properties of the industrial mould (Larouche, 2005) 58 Table 5-2 - Thermophysical properties of the casting simulator mould (Metals Handbook, 1990) 61 Table 5-3 - Data used for 1D transient heat conduction validation problem 61 Table 5-4 - Thermophysical properties used in steady state and transient validation problems. 63 Table 5-5 - IHC Results Steady State Sensitivity 66 Table 5-6 - Comparison between actual and calculated q(x,t) characteristics 68 Table 6-1 - Test matrix for the 2003 Dubuc plant trial 70 Table 6-2 - IHC parameter values used for industrial IHC analyses 71 Table 6-3 - Plant trial IHC tabulated results 72 Table 6-4 - Casting simulator test conditions 75 Table 6-5 - IHC parameter values used for casting simulator IHC analyses 76 Table 6-6 - Casting simulator IHC tabulated results 81 Table 6-7 - Industrial trial vs. casting simulator casting parameters 85 Table 6-8 - Qualitative differences between the industrial trial and casting simulator casting conditions 87 vii List of Figures Figure 1-1 - Worldwide production of primary aluminum (The Aluminum Association of Canada, 2006) 1 Figure 1-2 - North American light vehicle aluminum content (Ducker Worldwide, 2006) 2 Figure 1-3 - Schematic of a VDC casting system during steady state operation 4 Figure 1-4 - An axial cross section of an HDC casting machine during steady state operation. 6 Figure 1-5 - HDC casting machine mould; a) from view of mould and b) exploded cross section of mould at location indicated b—b 6 Figure 2-1 - Enlarged cross section of a HDC casting mould and ingot. The primary and secondary cooling regions are highlighted 8 Figure 2-2 - Enlarged cross section of a HDC casting mould and ingot: a) meniscus zone, b) metal/mould contact zone c) air gap zone 9 Figure 4-1 - T-ingot mould front view. General location of T/c placement is shown 20 Figure 4-2 - Cross section of the T-ingot mould showing the position of embedded T/c's used in 2003 Dubuc plant trial 20 Figure 4-3 - Raw temperature data (small time scale shown), obtained from industrial plant trial 21 Figure 4-4 - Raw temperature data obtained from industrial plant trial for 4 selected T/c's 22 Figure 4-5 - Variation in T/c signal as a function of distance from the refractory plate. Data taken from Dubuc 2003 plant trial 22 Figure 4-6 - T/c data prior to industrial plant trial cast startup. The industrial temperature measurement precision was approximately +/- 1°C 23 Figure 4-7 - Sample raw thermocouple data obtained during plant trial. The regions defined as the steady operating regions for casting tests 1 and 2 are shown 24 Figure 4-8 - Steady state mould temperature measurements measured during the industrial trial 25 Figure 4-9- Preliminary design concepts; a) cold finger "dip" test, b) static casting, c) shell extractor apparatus and d) casting simulator 26 Figure 4-10 - General design of the casting simulator apparatus; a) side section b) exploded side section of the casting simulator assembly 28 Figure 4-11 - Bird's eye view of casting simulator apparatus after final build 29 Figure 4-12 - Side view of the initial configuration of the casting mould assembly. In later tests, the top chill was replaced with one identical in dimension to the bottom chill 29 VI I I Figure 4-13 - Front view of the casting simulator mould assembly with refractory sides and T/c holes shown 31 Figure 4-14 - Bottom surface of failed casting tests; a) folds present on surface, b) inconsistent and large lapped structure and c) significant and prolonged tearing of large surface laps. 34 Figure 4-15 - Bottom surfaces of castings conducted using increased metal head pressure; a) Test 1 casting, b) Test 3 both casting (right side) and torn cast section (left side), c) Test 5 both casting (right side) and torn cast section (left side) and d) Test 8 casting. All surfaces show similar surface structure 35 Figure 4-16 - Mould assembly used in final casting trials. Top and bottom Cu chills are similar in length 36 Figure 4-17 - Side view of the copper chill with T/c locations shown 39 Figure 4-18 - Raw temperature data for a) Test 1 and b) Test 4 from four selected T/c's in the copper chill. T/c 1 is closest to the front of the chill whereas T/c 13 is farthest from the front of the chill. (Note: data was acquired at a rate of 10 Hz, whereas the data shown above is displayed as 1 Hz data for clarity purposes.) 41 Figure 4-19 - Filtered temperature data for Test 1 from all T/c's in the copper chill. Data shown has been smoothed 43 Figure 4-20 - Filtered temperature data for Test 3 from all T/c's in the copper chill. Data shown has been smoothed 43 Figure 4-21 - Filtered temperature data for Test 4 from all T/c's in the copper chill. Data shown has been smoothed 44 Figure 4-22 - Filtered temperature data for Test 5 from all T/c's in the copper chill. Data shown has been smoothed 44 Figure 4-23 - Filtered temperature data for Test 8 from all T/c's in the copper chill. Data shown has been smoothed 45 Figure 5-1 - Sample 2D heat conducting domain with external boundaries and boundary conditions shown. The external boundaries are marked by dashed black lines 48 Figure 5-2 - Sample inverse heat conduction problem 50 Figure 5-3 - a) Estimation of the actual q(t) using a series of discrete flux values; b) the constant heat flux assumption, used over time period RAO, required to add stability to the iteration procedure when solving for a discrete flux (in this figure g,) 51 Figure 5-4 - Inverse Heat Conduction algorithm flow chart 52 Figure 5-5 - HDC geometry and mesh, along with definitions of the applied heat transfer boundaries conditions 55 Figure 5-6 - Metal/mould heat flux boundary conditions used in the HDC inverse heat conduction model 56 Figure 5-7 - Casting simulator mould: geometry, mesh, and external heat transfer boundary regions 58 IX Figure 5-8 - Metal/mould heat flux boundary condition used in the casting simulator inverse heat conduction analysis 59 Figure 5-9 - The temperature evolution for the case of a semi-infinite solid subjected to a constant surface heat flux at time t > 0, calculated via analytical and FE methods 62 Figure 5-10 - Geometry and boundary conditions used for the steady state forward problem.. 63 Figure 5-11 - Steady State IHC calculated flux distributions compared with applied flux. Sensitivity to flux distribution outside of region is shown 65 Figure 5-12 - Steady State IHC calculated flux distributions compared with applied flux. Sensitivity to flux distribution outside region q 1 4 is shown 65 Figure 5-13 - Geometry and boundary conditions used for the transient forward problem 67 Figure 5-14 - Comparison between actual and calculated heat flux distributions for selected times 68 Figure 6-1 - Calculated heat flux distributions obtained from Plant trial tests 72 Figure 6-2 - The effect of degree of regularization on the q(x) steady state distribution, obtained using test 1 plant trial data 73 Figure 6-3 - Smoothed and raw T/c data for Test 1. The dashed lines represent the start and end of the IHC analyses 74 Figure 6-4 - Filtered T/c data for Test 4. The dashed lines represent the start and end of the IHC analyses 75 Figure 6-5 - Test 1 T/c data and transient IHC results. The different curves represent the calculated fluxes q-, thru q-,3 respectively. The dashed line indicates the onset of the quasi-steady casting period 77 Figure 6-6 - Test 3 T/c data and transient IHC results. The different curves represent the calculated fluxes thru q 1 3 respectively. The dashed line indicates the end of the casting test 78 Figure 6-7 - Test 4 T/c data and transient IHC results. The different curves represent the calculated fluxes q, thru q 1 3 respectively. The dashed line indicates the end of the casting test 78 Figure 6-8 - Test 5 T/c data and transient IHC results. The different curves represent the calculated fluxes q, thru q 1 3 respectively. The dashed line indicates the end of the casting test 79 Figure 6-9 - Test 8 T/c data and transient IHC results. The different curves represent the calculated fluxes thru q 1 3 respectively. The dashed line indicates the onset of the quasi-steady casting period 79 Figure 6-10 - Calculated heat flux distributions obtained from casting simulator tests 81 Figure 6-11 - The calculated flux history for q-i for Test 1 for various values of a. The corresponding temperature history for T/c-i is plotted in black 82 X Figure 6-12 - Calculated heat flux distributions obtained from Test 1 for various values a 83 Figure 6-13 - Heat flux distribution comparison. Industrial trial vs. casting simulator results. . 84 Figure 6-14 - Schematic depicting initial metal solidification within the casting mould for both the a) HDC casting machine and b) casting simulator apparatus. The solid shell is shown as the grey curved line and the mould conduction path L1 denotes the heat flux pathway from mould cooling water to the meniscus zone 86 Figure 6-15 - Surface structure of lab test castings compared with industrial T-ingot surface structure, for aluminum A356 alloy 88 xi Acknowledgements I would like to thank my supervisors Daan Maijer and Steve Cockcroft, for their mentorship throughout the project. They have taught me well and have treated me fairly over the past ~3 years. Many thanks to Malcolm Lane and Andre Larouche for the many useful discussions concerning my project. I am grateful for the help of Riley Shuster, Jason Mitchell and Bin Zhang during casting. Furthermore, the work in this project could not have been completed without the efforts of the various technicians at the Department of Materials Engineering at UBC: Ross McLeod, Carl NG, Dave Torok, Serge Milaire, Rudy Cardeno and Glenn Smith. Lastly, the camaraderie between students, faculty and staff at the Materials Engineering Department at UBC can not be understated; without it I surely would not have completed my thesis. 1 : Introduction 1 Introduction 1.1 Aluminum Production The 2005 world production of aluminum metal from primary ore (primary aluminum) was in excess of 31 million tones. Figure 1-1 shows the trend in worldwide production over the last fifteen years (The Aluminum Association of Canada, 2006). Production in Canada was 2.9 million tones, making Canada the third largest primary aluminum producer in the world. A 1998 survey counted a total of 156 primary aluminum facilities worldwide (Plunked, 1999), with 12 in Canada including those planned to be in operation by 2003. 40 35 o T 3 </> O (U £ i 30 < s > o 25 ro c E ° E = 20 Q- £ * 15 10 • • • • • 1985 1990 1995 2000 2005 2010 year Figure 1-1 - Worldwide production of primary aluminum (The Aluminum Association of Canada, 2006) Primary aluminum is sold principally in two forms, ingot (wrought alloys) or re-melt stock (for use by foundries). The semi-continuous vertical Direct Chill (DC) casting process is one of the predominant methods used to produce wrought ingots in both round and rectangular cross sections. Horizontal DC and Carousel-type casters are examples of casting processes use to produce re-melt stock. Other examples of primary consolidation casting processes include twin-roll and belt/wheel casters. 1 : Introduction 2 In 2000, 32% of the total aluminum product shipments in the United States were made by the automotive industry (The Aluminum Association, 2006), making the transportation sector the largest end-user of aluminum. The steady increase in aluminum content per vehicle in the North American market over the past twenty years, shown in Figure 1-2, is the primary factor for the increase in primary aluminum production worldwide. This increase in the automotive sector in turn is being driven by the desire to reduce vehicle weight and increase fleet fuel efficiencies. 160 140 i 120 o (D fc 1 0 0 £ ou B* 60 40 20 1985 1990 1995 2000 year 2005 2010 Figure 1-2 - North American light vehicle aluminum content (Ducker Worldwide, 2006). Looking at the worldwide number of aluminum components sold in the automotive industry in 2006, shown in Table 1-1, cast components such as wheels and heads make up the majority of sales in terms of quantity. The raw material used by foundries is supplied as "foundry" or "re-melt" ingots. They come in various shapes and sizes; from large continuously cast T-ingots with cross sections close to 1 m2 and weight in excess of 500 kg, to individually cast small ingots weighing closer to 10 kg. In response to the noted increase in aluminum foundry production, Horizontal Direct Chill (HDC) casting of re-melt ingots has emerged as an efficient means to supply foundry ingots to the marketplace. The HDC casting process offers distinct advantages over Carousel-type casters both in terms of productivity and ingot quality. 1 : Introduction Table 1-1 - 2006 worldwide sales of aluminum car parts (Ducker Worldwide, 2006). Component Millions of Aluminum Units Sold (Worldwide) Wheels 99 Heads 55 Suspension Arms and Links 44 Transmission Cases 43 Brake Calipers 33 Steering Knuckles 33 Blocks 22 Bumper Beams 14 Closures 14 Subframes 9 Transfer Cases 3 IP Beams 2 Front Structures 2 Complete B/W 0.1 1.2 DC Casting A large fraction of the primary aluminum produced worldwide is consolidated using a form of DC casting technology. DC casting was first invented (independently) in the 1930's by both VAW and Alcoa (Roth, 1936; Ennor, 1942). Initially, ingots produced using DC casting technology were vertically cast, hence the acronym VDC casting was adopted. Later on in the 1950's, a Horizontal DC (HDC) casting process was invented by Societe Ugine at Venthon for making aluminum busbar (Angleys, 1960). In a VDC casting process, liquid metal is fed at a constant rate into an open ended mould. Figure 1-3 displays a schematic of a typical VDC casting machine during steady state operation. The liquid metal inflow rate is set equal to the ingot withdrawal (i.e. casting) rate to maintain a constant level within the mould. The section of the mould can be circular (billet or rod), rectangular (ingot), T-shaped (T-ingot), or square. The liquid metal, while in the mould region, is cooled by the mould and thus solidifies from the outside inward. As the cast is withdrawn, the growing solid shell contains the liquid metal sump. Rupture of the shell during operation can lead to a liquid metal breakout which can be extremely dangerous. To prevent shell sticking and tearing in the mould, the casting mould is lubricated. Typically, a free flowing 1 : Introduction 4 oil based lubricant such as castor oil (Laemmle and Bohaychick, 1992) is hydrostatically fed into the mould through porous graphite inserts (Angleys, 1964) or oil weeping channels machined into the mould. The location in the mould where the lubricating fluid first contacts the metal is close to or above the metal meniscus level. At the exit of the mould, the partially solidified casting is subject to further cooling by water which is sprayed directly onto the solid surface (shell), providing the necessary cooling to complete solidification of the ingot (interior). Typically, a DC casting mould is designed such that the water pumped through the internal channels within the mould is ejected through holes along the periphery of the mould; thereby providing the water required to "directly chill" the ingot surface. The casting process continues until the ingot reaches a predetermined length which is typically determined by factory height and "casting pit" depth limitations. Once the predetermined ingot length is obtained, the casting process is terminated. The ingot is then allowed to cool to room temperature prior to removal from the casting pit. The machine is then prepared for another casting run. Thus, VDC casting is considered a semi-continuous process. Water Cooled Mould Liquid Metal Inflow Figure 1-3 - Schematic of a VDC casting system during steady state operation. 1 : Introduction 5 1.3 HDC Casting By turning the process on its side, Horizontal DC casting offers significant production benefits through the possibility of continuous operation. A schematic of an HDC casting machine is shown in Figure 1-4. During steady state operation, molten metal from a holding furnace is transferred into the tundish via a runner system (not shown in Figure 1-4). The liquid level in the tundish is monitored during casting, and a feedback system is used to maintain a constant height. The tundish delivers the molten metal to the HDC mould via a series of refractory transfer tubes. Typically, moulds such as the T-ingot mould shown in Figure 1-5, are water cooled and made of copper alloys. Aside from startup operations; the mould, along with a refractory backing plate, confines the liquid metal. An initial shell solidifies around the periphery of the ingot prior to exit from the mould. Similar to VDC casting, continuous oil lubrication of the mould reduces mechanical friction between the solidifying shell and mould surfaces. Upon exiting the mould, the ingot surface is cooled by water jets emanating from the mould. These water jets are the major source of cooling in the process. Further downstream, where the ingot section has fully solidified, a flying saw cuts the ingot into manageable sizes while not disrupting the casting process. With the exception of process startup procedures, the process is operated continuously with cast material being withdrawn from the mould at a constant rate (i.e. casting velocity). During steady operation, typically HDC casting machines can produce ingots of size -700 mm wide by ~250 mm high at a rate of ~2 mm/s. Currently, Alcan is using two three-strand HDC casting machines at its Alma plant to produce T-ingot from A356 alloy and commercially pure aluminum for re-melt applications. 1 : Introduction Water Cooled Copper Mould Water Spray Cooling Backing Plate AL Casting Direction u Conveyor Figure 1-4 - An axial cross section of an HDC casting machine during steady state operation. Water Inlet t Ingot Cross Section Water Inlet Copper Mould Water Channel Channel Casting Direction Mould t Figure 1-5 - HDC casting machine mould; a) from view of mould and b) exploded cross section of mould at location indicated b—b. In order to obtain the full benefit from continuous casting operation using HDC technology, process optimization and development must continue. Key areas for improvement include extending campaign duration (the length of time/tonnage that can be continuously cast without interruption), casting rates, the ability to change alloys on the fly and the minimization of defects. To this end, Researchers at the University of British Columbia and Alcan's Arivida Research and Development Centre have entered into a collaborative research program to 1 : Introduction 7 develop a physical/fundamentally-based mathematical model to describe energy transport and solidification in the HDC casting process that can be used to assist in process optimization (NSERC CRD grant "Mathematical Modeling of Horizontal Direct Chill Casting for T-ingot Production", 2005-2007). As part of the overall objective to develop and validate a thermal-fluid model of the HDC casting process, various sub-tasks were defined for completion including acquiring validated thermal boundary conditions for both the primary and secondary cooling regions of the HDC casting machine. The use of valid boundary conditions in mathematical models becomes essential when accurate numerical results and trends are desired. When boundary conditions are inferred; for example, if conditions from a VDC casting machine are used as approximate boundary conditions for a HDC casting machine, then the resulting modeling calculations lose value. This thesis is focused on understanding aspects of the heat transfer that occurs within the mould region of the HDC caster. 2 : Background Information and Literature Review 8 2 Background Information and Literature Review 2.1 Introduction On a macroscopic scale, the energy flow during solidification of an ingot being DC cast is relatively easy to identify/understand. During operation, fresh molten metal flows from the tundish (liquid metal reservoir) to the sump region within the solidifying ingot. This molten metal represents the energy input to the ingot. The rate of energy input to the ingot can be raised by increasing either the casting velocity or metal superheat. The sensible heat of the solid represents the largest fraction of the total enthalpy of the incoming molten metal (~ 60 %); the latent heat of solidification (-35 %) and molten metal superheat (~5 %) make up the remainder (Grandfield and McGlade, 1996). Energy is extracted from the ingot by the primary cooling and secondary cooling, see Figure 2-1. Primary cooling is defined as the region where the ingot contacts (or is close to) the casting mould, whereas secondary cooling begins at the point where water sprays first impinge onto the ingot surface. It is understood in DC casting that the majority of cooling required for ingot solidification is provided by the secondary cooling. In VDC casting of Mg billets, the split between primary and secondary cooling has been reported as 4-11% to 96-89% (Adenis et al, 1963). Casting Mould Primary Cooling Secondary Cooling j * * Refractory Figure 2-1 - Enlarged cross section of a HDC casting mould and ingot. The primary and secondary cooling regions are highlighted. 2 : Background Information and Literature Review 9 2.2 Primary Cooling Phenomenon in DC Casting The heat transfer phenomena that occur in the primary region of a DC casting system are fairly well understood (qualitative). With respect to VDC casting, there is a large body of experimental work and numerical studies available. In HDC casting, few studies are available; however the phenomenon occurring in the primary cooling zone is expected to be similar. Detailed quantitative studies of the process parameters affecting the heat flux within the primary cooling region in DC casting (both HDC and VDC) have not been reported. In early DC casting modeling literature (Adenis et al, 1963), the heat transfer within the DC casting mould was classified into 3 zones: 1) a meniscus zone; 2) a contact zone and 3) a gap zone. Figure 2-2 illustrates these 3 zones within the primary cooling region. la': b : c |: Figure 2-2 - Enlarged cross section of a HDC casting mould and ingot: a) meniscus zone, b) metal/mould contact zone c) air gap zone. In the meniscus zone, liquid metal is in direct contact with the casting mould. High heat fluxes are expected as this is the first point of contact between the molten metal and the casting mould. On a macro-scale, contact between the ingot surface and mould at the meniscus, is good; creating an ideal path for heat to flow across the interface leading to relatively high heat extraction rates. Indeed, there is a general consensus that the heat fluxes in the meniscus zone are high and on the order of 0.6-3 MW/m2 (Bakken and Bergstrom, 1986; Drezet et. al, 2000; Fjaer et al, 2000; Grandfield and Dahle, 2000; Rabenberg et. al, 2000). 2 : Background Information and Literature Review 10 On a smaller scale it appears to be a rather dynamic region characterized by repetitive formation and withdrawal of a thin solid shell leading to periodic contact between the liquid metal and the mould. Through thermocouple measurements (cast in ingots) and metallographic studies (Bergmann, 1970; Weckman and Niessen, 1984c), it has been shown that the meniscus zone is only a few mm in length. Additionally, there is also general agreement that the heat transfer in the meniscus region is prone to fluctuations and/or periodicity. In non-ferrous VDC casting it is expected that this is due largely to metal level fluctuations (Fjaer et al, 2000). Similar observations have been made in steel continuous casting, where detailed studies of meniscus heat transfer also point to metal level being a critical parameter controlling meniscus heat transfer (Kumar et al, 1995). In early studies on cold shut formation in DC casting, Weckman and Niessen outlined 7 critical parameters that affect cold shut formation which are all linked to meniscus region heat transfer. The parameters are: casting speed, alloy freezing range, liquid metal superheat, oxidation influences, metallostatic head, mould-insert geometry and mould lubrication (Weckman and Niessen, 1984a and 1984b). The shell/mould contact zone is the area between the meniscus and gap regions. Numerical studies indicate that the heat flux in this intermediate region is on the order of 0.2-1 MW/m2 (Bakken and Bergstrom, 1986; Drezet et al, 2000). Typically, the heat flux in this region decreases with distance from the meniscus (in the direction of casting), due to the increasing thickness of the solidified shell. Furthermore, thermal contraction of the ingot reduces the contact pressure between the shell and mould wall, thus increasing the resistance to heat flow across the interface. Measuring the length of the contact region is a difficult task, although it has been inferred using thermocouple measurements to be around 5-20 mm (Jensen, 1984; Baker and Grandfield, 1987; Drezet et. al, 2000; Rabenberg et. al, 2000). Similar to the meniscus zone, the length of this contact zone may also fluctuate due to complex shell dynamics in the mould region (Collins, 1967). The surface roughness (both mould and metal shell), mould lubrication and alloy type have been shown to alter heat transfer measured during static casting of aluminum alloys (Muojekwu et al, 1995), presumably by affecting the contact 2 : Background Information and Literature Review 11 conditions at the shell/mould interface. Similarly, these variables should affect shell/mould heat transfer in DC casting, although no studies have been reported. Using similar logic, the metallostatic head pressure could also affect heat transfer in this intermediate region. Temperature measurements from VDC moulds (Fjaer et al, 2000) and ingots (Drezet et al, 2000) show that a gap region exists within the mould; which is largely attributed to thermal contraction of the ingot. This is analogous to the situation in static castings where the surface of the cast pulls away from the mould to form an air gap. Considering both the scale of the gap (< 1 mm) and the thermo-physical properties of the gases which exist in the gap, one can assume that heat is primarily transferred via conduction through the gas phase in the gap region (Grandfield and Dahle, 2000). Therefore, the resulting heat transfer in the air gap region is significantly reduced. Values for the metal/mould heat flux in the gap region have been calculated on VDC cast Al ingots as 2 kW/m2 (Drezet et al, 2000). Comparing this with static casting experiments; gaps forming between Al castings in metallic moulds result in interfacial heat fluxes of 10-50 kW/m2 (Ho and Pehlke, 1985). These values are considerably different; however they are still negligible in comparison with the high flux region of the mould. Temperature measurements from HDC moulds (Grandfield and Dahle, 2000) also indicate that an area of decreased heat transfer, associated with gap formation, occurs near the end of the mould. Using pool profile measurements, the heat fluxes in the gap region were reported between ~50-160 kW/m2 for pure Mg cast bars. 2.3 Experimental Methods for Determining Heat Fluxes during Casting To experimentally determine the heat flux from a solidifying metal to a mould during casting, a common methodology has been employed. Thermocouples are embedded very close to the interface of interest and temperature measurements are taken during a casting trial. Utilizing the test measurements, an inverse heat conduction algorithm' is coupled with a heat transfer model of the system, with the objective of matching the test data with the model 2 : Background Information and Literature Review ; 12 predictions. By matching the predicted temperature data with the measured temperatures, the heat fluxes can be inferred. INDUSTRIAL MEASUREMENTS A number of researchers have reported studies where thermocouples were 'cast' into DC cast ingots (Peel et al, 1970; Baken and Bergstrom, 1986; Jensen et al, 1986; Grandfield and Baker, 1988; Drezet et al, 2000; Rabenberg et al, 2000). Using this technique both the heat fluxes in the primary and secondary cooling zones can be determined, since the obtained measurements capture temperature data throughout within both cooling regimes. In an early study on VDC cast Al extrusion billets (Bakken and Bergstrom, 1986), a series of thermocouples were embedded into billets during casting, each a different depth from the casting surface (known as the "Harp Method"). Using temperature data from the embedded thermocouples, Bakken and Bergstrom were able to calculate the steady state heat flux occurring on the surface of the billets. The numerical procedure used to calculate surface heat fluxes and temperatures involved extrapolation and curve fitting of the original thermocouple data. The surface heat fluxes reported for the primary cooling region were around 1 MW/m2. In this study, error estimates were not reported. In a recent study on VDC cast Al alloy ingots (Drezet et al, 2000), thermocouple data was obtained in a manner almost identical to that of Baken and Bergstrom. The numerical approach to calculate the surface heat fluxes employed an inverse technique coupled with a finite element model of the casting process. The surface heat fluxes in the primary region calculated in this investigation were of a similar magnitude to that of Bakken and Bergstrom, with a maximum heat flux reported of about 1.2 MW/m2. Table 2-1 summarizes various results reported from literature. The procedure for casting thermocouples into an ingot/billet is technically challenging. To obtain meaningful data, the thermocouples should be placed at a known depth close to the ingot surface. Typically, this is achieved by mounting thermocouples onto a rigid frame and casting the frame into the ingot during operation. In addition, to minimize the perturbation of the 2 : Background Information and Literature Review 13 local thermal field, the thermocouples should have a relatively small thermal mass. In open top casting configurations such as VDC casting (see Figure 1-3) access to the ingot liquid sump is relatively straightforward making these measurements feasible. In HDC casting configurations (see Figure 1-4), access to the liquid portion of the ingot is difficult, since it must be achieved through the transfer tubes. Consequently, only one study involving casting thermocouples into an HDC cast ingot has been reported (Grandfield and Dahle, 2004). Unlike the ingot/billet; the mould is relatively accessible and thermocouples can be placed within it to collect mould temperature data suitable for calculation of primary heat transfer (surface heat fluxes) via an inverse heat conduction methodology. A number of studies in the non-ferrous literature have used this methodology (Jensen, 1984; Baker and Grandfield, 1988; Fjaer et al, 2000; Grandfield and Dahle, 2000). In the study by Jensen on DC cast Al billets, mould temperatures were used to calculate heat fluxes in the meniscus and the shell/mould contact regions of the mould. Model equations relating the total amount of heat transfer to the contact length, average metal/mould heat flux and temperature difference between the metal/mould surfaces were fit by trial and error using internal mould temperature data. By further assuming that the total amount of heat transferred to the mould remained fixed (an amount measured as 16 kW) Jensen's calculated contact lengths and heat fluxes were within the ranges of 1-4 mm and 2-10 MW/m2. Using this method, the calculated heat fluxes may have been inaccurate, thus leading to unreasonably high primary zone heat fluxes. In a recent study using inverse modeling techniques, Fjaer calculated the primary zone heat fluxes in VDC casting of Al ingots to be of the order 0.8-1.2 MW/m2. In the work by Grandfield and Dahlle, analysis of primary heat transfer of HDC cast pure and AZ91 alloy Magnesium rods was performed by two different methods. Using inverse techniques and mould temperature measurements, heat fluxes in the mould were reported as 0.2-0.9 MW/m2 for pure Mg and 1-3 MW/m2 for Mg alloy ingots cast in an HDC process; however, a clear description of the inverse technique used was not given. As a validation of the inverse calculations, the average mould heat fluxes were also obtained by measuring the solid shell 2 : Background Information and Literature Review 14 profile angles, following alloy doping of the liquid metal sump. These measurements were used to estimates the solidification rate of the shell region, and from this an average mould heat flux and heat transfer co-efficient were calculated. The average heat fluxes were reported as 1.2-1.8 MW/m2 for pure Mg. Table 2-1 - Results from industrial characterization of primary zone heat fluxes in aluminum and magnesium DC casting systems. Source Alloy(s) System Experimental Method Numerical Method Max flux (MW/ m2) . Contact length (mm) Fit Adenis et al AZ80A and ZK60A VDC billet cast in T/c's measurements to model by trial and error 0.15 NA Fit Jensen AA6063 VDC billet mould T/c's measurements to model by trial and error 2-10 4 Jensen et al AA6063 VDC billet cast in T/c's T/c data extrapolation 0.6-2 NA Bakken and Bergstrom Al-Mg-Si-Fe alloy VDC billet cast in T/c's T/c data extrapolation 0.8 NA Baker and Grandfield Al alloy VDC mould T/c's Fit to water temperature measurements NA 10 Drezet et al AA5182 VDC ingot cast in T/c's Inverse technique 1.2 10-20 Grandfield and Dahle pure Mg HDC ingot Pool profiles Fit to heat transfer model equation 1.2-1.8 NA Grandfield and Dahle pure Mg HDC ingot mould T/c's Inverse technique 0.2-0.9 NA Grandfield and Dahle AZ91 HDC ingot mould T/c's Inverse technique 1.0-3.0 NA Fjaer et al AA6xxx alloy VDC ingot mould T/c's Inverse technique 0.8-1.2 NA Rabenberg et al AA7075 VDC ingot cast in T/c's Inverse technique 1.3 5 LABORATORY MEASUREMENTS With respect to non-ferrous casting, there have been numerous studies aimed at characterizing the heat flux occurring at the metal mould interface during casting. Several 2 : Background Information and Literature Review 15 experiments have been conducted in order to characterize the interfacial heat transfer between a casting and mould during static casting of aluminum alloys (Ho and Pehlke, 1984,85; Nishida et al, 1986; Kumar and Prabhu, 1991; Rappaz et al, 1995; Krishnan and Sharma, 1996; Loulou et al, 1999a and 1999b; Velasco et al, 1999; Trouvant and Argyropoulos, 2000a and 2000b; Prabhu et al, 2002). In these tests, molten Al alloys were poured into a static mould, and measurements from embedded T/c's are used to calculate the heat flux across the metal/mould interface. The parameters affecting heat transfer, such as: mould material, mould roughness, mould lubrication, alloy type, alloy superheat as well as casting orientation have been examined. Unfortunately, these experiments were only able to characterize transient interfacial heat flux phenomena. As continuous casting machines are known to operate with steady state conditions, knowledge of how the metal/mould interface varies spatially, not temporally (i.e. a steady state heat flux distribution) is of more importance when modeling steady state continuous casting processes. In this respect, static casting experimental results are of limited applicability with respect to modeling of continuous casting processes. In an attempt to make lab tests more relevant to DC casting certain apparatus have been developed with the aim of mimicking conditions which occur during DC casting. These include cold finger "Dipping" tests and mould simulator tests. In the cold finger method, a cooled metal 'finger' is immersed into a molten metal pool and a metal shell solidifies against the finger. Using thermocouples embedded in the 'finger', the interfacial heat flux can be back calculated using inverse algorithms. Two examples of this technique can be found in non-ferrous literature (Muojekwu et al, 1995; Bouchard et al, 2001) and one in the steel literature (Machingawuta et al, 1991). Muojekwu et al present an in depth analysis of the effect of lubrication, mould roughness and alloy superheat on the interfacial heat transfer during aluminum casting. Although this is a very thorough study, the relevance to continuous casting of aluminum is limited as the experiment fails to simulate the physics which occur within the primary cooling region of a DC caster (i.e. liquid metal renewal). Additionally, like the static casting experiments, the test is transient. Lastly, depending on the geometry of the cold finger, 2 : Background Information and Literature Review 16 the thermal contraction of the solidifying shell may occur in such a way that the solid shell contracts against the finger, which is opposite to what happens in continuous casting (i.e. the shell pulls away from the mould). In using a mould 'simulator', the idea is to incorporate both shell solidification and extraction thereby simulating the phenomenon of liquid metal renewal at the metal/mould interface. In the case of continuous casting of steel, there have been a few studies where mould simulators were used to study initial solidification phenomenon (Badri et al, 2005; Saucedo, 1997; Suzuki et al, 1991). Very recently, Badri et. al have successfully replicated cast surface oscillation marks by continuously casting thin steel shells using a lab scale mould simulator (Badri et al, 2005). Specifically, their mould simulator exposes one side of a copper mould to molten steel. A computer, controlled linear actuator (driven by a motor) is used to withdraw the solidifying shell at a prescribed velocity, analogous to the casting velocity. The apparatus size allows for shells of 80-100 mm in length. With respect to non-ferrous literature, mould simulators have been built to simulate strip casting of Al (Li et al, 2006), however no tests to simulate DC casting moulds were found. 3 : Objective 17 3 Objective As one of the subtasks of the larger HDC model development program, the objective of this thesis is to characterize the heat transfer in the primary cooling region of a HDC casting system. To accomplish this, an industrial plant trial was completed. Mould temperatures measured during the plant trial were analyzed using inverse modeling techniques, enabling the estimation of the primary zone heat fluxes in the HDC casting machine. As part of this effort, a 2D heat conduction model of the industrial mould was formulated and coupled with an inverse heat conduction algorithm. Furthermore, by varying the casting velocity, metal pouring temperature and cooling water flow rate during the plant trial, their effects on primary cooling region heat fluxes could be determined. In addition to plant trial measurements, a secondary objective was to build a laboratory apparatus with the ability to characterize primary cooling heat transfer. The increased flexibility and reduced costs associated with the lab apparatus (in comparison to plant trials) make it a potentially attractive means for conducting studies on metal/mould heat transfer. To accomplish the secondary objective, a casting simulator was commissioned which would replicate, to the extent possible, primary cooling phenomena in a commercial HDC caster. Using mould temperature measurements taken from the casting simulator, inverse heat conduction analysis was used to calculate primary cooling heat fluxes. To validate the applicability of the laboratory results, the plant trial fluxes and trends were compared with those found in the lab. 4 : Experimental Methods and Measurements 18 4 Experimental Methods and Measurements 4.1 Industrial HDC Casting Machine Plant Trial In 2003 an industrial trial was performed by Alcan, on one of their Horizontal Direct Chill (HDC) casting machines (at the Dubuc plant). The experimental data obtained during this plant trial was analyzed in this thesis. The plant trial consisted of one casting campaign where aluminum alloy A356 (Al; 7%wt Si; 0.3%wt Mg) T-ingot was cast continuously. To assess the effect of variations in process parameters such as cooling water flow rate, in-coming metal temperature and casting velocity on the cast product eight casting tests were conducted. For characterization purposes, the casting mould was instrumented with thermocouples in order to study the effects of process parameters on the primary cooling zone heat transfer. In order to obtain boundary conditions representative of the commercial HDC process the operating parameters used during the trial did not differ widely from that of standard industrial practice. Additionally, safety and technical issues limited the range of operating parameters that were explored using the industrial equipment. Safety also was a determining factor in the extent of instrumentation used throughout the plant trial. For example, the number of thermocouples embedded into as well as their placement in the casting mould were limited in order to minimize the risk of water leaks. Water leaking from the internal cooling channels to the exterior surfaces of the mould is a major safety concern, as contact between water and large volumes of liquid metal can lead to explosions. 4.1.1 Experimental Matrix The casting conditions tested during the plant trial are listed in Table 4-1. A single casting campaign was employed to assess the effects of these conditions. Each set of conditions were tested in the sequence shown. The three parameters which were varied over the eight tests were: casting velocity, tundish metal temperature and the cooling water flow rate. 4 : Experimental Methods and Measurements 19 The effect of casting velocity was of primary importance (as this directly affects production rates). Secondary importance was placed on the effect of pouring temperature (as decreasing pouring temperature translates into power savings). Throughout the casting campaign, transition from the current test condition to the next was made slowly once steady-state for the current test was reached. For each test condition, steady state operation of the casting process was observed for 300-1000 seconds. Table 4-1 - Test Matrix for the 2003 Dubuc plant trial (% of baseline condition). Test Num Tunish Metal Temp (%) Casting Speed (%) Cooling Water Flow Rate (%) Tundish Metal Level (%) Alloy 1 101 80 88 2 101 100 88 3 101 100 83 4 100 100 100 100 A356 5 101 105 100 6 100 110 100 7 97 105 100 8 102 100 100 The liquid metal level, measured as the difference from the top of the metal in the tundish to the bottom of the T-ingot, was kept constant for all tests. Additionally, the mould lubrication and the geometry of the mould/refractory backing plate were constant throughout the duration of the test. Varying lubrication rates during testing could make the ingot prone to tearing, thus safety considerations prohibited testing the effects of oil lubrication. 4.1.2 Mould Instrumentation To measure mould temperatures during the plant trial, 7 K-type thermocouples (T/c's) were placed in the mould, at a depth of 2 mm from the hot face and at various distances from the refractory backing plate. Thermal paste was used to improve thermal contact between the thermocouple tip and the casting mould. The positions of the T/c's are listed in Table 4-2. All 7 T/c's were positioned near the top centre of the T-ingot (see Figure 4-1). Figure 4-2 shows a 4 : Experimental Methods and Measurements 20 cross-section of the mould depicting how the T/c's were installed. During the plant trial, temperature values were logged at a rate of 1 Hz by a data acquisition system. Table 4-2 - Locations of T/c placement in the industrial HDC casting mould. T/c# Distance From Front Edge of Mould (mm) T/c Depth From Surface of Mould (mm) 1 2 2 2 5 2 3 8 2 4 11 2 5 14 2 6 18 2 7 33 2 Water Inlet i/c location Water Inlet ll * * • • Ingot Cross Section hi •i Ln:::::;:;:;::::::::::::::::::::::::::::::::::v::::::: i Copper Mould W a t e r Channel Figure 4-1 - T-ingot mould front view. General location of T/c placement is shown. Thermocouple Installation Casting Mould Refractory Plate Figure 4-2 - Cross section of the T-ingot mould showing the position of embedded T/c's used in 2003 Dubuc plant trial. 4 : Experimental Methods and Measurements 21 4.1.3 Results A sample of the raw data obtained from the T/c's during the plant trial is shown in Figure 4-3. For each casting test condition, the temperature data is never constant and fluctuates with time, for short time scales. This is shown more clearly in Figure 4-4, where data from 4 selected T/c's are displayed. Moreover, the magnitude of the scatter varies depending on the position of the thermocouple. For T/c 1 located 2 mm from the backing plate, the scatter is between -20-50 °C. Whereas for Tc-7, located 33 mm from the back plate, the scatter is approximately 5-10 °C. Plotting the standard deviation of the steady state temperatures vs. distance from the refractory backing plate, shown in Figure 4-5, confirms this. -*-T/c 1: 2 mm T/c 2: 5 mm -*- T/c 3: 8 mm -*- T/c 4: 11 mm -e-T/c 5: 14 mm T/c 6: 18 mm -A-T/c 7: 33 mm 200 50 —— —— 5950 6000 6050 6100 6150 6200 6250 Time (s) Figure 4-3 - Raw temperature data (small time scale shown), obtained from industrial plant trial. 4 : Experimental Methods and Measurements 22 T/c 2: 5 mm • T/c 4: 11 mm -e-T/c5: 14 mm - T/c 6: 18 mm 200 O 175 CD rs -»—< CO i_ 01 Q-E CD 150 125 100 5950 6000 6050 6100 6150 6200 6250 Time (s) Figure 4-4 - Raw temperature data obtained from industrial plant trial for 4 selected T/c's. g to > CD Q CD T5 C CD CO CD E CD L_ </) CD CD CD Z! TO CD Q. E CD 8 7 6 5 4 3 2 1 0 o Test 1 * Test 2 A Test 3 x Test 4 x Test 5 - Test 6 • Test 7 o Test 8 s A | ° 8 o O 1 A O 0 O o ^ Q 1 10 20 30 Distance from Refractory Plate (mm) 40 Figure 4-5 - Variation in T/c signal as a function of distance from the refractory plate. Data taken from Dubuc 2003 plant trial. 4 : Experimental Methods and Measurements 23 Previous studies on continuous casting of steel suggest that the large temperature fluctuations within the steady state operation of the HDC casting machine mould are due to physical phenomenon occurring during initial solidification (Kumar et al, 1995). The physical process explaining these temperature fluctuations are qualitatively understood. It involves the repetitive freezing of the metal at the meniscus, withdrawal, rupture of the meniscus and renewal of liquid metal. Examination of the T/c variability prior to casting (see Figure 4-6) and the variation in the noise during transition in the casting parameters (see Figure 4-7) suggest that the temperature fluctuations observed are due to real processes and not random instrumentation noise. Unfortunately, lack of temporal resolution in the T/c data inhibited further study of the meniscus solidification behavior. 50 100 150 200 250 Time (s) 300 Figure 4-6 - T/c data prior to industrial plant trial cast startup. The industrial temperature measurement precision was approximately +/- 1°C. Looking at a larger time scale - i.e. the scale shown in Figure 4-7 - it appears that although the temperature measurements fluctuate over a short time scale (with a scatter in measured temperature of ~20-50 °C), they reach a steady state profile. The temperature data shown in Figure 4-7 displays the long term temperature response for 3 selected T/c's. In this 4 : Experimental Methods and Measurements 24 figure, two steady state operating regions can be seen, one at a time index of 4000-5000 seconds and another at 7000-8000 seconds. Within these regions, long term temperature stability was observed for all T/c's in the mould. The transition between casting conditions 1 and 2, shown in Figure 4-7 at the time index of ~ 5000 s, clearly shows a change in temperature for all thermocouples as well as a change in the scatter of measured temperatures. This trend was observed for all T/c's in the casting mould during casting test transitions. The most pronounced transition observed was the one shown between tests 1 and 2. 250 + T/c 7 : 33 mm < T/c 5 : 18 mm • T/c 1 : 2 mm Steady Region I-*— » 1 4000 Operating parameter change 5000 6000 Time (s) Steady Region 7000 8000 Figure 4-7 - Sample raw thermocouple data obtained during plant trial. The regions defined as the steady operating regions for casting tests 1 and 2 are shown. Due to the lack of temporal resolution in the thermocouple data, it was necessary to use time averaged steady state temperature measurements for subsequent analysis. In order to extract the steady state temperature measurements for T/c's in the mould, a stable period 4 : Experimental Methods and Measurements 25 just prior to making a casting change was defined as the steady state operating time period for each test condition. This period varied test to test from 300-1000 seconds (see Table 4-1). Within the steady state operating period, data taken from each T/c was averaged, yielding the steady state operation temperatures for each test. This data was used in subsequent inverse analyses. Figure 4-8 shows the steady state temperatures measured in the HDC casting mould during the plant trial tests. The data indicates that temperature is highest near the front of the mould. The temperature data from Test 1 appears to be significantly lower then the other tests. The casting velocity for Test 1 - the lowest of all tests performed - may account for these low mould temperatures. Furthermore, no clear distinction between steady state mould temperatures with observed from Tests 2 thru 8. O o CD I =3 oo i _ CD Q_ E 0) 160 140 120 100 80 60 40 - 1 1 o Test 1 * Test 2 A Test 3 x Test 4 x Test 5 - Test 6 • Test 7 o Test 8 ° 1 : A i i 10 20 30 Distance from Refractory Plate (mm) 40 Figure 4-8 - Steady state mould temperature measurements measured during the industrial trial. 4 : Experimental Methods and Measurements 26 4.2 Lab Scale Characterization of Primary Zone Heat Transfer In addition to the plant trial, a lab-scale apparatus was built to characterize primary (mould) heat transfer conditions in horizontal continuous casting. Testing in a lab allows for a much broader range of test conditions to be examined and far greater flexibility in terms of access, as the facility is not bound by the constraints of commercial production. Additionally, greater flexibility in instrumentation is permitted allowing increased spatial resolution in the data. The design objective for the apparatus was to mimic as close as possible the initial solidification behavior in an HDC casting machine. If achieved, one would expect consistency between lab and plant trial tests - i.e. the heat fluxes in the mould region of the lab apparatus should approximately match or show the same trends as those of its industrial counter part. Preliminary design considerations combined with a literature review yielded four concepts for the lab apparatus: 1) a cold finger "dip" apparatus; 2) a static casting test; 3) a shell extractor apparatus and 4) a casting simulator. These concepts are depicted in Figure 4-9. 0 Refractory A l (liquid) A l (solid) • Copper Chil l Steel Extractor Figure 4-9- Preliminary design concepts; a) cold finger "dip" test, b) static casting, c) shell extractor apparatus and d) casting simulator. 4 : Experimental Methods and Measurements 27 Initially, the cold finger and static casting designs were rejected, on the basis that they do not allow for liquid metal renewal at the mould metal interface. In both setups there is only one instance per test where liquid metal contacts the mould - at the test start. This would severely limit the applicability of any experimental results obtained using these designs, as they do not replicate HDC conditions. As for the shell extractor, preliminary design calculations showed that it would be hard to maintain a constant metal temperature (analogous to the tundish metal temperature) throughout the duration of a test. Additionally, concerns about re-melting and/or tearing of the shell once it left the chill region suggested that the casting simulator was the best option. Many experimental benefits can be realized with the casting simulator design concept. An operational casting simulator design would have liquid renewal at the front of the mould, thus mimicking the metal meniscus in a DC casting mould. Second, with the casting simulator design the ability to test many variables exists, such as: metallostatic head pressure, mould orientation, casting superheat, casting velocity, mould material and mould surface roughness. Last, the possibility of running a test for an extended period of time (and achieving steady state conditions in the lab) exists if the apparatus design includes a large enough supply of hot liquid metal and a system capable of handling extended withdrawal of solid material from the mould. 4.2.1 Casting Simulator Design In designing the casting simulator, the goal was to replicate primary mould cooling in a safe manner while maintaining as much similarity to industrial conditions as possible. For the preliminary implementation it was felt that safety would be significantly enhanced if no direct water spray cooling was used. The general design of the apparatus is shown in Figure 4-10. In operation, molten aluminum from the crucible enters the casting simulator assembly through a transfer tube. The casting simulator assembly is lined with refractory (see Figure 4-10) to minimize heat loss and give the incoming liquid metal time to stabilize. Two offset water cooled copper chills (see Figure 4-10) provide the cooling necessary for solidification. 4 : Experimental Methods and Measurements 28 The concept was that solidification would be initiated within the "region of interest" by the bottom chill only, shown highlighted in Figure 4-1 Ob. To ensure full solidification of the Al casting before it leaves the mould there is a second water-cooled copper mould located on the top. The offset distance for the top chill was made similar to the length of the industrial casting mould. Mould Simulator Linear Slide Refractory Starter Block Block Frame l n i t i a l Metal Solidification Copper Chill a b Figure 4-10 - General design of the casting simulator apparatus; a) side section b) exploded side section of the casting simulator assembly. At the beginning of the test, a copper starter block is inserted into the mould. Molten metal is released from the crucible into the mould, and after a prescribed time, the block is withdrawn from the mould at a predefined speed using a linear drive system. As the starter block is withdrawn, the region near the inlet on the bottom chill should have liquid renewal, thus replicating the meniscus region of a continuous casting mould and therefore the heat fluxes (see Figure 4-10) should approximate those observed in the HDC casting machine mould. In Figure 4-11 and Figure 4-12, the casting simulator apparatus is shown, as originally, built. 4 : Experimental Methods and Measurements 29 Figure 4-11 - Bird's eye view of casting simulator apparatus after final build. water cooled Cu moulds Figure 4-12 - Side view of the initial configuration of the casting mould assembly. In later tests, the top chill was replaced with one identical in dimension to the bottom chill. 4 : Experimental Methods and Measurements 30 APPARATUS SIZING CONSIDERATIONS In sizing the casting apparatus, a constraint was imposed to have a solidification profile such that the Al temperature at the top of the cast section would not drop significantly below the liquidus temperature until the metal reaches the second (offset) chill, refer to Figure 4-1 Ob. Based on design calculations using different casting section geometries, a section height of 50 mm was selected. With this height, calculations suggested that the operating casting velocity for the simulator could vary from 1-2.5 mm/s without significant solidification occurring at the top of the casting prior to it being exposed to the second offset chill. HEAT FLOW CONSIDERATIONS In an attempt to simplify the heat flow in the casting to 2 dimensions, the mould assembly sides were lined with refractory (see Figure 4-13). The idea being that the majority of the heat flow in the Al would be to either the top or bottom copper chills only, thus achieving 2-dimensional heat transfer and solidification in the casting. Additionally, by using a casting section width of ~100 mm any heat flow into the refractory sides should have negligible effects with respect to the heat flow along the midsection of the casting. By simplifying the heat flow in the casting in this manner the data collected lends itself to a 2D inverse analysis and also better replicated the heat flow occurring within the top centre region of the commercial caster, where temperature data was obtained during the plant trial. INSTRUMENTATION CONSIDERATIONS In an attempt to minimize thermal field distortion in the copper chill the T/c hole orientation/placement, spacing and depth (see Figure 4-13) were carefully assessed. T/c holes were drilled parallel to the mould surface, such that heat flow from the mould surface to the mould water cooling channel would not be impeded. Furthermore, the T/c holes were spaced 6.35 mm apart from each other and staggered (i.e. odd and even numbered T/c holes were drilled from opposite ends of the mould), thus minimizing interference between adjacent T/c 4 : Experimental Methods and Measurements 31 holes. Calculations suggested that the T/c holes did not cause significant thermal field disruption. Figure 4-13 - Front view of the casting simulator mould assembly with refractory sides and T/c holes shown. 4.2.2 Initial Casting Trials: Operating Parameter Investigation Following fabrication and some early problems with leaking, commissioning of the casting simulator began in earnest in May, 2006. Tests with the casting simulator continued for roughly five and a half months, over which close to forty casting trials were run. Table 4-3 is a summary of the various issues encountered with the casting simulator and the actions taken to try and resolve them. 4 : Experimental Methods and Measurements 32 Table 4-3 - Summary of experimental troubles encountered with the casting simulator. Chronology Problem Most probable reason(s) for occurrence of problem (at that time) Solution(s) May 2006 Liquid aluminum leaking out of mould assembly (assembly) -gaps present in mould assembly joints -switched from using a gasket material in the assembly joints to a refractory glue compound. June-July 2006 Inconsistent surface structure on casts, large tears (procedural) -large amount of mushy material present before motor is switched on, possibly due to insufficient preheat of the mould assembly. -ramp the speed of the motor from zero to desired casting velocity -position the starter block closer to the front of the copper chill, reducing the amount of initial mushy material present prior to starting the motor -stronger mould preheat attained by using an industrial sized propane torch and preheating for 50-60 minutes -reduce the amount of refractory in the mould by shortening the length between the metal inlet and the copper chills July-August 2006 Motor jamming shortly after motor starts pulling (assembly) -tolerance between starter block and mould too small -improper alignment of starter block -excessive wear on screw assembly, causing slide to skip -tapering the starter block -consistent measurement of tolerances between mould assembly and starter block -consistent alignment of mould assembly -consistent application procedure of starter block 'gasket' material -checking linear slide screw assembly for any signs of wear on threads before each test September 2006 Inconsistent surface structure on casts, large tears (procedural) -insufficient metallostatic head pressure, as evidenced by large amounts of mushy material large voids present -increase metal head from 90 mm to 175 mm -make length of top mould equal to length of bottom mould, i.e. symmetric design. October 2006 Consistent surface structure on casts but tearing of shell persists for large percentage of tests (design) -insufficient mould lubrication -sharp corners of casting shape -insufficient secondary cooling -New design of mould assembly In terms of setup, the most prominent problem was jamming of the motor during testing. This problem occurred more than ten times. In the end, consistent setting of the starter block/mould tolerances and inspection of the linear slide screw assembly for wear were instrumental in avoiding jamming problems. The procedural change which enabled successful castings was increasing the metallostatic head pressure of the apparatus. This was done by raising the crucible and using 4 : Experimental Methods and Measurements 33 an angled transfer tube to deliver the liquid metal to the mould assembly. Originally, the metal head was kept low for safety concerns, however; inconsistency in the surface structure of the casts, as shown in Figure 4-14, as well as large voids present in the casts led to the idea that the liquid metal feeding into the cast did not have enough pressure to properly penetrate the mush of the solidifying metal. Increasing the metal head pressure of the system by -100%, to a value of 175 mm, dramatically improved the casting results. The laps and folds previously seen in many of the casting tests disappeared. Additionally, cast surfaces for the eight tests conducted using an increased metal head all appeared macroscopically similar, selected results from four of the eight tests are shown in Figure 4-15. 4 : Experimental Methods and Measurements 34 Casting Direction extended tearing Figure 4-14 - Bottom surface of failed casting tests; a) folds present on surface, b) inconsistent and large lapped structure and c) significant and prolonged tearing of large surface laps. 4 : Experimental Methods and Measurements 35 Casting Direction C f->i (})! XV'  1 • *'-,•-;»• similar cast surface structure Figure 4-15 - Bottom surfaces of castings conducted using increased metal head pressure; a) Test 1 casting, b) Test 3 both casting (right side) and torn cast section (left side), c) Test 5 both casting (right side) and torn cast section (left side) and d) Test 8 casting. All surfaces show similar surface structure. 4 : Experimental Methods and Measurements 36 4.2.3 Scope of Experiments The original intent of the experiments was to examine the effects of: casting velocity, incoming metal temperature and water cooling flow rate on the primary zone heat transfer. As noted in the above section, successful castings were achieved after increasing the metal head pressure of the system. Due to commissioning problems, a limited number of "successful" tests were conducted. In total, eight experiments were conducted while using an increased metal head pressure. For all eight tests completed, the following test procedure was used. The casting simulator mould cavity was carefully assembled in an attempt to avoid metal leakage in the mould cavity and crucible assemblies, water leakage in the cooling water lines and jamming of the linear drive in the mould cavity. Unlike the original design, the top and bottom chills used in these tests were of similar length. Results from the commissioning tests suggested that the offset chill design was causing tearing. The mould assembly used for these tests is schematically shown in Figure 4-16. refractory Inflow Cu chill Casting Direction Cu chill region of interest start block Figure 4-16 - Mould assembly used in final casting trials. Top and bottom Cu chills are similar in length. After assembly, 6.3 kg of Al was melted in a furnace at the temperature required for the specific test. Prior to the beginning of the test, the mould cavity was preheated using a propane torch, for ~1hr. After preheating, the copper starter block was inserted into the mould 4 : Experimental Methods and Measurements 37 to a set distance such that only the front 15 mm of both the top and bottom copper chills were initially exposed to liquid metal. A steel plug was installed in the crucible, isolating it from the mould cavity. Using two smaller crucibles, the molten metal was taken from the furnace and poured into the casting simulator crucible. Once the metal settled in the crucible (a few seconds), the plug was removed from the crucible, releasing the molten metal into the mould cavity. Water lines to the mould were then opened to initiate mould cooling. After a prescribed time of 10 seconds, the starter block was withdrawn from the mould by a linear drive system. The motor for the linear drive system was ramped to its predetermined casting velocity manually over a time period of 15 seconds. The linear drive system is capable of providing constant torque output throughout its entire velocity range of 0.5-2.5 mm/s. As the starter block was withdrawn, molten metal from the crucible fed into the mould cavity, thereby facilitating liquid renewal at the front of the mould. During the test, the rotational speed of the motor (thus the casting velocity) was measured manually using a digital, hand held, non-contact tachometer (Lutron DT-2236). The water flow rates in the mould water channels were measured using an in-line, piston type, variable area flow meter (Omega FL-6000 series flow meter). Casting continued until the metal supply was depleted. If tearing of the ingot was observed, the test was aborted by pulling a drain plug installed in the crucible and allowing the remaining liquid metal to drain out of the casting simulator mould cavity and crucible. The mould cavity for all tests (and hence the casting cross section) was 100 mm wide by 50 mm high. To delineate between an unsuccessful and successful cast, a set of criteria were developed. To be considered a successful cast, two criteria had to be achieved: 1) no assembly failures during testing; and 2) a cast duration of at least 1 minute. Table 4-4 is a list of the eight casting trials run using the increased metal head pressure. Of the eight trials five were considered successful. 4 : Experimental Methods and Measurements 38 Table 4-4 - Final eight experimental trials of casting simulator (increased metal head pressure). Test Casting velocity (mm/s) Metal Temp in Crucible (°C) 1 1.21 +/-0.02 745 2 1.47 +/-0.02 745 3 0.88 +/-0.02 745 4 1.20 +/-0.02 745 5 , 1.24 +/-0.02 700 6 1.21 +/-0.02 745 7 1.19 +/-0.02 745 8 1.20 +/-0.02 790 Water Cooling Flow Rate (LPM) Metal Head Height (mm) Cast Length mm Successful Casting Reason for Stoppage 300 YES Tear 80 NO Short casting duration . 85 YES Tear 90 YES Tear 90 YES Tear NA NO Excessive metal leak NA NO Motor jam 320 YES End of Test 15 +/-0.5 180 +/-10 (the difference between the top of the metal level in the crucible to the bottom of the casting surface) 4.2.4 Instrumentation of Copper Chill Thermocouple holes were drilled in the copper chill close to the hot face of the chill and the water channel (see Figure 4-17). The locations of the T/c holes near the chill hot face are listed in Table 4-5. The T/c holes were cut with a flat bottom to ensure good contact between the T/c junction and hole. Half of the T/c holes were drilled from one side of the chill (odd numbered T/c's), and the other half were drilled from the opposite side (even numbered T/c's). Both sets of T/c holes (odd and even) were drilled to a z-axis depth of 3.2mm from the center plane of the mould such that the T/c tips of both sets would be a distance of 6.4 mm from each other along the z-axis (see Figure 4-13). 4 : Experimental Methods and Measurements 39 Table 4-5- Locations of T/c placement in copper chill. T/c# Distance From Front Edge of Mould (mm) T/c Depth From Surface of Mould (mm) 1 3.2 3.2 2 6.4 3.2 3 9.5 3.2 4 12.7 3.2 5 15.9 3.2 6 19.1 3.2 7 22.2 3.2 . • 8 25.4 3.2 9 28.9 3.2 10 31.8 3.2 11 34.9 3.2 12 38.1 3.2 13 41.3 3.2 14 47.6 3.2 T/c locations Depth / \ Refractory ! / Water \ M o u | d J ( Channel ] •-<#»» Distance from Refractory Figure 4-17 - Side view of the copper chill with T/c locations shown. Stainless steel sheathed type-E Special Limit Error (SLE) T/c's were used, along with type-E SLE thermocouple grade extension wire. Compared with type K T/c's, type E T/c's produce higher EMF values at low temperatures, thereby achieving better signal to noise ratios and cleaner data. Furthermore, SLE T/c wire is calibrated to a higher precision then regular thermocouple wire. Temperature measurement accuracy for SLE T/c wire is specified as +/-1°C or 0.4 % of the reading; compared with +/- 1.7°C or 0.5 % for standard T/c wire. Thermocouple junctions were made by exposing a small portion of the thermocouple wires from its sheathing and spot welding a junction. The T/c tip was then straightened and inserted into 4 : Experimental Methods and Measurements 40 the T/c hole. A small wedge was tapped into the end of the T/c hole to prevent the T/c from slipping out of the T/c hole. T/c data was acquired using a National Instruments data acquisition (hardware and software) system. The T/c data acquisition rate was set to 10 Hz for all experiments. 4.2.5 Results Raw temperature data measured during Test 1 and Test 4 are shown in Figure 4-18 a and b. At the beginning of the test, molten metal enters the casting simulator cavity. Initial contact between the liquid metal and the mould causes the temperature in the mould to increase rapidly. Contraction of the initial solid shell and initiation of water cooling within the mould, cause the temperature in the mould to drop shortly after this rapid increase. The temperatures in the mould continue to drop as the metal solidifies. Initiating starter block withdrawal and ramping up the withdrawal speed to the desired casting velocity moves the shell and exposes fresh metal to the mould surface. In turn, this causes the mould to heat up once again. Mould heating continues for a period of time. In Test 1 and 8, the casting time was long enough that mould temperatures leveled off. This was not observed in Test 3, 4 or 5. The termination of the casting tests, either by tearing of the ingot section or due to insufficient metal supply, is indicated by a sudden drop in mould temperatures. 4 : Experimental Methods and Measurements 41 Liquid Al Enters Mould Motor Ramping Period 180 160 140 0 o 120 0 i— =3 -t—« 100 _ o_ E 80 a; h-60 40 20 Mould Heating Period End of test -25 25 75 125 175 Cast Time (s) c-T/d x T/c 5 - T/c 9 o T/c 13 225 275 a) Liquid Al Enters Mould 180 160 140 o o 120 0) 100 _ Q_ E 80 (D h- 60 40 -20 -25 Motor Ramping Period 25 75 125 175 Cast Time (s) 225 275 b) Figure 4-18 - Raw temperature data for a) Test 1 and b) Test 4 from four selected T/c's in the copper chill. T/c 1 is closest to the front of the chill whereas T/c 13 is farthest from the front Of the Chill . (Note: data was acquired at a rate of 10 Hz, whereas the data shown above is displayed as 1 Hz data for clarity purposes.) 4 : Experimental Methods and Measurements 42 As seen from Test 1 data, after ~110s of casting the temperature measurements plateau into a quasi-steady state region. This behaviour was observed in Tests 1 and 8. For these tests, the casting was sufficiently long enough to allow the temperature within the mould to approach steady state. However, within this quasi steady state region large temperature fluctuations were observed, possibly due to variability in the ingot cast-surface morphology. The region in time during Tests 1 and 8 in which the mould temperatures plateau is therefore assumed to represent a quasi-steady state condition. In Tests 3, 4 and 5, a quasi-steady casting period was not observed. As seen from the Test 4 sample data, the measured temperatures are continuing to increase, but due to the short test duration, steady state conditions were not achieved. Similar behaviour was observed in Tests 3 and 5. Within the transient casting period it was observed that the temperature data consistently followed a trend. Specifically, the T/c closest to the front of the copper chill always measured the highest temperature and the temperatures decreased with increasing distance from the front of the mould. During the quasi-steady periods of Tests 1 and 8, this trend was not always observed do to the fluctuations in temperature, believed to be associated with cast surface variability. Examining the T/c data prior to a casting test provides an assessment of the inherent signal noise in the data acquisition system. As expected, the precision in the lab +/- 0.25 °C was greater than the industrial measurement precision +/- 1°C. Figure 4-19 thru 4-24 display the complete sets of mould temperature data collected during casting trials 1,3,4,5 and 8. 4 : Experimental Methods and Measurements 43 140 i -50 0 50 100 150 200 250 300 350 Cast Time (s) Figure 4-19 - Filtered temperature data for Test 1 from all T/c's in the copper chill. Data shown has been smoothed. 140 i Cast Time (s) Figure 4-20 - Filtered temperature data for Test 3 from all T/c's in the copper chill. Data shown has been smoothed. 4 : Experimental Methods and Measurements 44 140 -i ~ 120 O Cast Time (s) Figure 4-22 - Filtered temperature data for Test 5 from all T/c's in the copper chill. Data shown has been smoothed. 4 : Experimental Methods and Measurements 40 -| , , , , 1 1 1 -50 0 50 100 150 200 250 300 Cast Time (s) Figure 4-23 - Filtered temperature data for Test 8 from all T/c's in the copper chill. Data shown has been smoothed. 4.3 Chapter Summary 4.3.1 Plant Trial In 2003 a plant trial was conducted on an industrial HDC casting machine. T/c's embedded in the HDC mould enabled the collection of mould temperature data. Specifically, T/c's were placed near the hot surface of the casting mould, all of which were located near the top centre (see Figure 4-1) of the casting mould cross section and at various distances from the refractory plate (see Table 4-2). In all, 8 different operating conditions were tested. For each casting condition, the system achieved steady state operational conditions for a minimum duration of 300 seconds. The parameters varied were: casting velocity, tundish metal temperature, and cooling water flow rates. Other parameters known to effect heat transfer such as: metallostatic head pressure, alloy type, mould lubrication and mould/refractory geometry were all kept constant throughout the duration of the trial. 4 : Experimental Methods and Measurements 46 4.3.2 Lab Experiments A literature survey yielded four possible designs for an apparatus which could be used to examine aspects of primary heat transfer occurring in horizontal continuous casting. In the end, a design was selected that could reproduce continuous liquid metal renewal at the meniscus and also allow for thermal-contraction induced loss of heat transfer. The major design considerations included sizing of the mould assembly and consideration of the heat flow within the copper chill. During commissioning, assembly and procedural problems were encountered. The biggest assembly problem was jamming of the starter block inside the mould assembly. The largest procedural problem was solved by increasing the metal head pressure of the system; this resulted in more consistent and successful castings. In total, five tests were defined as successful. The bottom copper chill of the casting simulator was instrumented with T/c's along the hot face. The data collected during casting trials displayed consistent trends with respect to the temporal and spatial variation in temperature. After an initial rapid transient associated with the introduction of the liquid metal and initiation of water cooling, all of the responses showed a steady increase in temperature. In several instances quasi steady state conditions were achieved when the temperatures were observed to level-off prior to termination of the casting. The temperatures within the mould were consistently hotter near the liquid metal inlet and decreased with increasing distance from the front of the chill. Additionally, T/c measurement precision in the lab was greater then that of the plant trial. 5 : Inverse Heat Conduction Analysis Technique 47 5 Inverse Heat Conduction Analysis Technique Temperature measurements taken from within the mould can be related to the surface heat flux (quantity of interest) by constructing a heat conduction model of the casting mould and coupling this model to an inverse heat conduction algorithm. This chapter outlines the basic numerical methods needed to perform both the forward and inverse heat conduction calculations. First, forward and inverse heat conduction problems are overviewed. The models developed for this study are then described and finally, a series of heat transfer problems are solved to ensure that the numerical calculations made in this thesis are accurate. 5.1 Forward Heat Conduction Problems Forward heat conduction problems are defined as those in which the temperature in a body or domain is calculated by solving the heat transport equation subject to the appropriate boundary conditions and initial conditions (if transient). In certain cases the energy transport equation can be solved analytically, whereas for more complex cases numerical methods such as the finite difference or finite element methods must be used. 5.1.1 The Heat Conduction Equation The general form of the heat transport equation can be written as: I a** + y~dy J + ~dz~ p c p ^ - + pcpu-VT + Q eq 5-1 This equation can be derived by performing an energy balance on a differential volume element. The term on the LHS accounts for energy transport by diffusion or conduction (Fourier's law). The 1st term on the RHS represents the rate of energy storage or accumulation. The 2 n d term on the RHS accounts for advective transport of energy and the 3rd term is a heat generation/consumption term. The 1st term is included for transient problems in 5 : Inverse Heat Conduction Analysis Technique 48 which the temperature field varies with time. The 3rd term is included in problems in which there is a significant volumetric source or sink of energy such as may be associated with the heat released/consumed during a phase transformation in a material. The 2 n d term is present in problems that include advection (flow of material) within or through the problem domain. As only the mould is considered in the analysis of the thermal data, as shown in Figure 5-1, consequently the following conditions apply to the current application: 1) There is no advective transport and no volumetric heat source or sink, hence the 2n d and 3rd terms on the RHS of Equation 1 are set to zero; and 2) Both transient and steady state problems are analyzed in this project. Problem Domain k, P, cp . . . . . External Boundaries | | | | | * * — External Boundary Condition Figure 5-1 - Sample 2D heat conducting domain with external boundaries and boundary conditions shown. The external boundaries are marked by dashed black lines. For non-linear steady state problems, it is often beneficial to use a transient formulation when solving the problem numerically as the time independent temperature field solution can be "evolved" slowly using a dummy time variable, thereby improving solution convergence. This approach has been adopted in this work hence a transient formulation is applied throughout the work that appears in the following sections. 5 : Inverse Heat Conduction Analysis Technique 49 5.1.2 Finite Element Method for Solving Heat Conduction Problems The finite element method has been used to solve the problem described above subject to a set of boundary and initial conditions (to be described later). The method is a numerical technique often used to solve partial differential equations including the heat conduction problem. The method involves discretization of the problem geometry into small elements. A trial function is defined that describes the variation of field variables (in the present case temperature) over each element. Application of the Method of Weighted Residuals using the shape functions in both the trial function and the weighting function yields the so-called finite-element equations after a series of algebraic manipulations. The solution of the finite element equations can be performed using standard matrix decomposition techniques, which yields an approximation to the exact solution of the original problem, (Zienkiewicz and Taylor, 2000). 5.2 The Inverse Heat Conduction Problem An inverse heat conduction problem is a heat conduction problem where one of the following is unknown (or undefined): a) initial conditions (for transient problems only), b) boundary conditions or c) thermophysical properties (such as density, thermal conductivity or heat capacity). The goal in solving an.inverse heat conduction problem is to find the unknown quantity using known temperatures from the interior of the heat conducting body. Various inverse algorithms have been developed for solving inverse heat conduction problems that vary in complexity and practicality. For example, the first six chapters of the Inverse Engineering Handbook (Woodbury, 2003) present different inverse solution methodologies. For engineering purposes, the non-linear sequential estimation technique (with regularization) proposed by Beck (Beck, 1970), is simple to understand and easy to couple to an existing heat conduction code. In its most general form, Beck's method can be used to 5 : Inverse Heat Conduction Analysis Technique 50 solve non-linear, multi-dimensional, transient inverse problems where more then one unknown heat flux is to be determined. 5.2.1 Beck's Technique To understand how Beck's algorithm works, consider the case of a flat plate subject to time varying heat flux at x=0 and insulated at x=L (see Figure 5-2). A thermocouple sensor, located at x=xr/c, records data at a time interval of AtT/c. The objective is to estimate q(t) using the sensor measurements, given the thermophysical properties and initial conditions of the system. Solid conducting medium; (thermophysical properties known) q = q (t) (Unknown) Figure 5-2 - Sample inverse heat conduction problem. In Beck's method, q(t) is estimated as a series of discrete fluxes - q, = q1: q2, c/w -each over a time interval AO, as shown in Figure 5-3. The normal procedure is to assign AO a value that is an integer value greater than or equal to Atm. This reduces the computational difficulty which may arise if AtT/c ^ AO. Starting at t=0, a value for ^ i is needed which minimizes the discrepancy between the thermocouple measurements and the model predictions. To do this, an initial guess for <7i is employed and assumed to remain constant for a period of time RAO, (where R is an integer). Beck's method uses the idea of R future times as a means to stabilize the estimation procedure. The resulting forward heat conduction problem is solved 5 : Inverse Heat Conduction Analysis Technique 51 (with our initial guess for <i\ as the surface flux) over the period RA9. The sum of squared differences between the thermocouple measurements and the model predictions is then calculated (this is called the objective function). Through iteration with the initial guess, the objective function can be minimized, thus yielding a best estimate for c^ . Once the best estimate for q1 is obtained, time is incremented by the interval Ad and the process is repeated; looking to obtain an estimate for the flux q2. Repetitive application of this technique yields the full heat flux history q(t). discrete estimates assembled to give q(t) a s s u m e <* i s c o n s t a n t f o r i n t e r v a l Figure 5-3 - a) Estimation of the actual q(t) using a series of discrete flux values; b) the constant heat flux assumption, used over time period RA6, required to add stability to the iteration procedure when solving for a discrete flux (in this figure qi). An algorithm flow chart which uses Beck's method to solve an inverse heat conduction problem is shown in Figure 5-4. For the general case of P unknown heat fluxes and NTc temperature sensors used to measure temperatures at the rate of AtT/c the following values must be defined: number of future time steps, R\ the heat flux time step increment, AO; the regularization value, a; the time step convergence criterion; the number of time steps to calculate; the initial temperature field; and an initial guess for the heat flux unknowns at t-0. Once these terms have been defined, the solution procedure can begin, shown as the outer loop in Figure 5-4. To more to the next increment in this loop, iterations of q are performed until the value of the iteration Aq, satisfies the time step convergence criterion. 5 : Inverse Heat Conduction Analysis Technique 52 If j > MAXITER Then Check for Problem Formulate IHC Model Define: NT/C,P, AtT/c, A9, R, a, Max Iter, Conv Crit., NSTEPS wo Set Initial T field for i=1,NSTEPS Set Initial guess for flux for j =1, MAXITER Calculate: S, G,, A, b, Aqi+ 1 Update q YES Move fon/v £. ard in time Update T history Upd ate q Figure 5-4 - Inverse Heat Conduction algorithm flow chart. To make an iteration, Aq, the following must be calculated: the sensitivity matrices, G,, and the current model predictions, T, . The model predictions, T,, are the calculated temperatures that correspond to the values measured by the temperature sensors, V,. For each iteration of q the model predictions must be re-calculated, however; it is sufficient to calculate the sensitivity matrix once (before the first iteration) per time increment, AO (for highly non-linear problems this may be troublesome). The sensitivity matrix is the variation in temperature predictions, T,, with respect to a change in the unknown heat flux q. Its dimension is determined by the number of unknown heat fluxes, P, and the number of temperature sensors, NTc. It can be calculated by 5 : Inverse Heat Conduction Analysis Technique 53 approximating the derivative using numerical differentiation. The calculation for each sensitivity co-efficient in the matrix is performed using: dTk _ 7 * ( g « + f i f t ) - ^ ( g f ) — = h,i = • e c l 5 " 2 where i=1,2,...,P and k=1,2,...,NT/c • The value of £ is a small value used for numerical differentiation. A suggested value is 0.001 (Beck et al., 1985; pg 221). The full set of sensitivity matrices, Gt, can be written as: .eq 5-3 With the values for G,, 7, and V, known, iteration of q can be calculated by application of the following equations: AqJ+l = A~]b A l Ad \AtTc. l=\ + al A0 {AtTc l=\ .eq 5-4 .eq 5-5 .eq 5-6 For additional stability, a regularization term, a, is added to the matrix A. This implementation is deemed zeroth order regularization. The value used for a is problem dependant. Increasing 5 : Inverse Heat Conduction Analysis Technique 54 the value of a will increase its effect, with large non-zero values of Of resulting in reduced magnitudes of q (Beck etal., 1985; pg 136). Updating the current value for q is simply calculated by adding the iteration value, Aq, to the current value. A damping factor, /j, can be used to avoid over-stepping and is usually set to a value close to but less than 1. The iteration equation is written as: qJ + l =qJ + ^ q J + [ .eq 5-7 A criterion used to determine if the estimate for q has converged for the current time increment is shown below. The convergence criterion value chosen will be problem dependant. A typical value given by Beck as a suitable measure of convergence for inverse heat conduction problems is 0.001 (i.e. NSIG = 3). 1 p P k = l Mi < i o - ^ / G .eq 5-8 Once the convergence criterion is met for the current time increment, the value of q is retained as the heat flux for that time interval. The inverse problem moves forward to the next time step and the process is repeated. The initial guess for q for this next step is chosen to be the converged heat flux from the previous time step. 5.3 IHC Model of an Industrial HDC Mould As a first step in calculating the heat flux distribution along the hot face of the industrial HDC casting mould, a model for the mould was developed. To constructing the IHC model of the industrial HDC mould, the following assumptions were made: 1) 2) the temperature field in the mould is not disrupted by the T/c holes; the heat transfer was confined to two dimensions, with no heat flowing along the width of the T-ingot mould (z-axis); 5 : Inverse Heat Conduction Analysis Technique 55 3) the heat transfer in the mould and T-ingot is consistent (i.e. equivalent) over the distance (z-axis) containing the T/c's; and 4) the water flow within the cooling channel is uniform (both velocity and pressure) over the distance containing the T/c's. With these assumptions made, the T/c measurements were superimposed onto a single cross section of the mould. This 2D inverse heat conduction problem was used to solve for the heat flux on the mould surface - i.e. the primary region heat flux distribution in the HDC casting machine. 5.3.1 Geometry and Mesh The 2D cross-sectional geometry of the HDC mould is shown in Figure 5-5. This geometry was meshed using 4-node linear elements with the aid of the commercial FE software package ABAQUS. The mesh in the region where the T/c's are located is structured, with an element size of 0.5mm. Overall, there are 1953 elements and 2113 nodes. External Boundary External Boundary , \ , S External -A X 0 M] B o u n d a r y Water channel M Refractory/mould \ interface approx T/c locations-Metal/mould interface Figure 5-5 - HDC geometry and mesh, along with definitions of the applied heat transfer boundaries conditions. 5 : Inverse Heat Conduction Analysis Technique 56 5.3.2 Boundary Conditions The bounding surfaces of the mould were divided into 4 regions: 1) the metal/mould interface (where the ingot is in contact with the mould); 2) the water cooling channel/mould interface; 3) the refractory/mould interface; and 4) the external surfaces of the mould. METAL/MOULD INTERFACE The heat flux distribution along this boundary was assigned six unknown fluxes q1: q2, Qa q4, 95, qe each centered over the a T/c (x-axis) location. Between these locations, the heat flux was assumed to vary linearly and was determined through interpolation. In the region upstream of the first thermocouple, the heat flux was set to a constant value (equal to g,), and in the region downstream of the sixth thermocouple the flux was set to 5% of the value of q6. The heat flux in the region past the 7th T/c was set to zero. An example heat flux distribution including the bounding fluxes is shown in see Figure 5-6. T/C locations Figure 5-6 - Metal/mould heat flux boundary conditions used in the HDC inverse heat conduction model. 5 : Inverse Heat Conduction Analysis Technique 57 WATER CHANNEL A convective boundary condition was applied to the water cooling channel/mould interface: To determine a suitable heat transfer co-efficient, an estimate of the average Reynolds number was made for the water flow rate reported in the mould. Using this estimate and thermophysical data for water; a convective cooling correlation was used to calculate a local heat transfer co-efficient (see Appendix 1). The heat transfer co-efficient was dependant on flow rate and varied from 9650 to 11250 W/m2K. The bulk water temperature was set to 25°C. REFRACTORY/MOULD INTERFACE AND EXTERNAL BOUNDARIES The refractory/mould interface and the remaining external boundaries were all defined to be adiabatic. This assumption is reasonable since heat losses from the refractory to the surrounding air are negligible compared to the heat extraction from the mould to the water channel. eq 5-9 dT dT = <7 = 0 dx dy eq 5-10 J 5.3.3 Thermophysical Properties The HDC mould was made from a Copper alloy. The thermophysical properties used in the IHC analysis were provided by Alcan and are shown in Table 5-1. Note: they were assumed to be independent of temperature. 5 : Inverse Heat Conduction Analysis Technique 58 Table 5-1 - Thermophysical properties of the industrial mould (Larouche, 2005). Property Value Thermal Conductivity (W/m K) 320 Density (kg/mJ) 8900 Heat Capacity (J / kg K) 380 5.4 Casting Simulator Chill Using heat flow assumptions similar to those applied to the HDC mould (in section 5.3), a 2D inverse heat conduction analysis of the casting simulator chill/mould was constructed. 5.4.1 Geometry and Mesh The 2D cross-sectional geometry of the instrumented mould is shown in Figure 5-7. It was meshed using 4-node linear elements with the aid of the commercial FE software package ABAQUS. The mesh in the region where the T/c's are located is structured, with an element size of 0.8 mm. Overall, there are 1547 elements and 1644 nodes. Metal/Mould Interface T/c locations • Refractory/MoL Interface «.*.«•«; • » « • •. .* »:*.••• *,i <••{—!-,{ A i""'"7"-/ V - \ •' "V External Boundary Water Channel Water channel t-1 \ J4-External Boundary Figure 5-7 - Casting simulator mould: geometry, mesh, and external heat transfer boundary regions. 5.4.2 Boundary Conditions The bounding surfaces of the mould were divided into 4 regions: 5 : Inverse Heat Conduction Analysis Technique 59 D 2) 3) 4) the metal/mould interface; the water cooling channel/mould interfaces; the refractory/mould interface; and the external boundaries of the mould. METAL/MOULD INTERFACE The heat flux distribution along the metal/mould interface was assigned fourteen unknown heat fluxes q:, q2... q14, each centered over the T/c (x-axis) location. Between these locations, the heat flux was determined through linear interpolation. In the region upstream to the 1st thermocouple the heat flux was set to a constant value (q,), and in the region downstream of the last thermocouple (q14), the heat flux was ramped to zero at the end of the mould. An example of this heat flux variation is shown in Figure 5-8. Note that data from the T/c located at x=44.46 mm was omitted as its temperature readings were found to be erroneous due to a faulty extension wire; thus, only fourteen heat flux unknowns (not fifteen) were used. 9 Casting Direction 1 I I I I " q = 0 x T/C locations' Figure 5-8 - Metal/mould heat flux boundary condition used in the casting simulator inverse heat conduction analysis. 5 : Inverse Heat Conduction Analysis Technique 60 WATER CHANNELS A convective boundary condition was applied to the interface with the mould for each water cooling channel, see equation 5-8. The average Reynolds number was calculated for each water channel using the measured water flow rates. Using the average Reynolds number (and thermophysical data for water), a convective cooling correlation was selected and used to calculate the local heat transfer coefficient (Appendix 1). The heat transfer coefficient used for channel on the left hand side was 6400 W/m2K, and 11700 W/m2K for the channel on the right hand side. The bulk water temperature was measured to be 16.5°C, which was adopted for use in the model. REFRACTORY/MOULD INTERFACE AND EXTERNAL BOUNDARIES As the thickness of refractory behind the refractory/mould interface is large and the refractory material used had a comparatively low thermal conductivity, the thermal resistance is expected to be high and negligible heat flow should occur across this boundary. In addition, since the remaining external boundaries are all far from the region of interest within the mould, the inverse analysis results are largely insensitive to the conditions along these external boundaries due to the diffusive behaviour of transient heat conduction. Consequently, it was assumed that the mould/refractory interface boundaries and the mould/ambient environment boundaries were adiabatic, see equation 5-10. 5.4.3 Thermophysical Properties The thermophysical properties for the copper used in the casting simulator mould are shown in Table 5-2. They are consistent with the thermophysical properties of pure Copper and are similar to the values reported from supplier data sheets. In the analysis, the copper was assumed to have temperature independent properties. 5 : Inverse Heat Conduction Analysis Technique 61 Table 5-2 - Thermophysical properties of the casting simulator mould (Metals Handbook, 1990). Property Value Thermal Conductivity (W/m K) 391 Density (kg/m3) 8940 Heat Capacity (J / kg K) 384 5.5 Validation Various calculations were performed to validate the numerical methods employed in this thesis. The finite element heat conduction model was compared with an analytical solution while the inverse heat conduction algorithm was used to predict a series of heat flux distributions using thermal data generated from a known applied heat flux. 5.5.1 FE Validation The finite element code written for this project was validated through comparison with an analytical solution to a 1D transient heat conduction problem. For the case of a semi-infinite solid subjected to a constant surface heat flux at time t s 0, the analytical solution for the temperature evolution in the solid is (Incropera and DeWitt, 2002): 12 ( _.2\ " / .. \ T(x, t) - Tj = exp • x Aat q0x x ^erfc 2jat eq 5-11 Table 5-3 - Data used for 1D transient heat conduction validation problem. Property Symbol Value Surface flux (W/m') Qo 10000 Thermal conductivity (W/mK) k 30 Heat capacity (J/kgK) cn 800 Density (kg/m3) P 7500 Using the values given in Table 5-3, the temperature distributions in the solid after 1, 5, 10 and 20 seconds were calculated using the analytical relation (eq 5-11) and a FE model. The FE model had a mesh density of 2.5-10 mm and used a time step increment of 0.25 s. The FE 5 : Inverse Heat Conduction Analysis Technique 62 calculated solution is compared with the analytical result in Figure 5-9. The comparison shows excellent agreement thus confirming the ability of the conduction code to accurately solve the transient heat conduction equation. - • • Analytical: t= 1s o Calculated — Analytical: t= 5s A Calculated — - Analytical: t= 10s O Calculated Analytical: t= 20s • Calculated 0 0.02 0.04 x(m) 0.06 Figure 5-9 - The temperature evolution for the case of a semi-infinite solid subjected to a constant surface heat flux at time t > 0, calculated via analytical and FE methods. 5.5.2 Steady State IHC Validation A first step in validation of the IHC analysis procedure is to predict the steady state heat flux using simulated temperature data based on a known heat flux. By constructing and solving a steady state forward heat conduction problem, virtual T/c data was generated. This data was then used as input for the IHC analysis. The geometry and boundary conditions used for the forward problem are shown in Figure 5-10. Note that the geometry used is consistent with the geometry of the casting simulator mould. The thermophysical properties used are given in Table 5-4. 5 : Inverse Heat Conduction Analysis Technique 63 2.0E+06 h = 6400 W/m2K h = 6400 W/m2K T w = 298 K T w = 298 K Figure 5-10 - Geometry and boundary conditions used for the steady state forward problem Table 5-4 - Thermophysical properties used in steady state and transient validation problems. Property Value Thermal Conductivity (W/m K) 400 Density (kg/mJ) 8940 Heat Capacity (J / kq K) 384 The calculated steady state heat flux distribution is compared with the applied heat flux in Figure 5-11 and Figure 5-12. Figure 5-10 presents the results for the upstream end of the mould and Figure 5-11 for the downstream region. Over most of the surface of the mould the inverse algorithm is able to accurately reproduce the applied heat flux. However, at both ends there is variability in the success which is dependent on the assumptions made with respect to the variation of surface heat flux outside the range of the thermocouples. To determine an accurate method to estimate the heat flux in the region upstream of the 1st thermocouple, two approaches were used. The first method used a constant heat flux while the second method 5 : Inverse Heat Conduction Analysis Technique 64 extrapolated the slope of the heat flux distribution for the region between the 1st and 2 n d T/c's, see Figure 5-11. From these results, it appears that extrapolating the heat flux produces a slightly better overall result ahead of the 1st T/c, but diminishes the solution accuracy within the region where the T/c's are located. Similarly, two approaches were used to determine the best way to describe the heat flux distribution in the region downstream of the final thermocouple. The first method assumes no heat flow occurs across the boundary in this region while the second method ramps the heat flux linearly over the region down to a value of zero corresponding to the end of the mould, see Figure 5-12. The results suggest that ramping the heat flux to a value of zero gives a better result than using an adiabatic approximation for that region which results in overcompensation in the flux at qi4. This overcompensation leads to an oscillatory behaviour in the calculated heat flux solution. As indicated in Table 5-5, when the heat transfer coefficient varies by a factor of +/-20%, the calculated mould cooling power can vary as much as 10%. Considering the accuracy, +/- 5%, of the water channel heat transfer co-relation used throughout this thesis (Appendix 1); it is reasonable to assume that IHC calculations will be relatively insensitive to heat transfer co-efficient inaccuracies (compared to temperature measurement error effects on IHC calculations). Overall, with the optimal modeling parameters chosen, the steady state heat flux distribution can be approximated to within 5% of the actual value, for cases where the experimental data contains no error. 5 : Inverse Heat Conduction Analysis Technique 65 Figure 5-11 - Steady State IHC calculated flux distributions compared with applied flux. Sensitivity to flux distribution outside of qi region is shown. 2.0E+06 1.5E+06 | 1.0E+06 X 3 - a - Linear Ramp to q=0 q = 0 Actual TO I 5.0E+05 0.0E+00 -5.0E+05 20 40 60 80 100 120 140 Distance From Front of Mould (mm) Figure 5-12 - Steady State IHC calculated flux distributions compared with applied flux. Sensitivity to flux distribution outside region q 1 4 is shown. 5 : Inverse Heat Conduction Analysis Technique 66 Table 5-5 - IHC Results Steady State Sensitivity Peak Heat Flux (3.2 mm) (W/m2) % Heat Flux % Total Mould la Change (41.3 mm) (W/m2) Change Cooling Power (W/m) Change ACTUAL q(x) 1.35E+06 IMEsHII 1.00E+05 — 2.74E+04 — Heat Conduction Modeling Parameters q(x) distribution Linear-ramp 1.23E+06 -8.7 1.11E+05 11.4 2.6E+04 -4.5 Constant-ramp 1.30E+06 -4.0 1.11E+05 11.4 2.6E+04 -4.5 Linear-zero 1.25E+06 -7.8 3.12E+05 212.2 2.5E+04 -10.5 Constant-zero 1.31E+06 -3.0 3.12E+05 212.3 2.5E+04 -10.5 Water Cooling Convection Co-efficient 5120 (W/m2k) 1.26E+06 -3.1 8.25E+04 -25.7 2.3E+04 -11.5 6400 (W/m2k) 1.30E+06 base 1.11E+05 base 2.6E+04 Base 7680 (W/m2k) 1.33E+06 +2.3 1.38E+05 +24.3 2.9E+04 +11.5 5.5.3 Transient IHC Validation By constructing and solving a transient forward heat conduction problem, virtual T/c data was generated. This virtual T/c data was used as input for a transient IHC analysis. The geometry and boundary conditions used for the forward sample problem are shown in Figure 5-13. The initial temperature field was set to 25°C. Note that the geometry used is consistent with the geometry of the casting simulator mould. The thermophysical properties used are listed in Table 5-4. The applied flux (see Figure 5-13) is the product of a transient triangular heat flux ramp, qrft), and a spatially varying exponentially decaying heat flux term, q2(x). After solving the problem, the temperatures at locations, corresponding to the T/c locations in the casting simulator were extracted with a time increment of 0.1 s, yielding virtual T/c data for use as a validation problem. 5 : Inverse Heat Conduction Analysis Technique 67 0 2x10 s 2xlC 0 t<5 -\ 1-5] ; 5</<15 k 10 J 2 5 - ^ ; 15^;<25 10 J ; l>25 • -150 x 8fe A 1 V ± t U r V > < TSc f s - r v q=0 h= 8000W/m3< T =298 K w q=0 h= 1500 W/m3< T =298 K w Figure 5-13 - Geometry and boundary conditions used for the transient forward problem. Using the virtual data as input into the IHC analysis, the complete metal/mould surface heat flux history was calculated. Selected IHC results are compared to the imposed heat flux distribution at 7, 11 and 15 seconds in Figure 5-14 and Table 5-6. Discrepancies in the results are attributed to inaccuracies inherent in the heat flux discretization (linear variation as opposed to exponential variation) and to insufficient T/c resolution near the left side of the mould (i.e. the first T/c is positioned 3.2 mm from the left side of the mould). Overall, the agreement is good and the discrepancy between calculated and imposed heat fluxes are within 5 %. 5 : Inverse Heat Conduction Analysis Technique 2.0E+06 1.5E+06 | 1.0E+06 <u I 5.0E+05 0.0E+00 • precited: t=15s actual: t=15s o precited: t=11s actual: t=11s A predicted: t=7s actual: t=7s •ei i m—a—e-10 20 30 40 Distance From Front of Mould (mm) 50 Figure 5-14 - Comparison between actual and calculated heat flux distributions for selected times. Table 5-6 - Comparison between actual and calculated q(x,t) characteristics. time (s) Total Mould Cooling Power (W/m) Applied Predicted % difference 7 2667 2721 2.0 11 8000 7999 -0.003 15 13333 13145 -1.4 19 8000 8125 1.6 23 2667 2798 4.9 5 : Inverse Heat Conduction Analysis Technique 69 5.6 Summary By coupling a 2D transient heat conduction analysis with Beck's non-linear sequential estimation technique, a method for solving inverse heat conduction problems has been developed. The details of applying this technique to the industrial HDC and the casting simulator problems have been presented. Furthermore, various calculations were presented as validation of: 1) the FE transient heat conduction code used in this thesis; and 2) the IHC algorithm code used in this thesis for both the steady state and transient cases. Overall, the IHC model accurately predicts the heat flux distribution for both transient and steady state cases, however; it was shown (via the steady state IHC validation problem) that thermocouple resolution can limit the solution accuracy. The steady state validation problem showed that approximating the region prior to the 1st T/c with a constant heat flux was preferred. Additionally, it showed that by ramping the flux to zero for the low heat flux region beyond the location of the last thermocouple the accuracy of the results could be improved. 6 : Results and Discussion 70 6 Results and Discussion Using the temperature data obtained during the plant trial and lab tests, IHC analyses were performed to calculate the heat flux distributions along the hot faces of the casting moulds. Both the plant trial and casting simulator results are presented individually, with some short discussion. Comparison of the results follows, with discussion regarding their similarities and differences. 6.1 Industrial IHC Analysis The steady state temperature measurements obtained during the plant trial were used as input into the industrial model (see Figure 4-8). For each casting condition, the IHC analysis was performed (with the appropriate T/c data), and the heat flux distribution for that test was determined. The experimental matrix for the plant trial is shown in Table 6-1. Table 6-1 - Test Matrix for the 2003 Dubuc plant trial (% of baseline condition). Tunish _ . Cooling Tundish T . . . Metal e IF W a t e r Metal ... Test Num T _ Speed ,., n . . . A by Temp jj,.. Flow Rate Level ' 1 101 80 88 2 101 100 88 3 101 100 83 4 100 100 100 100 A356 5 101 105 100 6 100 110 100 7 97 105 100 8 102 100 100 The IHC analyses were performed using a transient heat conduction formulation and a dummy time step. Doing so, the inversely calculated steady state heat flux profiles were allowed to evolve over a period of time. This method is commonly used to improve convergence behaviour of steady state heat transfer calculations. The IHC parameter values used for the industrial IHC analyses are listed in Table 6-2. 6 : Results and Discussion 71 Table 6-2 - IHC parameter values used for industrial IHC analyses. IHC Parameter Value Used Number of Future Time Steps, R 2 Dummy Time Interval Size, A9 (s) 0.2 Regularization parameter, a 2x10" a Overall Convergence Criterion 5 x10 s 6.1.1 Industrial IHC Results The calculated heat flux distributions for Tests 1 thru 8 are shown in Figure 6-1 and summarized in Table 6-3. Shown in the figure, the steady state heat fluxes q1 thru q6 are plotted as a function of distance from the front of the mould. As expected, the maximum heat flux occurs near the front end of the mould. The magnitude of the heat flux at the hot (upstream) end of the mould is in the range of 2.2-2.6 MW7m2 for all tests. The heat fluxes steadily decrease with distance along the mould. There is no distinct drop in the heat flux that may be associated with the onset of gap formation; rather there is a continuous decrease in the flux consistent with a continuous increase in contact resistance across the metal/mould interface. Grandefield and Dahle measured heat fluxes of 50-160 kW/m2 in air gap region within an HDC mould (Grandefield and Dahle, 2000). Due to lack of thermocouples located between 20-40 mm along the length of the mould, the minimum heat fluxes observed, at a distance of 18 mm from the front of the mould, were substantially higher then those cited. In future plant trials, the number of thermocouples along the length of the mould should be increased such that the air gap fluxes can be characterized with greater detail. The heat flux distribution for the low casting velocity test (Test 1) is clearly lower than all the other tests. The heat flux distribution can be integrated to provide a measure of the cooling power per unit width of mould, shown in Table 6-3. These calculated values further support the conclusion that of the factors considered, casting velocity has the most significant effect on mould heat transfer. 6 : Results and Discussion 72 3.0E+06 n 2.5E+06 -?P o | 2.0E+06 - 1 x o ^ .2 1.5E+06 - - * LL m ro o 9 £ 1.0E+06 - ° | + 5.0E+05 - & 0.0E+00 -I , 0 10 20 30 40 Distance From Front of Mould (mm) Figure 6-1 - Calculated heat flux distributions obtained from Plant trial tests. Table 6-3 - Plant trial IHC tabulated results. Test Max Heat Flux @ 2 mm (W/m2) Mould Cooling Power (W/m) 1 2.2E+06 2.5E+04 2 2.5E+06 3.0E+04 3 2.4E+06 2.9E+04 4 2.5E+06 3.1E+04 5 2.5E+06 3.0E+04 6 2.5E+06 3.1E+04 7 2.5E+06 2.9E+04 8 2.4E+06 3.0E+04 6.1.2 Model Sensitivity to Regularization Parameter The sensitivity study (shown in section 5.5.2) using the steady state validation problem suggested that with noise free thermocouple measurements, the heat fluxes calculated were within +/- 5% of the applied values. However, error associated with the real thermocouple measurements may act to further decrease the accuracy of the IHC calculations. Although a proper statistical analysis of the IHC calculations was beyond the scope of this project, a o Test 1 • Test 2 x Test 3 + Test 4 x Test 5 A Test 6 o Test 7 - Test 8 6 : Results and Discussion 73 sensitivity study using the regularization parameter (a) (required to stabilize the IHC algorithm) gives some insight into calculation accuracy. By varying the regularization parameter around the value used in the above analysis, 2 x 10"9, the calculated heat flux distribution is affected as shown in Figure 6-2. However, the general shape of the heat flux distribution and magnitudes are consistent over the range of a tested. Depending on the degree of regularization, the calculated peak heat flux will change. This result is expected, as large non-zero values of zeroth order regularization reduce heat flux magnitudes (Beck et al, 1985: pg 136). Overall, the central value of 2 x 10"9, used in the industrial IHC analysis, yields optimal IHC results. 3.0E+06 2.5E+06 E 2.0E+06 § 1.5E+06 | 1.0E+06 5.0E+05 0.0E+00 0 " A X o a = 1 x 10"8 x q = 2 x 10"9 A q =1 x 10- 1 0 o A R _ A X o * o 10 20 30 Distance From Front of Mould (mm) 40 Figure 6-2 - The effect of degree of regularization on the q(x) steady state distribution, obtained using test 1 plant trial data. 6 : Results and Discussion 74 6.2 Casting Simulator IHC Analysis To calculate the heat flux distributions, q(x), for the casting simulator tests, the transient T/c data was first filtered to smooth out any noise. This was done using a Savitsky-Golay filter (Press, 1992) with a filter window size of 40. Using the filtered data, shown for example in Figure 6-3, a transient IHC analysis was run for each test. The starting point for the analyses was chosen for each test to be a point in time just after the linear motion of the starter block had commenced (i.e. the start of continuous casting). The end point for the analyses was chosen as the point just prior to the end of the casting test. The start and end points for Test 1 and Test 4 along with the filtered thermocouple data used in the IHC analyses are shown in Figure 6-3 and Figure 6-4. Table 6-4 lists the experimental casting conditions used for the tests analyzed using IHC analysis. -50 0 50 100 150 200 250 Cast Time (s) Figure 6-3 - Smoothed and raw T/c data for Test 1. The dashed lines represent the start and end of the IHC analyses. 6 : Results and Discussion 75 140 -, Cast Time (s) Figure 6-4 - Filtered T/c data for Test 4. The dashed lines represent the start and end of the IHC analyses. Table 6-4 - Casting simulator test conditions. Test Casting velocity (mm/s) Metal Temp in Crucible (°C) Water Cooling Flow Rate (LPM) Metal Head (mm) Cast Length (mm) 1 1.21 +/-0.02 745 300 3 0.88 +/-0.02 745 85 4 1.20 +/-0.02 745 15 +/-0.5 180 +/-10 90 5 1.24 +/-0.02 700 90 8 1.20 +/-0.02 790 320 To determine the IHC parameter values to be used for the casting simulator analyses, preliminary numerical trials were performed using real test data. The IHC parameters values, such as number of future time steps, R, and the regularization parameter, a, were chosen based on a qualitative assessment of the preliminary numerical test results and the 6 : Results and Discussion 76 convergence behaviour for each numerical trial. The IHC parameter values used for the casting simulator IHC analyses are listed in Table 6-5. Table 6-5 - IHC parameter values used for casting simulator IHC analyses. IHC Parameter Value Used Number of Future Time Steps, R 2 Time Interval Size, A8 (s) 0.2 Regularization parameter, a 2x10"u Time Step Convergence Criterion 10* 6.2.1 Casting Simulator IHC Results The transient heat flux results for Tests 1, 3, 4, 5 and 8 are shown in Figure 6-5 thru 6-9. In the figures, the heat fluxes q-, thru q13 are plotted along with the temperature data. For the most part, the heat flux evolution follows the same trajectory as the temperature evolution. For example, c/r follows the path of T/c^ and q2 the path of T/c2. This is expected, as the calculated heat fluxes are greatly affected by the nearest temperature sensor (Beck et al, 1985; pg 35). In order to facilitate comparison to the industrial plant trial results, steady state heat flux distributions from the casting simulator test results are needed. For Tests 1 and 8, due to the relatively long casting duration, a quasi-steady state casting period was achieved during testing (defined in chapter 4). The onset of this casting period is indicated -for Tests 1 and 8- in Figure 6-5 and Figure 6-9. As observed, the calculated heat fluxes within this region do not follow the same trajectory as the temperature evolution. Fluctuations in temperature observed during the quasi-steady periods of Tests 1 and 8 may cause deviations between the heat flux and temperature trajectories. Due to the limited test results, these heat flux/temperature trajectory deviations could not be studied in great detail. As the heat flux trajectories for Tests 1 and 8 followed the temperature evolution closely in the time leading up to this period (left of the dashed lines in Figure 6-5 and Figure 6-9) results from this period were used to approximate the steady state heat flux distribution. Specifically, the heat flux distribution corresponding to the time where the overall maximum heat flux was observed was used as the steady state heat flux approximation. For Test 1 the 6 : Results and Discussion 77 maximum overall heat flux was observed at the cast time of ~ 110 s, for Test 8 at -125 s (see Figure 6-5 and Figure 6-9). Figure 6-5 - Test 1 T/c data and transient IHC results. The different curves represent the calculated fluxes q 1 thru q 1 3 respectively. The dashed line indicates the onset of the quasi-steady casting period. 6 : Results and Discussion 78 50 100 150 Cast Time (s) 200 250 3 03 CD Figure 6-6 - Test 3 T/c data and transient IHC results. The different curves represent the calculated fluxes thru q 1 3 respectively. The dashed line indicates the end of the casting test. — T/c data • Hea t flux -50 50 100 150 200 Cast Time (s) 1 4E+06 1 2E+06 1 OE+06 3 8 OE+05 > 3 6 OE+05 X 4 2 OE+05 OE+05 0 0E+00 250 Figure 6-7 - Test 4 T/c data and transient IHC results. The different curves represent the calculated fluxes thru q 1 3 respectively. The dashed line indicates the end of the casting test. 6 : Results and Discussion 79 — T/c data • Heat flux Cast Time (s) Figure 6-8 - Test 5 T/c data and transient IHC results. The different curves represent the calculated fluxes q, thru q 1 3 respectively. The dashed line indicates the end of the casting test. Figure 6-9 - Test 8 T/c data and transient IHC results. The different curves represent the calculated fluxes thru q 1 3 respectively. The dashed line indicates the onset of the quasi-steady casting period. 6 : Results and Discussion 80 Similarly, for Tests 3 - 5 the heat flux distributions corresponding to the point in time where the overall maximum heat flux was observed was chosen to approximate a steady state heat flux distribution. From observation of the calculated heat fluxes for Tests 3-5 (see Figure 6-6 thru 6-8), the maximum flux occurs just before the termination of the casting run (i.e. test end). This was observed for Tests 3 - 5, and is an indication that the mould was still heating during testing (i.e. steady state was not achieved). This should be considered when comparing tests; as results obtained from Tests 3-5 may suggest lower heat flux values in comparison to Tests 1 and 8. As the time derivative of the heat flux at the end of the casting period is greatest for Test 4 (in comparison to Test 3 and 5), the bias associated with this approximation method should be highest for the results presented for Test 4. For Tests 3 and 5, the calculated heat flux appears to have leveled off (in comparison with Test 4) just prior to the end of casting. Similarly, the bias associated with the steady state heat flux approximation for Tests 3 and 5 may not be as significant. APPROXIMATE STEADY STATE HEAT FLUX DISTRIBUTIONS Using the methodology stated, the extracted heat flux distributions for Tests 1, 3, 4, 5 and 8 are shown in Figure 6-10 and summarized in Table 6-6. The maximum heat flux for each test occurs at the hot end of the mould and ranges from 1.1-1.4 MW/m2. The heat flux steadily decreases with distance from the front of the mould. Similar to the industrial results, the heat flux appears to be insensitive to the process parameters examined. Test 3 appears to have a reduced heat flux distribution which at first may be attributed to lower casting velocity, however; this result should be considered inconclusive because the heat fluxes were still rising at the end of casting. The heat flux magnitudes in the 20-40 mm region correspond well to the suggested air gap fluxes 50-160 kW/m2 reported in previous HDC literature (Grandfield and Dahle, 2000). 6 : Results and Discussion 81 2.0E+06 1.5E+06 IE * 1.0E+06 X x. 5.0E+05 O.OE+00 o o Test 1 x Test 3 A Test 4 o Test 5 • Test 8 10 20 30 Distance From Front of Mould (mm) 40 Figure 6-10 - Calculated heat flux distributions obtained from casting simulator tests. Table 6-6 - Casting simulator IHC tabulated results. Test Max Heat Flux @ 3.2 mm (W/m2) Mould Cooling Power (W/m) 1 1.32E+06 2.29E+04 3 1.13E+06 1.72E+04 4 1.15E+06 1.96E+04 5 1.23E+06 2.13E+04 8 1.26E+06 2.19E+04 6.2.2 Sensitivity The transient IHC calculations should exhibit a strong dependency on both the regularization parameter (or) and the number of future time steps (R) used as they both act to stabilize the algorithm. By varying the regularization parameter around the value used for the casting simulator IHC analysis, 2 x 10"9; the evolution in heat flux is affected. For example, the effect of or on the calculated values of c/r is illustrated in Figure 6-11, using data and results from Test 1. Concentrating on casting times less than 150 seconds, a high value of a acts to constrain the calculated heat fluxes, requiring more time for the heat fluxes to change. This 6 : Results and Discussion 82 effect is reduced as the value of a decreases. For casting times greater than 150 seconds, it is unclear how the value of a affects the calculated heat fluxes. Within this time period, large temperature fluctuations from other thermocouples (not shown in Figure 6-11) also have an effect on the heat flux evolution, see for example Figure 6-5. — T/c 1 Heat flux q1: * a=4x10 9 c a=2x10" 9 * a=1x10"9 5.0E+05 -25 25 75 125 Cast Time (s) 175 225 Figure 6-11 - The calculated flux history for for Test 1 for various values of a. The corresponding temperature history forT/Ci is plotted in black. Figure 6-12 shows the effect a has on the approximate steady state casting heat flux distribution, extracted with the method described previously for Test 1. Like the industrial IHC analysis, the peak heat flux (corresponding to the T/c closest to the front of the mould) is sensitive to or, however the heat flux distribution is not greatly effected. Similarly, the central value of 2 x 10"9, used in the casting simulator IHC analysis, yielded an optimal result. 6 : Results and Discussion 83 CO <D X 2.0E+06 1.5E+06 1.0E+06 5.0E+05 0.0E+00 x o x o 8 o a =4 x 10"9 x a =2x 10-9 A a =1 x 10-9 o a =8 x 10"10 9. 2 10 20 30 Distance From Front of Mould (mm) 40 Figure 6-12 - Calculated heat flux distributions obtained from Test 1 for various values a. 6.3 Comparison of Results By comparing the IHC results from the industrial plant trial and casting simulator, the viability Of casting simulator to reproduce HDC conditions can be assessed. The lab test and plant trial results for slow and fast casting velocities are plotted in Figure 6-13. The peak heat fluxes, although higher in the plant trial case, are of similar order -1.1-2.6 MW/m2. As expected, this suggests that the same basic physical conditions are present in both tests. Comparison of the casting parameters used in the two tests, shown in Table 6-5, reveal that although the tests differed in size scale; as evidenced by the large discrepancy in casting rate and mould water flow rates, the parameters critical to initial solidification and primary zone heat transfer were similar. Specifically, the casting velocity, metal head pressure and metal superheat were comparable between the two tests. Additionally, in both tests the heat flux increases with increasing casting velocity, however; this should be confirmed by more testing with the casting simulator. In the region 0-20 mm from the front of the mould, the heat flux distributions show similar trends; steadily decreasing with distance from the upstream end of 6 : Results and Discussion 84 the mould. The slopes of these curves are steeper for the industrial cases shown. Due to the lack of spatial thermocouple resolution in the latter portions of the industrial casting mould, comparisons of the onset of gap formation in the two tests cannot be made. Comparing the calculated mould cooling powers for the industrial mould tests, 25000-31000 W/m, with the casting simulator tests 17000-23000 W/m, shows they are of comparable magnitude. In general, the agreement between the plant trial and lab results is favorable, as the trends in q(x) distributions are the same and the calculated heat fluxes and mould cooling powers are within an order of magnitude of each other. 3.0E+06 2.5E+06 N£ 2.0E+06 x 1.5E+06 3> 1.0E+06 x 5.0E+05 0.0E+00 -Q- HDC: slow cast —e— HDC: fast cast - -+•- lab: fast cast -X- lab: slow cast 0 10 20 30 Distance from front of chill (mm) 40 Figure 6-13 - Heat flux distribution comparison. Industrial trial vs. casting simulator results. 6 : Results and Discussion 85 Table 6-7 - Industrial trial vs. casting simulator casting parameters. Parameter HDC Process* Casting Simulator Casting Velocity (mm/s) 0.9-1.2 Casting Temp CC) warn 700-790 Metal Head Height (mm) • i -180 Casting Rate (kg/s) 0.006-0.008 Water Flow rate per unit length of mould (L/min/m) 150 * HDC process conditions removed at the request of the industrial sponsor. Assuming primary region heat transfer is limited by the heat flow within the mould (not the ingot); comparing the thermal resistances of the HDC and casting simulator moulds provides insight into the differences expected in heat flux magnitudes between the two moulds. Taking the distance from the water channel to the front of the mould for both setups, denoted as LT in Figure 6-14, and assuming the heat transfer in the mould to the cooling water is 1D along the path indicated by the heat fluxes can be approximated by summation of the thermal resistances: AT k h eq 6-1 Assuming the thermal gradients in the mould are similar, the ratio of the thermal resistances for the two moulds suggest that the steady state heat flux magnitude for the HDC mould should be approximately 1.4 times larger than that of the casting simulator mould, at the front of the mould. Considering the difference in water channel diameter and water heat transfer co-efficients between the two tests the maximum cooling power per unit length of mould, defined as Q/, can be approximated by the following relation: Q,~hnD{Ts-Tw) eq 6-2 6 : Results and Discussion 86 Again, assuming the thermal gradients in the mould are similar, the approximate HDC mould cooling capacity per unit length of mould would be approximately 3.5 times larger then the casting simulator mould. The ratios of these simple heat flux values (1.4 and 3.5) are similar to the discrepancy observed in heat flux magnitudes between the two tests, suggesting that mould geometry may be a significant factor to consider in future lab testing. Figure 6-14 - Schematic depicting initial metal solidification within the casting mould for both the a) HDC casting machine and b) casting simulator apparatus. The solid shell is shown as the grey curved line and the mould conduction path L: denotes the heat flux pathway from mould cooling water to the meniscus zone. Specific casting parameters that differed in the plant trial and lab tests are shown in Table 6-8, all of which affect initial solidification behaviour in DC casting. The lack of oil lubrication in the casting simulator may have reduced heat fluxes near the meniscus and in the metal/mould contact regions. Advance cooling effects (brought about by the direct water spray) present in the HDC cast ingot may lead to larger shell growth rates in comparison to the casting simulator, see Figure 6-14. Larger shell growth rates within the primary region lead to a steeper q(x) slope in the mould, as the resistance to heat flow from the ingot to the mould would increase with increasing shell thicknesses. This agrees with the heat flux observations Melt Inflow a) b) 6 : Results and Discussion 87 reported in this thesis. Additionally, the lack of secondary cooling in the lab test setup result in reduced thermal gradients in the lab castings (w.r.t. to the HDC cast ingot), thus reducing the extent of thermal contraction of the solid shell. This difference will affect the onset of gap formation in the lab casting and could explain why the slopes of the q(x) results were shallower for the casting simulator results. Table 6-8 - Qualitative differences between the industrial trial and casting simulator casting conditions. Parameter HDC Process Casting Simulator Secondary Cooling Water spray on ingot None Lubrication Oil None Angle formed at the intersection of the Copper mould and refractory backing plate 90° 0° The difference in initial solidification heat fluxes may also be related to the surface structure. The surface morphology from both industrial and lab tests is shown in Figure 6-15. The industrially cast surface clearly exhibits a fine lapped structure. The thickness and length of these (laps) ridges show some consistency over short distances. Considering that a 90° angle forms at the intersection point of the Copper mould and the refractory backing plate for the HDC casting machine (see Figure 6-14), the observed surface structure is expected to occur when shell thickness at the front of the mould is greater than zero; as it leads to a periodic shell stick and release mechanism similar to cold shutting mechanisms described in previous studies on DC casting of aluminum (Weckman and Niessen, 1984a and 1984b). This periodic shell stick and release mechanism is also consistent with the large temperature oscillations observed in the mould. Furthermore, liquid metal renewal at the meniscus occurs with short sudden bursts, possibly leading to enhanced heat transfer at the meniscus. In the lab tests, the surface ridges and crevices are not as well defined and are less uniform in thickness and length. In the casting simulator setup the Copper mould - refractory plate intersection point forms a angle of 0°, thus flattened surface laps are expected with less 6 : Results and Discussion 88 uniformity between laps. Additionally, due to the 0° mould/ refractory angle, a shell stick and release mechanism would not occur to the same degree observed in the HDC cast ingot. If shell growth at the front of the mould was greater then zero during lab tests, it is possible that the shell could have extended back into the refractory portion of the mould assembly, thus offsetting the metal meniscus. This could be another possible explanation for the lower heat fluxes observed in the meniscus region of the casting simulator. Casting Direction Figure 6-15 - Surface structure of lab test castings compared with industrial T-ingot surface structure, for aluminum A356 alloy. 6.4 Summary of Results The heat flux distributions along the hot faces of both the industrial and casting simulator moulds were calculated via inverse heat conduction analysis using T/c test data as input. For the plant trial tests, the maximum calculated heat flux in the mould was 2.2-2.6 MW/m2; in the casting simulator the maximum was found to be 1.1-1.4 MW/m2. The heat flux 6 : Results and Discussion 89 distributions from both cases show similar trends where heat flux magnitude decreases with increasing distance from the upstream end of the casting mould, as would be expected. The mould cooling power for the industrial mould was calculated as 2.5-3.1 x 104 W/m whereas the values for the casting simulator mould were lower, 1.7-2.3 x 104 W/m. The casting speed affects the heat flux in the mould, as decreasing the casting speed resulted in lower heat fluxes for the industrial tests. This behaviour was observed in the casting simulator tests; however additional tests should be done to confirm this result. The other variables of interest, i.e. casting temperature and mould water flow rate did not significantly change the calculated heat flux distributions. Comparing the industrial heat fluxes with the casting simulator heat fluxes suggest that the same basic heat transfer phenomenon occurring in the industrial casting mould were reproduced with the laboratory apparatus. The heat fluxes were of similar order of magnitude, and the heat flux distributions showed similar behaviour. Thus, the casting simulator is a viable method for characterizing primary heat transfer in HDC casting. 7 : Conclusions and Future Work Recommendations 90 7 Conclusions and Future Work Recommendations 7.1 Conclusions SUMMARY OF TASKS A 2-D inverse heat conduction (IHC) model of an industrial HDC casting mould has been developed. Using mould temperature measurements taken from an industrial mould during a 2003 plant trial, an IHC analysis was performed to determine the heat fluxes occurring along the hot face of a HDC casting mould during continuous casting of aluminum A356 alloy T-ingots. Additionally, an apparatus was designed and built for the purpose of simulating primary region heat transfer in a HDC casting machine. After an initial experimentation period, the parameters required for successful operation of the apparatus were found. Several experiments were conducted, of which 5 tests yielded useful data. Similar to the industrial case, a 2-D IHC model of the test apparatus was developed. IHC analysis was done using temperature measurements taken from the casting simulator tests. This analysis yielded the heat fluxes occurring along the hot face of the casting simulator mould. SUMMARY OF RESULTS The heat flux distributions, q(x), along the hot faces of both the industrial and casting simulator moulds were calculated using inverse heat conduction calculations and mould temperature data. For the plant trial tests, the maximum calculated heat flux in the mould ranged 2.2-2.6 MW/m2; in the casting simulator the maximum was found to be 1.1-1.4 MW/m2. The observed heat flux distributions all decreased with increasing distance from the front edge of the casting mould. 7 : Conclusions and Future Work Recommendations 91 The mould cooling power for the industrial mould was calculated as 2.5-3.1 x 104 W/m whereas the value for the casting simulator mould was lower 1.7-2.3 x 104. The casting velocity affected the resulting heat fluxes in the industrial mould, as decreasing the casting velocity resulted in lower heat fluxes. This was also observed in the casting simulator results; however more tests should be performed to confirm this. The other variables of interest, i.e. casting temperature and mould water flow rate did not significantly affect calculated heat flux distributions. Heat flux results suggest that the same basic heat transfer phenomenon occurring in the industrial casting mould were reproduced with the casting simulator. The heat fluxes in both tests were of similar order of magnitude, and behaved in a similar manner, suggesting that testing with the casting simulator is a viable method for characterizing primary heat transfer in HDC casting. 7.2 Future Work Recommendations INDUSTRIAL PLANT TRIAL It is recommended that a second plant trial be conducted. In a second plant trial, the following suggestions could improve the quality of the test results. These suggestions include: 1) Ingot temperature measurements (i.e. T/c's cast into an ingot); 2) Installing more then 7 T/c's along the hot face of the mould, to improve the spatial resolution of the resulting heat flux calculations; 3) Installing T/c's in various regions around the mould periphery (to check for differences in cooling at top, bottom, side and corner locations of the mould/ingot); 4) Using measurements to precisely locate thermocouples in the mould; 5) Monitor the metallostatic pressure (i.e. metal level in the tundish) during testing; 6) Measure the water temperature in the mould and in the re-circulation area and 7) Measure water flow rates in the mould. 7 : Conclusions and Future Work Recommendations 92 LABORATORY EXPERIMENTS A redesign of the casting simulator is suggested. Specifically, the following modifications to the casting simulator design should improve the ability to cast test ingots: 1) re-dimension the mould so that it matches the HDC mould geometry 2) round the corners of the casting cross section, thus reducing the chances of corner cracking; 3) introduce a way to control the metal superheat, thus reducing the likelihood of freeze up of the hot metal before it comes into contact with the copper mould and 4) re-design of the mould assembly to decrease setup time without sacrificing test repeatability. Additionally, incorporating secondary cooling (i.e. direct water spray) and a mould lubrication system in the casting simulator would minimize discrepancy between laboratory and industrial tests. Finally, an effort should be made to enhance the quantity and quality of measurements taken during any future tests (see suggestions from previous section). References 93 References Adenis, D.J.-P., Coats, K.H. and Ragone, D.V. 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"A New Explanation of the Surface Structure of Direct Chill Ingots". Metallurgia, 1967. 76(456): p. 137-144. Drezet, J.M., et al. "Determination of thermophysical properties and boundary conditions of direct chill-cast aluminum alloys using inverse methods". Metallurgical and Materials Transactions A, 2000. 31 A(6): p. 1627. References 94 Ducker Worldwide, "Aluminum Content for Light Non-Commercial Vehicles Assembled in North Amreica, Japan, and the European Union in 2006" [pdf]. Available from the Automotive Aluminum Inc. Website, http://www.autoaluminum.org/ Ennor, W.T., US patent 2301027, Nov. 3, 1942. Fjaer H.G., et al. "Investigations of the Primary Cooling in Sheet Ingot Casting", in Internationl Congress "Continuous Casting". 2000. Frankfurt: WILEY-VCH Verlag CmbH. Grandfield, J.F. and Dahle, A.K. "Modelling and Measurement of Mould Heat Transfer During Horizontal Direct Chill Casting of Magnesium", in 4th Pacific Rim International Conference on Modelling of Casting & Solidification Processes. 2000. Centre for Computer-Aided Materials Processing; Yonsei, Korea. Grandfield, J.F. and McGlade, P.T. "DC casting of aluminium: process behaviour and technology". Materials Forum (Australia), 1996. 20: p. 29-51. Ho, K. and Pehlke, R.D. "Mechanisms of Heat Transfer at a Metal/Mold Interface". (Retroactive Coverage), in Transactions of the American Foundrymen's Society. 1984. St. Louis, Missouri; USA. Ho, K. and Pehlke, R.D. "Metal/Mold Interfacial Heat Transfer". Metallurgical and Materials Transactions B., 1985. 16B(3): p. 585-594. Incropera, F.P., DeWitt, D.P. Fundamentals of Heat and Mass Transfer. Fifth Edition. John Wiley and Sons, 2002. New York Inverse Engineering Handbook, K.A. Woodbury, Editor. 2003, CRC Press. Jensen, E.K. "Mold Temperatures During DC Casting of 8 In. Dia. Extrusion Ingots in Alloy 6063". in Light Metals 1984. 1984. Los Angeles, Calif; U.S.A. Jensen, E.K., et al. "Heat Transfer Measurements During DC Casting of Aluminium. II. Results and Verification for Extrusion Ingots", in Light Metals 1986. 1986. New Orleans, Louisiana; USA. Krishnan, M. and Sharma, D.G.R. "Determination of the interfacial heat transfer coefficient h in unidirectional heat flow by Beck's non linear estimation procedure". International Communications in Heat and Mass Transfer, 1996. 23(2): p. 203. Kumar, T.S.P. and Prabhu, K.N. "Heat Flux Transients at the Casting/Chill Interface During Solidification of Aluminum Base Alloys". Metallurgical and Materials Transactions B, 1991. 22B(5): p. 717-727. Kumar, S.W., Samarasekera, I.V., Brimacombe, J.K. "Chaos at the meniscus--the genesis of defects in continuously cast steel billets", in Process Technology. Vol. 13. Continuous Casting. 1995. Nashville, Tennessee; USA: Iron and Steel Society. Laemmle, J.T., Bohaychick, J. "Mold Lubricants for Casting Aluminum and its Alloys". Lubrication Engineering 1992: p.858-863. Larouche, Andre. Thermophysical Data for Copper Alloy used in HDC moulds. Personal Email Communication to Massimo Di Ciano, October 19th, 2005. References 95 Li, D., Shabestari, S.G., Isac, M., Guthrie, R.I.L. "Studies in the Casting of AA6111 Strip on a Horizontal, Single Belt, Strip Casting Simulator", in Light Metals 2006. San Antonio, TX; USA. a) Loulou, T., Artyukhin, E.A. and Bardon, J.P. "Estimation of thermal contact resistance during the first stages of metal solidification process. I. Experiment principle and modelisation". International Journal of Heat and Mass Transfer, 1999. 42(12): p. 2119. b) Loulou, T., Artyukhin, E.A. and Bardon, J.P. "Estimation of thermal contract resistance during the first stages of metal solidification process. II. Experimental setup and results". International Journal of Heat and Mass Transfer, 1999. 42(12): p. 2129. Machingawuta, N.C., Bagha, S., Grieveson, P. "Heat Transfer Simulation for Continuous Casting". In Steelmaking Conference Proceedings, 1991: p. 162-170. Metals Handbook, ASM International, Materials Park, OH, 1990, vol 2, pg 152-177. Moody, L. F. (1944). "Friction Factors for Pipe Flow", Trans. ASME, 66, 671-684. Muojekwu, C.A., Samarasekera, I.V. and Brimacombe, J.K.. "Heat transfer and microstructure during the early stages of metal solidification". Metallurgical and Materials Transactions B, 1995. 26B(2): p. 361-382. Nishida, Y., Droste, W. and Engler, S. "The Air-Gap Formation Process at the Casting/Mold Interface and the Heat Transfer Mechanism Through the Gap". Metallurgical and Materials Transactions B, 1986. 17B(4): p. 833-844. Peel, D.A. and Pengelly, A.E. "Pilot Plant Studies of Heat Transfer, Solidification and Resultant Structure of Continuously Cast Aluminum", in AIME Conference. 1970. Denver, Colorado. Petukhov, B. S., and Kirilov, V. V. (1958). "The Problem of Heat Exchange in the Turbulent Flow of Liquids in Tubes". Teploenergetika, 4(4), 63-68. Plunked, P.A. "Primary Aluminum Plants Worldwide - 1998: Part 1 - Detail". U.S. Department of the Interior and U.S. Geological Survey. July 1999. Available from the U.S. Geological Survey website, http://www.usqs.gov/. Prabhu, K.N., Kumar, S.T. and Venkataraman, N. "Heat transfer at the metal/substrate interface during solidification of Pb-Sn solder alloys". Journal of Materials Engineering and Performance (USA), 2002. 11(3): p. 265-273. Press, W.H. Numerical Recipes in FORTRAN: The Art of Scientific Computing. Cambridge University Press, 1992. New York Rabenberg, J.M., et al. "Determination of Material Properties and Thermal Bouundary Condtiions from Casting Trial on Alloy AA7075". in Internationl Congress "Continuous Casting". 2000. Frankfurt: WILEY-VCH Verlag CmbH. Rappaz, M.D., Drezet, J.L, Gandin, J-M, Jacot, A, Thevoz, P. 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Elsevier. 2000. Appendices Appendix 1 - Calculation of Water Cooling Heat Transfer Co-efficients 98 Appendix 1 - Calculation of Water Cooling Heat Transfer Co-efficients Industrial Mould To calculate the convective heat transfer co-efficient for water flowing through the mould, the local water velocity must be known. Fluid modeling (performed at Alcan research centre) of water within the mould region indicated that the local water velocity in the upper region of the water channel to be in the range 3 - 3.5 m/s; for the case of a total water flow rate of 60 m3/hr. For the other water flow rates, the local water velocity was linearly scaled according to this result. Doing so, the approximate local water velocities were calculated, along with the Reynolds numbers. Table A1 - Water velocities used for calculation of heat transfer co-efficients. Total Water Flow Rate (m3/hr) Local water velocity (m/s) Reynolds Number 50 2.75 6.12 x 10" 53 2.9 6.45 x 104 60 3.3 7.35 x 104 The Reynolds number were calculated from the following relation:. >' eq A1 The magnitude of the Reynolds number indicated turbulent flow. Assuming that the flow within the mould was fully developed and turbulent, the following correlation by Petukhov and Kirilov (1958) (as shown in (Bejan and Kraus, 2004) ) was used to calculate the Nusselt number (NuD) for each case : Appendix 1 - Calculation of Water Cooling Heat Transfer Co-efficients 99 N u d = ( / / 2 ) R e 0 P r 1.07 + 9 0 0 / R e D - 0 . 6 3 / ( l + 10Pr) + 1 2 . 7 ( / / 2 ) , / 2 ( P r 2 / 3 - l ) eqA2 valid for (4OOO < R e ^ < 5 x 1 0 6 ) The accuracy of the above equation has been stated to be within +/- 5%; however, the actual accuracy is expected to be lower then the stated accuracy when this co-relation is applied to non-ideal heat/fluid flow configurations. The friction factor (f), can be estimated using the relation developed by Moody (1944) (as shown in (Bejan and Kraus, 2004)): / * 0.046 R e ~ 1 / 5 , u s eq A3 valid for ( 2 x l 0 4 < R e D < 1 0 6 ) By definition of the Nusselt number, the calculated NuD values can be used to estimate the convective heat transfer co-efficient: Nu r>k "D ~ D eq A4 The final values used in the industrial inverse heat transfer model are given below. Table A2 -Heat transfer co-efficients used in industrial IHC model. Total Water Flow Rate (m3/hr) Heat transfer co-efficient (W/m2K) 50 9650 53 10100 60 11250 Casting Simulator Mould The same method was used to calculate the convective heat transfer co-efficient for water flowing through the mould, however; in this case the local water velocity was measured using flow meters attached to the mould water cooling plumbing lines. The values used in the model are given in the table below. Appendix 1 - Calculation of Water Cooling Heat Transfer Co-efficients 1 Table A3 -Heat transfer co-efficients used in casting simulator IHC model. Total Water Flow Rate (LPM) Heat transfer co-efficient (W/m2K) 15 6400 30 11700 

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