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Mathematical modeling of heat transfer in the meniscus region of the continuous slab casting mould Wang, Yan 1994

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Mathematical Modeling of Heat Transfer in the Meniscus Regionof the Continuous Slab Casting MouldbyYAN WANGB.A.Sc., The University of Science & Technology of Beijing, China, 1987M.Sc., The University of Science & Technology of Beijing, China, 1990A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF APPLIED SCIENCEinTHE FACULTY OF GRADUATE STUDIESDepartment of Metals and Materials EngineeringWe accept this thesis as conforming)therequired standardTHE UNIVERSITY OF BRITISH COLUMBIAFebruary, 1994©Yan Wang, 1994In presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.(Signature)__________________________Department of ‘%‘L&&L ,ikewti,FThe University of British ColumbiaVancouver, CanadaDate i??7A,-L 2c i9,94DE-6 (2J88)AbstractThe objective of this investigation was to characteristize the heat transfer phenomena related tothe Submerged Entry Nozzle (SEN) and its role on the heat transfer of the liquid steel in themeniscus region of the mould broad face. The investigation has been conducted based on aprevious plant trial at Stelco’s Lake Erie.A mathematical model, which includes the SEN and the liquid steel, was formulated. The heattransfer in the SEN was examined by performing a two - dimensional finite difference modelwith the Alternating Direction Implicit (ADI) method. The influences of the SEN on the steelheat transfer in the meniscus region was studied under various conditions. The heat transfer ofthe liquid steel was investigated (i) by a plug flow model for the liquid steel flowing through theSEN tube and (ii) by a one-dimensional finite difference model for the liquid steel in themeniscus region.The modeling results revealed that the SEN absorbs heat from the liquid steel both inside theSEN tube and in the meniscus region, and loses heat to the atmosphere through its exposedsurface above the meniscus; the liquid steel falling through the SEN tube has a temperature dropof about 2.4°C from the SEN entrance to exit for a SEN length of 0.7 m; about 30% of thesuperheat extracted of the liquid steel in the meniscus region is absorbed by the SEN. Manyfactors, such as the thermal properties of the SEN sleeve and body materials and the mould fluxinsulation depth and performance, have influences on the heat transfer of the SEN and then onthe heat transfer of the liquid steel in the meniscus. The distance between the mould broad faceand the SEN is also an important factor which influences the severity of the cooling effect of theliquid steel in the meniscus caused by the SEN heat transfer. With the shorter distance between11the mould broad face and the SEN, the cooling effect of the liquid steel is more pronounced. TheSEN tube length, especially the length above the meniscus, has an effect on the temperature dropof the liquid steel inside the SEN.The results of this work showed the importance of the heat transfer of the SEN regarding to thecasting process and provided guidelines for improvements on slab surface quality and operatingpractice.111Table of ContentsAbstract.iiTable of Contents ivList of Symbols viiiList of Figures xList of Tables xiiiAcknowledgment xivChapter 1 Introduction 1Chapter 2 Literature Review 42.1 The Continuous Casting Mould 42.1.1 General Features of the Continuous Casting Mould 42.1.2 Heat Transfer in the Mould 52.2 The SEN for Continuous Slab Casting 72.2.1 The SEN Design for Slab Casting 72.2.2 SEN Materials and Physical Properties 82.2.3 Effects of the SEN Heat Transfer on Steel Slab Surface Quality 92.3MouldFlux 102.3.1 Introduction to Mould Flux in Continuous Casting 102.3.2 Functions of the Mould Flux 112.3.2.1 Thermal Insulation and Oxidation Prevention 112.3.2.2 Inclusion Absorption 112.3.2.3 Lubrication at Strand/Mould Interface 122.3.2.4 Control of the Rate and Uniformity of Heat Transfer to the Mould..132.4 Quality Aspects of Continuously Cast Slabs 142.4.1 Oscillation Marks 14iv2.4.2 Longitudinal Midface Surface Defects 16Chapter 3 Scope and Objectives of the Present Work 29Chapter 4 Mathematical Models 314.1 The SEN Heat Transfer Model 324.1 .1 Assumptions in the Heat Conduction Model of the SEN Wall 324.1.2 Mathematical Formulation of Heat Flow in the SEN WaiF 334.1.3 Boundary Conditions 334.1.4 Solution of the Differential Equation 354.1.5 Input Datato the Model 354.1.6 Sensitivity Analysis 374.2 Mathematical Model of the Steel Flowing Through the SEN (Plug Flow) 384.2.1 Assumptions 384.2.2 Governing Equation 384.2.3 Initial Condition 384.2.4 Solution of Steel Temperature Drop 394.2.5 Input Data 394.3 Heat Transfer Model of Steel in the Meniscus Region 404.3.1 Assumptions for Steel Heat Transfer Model 404.3.2 Governing Equation of Steel Heat Flow 404.3.3 Boundary and Initial Conditions 404.3.4 Input Parameters 414.3.5 Meniscus Shape 424.3.6 Removal of Latent Heat in the Solidification Range 424.3.7 Calculation of Extraction Rate of Latent Heat and SuperheatRemoval 434.3.8 Calculation of the Average Drop in the Superheat Temperature ofSteel 44V4.3.9 Sensitivity Analysis .44Chapter 5 Model Predictions and Discussions 545.1 Models Predictions 545.1.1 Heat Transfer Characteristics of the SEN Wall 545.1.2 Steel Temperature Drop from the SEN Entrance to Exit 585.1.3 Average Temperature Drop at the Meniscus Region 585.2 Variables Affecting the Heat Transfer 595.2.1 Thermal Conductivity of the SEN Wall 615.2.2 Thickness of the SEN Wall 635.2.3 SEN Sleeve Length 645.2.4 Unmelted Mould Flux Depth 655.2.5 Depth of the Liquid Mould Flux 665.2.6 Steel Pouring Temperature 675.2.7 The SEN Tube Length 675.2.8 Distance Between the Mould Plate and the SEN 68Chapter 6 Conclusions and Recommendations 856.1 Conclusions from the Present Model 856.2 Suggestions for Future Work 88Appendix I 901. Correlations for Liquid Metal Convective Heat Transfer 901.1 Liquid Metal Flow Over Plane Surface ---Dissipation Neglected 901.2 Liquid Metal Flow Through Tube and Pipe 902. Heat Transfer Coefficient at Steel - SEN Interface 912.1 Outer SEN Surface ---Steel 912.2 Inner SEN Surface ---Steel 92Appendix II 94Effective Heat Transfer Coefficient 94viAppendix111.951. Heat Transfer Coefficient at Liquid Flux SEN Outer Wall Interface 95References 97viiList of SymbolsCp, Cp,, Cpa, Specific heat, J/kg°CD Distance, mDiiq Liquid flux pooi depth, mD501d Solid flux depth, mdt Time step, sg Gravitational acceleration, mIs2heff Effective heat transfer coefficient at SEN/atmosphere interface, W/m2°CHeat transfer coefficient at liquid flux/SEN interface, W/m2°CHeat transfer coefficient at liquid steel/SEN interface, W/m2°CK Thermal conductivity, W/m°CL Latent heat, kJ/kgLm Mould broad face width, mLmold Distance below the meniscus, mL0 SEN length, mLsieeve Sleeve length, mq, Q Heat flux, W/m2Qc(y) Heat flux along the mould broad face, W/m2Convective heat flux, W/m2Qrad Radiative heat flux, W/m2Q1 Rate of heat absorbed by the SEN from steel in the meniscus region, WR Resistance, oCm2/WR0 SEN inside radius, mT Temperature, °CTa Atmosphere temperature, °CviiiTjq Liquidus temperature, °CT01 Solidus temperature, °CT111 Initial temperature, °CT0 SEN temperature, °CTpour Steel pouring temperature, °CTsiag Liquid flux temperature at sintered/liquid interface, °CTsteei Steel temperature, °CTsmei Melting temperature of mould flux, °CAT Temperature drop, °CAT1 Steel temperature inside SEN, °CAT2 Average temperature drop of steel at the meniscus, °CAl’S Superheat temperature of steel, °CV Casting speed, misV5 Steel flowing velocity inside the SEN, misWm Mould narrow face width, mWmold Distance between the mould and the SEN, mSEN wall thickness, rnP Ps’ Pf Density, kg/m311 Viscosity of mould flux, poiseLaminar viscosity, kg/rn so Ferrite phase of steely Austenite phase of steel9 Circumferential coordinater Radial coordinatex Horizontal coordinatey Axial (longitudinal) coordinateixList of FiguresFigure:1.1: Schematic illustration of the continuous casting process 32.1: Schematic sections through an adjustable mould 202.2: Schematic representation of the thermal resistances to heat flow in mould 202.3: Schematic diagram showing the longitudinal section (parallel to the broad face) of acontinuous casting mould 212.4: A typical example of heat flux profiles at the narrow face and broad face (inside radius)of a slab caster 212.5: Effect of casting speed on the axial heat flux profiles at the narrow face of a slab casting..mould 222.6: Influence of the type of the mould flux on the axial heat flux profiles (narrow face) in aslab caster 222.7: Two kinds of SEN used in continuous casting of slab 232.8: Relationship between the occurrence of longitudinal cracks and immersion depth 232.9: Influence of refractory material in the bath level zone on the occurrence of longitudinalcracks [30] 242.10: Typical variation of the thickness of flux layers during a cast 242.11: Relationship between A1203absorption rate of the molten mould flux and basicity Bi 252.12: Change in viscosity of the molten mould flux as a function ofA1203content 252.13: The optimum range of solidification temperatures for slab casting of aluminum-killedsteels at speed of 1.0 to 1.7 rn/mm 262.14: Relationship between crystallization temperature and longitudinal crack index 262.15: The variation in 1) liquid film thickness, 2) heat transfer and 3) mould temperature as afunction of the parameter 272.16: Temperature distribution of molten steel in mould in depth direction 27x2.17: The effect of the fluid flow control on slab surface quality 284.1: A Typical SEN design used in modeling 474.2: Modeling domain and dimension of the SEN wall 474.3: Thermal conductivities of SEN materials as functions of temperature 484.4: Specific heat of SEN materials as functions of temperature 484.5: Steel flow pattern in the modeling plane 494.6: Axial surface temperature profile of SEN outer wall for different node sizes 504.7: Axial surface temperature profile of SEN for different heat transfer coefficients betweenthe steel and the SEN wall outer surface 504.8: Control volume of steel inside SEN tube 514.9: Thermal conductivity of steel as a function of temperature [12] 514.10: Enthalpy of steel as a function of temperature [12] 524.11: Calculation domain of steel heat flow model in mould 524.12: Assumed linear latent heat release in the mushy zone by artificially increasing thespecific heat 534.13: Heat flux profile along the mould broad face 535.1: Temperature contour of the SEN wall (standard case) 735.2: Temperature contour of the SEN wall 745.3: Predicted axial profiles of the SEN wall temperature at different depths from the SENouter surface (standard case) 755.4: Transverse temperature profile in the SEN wall at the meniscus (standard case) 755.5: Axial profiles of transverse heat flux in the SEN wall at different depths from the outersurface of the SEN (standard case) 765.6: Axial heat flux profiles in the SEN wall at different axial locations from the meniscus(standard case) 775.7: Calculated heat loss of steel to the SEN wall at the meniscus in different cases 785.8: Steel temperature drop inside the SEN tube in different cases 78xi5.9: Transverse temperature profiles at the meniscus with different thermal conductivities ofthe SEN sleeve and body 795.10: Axial temperature profiles at the outer surface of the SEN wall with different thermalconductivities for the sleeve and body 795.11: Axial temperature profiles at mid-thickness of the SEN wall with different thermalconductivities for the sleeve and body 805.12: Axial temperature profiles at the inner surface of the SEN wall with different thermalconductivities for the sleeve and body 805.13: The SEN wall transverse temperature profiles at the meniscus plane with different wallthicknesses 815.14: Axial temperature profiles at the outer surface (o), mid-thickness (m) and inner surface (i)with different wall thicknesses 815.15: Transverse temperature profile in the SEN wall at the meniscus for different sleevelengths 825.16: Axial temperature profiles at outer surface (o), mid-thickness (m) and inner surface (i) ofthe SEN for different sleeve lengths 825.17: Transverse temperature profiles in the SEN wall at the meniscus for different depths ofthe unmelted mould flux 835.18: Axial temperature profiles at the outer surface (o), mid-thickness (m) and inner surface (i)of the SEN for different depths of the unmelted mould flux 835.19: Transverse temperature profiles at the meniscus for different liquid mould flux depths 845.20: Axial temperature profiles at the outer surface (o), mid-thickness (m) and inner surface (i)of the SEN for different liquid mould flux depths 84xiiList of TablesTable:2.1: Chemical analysis ranges of SEN refractories 194.1: The Modeling Flow Chart 454.2: Variables Used in Models 465.1: Steel Temperature Drop Inside the SEN Under Different Conditions 705.2: Average Temperature Drop of Steel in the Meniscus Region with Different Distancesbetween the SEN Wall and the Mould Plate 715.3: Thermal Conductivity of the SEN Materials Used in Calculations 715.4: Variables tested in the model 72xliiAcknowledgmentI would like to express my sincere thanks to my supervisors, Dr. J.K.Brimacombe andDr. I.V.Samarasekera, for their invaluable guidance and advice throughout the course of thisresearch. The funding for this work from the Natural Science and Engineering Research Councilof Canada is greatly acknowledged.The help from Mr. Neil Walker is deeply appreciated. It is also my obligation and pleasure tonote that many friends in the Department of Metals and Materials Engineering gave me greathelp.Finally I would like to thank my husband and my parents for their constant support,understanding and encouragement throughout the course of this work.xivChapter 1 IntroductionFrom the middle of this century, the continuous casting of steel has become the most significanttechnology to replace traditional ingot casting. As illustrated in Figure 1.1, continuous steelcasting is performed with a water-cooled open-end copper mould which oscillates along the axisof the moving strand. During the continuous casting of slabs and blooms, the hot steel is pouredinto the mould from the tundish through a SEN (Submerged Entry Nozzle) made of refractorymaterial. Also, mould flux is used in continuous slab casting to provide lubrication between themould wall and the steel to control the heat transfer in the mould. The steel in the mould forms athin shell against the mould wall and gradually solidifies as the strand moves down through themachine. This process has been adopted widely in the world owing to its advantages of low cost,high yield, flexibility of operation and ability to achieve high quality products. Recently, as aresult of directly connecting the continuous casting and the hot rolling processes, more emphasishas been placed on the quality aspects of the cast product, especially the surface quality.Many researchers and engineers have investigated the formation of surface defects, such astransverse and longitudinal facial cracks and attempted to identify influencing factors.Transverse cracks often form at the base of deep oscillation marks. It has been shown that theformation of oscillation marks and many of the surface defects are related to meniscus heattransfer which is influenced by a number of factors. High and nonuniform heat flux in themeniscus region is the main reason for the formation of longitudinal cracks, while the mould fluxperformance, as well as heat transfer, determines the depth of the oscillation marks. Although asignificant amount of work has been done to study the influence of process variables, namelycasting speed, metal level fluctuation, steel fluid flow pattern, SEN submergence depth, andmould flux lubrication etc., the surface problems of cast products have not disappeared1completely. For example, several steel companies [32] have observed occurrences oflongitudinal cracks on the cast slab surface, and these cracks were obviously linked to the usageof the SEN. However, to the autho?s knowledge, insufficient work has been conductedpreviously to elucidate the linkage between the SEN and the slab surface problems. In most ofthe previous work carried out by many researchers, the influence of the SEN on the steel heattransfer, especially in the meniscus region, has been neglected.Thus, the primary objective of this work is to identify the influence of the SEN (material anddesign) on the heat transfer characteristics of steel in the meniscus region of the mould broadface, and to clarify the potential linkage between slab surface cracks, depth of oscillation marksand the SEN design. A mathematical model was formulated to study the heat flow inside theSEN wall, the steel flowing through the SEN and in the meniscus region of the mould. Thetypical heat flux density data for continuous slab casting obtained from a plant trial conducted atStelco’s Lake Erie Works was applied in the mathematical model. This study has led to a betterunderstanding of the role of the SEN in the continuous slab casting process and on heat flow andlubrication in the mould. It also provides guidelines for the improvement of slab surface qualityand operating practice.2Steel from TundishMeniscusVoter CooledCopper MoldLiquidPool Solid SteelShell..q-Woter Sprays— --Radiant CoolingFigure 1.1: Schematic illustration of the continuous casting process.3Chapter 2 Literature Review2.1 The Continuous Casting MouldThe primary role of the casting mould is to act as a heat exchanger with a high heat flux density1 MW/rn2 and to promote the formation of a solid shell. The mould provides support for thenewly solidified steel shell in the shape of a bloom, slab or billet. The surface quality and theshape of the cast product are strongly influenced by the design and operation of the mould.Besides all the roles mentioned above, the casting mould is also a chemical reactor whichseparates non-metallic inclusions from the liquid steel.2.1.1 General Features of the Continuous Casting MouldStraight and curved moulds are used in the continuous casting process with the latterdevelopment directed at reducing machine height. Whether moulds are curved or straight, theirbasic designs are the same. For continuous slab casting, the mould consists of two large platesfor the broad faces, and two narrow-face plates located between the broad faces. The narrowfaces (frequently only one) can be moved in and out to adjust the broad face width. As shown inFigure 2.1, the plates are supported by stiff water boxes with bolts. The water box controls thecirculation of the cooling water needed to dissipate the heat from the mould. Vertical coolingwater channels are machined on the back of the copper plates to enable cooling water to flowthrough it. The water boxes are connected to a steel frame on which the gear boxes for narrowface adjustment and clamping mechanism are mounted. Copper alloys are used as the mouldplate material primarily because of their advantages, such as high thermal conductivity.As the strand is withdrawn, the heat from the strand surface is transferred via the mould wall tothe cooling water. As the strand shell cools and shrinks, it moves away from the copper wall to4form an air gap which gives rise to a drop in the local heat extraction. In order to compensate forthe slab shrinkage, the slab mould plates are usually tapered to improve heat transfer. Unlike thebillet casting mould, the taper of the slab mould is only provided on the narrow faces because theshell contraction mainly occurs on the broad faces. As reported [41], tapers of 0.6 to 1% havebeen successful for the 700 mm long standard mould.Another feature in continuous casting is the mould oscillation which was a key factor inrendering the process feasible. The purpose of mould oscillation together with lubrication is toprevent the newly formed shell from sticking to the mould wall. In the past, a sinusoidal patternhas been employed for mould movement while, recently, some investigators [27] found that atriangular mould oscillation motion is even better than the old mode from the point view of slabsurface quality. The other important factor for mould oscillation is the negative-strip time. Thisis defined as the time period in which the downward velocity of the mould exceeds thewithdrawal speed of the strand. It is well known that the cast strand surface quality depends onthe negative strip time. Although a very short negative-strip time is desirable, Brimacombereported that a value of about 0.17 seconds may be a minimum to reduce sticker breakouts fromexperience.2.1.2 Heat Transfer in the MouldTo convert the molten steel into a solid semi-finished shape in the casting mould, the enthalpystored in the liquid steel must be removed. As shown in Figure 2.2, the heat from the steel istransferred to the mould cooling water via a series of thermal paths: conduction through the solidsteel shell (iv), conduction through the air gap(iii), conduction through the mould wall (ii) andconvection from the mould to the cooling water (i). Of all these, the air gap forms the largestresistance to heat flow ( 84% [75]), which results in a large temperature drop from the strandsurface to the hot face of the mould copper plate. In the slab caster, Figure 2.3, the mould/strandinterface is filled with a molten mould flux film which aids lubrication. One of the functions of5this flux film is to localize the shear stress between the mould and the strand brought about bythe oscillation of the mould and adjust the interface resistance to the desired level. Because ofthe infiltration of the liquid flux, an air gap does not develop in the upper part of mould becausethe flux fills the gap. The heat transfer in the flux film is very complex involving bothconduction and radiation. The overall thermal resistance between the strand and mould wasreported to be about 0.0004 0.0008 m2K!W [53].Strand surface quality is closely linked to heat transfer in the mould, especially in the meniscusregion. Uneven and high heat flux density was reported by several investigators [47, 52, 62] tocause the formation of longitudinal cracks. Other features, such as the depth of oscillationmarks, are also affected by heat transfer in the meniscus. Heat flux in the mould can becalculated from mould temperatures, measured by embedding thermocouples in the copper wall.A typical heat flux profile for slab casting calculated by Mahapatra [28] is shown in Figure 2.4.On both the narrow and broad faces, the heat flux density is highest at the meniscus, about 2.6MW/rn2in this case, while it decreases down the mould because of the air gap formation.The heat flux can be affected by a number of process variables. The main casting parameterscontrolling the heat extraction rate are the casting speed and the performance of the flux.Figures 2.5 and 2.6 show the heat flux density variations at different casting speeds and fordifferent lubricants. It is clear seen from Figure 2.5 that, with a casting speed increase from0.5 rn/mm. to 0.8 rn/mm., the heat flux at the meniscus increased more than 700 kW/m2. Also inFigure 2.6, an increase of about 450 kW/m2 in the heat flux density occurred when the lubricantwas changed from the high viscosity flux to the low viscosity flux. Besides these two factors, thesteel carbon content, metal level and the submergence depth of the SEN also influence heattransfer in the mould.62.2 The SEN for Continuous Slab CastingIn the continuous casting process, steel is transferred from the tundish to the casting mouldthrough a refractory nozzle. The submerged entry nozzle (SEN) has been widely used in thecontinuous slab casting process. In this practice, a mould flux is used in the mould to enhancelubrication and heat transfer between the mould plate and the strand surface as indicated earlier.The adoption of mould flux in the mould reduces operating problems, such as breakouts, andimproves product surface quality. Moreover, the working conditions around the mould area aresignificantly improved as there is less radiated heat and less metal splash from the steel streamand mould surface.2.2.1 The SEN Design for Slab CastingThe SEN’s used in the continuous slab casting process basically are of two types, as shown inFigure 2.7:1) The two-piece SEN: The upper section of the SEN is installed in the well block of thetundish, and the bottom section of the SEN is held in position against the upper section, as seenin Figure 2.7 (a). This type of SEN design allows the bottom section to be replaced with a newone during casting. However, a disadvantage is the joint between the sections, allowing airingress, even in the case of small gaps. Therefore, argon protection is used.2) The single piece SEN: In this design, the SEN is fitted to the tundish from the inside and cannot be replaced during the casting process, shown in Figure 2.7 (b).The geometrical shape of the SEN, as seen in Figure 2.7, is a ceramic tube with two or moreoutlet ports. A significant number of changes have been made mainly in the design of port angleand shape. Since the SEN material (usually alumina graphite) is attacked by mould flux,especially in the three phase zone (steel-mould flux-SEN), a flux line enhancement (also called‘sleeve’) in the meniscus region is used to protect the SEN from flux erosionlcorrosion. As7shown in Figure 2.7, both duplex and through-wall flux line enhancement are used [29,30]. Alsothe inlet head (throat) of SEN is enhanced to counteract the erosion from steel.The outlet port angle of the SEN is a key factor which influences the flow pattern of steel in themould. A number of investigators [11,20,30] have studied the flow pattern and heat transfer ofsteel inside the mould by physical and mathematical modeling. It is also reported [29] that theSEN with circular cross section and downward outlet ports is commonly used for the casting oflow carbon aluminum killed steels; there is also a move to a large cross section port in otherplants.2.2.2 SEN Materials and Physical PropertiesIn slab casting, the SEN is used not only to distribute steel from the tundish to the casting mouldwith a particular flow pattern, but also to protect the steel against contact with air, and deliverclean steel to the mould. Therefore, high wear-resistant, low porosity material is used for theSEN. The material also must be resistant to thermal shock.The main refractory used for the production of the SEN has been changed from fused silica tographitised alumina because of its good erosionlcorrosion performance. But the limitation ofgraphitised alumina still remains mainly in the area of the mould flux /steel/SEN contact zone.The graphitised zirconia was found to have even better resistance to wear and can reduce the rateof wear by a factor of 3 [29], and it is used in the flux line enhancement (sleeve). But because ofits adverse response to thermal shock, a well controlled pre-heating of the SEN is necessary toprotect SEN failure.As an alternative, graphitised magnesia can be used for the sleeve material [29]. This has lowercost and less critical pre-heating requirements than zirconia. Boron nitride is another choice. It8has been reported [30] that 10% BN can reduce the wear rate by a factor of 1.5 to 1.8. Table. 2.1shows the typical ranges of chemical compositions for the manufacture of SEN refractories.2.2.3 Effects of the SEN Heat Transfer on Steel Slab Surface QualityA number of studies have been undertaken on the effects of SEN design on slab surface quality.For example, a large amount of work was carried out on the port angle and the submergencedepth of the SEN [11, 30], because these parameters have significant effects on fluid flowpatterns and meniscus level fluctuations. They affect the entrapment of mould flux from themeniscus and the floating out of inclusions in steel. The work of Harris et al [40] showed that a150 upward port caused excessive surface turbulence at a shallow submergence depths, while a750 upward port angle promoted a quieter meniscus. Also, as the submergence depth decreased,the rate of mould flux entrapment increased. Submergence depths in the range of 100 mm150 mm were also examined [36], and it was observed that the incidence of longitudinal cracksincreased with an increase in the submergence depth of the SEN. This was considered to be dueto less heat reaching the steel meniscus from the SEN ports. This led to a cooled meniscus andencouraged the trapping of inclusions and gas bubbles. Hoffken et al [30] also found thesubmergence depth of the SEN had an appreciable influence on the occurrence of longitudinalcracks. As shown in Figure 2.8, with a submergence depth of around 120 mm, longitudinalcracks were found to be a minimum.The SEN material type also influences the strand surface quality. It was observed by Hofficen etal [30] that, as shown in Figure 2.9, under absolutely identical casting conditions, longitudinalcracking was a minimum when using the BN sleeve which has high thermal conductivity, whilethe greatest number of longitudinal cracks were observed when using the zirconia graphite sleevewith low thermal conductivity. Their explanation for this phenomenon was that, the thick-walledSEN has a large heat dissipating surface; the higher thermal conductivity of the sleeve increasesthe temperature of the entire SEN wall due to heat transfer from the steel, which thus reduces the9chilling effect of the SEN. Furthermore, this was explained [29] by considering the concept ofheat capacity. It was said that the SEN material with higher heat capacity enhances chilling ofthe mould flux in the vicinity of the SEN causing uneven melting of mould flux. This couldchange the mould flux lubrication between the mould and the strand surface resulting in theformation of cracks in the steel shell, such as longitudinal cracks.2.3 Mould Flux2.3.1 Introduction to Mould Flux in Continuous CastingMould fluxes used in the continuous casting process are usually fly-ash based powders, syntheticpowders or prefused and granulated materials. They usually belong to the system of CaO-Si02-A1203-Na-CaF.The main constituents are CaO and 5i02, and the ratio of CaO/Si02variesbetween 0.8 and 1.2 [16]. The mineralogical constitution of mould flux components hassignificant influence on the melting behavior of the lubricant. Carbon particles are also added tocontrol the melting rate. Some research has been conducted [16] to investigate the suitableamount, grain size and type of carbon in mould flux.As already shown in Figure 2.3, the mould flux is heated by hot steel at the meniscus andundergoes melting forming three different layers above the liquid steel meniscus: 1) an unmelted,dark, urireacted mould flux layer on top; 2) a carbon enriched or perhaps sintered layer in themiddle; 3) a liquid mould flux pool directly above the steel.The thickness of each layer can be monitored by immersing equal lengths of copper, aluminumand high carbon steel wires into the mould flux [48]. A typical variation of the thickness of fluxlayers during a cast is shown in Figure 2.10 It is reported [50] that a minimum thickness of25 imn of unmelted mould flux and 10 mm depth of liquid flux layer should be maintained10during the casting process. It was also proposed by Bommaraju [48] that the heat transfer fromthe SEN can accelerate the mould flux melting.The melted mould flux flows into the gap between the strand and the mould where the fluxsolidifies against the mould wall. Glassy and crystalline phases are observed in the solidifiedflux film. The solid flux layer formed against the mould wall in the initial stage of castingremains intact throughout the heat and has a decisive influence on the heat transfer, hence on thesurface quality of the strand [16]. A thin liquid film adjacent to the strand surface provides theactual lubrication.2.3.2 Functions of the Mould Flux2.3.2.1 Thermal Insulation and Oxidation PreventionThe mould flux spread over the steel meniscus gives good thermal insulation for the steel in themould. The unreacted mould flux (powder and sintered flux) provides a large thermal resistanceowing to its low thermal conductivity. As suggested by Mahapatra [28], the vertical heat fluxthrough various flux layers is as low as 40 kW/m2,while the heat flux in the horizontal directionthrough the mould wall is in excess of 2000 kW/m2. This solid mould flux layer prevents the‘bridging’ or solidification of the steel in the mould. The oxidation of steel is also prevented byinsulating the steel from the atmosphere. To maintain good insulation, a layer of ‘dark’, unmeltedflux must cover the steel surface in the mould completely at all times. As for good oxidationprevention and inclusion absorption, a liquid layer is also important.2.3.2.2 Inclusion AbsorptionThe mould flux can absorb harmful inclusions from the steel. The inclusions are assimilated bymould flux to form low melting point compounds which flow out of the mould with the flux.Alumina, due to its refractory nature, is the most harmful inclusion present in aluminum-killedsteel. The absorption rate of alumina inclusions is determined by the basicity of the flux, and11increases with an increase in the latter. The alumina pickup in the mould increases the fluxviscosity, then influences the heat transfer in mould and consequently the formation of surfacedefects. Therefore, the flux viscosity, liquid flux depth and flux consumption need to beoptimized to avoid excessive alumina content in the mould flux. Figure 2.11 shows therelationship between alumina absorption rate of the molten flux and basicity, while Figure 2.12shows the viscosity of molten mould fluxes at a temperature of 1300 °C as a function of aluminacontent. If the alumina can not be absorbed due to its large size, it may be entrapped in the steeland cause defects. Thus efforts must be made to avoid formation of large alumina clusters. AtInland Steel [48, 55], the alumina pickup for aluminum killed steel was reduced to 2 3%, andthe starting viscosity of the mould flux was increased to 1.1 poise so that an in-mould fluxviscosity of 2 2.5 poise (@ 1300 °C) was achieved and the incidence of longitudinal crackswas decreased.2.3.2.3 Lubrication at Strand/Mould InterfaceAs the mould oscillates and the strand moves downwards in the casting process, good lubricationis required at the mould/strand interface to prevent operational problems. In the upper part of themould, the infiltrated mould flux forms thin liquid flux film which provides hydrodynamiclubrication.With regard to the ability of a mould flux to lubricate, the thickness of the liquid flux film, themould flux viscosity and crystallization temperature play important roles. Emi [47] has foundthat the crystallization temperature has a direct effect on heat transfer in the mould andconsequently influences the surface quality of the strand. By decreasing the crystallizationtemperature and viscosity of a mould flux, better liquid flux lubrication is assured. The meltingrate of mould flux is another factor which also influences the flux lubrication. With lowermelting rate than the consumption rate, it is hard to keep an uniform liquid flux film between themould and the strand. Then the lubrication may fail.122.3.2.4 Control of the Rate and Uniformity of Heat Transfer to the MouldOne of the major functions of the mould flux is to control and provide uniform heat transferbetween the solidifring shell and the mould wall. Since the mould flux fills the gap, theconductivity across this gap is increased. In the upper part of mould, the liquid flux and strandsurface has excellent contact, while the contact between the solid flux and mould copper plate ispoor [42]. The thickness of the infiltrated flux film is a major factor which determines the heatflow to the mould, in addition to its effect on lubrication. Therefore, the heat extraction rate inthe mould can be better controlled by defining the desired properties of the mould flux.From a large number of studies [48, 51, 54], the mould flux viscosity, crystallization temperatureand solidification temperature have been found to be the major factors affecting the heat transferrate. The crystallization temperature determines how much solid flux film and liquid flux filmform between the mould and strand. Nakano et al [511 found that there was a close relationshipbetween the nonuniformity of heat removal and the product of casting speed, V, and fluxviscosity, q, for aluminum killed steel. In this case, the uniformity of heat removal was found tobe an optimum when the value of ri V is about 2 poise mlmin.. As shown in Figure 2.13,Bommaraju [48] suggested an optimum range for solidification temperature and viscosity forslab casting of aluminum killed steel, for the casting speed of 1.0 1.7 mlmin. In both cases, theviscosity of the mould flux was measured at a temperature of 1300 °C. The selection of thesolidification temperature of the mould flux is restricted by the occurrence of longitudinal cracksand the frictional forces. High solidification temperatures give rise to increased frictional forcesand a high propensity for sticker breakouts, while when the solidification temperature is too low,the heat transfer rate in the mould increases and leads to longitudinal cracks. It is also reportedin [54] that with high basicity, which results in the formation of more crystalline phase of mouldflux, and high solidification temperature, the overall heat flux density in the mould can bereduced. Therefore, longitudinal cracks are prevented more effectively.132.4 Quality Aspects of Continuously Cast SlabsSlab surface quality is very important because surface defects in the rolled product areunacceptable for many applications. As discussed earlier, the most common surface defectswhich occur in continuously cast slabs are transverse cracks and longitudinal cracks. Transversecracks usually form at the bottom of deep oscillation marks. It has been concluded that thesefacial defects and marks are initiated in the meniscus area and are related to the mould fluxperformance, casting parameters and steel casting temperature.2.4.1 Oscifiation MarksThe depth of oscillation mark is of concern since it influences slab surface quality. Theformation of transverse cracks is usually enhanced by the formation of deep oscillation marks.Segregation of phosphorus, manganese and entrapped mould flux which enhance crackformation, are found in the base of oscillation marks [33]. The oscillation marks increase theunevenness of the air gap and then lead to the nonuniform heat transfer. The uneven solid shellgrowth caused by a variation in heat transfer around the periphery of the slab may lead to abreakout during casting because of local shell thinning.A number of mechanisms for oscillation mark formation have been proposed in the literature [25,33,57,58,60]. Saucedo [25,60] and Tonomo et al [57,58] have suggested that the formation ofoscillation marks is governed by the partial solidification of the meniscus, or direct contact of thesteel with the mould. With this mechanism, they explained the formation of regular and irregularoscillation marks, but they were unable to rationalize the observed influence of mould flux onoscillation marks. The other mechanism proposed by Takeuchi and Brimacombe [33] is basedon the behavior of the partially solidified shell due to pressure developed in the flux channel dueto mould oscillation. A positive pressure is formed during the negative strip time and it is muchlarger than the shear stress acting in the flux channel. The meniscus is pushed away from mould14during the negative strip time and is drawn back towards the mould wall by negative fluxpressure during the positive strip time. Overflow may occur to form hooks at the beginning ofthe positive strip if the meniscus is partially solidified; otherwise overflow does not occur. Thepressure in the flux channel is influenced by the physical properties of the mould flux, themeniscus shape and flux rim thickness [28,331. They also found that the casting speed, metallevel fluctuation, as well as mould oscillation characteristics influence the formation ofoscillation marks.From the literature, it is very clear that the formation of oscillation marks is closely related to theinitial solidification of steel in the meniscus. Many studies have been carried out to identifymeasures to minimize the depth of oscillation marks. Birat et al [24] and Saucedo et al [25]proposed that the meniscus heat transfer should be reduced to maintain a ‘hot meniscus’. This canbe achieved by modification of the mould, such as welding an insert in mould in the meniscusregion [25]. Mould oscillation parameters also have a strong influence. Wolf et al [27] foundthat, for a wide casting speed range, the triangular mould oscillation motion with stroke changeduring casting is preferable for better slab quality. Ultrasonic mould vibration is also believed tohave the potential of improving lubrication. Mould flux performance is another important aspectbecause it influences heat transfer in the mould. Mahapatra et al [28] found that the flux rim,formed in the meniscus region, influences the depth of oscillation marks; a thicker flux rimresults in deeper oscillation marks. Tada et al [611 also examined the influence of flux rim sizeon the positive pressure developed in the flux channel and their results indicated that an increasein the size of the flux rim will increase the pressure and thereby enhance the formation ofoscillation marks. Therefore, the selection of mould flux for continuous casting becomesimportant.152.4.2 Longitudinal Midface Surface DefectsLongitudinal midface cracking is a particular problem in continuously cast slabs. It has beenfound that steel grades with a carbon content around 0.1% are most prone to longitudinal cracks[49]. The formation of longitudinal midface cracks is believed to be caused by thermal stressesin the shell resulting from differences in the thermal contraction of the &-ferrite and austenitephase [16]. Mills et al [16, 64] have proposed that the longitudinal cracks can be minimized byproducing a thin, uniform shell in the meniscus region. In other words, low and uniform heatflux in the meniscus region will benefit the reduction of longitudinal cracks. This point has beensupported by a number of researchers [47, 53, 54, 62, 64, 65].Heat transfer in the mould is affected by a number of factors from casting conditions to mouldflux performance. A considerable amount of research has been directed at finding ways toimprove slab surface quality. The ‘hot top mould’ is the most direct way of reducing heat flux inthe meniscus, and consists of introducing an additional heat resistance between the mould andthe strand. The first method is to machine vertical grooves on the mould wall, but difficultiesstill remain in designing, machining and maintaining the grooves. The second method is tomodify the copper mould by covering the upper surface with an insert which is made of lowthermal conductivity material [56]. In addition to the casting speed which was discussed earlier,the mould flux crystallization temperature was also considered an important factor by severalauthors [28, 47, 52, 53]. Figure 2.14 shows a strong correlation between crystallizationtemperature and longitudinal crack index. This phenomenon was related to the formation of airgaps in the mould. Yamauchi et al [53] found that high basicity flux with high solidificationtemperature is effective in reducing heat transfer and minimizing the longitudinal cracks. This isbecause that high basicity mould flux reduces thermal conductivity due to a structure change.Many authors have reported that the uneven flow of liquid flux from the meniscus into theshell/mould boundary and uneven heat extraction to the mould along the width direction result in16the local delay of shell formation and cause longitudinal cracks [47, 51, 52, 62, 64, 65]. Theuniformity of the initially solidified shell is strongly influenced by the performance of mouldflux and steel temperature distribution in the mould. Nakato et al [52] reported that thelongitudinal cracks occur at the position where the copper plate temperature is a minimum in thewidth direction, and the occurrence of longitudinal cracks increases with an increase in the timederivative of the temperature variation in the copper plate. Maintenance of an uniform and stableflux film between mould and strand is essential for obtaining uniform flow around the perimeterof the mould. In order to minimize the fluctuation in heat flux, Mills [64] recommended that it isnecessary to minimize the variation in both the flux infiltration and metal level control.Optimum surface quality can be obtained by choosing the casting speed and flux viscositycarefully; according to Mills, the value of ri J’ is between 1 and 3.5 poise rn/mm.. Nakano etal [51] also reported an optimum range of 3 and 7 poisem2/min., for Figure 2.15 showsthe variations in liquid flux film thickness, heat transfer and mould temperature as a function ofthe parameter r1V. This Figure clearly demonstrates that, in the optimum range of thevariation in heat flux and mould temperature is a minimum and the occurrence of longitudinalcracks can be minimized. This finding agrees well with the results of Nakato et al [52]. Theuneven flow of mould flux at meniscus can also be caused by improper design of SEN. Hofficenet al [30] has observed that a thick-walled SEN. which has a large surface for heat dissipation,could cool the steel between the mould broad face and the SEN, and influence the local meltingrate of mould flux.Meniscus cooling or freezing is detrimental to the formation of longitudinal cracks, as well as tooscillation marks. The steel superheat temperature in the meniscus is a definite factor whichaffects the crack formation. Recently, Yoshida and co-workers [62] found that the longitudinalcrack index is significantly influenced by the steel meniscus temperature distribution which wasaltered by changing the fluid flow pattern through the electromagnetic braking system (EMBr).Figures 2.16 and 2.17 are the temperature distribution of molten steel in the meniscus region, and17the effect of fluid flow (Types of A, B and C) on slab surface quality, respectively. Type A hasthe same fluid flow core as the conventional EMBr system; in type B, the EMBr brakes the SENconvection current except the flow in the vicinity of the meniscus, while in type C, the EMBrbrakes the downward flow in the mould only. This is a typical example of the relationshipbetween the meniscus cooling and longitudinal cracks. It is clearly seen from these two figuresthat the worst longitudinal cracking happened in type A which had the lowest steel temperaturein the meniscus.18Table 2.1: Chemical analysis ranges (pet.) of SEN refractories [29].Material Fused Silica Graphitised Graphitised GraphitisedAlumina Zirconia MagnesiaA1203 nil 40.0 -71.0 nil 0 - 8.0Si02 99.5 0 - 25.0 nil 0 - 10.0SiC nil 0 - 9.0 0 - 13.0 nilZr02 nil 0 - 7.0 63.0 - 82.0 nilMgO nil 0 0 - 3.5 54.0- 86.0C nil 23.0 - 34.0 13.5 - 19.0 12.0 - 25.019I Ig,aerIII[iJUa) Vertical sectionb) Horizontal sectionr 1[ii) (iiij [iv)Figure 2.1: Schematic sections through an adjustable mould [41].1500Q0Q[i] (iii) [IJ DistanceFigure 2.2: Schematic representation of the thennal resistances to heat flow in mould.20rrL_SubmergedWater-Cooled till NoZzleCopper MoldFlux IRim’________Molten FluxScidified Shell‘Flux—___________‘Film___——___Liqd Steel —Oscillation—1— — — —MarkStrand WithdrawalFigure 2.3: Schematic diagram showing the longitudinal section (parallel to the broad face) of acontinuous casting mould [50].2400 -_ _ __ __ __ _______-— Narrow Face--BroadFace-(Inside Radius)E1600-D--Metal level8000-- I I I0 200 400 600 800Distance Be’ow Top of Mou’d (mm)Figure 2.4: A typical example of heat flux profiles at the narrow face and broad face (insideradius) of a slab caster [28].212800 —___2400— Speed.50 minLz0 200 400 600 800Distance Below Top of Mould (mm)Figure 2.5: Effect of casting speed on the axial heat flux profiles at the narrow face of a slabcasting mould [281.2400 -______________________________________________________________I Low viscosity— High viscosityg 1600E1200 \S.—LL Metal Level/4000 I I I I0 200 400 600 800Distance Below Top of Mould (mm)Figure 2.6: Influence of the type of the mould flux on the axial heat flux profiles (narrow face) ina slab caster [28].22ThRCU3H WALL SLN3LINE ENHALICEMENTThROATE1’-IANCEMENTFigure 2.7: Two kinds of SEN used in continuous casting of slab [29).Cl)QC-)a00Cl)0Cr1Figure 2.8: Relationship between the occurrence of longitudinal cracks and immersiondepth [301.WP[EX SlAGUNE ENIW’ICEMENTSUMP(a) Two - piece (b) One - pieceo 2 4 6 8 10 12 14 16 18 20 22Depth of Submergence (D) in cm23crqECDrjcrc CDSlabs withLongitudinal Cracks in%“CDpCDCDThicknessofLayers(mm)oC)CD g 0o(tC-)0zCD0 3CDCDCDC,,5. 0 C/)IICD0N 0CD C,,0 CD-CD00CD CD 0MCA)00000Figure 2.11: Relationship between A1203 absorption rate of the molten mould flux and basicityBi [51].U,E0wa:z00a:0U)0840,A,,-r’7,— .- /7 /,_—:_,,—-- . ——.—— -. .- ——.--. —1.0 1.5 2.0BASICITY B— 1 .53CaO + 1.51 MgO+ I .S4Na2O+3.55Li+I .53CaF2— 1.48SiO+O.10A1032.5C.)C)C)()11>-I-U)0C.)U)>85420//77JP147— P15zz—[_0 5 10 15 20A120 (%)Figure 2.12: Change in viscosity of the molten mould flux as a function of A1203content [51].25Figure 2.13: The optimum range of solidification temperatures for slab casting of aluminum-killed steels at speed of 1.0 to 1.7 mlmin. [48].1120 1140 1160 1180 12C0 1220 1240CRYSTALLIZATION TEMPERATURE (C)Figure 2.14: Relationship between crystallization temperature and longitudinal crack index [47].Solidification Temperaturew0z00zaaz0-3264U(c)g p° 30EO EoCC 0o 1000 C> 00 2 4 6TV (poiseim mtn1J)Figure 2.15: The variation in 1) liquid film thickness, 2) heat transfer and 3) mould temperatureas a function of the parameter ‘i V [64].(mm)U,D0U,El00C,C)20-30 -20 -10 0Relative temperature in mould withrespect to that in turidish (°C)Figure 2.16: Temperature distribution of molten steel in mould in depth direction [62].27ECu,‘i-u,0-x2 .- .rEC—0—-C •0>0015 (b)10.00 2 4flV (poise[m mi-i1))0.1 I2 4 6TV (poiseLm mintJ)Figure 2.17: The effect of the fluid flow control on slab surface quality [62].28Chapter 3 Scope and Objectives of the Present WorkFrom the literature, it is evident that continuously cast slabs continue to be plagued by a numberof quality problems. It is also apparent from the literature that the formation of longitudinalfacial cracks is governed by heat transfer, which in turn is influenced strongly by mould fluxlubrication, in the meniscus region of the mould. Any factor which may influence the heat flowin this region will have an effect on the slab surface quality. As suggested by several researchers[28, 33, 34], the oscillation marks and midface longitudinal cracks are all related to the heattransfer of steel in the meniscus region which in turn is affected by the performance of mouldflux in the meniscus region. The submerged entry nozzle has been observed to influence theoccurrence of the slab surface defects by virtue of its design and the materials employed [30, 32].The reason for this is still not clear owing to an inadequate investigation of heat transfer of theSEN. A study of the influence of the SEN on heat transfer in the mould of a continuous slabcaster, therefore, is called for.Consequently, the main purpose of this research was to characterize heat transfer phenomenonrelated to the SEN and its role on the formation of slab surface quality problems. To accomplishthis goal, a mathematical model was formulated, and the following phenomena were examined:(1) The heat transfer in the SEN wall was examined, in particular heat transfer from thesteel to the SEN wall at the meniscus was determined.(2) The heat flow to the SEN tube from the steel as it flows from the tundish to the mouldwas investigated; the amount of heat loss to the atmosphere through the SEN wall was calculatedin the form of a steel temperature drop.29(3) The effect of heat loss to the SEN wall in the meniscus region and from the steelinside the SEN tube was further studied to assess the extent of cooling of the steel meniscus.(4) The influence of slab thickness, which determines the distance between the mouldplate and the SEN wall, on meniscus cooling by the SEN has been determined.30Chapter 4 Mathematical ModelsMathematical models were developed to study the interrelationship between heat transfer to theSEN wall and the steel temperature. The SEN in the current mathematical model, shown inFigure 4.1, is commonly used in North America; the SEN body is made of Alumina Graphite andthe SEN sleeve is made of Zirconia Graphite. The longitudinal midplane of the broad face of theslab casting mould was selected as the plane of interest, because the distance between the SENand mould broad face is the shortest and the SEN is likely to have the most significant influenceon the steel heat transfer in this plane. Due to symmetry, only half of this plane needs to bemodeled as shown in Figure 4.2. The slab mould size and other casting parameters are takenfrom earlier data [281.The mathematical model described above consists of three sub-models:1) The Model of the SEN Wall:This sub-model was used to calculate the temperature profile of the SEN wall. The heat fluxprofile along the inner surface of the SEN wall was calculated and employed as the inputboundary condition for the model of steel inside the SEN. The heat removed by the SEN fromliquid steel in the meniscus region is also an output which was used in the heat transfer model ofsteel in the meniscus region to calculate the average drop in superheat temperature of the steel.2) The Steel Model Inside the SEN:In this sub-model, the temperature drop of the steel from the top of the SEN (where the steeltemperature is assumed to be the pouring temperature) to the SEN exit was calculated. Inprevious studies, this temperature drop of steel inside the SEN has always been neglected.However, it is essential to evaluate the magnitude of this temperature drop.313) The Model of Steel Heat Transfer in the Meniscus Region:In order to examine the influence of the SEN on the steel temperature in the meniscus region, aheat transfer model of steel was developed. The average drop in superheat temperature of steelin the meniscus region caused by heat transfer to the SEN and mould cooling was calculated. Inthis model, the total steel superheat temperature drop caused by the SEN and the mould wasassumed to be the summation of the temperature drops in sub-models (2) and (3).These three sub-models are connected through the boundaries; Table 4.1 shows the flow chart ofthe model.4.1 The SEN Heat Transfer ModelThe principal mode of heat flow in the SEN wall is conduction in the through thickness andlongitudinal directions. The heat transfer of the SEN changes significantly in the longitudinaldirection around the steel meniscus and mould flux insulation region, because of differentboundary conditions along the outer boundary of the SEN wall. Far away from the steelmeniscus and mould flux insulation region, the heat transfer through the SEN is primarily one-dimensional. Therefore only part of the SEN wall, shown in Figure 4.2 as A-B-C-D-E-F-G, wasmodeled.4.1.1 Assumptions in the Heat Conduction Model of the SEN WallThe following assumptions have been made in the SEN wall heat transfer model.(1) Heat transfer inside the ceramic (SEN wall) is by conduction only.(2) The SEN body and sleeve are in perfect contact, thus the interface resistance RO.(3) The heat loss from the SEN wall to the atmosphere is by convection and radiation.(4) Heat transfer is uniform in the angular directions of the SEN tube (axial symmetry).32(5) The SEN is under steady state during the casting process.4.1.2 Mathematical Formulation of Heat Flow in the SEN WallThe differential equation which governs the SEN wall heat transfer, in the cylindrical coordinatesystem under steady state, is given by,Ô2T 1 aT 1 Ô2T 62T—+——+———+-——=O (4.1)2rãr r2ô0 2Assuming axial symmetry, the equation becomes,82T 1 aT Ô2T—+———+———=O (4.2)2 raray2Where, the coordinates are,r: radial coordinate.0: circumferential coordinate.y: axial coordinate.4.1.3 Boundary ConditionsThe Modeling domain of the SEN wall is shown in Figure 4.2. As stated before, the heat transferin the SEN wall in the steel meniscus region is likely to have influence on steel temperaturedistribution and slab surface quality. Therefore, the portion of the SEN wall which includes thesteel meniscus and mould flux insulation region is of most interest. The corresponding boundaryconditions are:A-B: Steel/SEN wall interface: r=r0(R y=O -L0/2,= htn(I;teei(Y)—70()) (4.3)r r=r0B-C: Liquid flux/SEN wall: r=r0(R W0), y=O=hsn(I;iag(Y)—Ioz(Y)) (4.4)r=r033where, h: heat transfer coefficient at liquid flux - SEN outer wall interface (naturalconvection assumed, see appendix III).Tsiag: liquid flux temperature at sintered flux -liquid flux interface was taken to beat 1200 °C.C-D: solid or unmelted mould flux/SEN wall interface:r=r0=(R+W,),(D,jq+D0ijj)very poor contact is assumed,=0 (4.5)r r=r0D-E: Ambient/SEN wall interface: r=r0=(R+W0), Y=(Diiq+Dsoiid)an effective heat transfer coefficient is used to account for both convection and radiationheat transfer.Kf-j = Qconv + Qrad =1’eff(Ta —10()) (4.6)r=r0where: heff effective heat transfer coefficient ( see appendix II)., atmosphere temperature.F-G: Hot steel/SEN inner wall: r=r=R0,y=-L0/2 L,/2,K =h(T(y)—7(y ) (4.7)r rrE-F: y=L0/2, G-A:y= -L0/2, and r=r1Based on the prior calculations, one dimensional heat transfer across the SEN wall isassumed in these two boundaries.=0 (4.8)T(y), temperature of steel inside the SEN at the corresponding position. The value of T(y)is calculated in the sub-model of hot steel flowing inside the SEN.344.1.4 Solution of the Differential EquationEquation (4.2) which describes the heat flow in the SEN wall was solved numerically with therelevant boundary conditions, equation (4.3) (4.8), by employing a finite difference technique.The SEN wall was divided into a large number of nodes and heat balances were performed oneach control volume. Therefore, an algebraic equation is generated for each node. TheAlternating Direction Implicit method (ADI) was chosen to solve the set of equations, because ofits stability and fast convergence. The SEN temperature profile and the heat absorbed by theSEN from the liquid steel in the meniscus region, Q1, are calculated. Also the heat flux dataalong the SEN inner boundary is stored and was used as an input to the steel model inside theSEN.4.1.5 Input Data to the Modela) The SEN Shape and Size:The SEN used for continuous slab casting mainly consists of the SEN body and the SEN sleevewhich is designed for the SEN wall protection from the mould flux corrosion as indicated earlier.There are different designs for SEN in different companies as discussed in Chapter 2, shown inFigure 2.7. In the current model, a simple SEN design shown as in Figure 4.1 is used. Themodeling domain and size are shown in Fig 4.2.b) Physical Properties of the SEN Materials:The variation of thermal conductivities of the SEN body material and the SEN sleeve materialwith temperatures are shown in Figure 4.3. Figure 4.4 is the specific heat data of the SENmaterials. These data were obtained from one of the SEN suppliers [13].35c) Heat Transfer Coefficient Between the outer Surface of the SEN Wall and Ambient:At the interface between the outer surface of the SEN wall and the air, heat is transferred mainlyby radiation and convection as well. The heat transfer coefficient is a strong function oftemperature. The detailed calculation of heat transfer coefficient is given in Appendix II.d) Heat Transfer Coefficient Between the Mould Flux and the SEN Wall outer Surface:Because of the loose packing of the mould flux and the poor contact between the SEN wallsurface and the unmelted mould flux, the interface resistance is assumed to be infinity. However,at the interface of liquid flux and the SEN, the heat transfer cannot be ignored and naturalconvection is assumed. The calculation of the heat transfer coefficient is illustrated in AppendixIII.e) Heat Transfer Coefficient Between Liquid Steel and the SEN Wall Surfaces:I) Interface between the liquid steel and the outer surface of the SEN wall in the meniscusregion.The heat transfer coefficient between the steel and the outer surface of the SEN wall is assumedto be constant and calculated at the interface which is in the plane of interest. According to fluidflow calculations [11], the direction of the steel flow in the plane of interest is uniformlydownwards as shown in Figure 4.5. Therefore, the influence of forced convection in this regionon heat transfer is negligible.II) Interface Between steel and the inner surface of the SEN wall.Inside the SEN tube, it is assumed that the steel is well mixed radically and in plug flow axially.The velocity of the molten steel through the SEN was calculated from the casting speed.Calculation of the heat transfer coefficient at the molten steel - inner SEN wall is shown inAppendix I.361) Steel Temperature at the Outer Surface of the SEN:The steel temperature along the SEN outer boundary in the meniscus region was calculated in themodel of steel in the meniscus region.4.1.6 Sensitivity AnalysisIn order to examine the effects of influencing factors, such as node size and heat transfercoefficient, on the accuracy and stability of the computations, calculations were performed undervarious conditions.1) Node sizeThe accuracy of the solution depends on the node size used in the finite difference mesh. Inorder to find the appropriate node size, the temperature of the SEN wall was calculated fordifferent mesh sizes; the effect of the total number of nodes on the SEN wall outer surfacetemperature is shown in Figure 4.6. It can be seen from this figure that the variation in the SENwall temperature becomes very small with further refinement of mesh size when the nodenumber is beyond 1335 (15 * 89); the dimensions of the finite difference nodes are 1.8 mm in boththe thickness (r) and the longitudinal (y) directions.2) Heat Transfer Coefficient Between the Steel and the Outer Surface of theSEN WallAs mentioned earlier, the heat transfer coefficient between the steel and the outer surface of theSEN wall was assumed to be constant. However, because of the differences in steel flowconditions around the SEN outer surface, the heat transfer coefficient varies with the steel flowpattern. Figure 4.7 shows the calculated temperature profiles along the SEN wall outer surfacefor different heat transfer coefficients. Thus it is clear that the variation in the SEN walltemperature is negligible. Therefore, a constant value of heat transfer coefficient could beemployed in the modeling.374.2 Mathematical Model of the Steel Flowing Through the SEN (Plug Flow)The magnitude of heat flow from the steel to the SEN inner wall was computed with the aid of anunsteady state heat transfer model for the steel. The heat flux along the SEN wall inner surface,which was calculated from the SEN wall model, was an input boundary condition to the steelmodel.4.2.1 AssumptionsThe assumptions made in this model are as follows:(1) Steel flow through the SEN is well mixed in the radial direction and in plug flow axially.(2) Steel flows at a constant velocity inside the SEN.(3) In the direction of the steel flow (y), heat transferred by conduction is negligible compared toheat transferred by bulk flow.4.2.2 Governing EquationConsidering the control volume shown in Figure 4.8 to be moving with the liquid steel at thesame velocity, the heat balance on this infinitesimal volume results in the following equation,pCp2L= Q = hffi(T—Tfl0(y)) (4.9)where: R0: SEN inside radius (m).Q: heat flux to SEN inner wall (W/m2).dt: time step and,dt= (4.10)vs4.2.3 Initial ConditionSince the calculation of steel temperature begins from the SEN entrance, the initial temperatureof the steel was taken to be the pouring temperature, Tour•IniTpour (4.11)384.2.4 Solution of Steel Temperature DropEquation (4.9) was solved easily with a simple program. At distance ofy from the SEN top, stepof Ay , the temperature of steel is:T(y)=T(y—Ay)—2Q At (4.12)PCPROZwhere: At is transferred from Ay, At =VsV is the steel velocity inside SEN.The temperature drop of steel from the SEN top to its bottom can be calculated as:A7 = Tpour — T(L0) (4.13)4.2.5 Input Dataa) Physical Properties of SteelThe physical properties of steel used in this study were taken from the literature [10]. Figure 4.9and 4.10 show the thermal conductivity and enthalpy of steel as a function of temperaturerespectively.b) Steel Flow VelocityThe time step, At, is related to the SEN length and the velocity of steel inside the SEN. Thevelocity of steel inside the SEN, V was calculated from the casting speed, the cross-sectionalarea of the mould and the cross-sectional area of the SEN and is shown in Appendix I. In thestandard case, the velocity of the steel inside the SEN is about 1 mIs.394.3 Heat Transfer Model of Steel in the Meniscus Region4.3.1 Assumptions for Steel Heat Transfer ModelThe modeling domain for steel heat flow is shown in Figure 4.11. The assumptions made in themodel are as follows:1) Heat transfer in the steel is by conduction only.2)Heat transferred by conduction in the casting direction is negligible compared to the heattransferred by bulk flow.3) The steel outside the SEN moves downwards at casting speed of V.4)Heat is extracted from the steel by cooling water passing through the mould.5) The latent heat is released in a linear fashion over the solidus and the liquidus temperaturerange.4.3.2 Governing Equation of Steel Heat FlowA one-dimensional unsteady state heat flow model, which is applicable to a slice of the strand ofunit thickness moving at the casting speed, was adopted to study the steel heat transfer in themeniscus region. The governing equation for the steel heat transfer model is,(4.14)dx dx dtwhere: K—f(T), thermal conductivity of steel (as in Figure 4.9).Cp=f(T), specific heat of steel (as in Figure 4.10).p. density of steel (constant number as 7200 kg/rn3).To solve equation (4.14), the finite difference method was chosen and one initial condition andtwo boundary conditions are required.4.3.3 Boundary and Initial ConditionsBoundary Condition:(1) Steel/mould interface, x=O,40=h11(T—Tnoz(y)) (4.15)dx(2) Steel/SEN wall interface, XWmold= h(T— Tnoz(y)) (4.16)Initial Condition:The initial temperature of steel at the meniscus is crucial to events in the meniscus region. Theconventional assumption, which is that the steel temperature at the meniscus is equal to the steelpouring temperature, is incorrect since the steel loses heat to the SEN and the mould prior toreaching the meniscus region. Thomas et al [11] have reported that the depth of submergenceand port angle of the SEN affect fluid flow as well as the temperature of the liquid steel at themeniscus. So, in the current model, the initial temperature of steel was assumed to be,(4.17)where: AT: temperature drop during travel from the SEN to the meniscus.4.3.4 Input ParametersThe values of thermo-physical properties of liquid steel, such as thermal conductivity, specificheat, density, and latent heat, were taken from the literature [101. The casting conditionsincluding casting speed, mould size, steel pouring temperature, steel solidus and liquidustemperatures were also obtained from literature[281. The heat flux boundary condition used inthe model was taken from an earlier study [281 and is shown in Figure 4.13. The data of physicalproperties for steel are shown in Figure 4.9, and Figure 4.10. Other details on the SEN are givenin Table 4.2.414.3.5 Meniscus ShapeThe ‘meniscus ‘refers to the curved liquid in contact with the mould, which is shaped by surfacetension effects. The vertical distance from the horizontal metal level, y, can be calculated byusing the following equation [33]:2 2+ ,J2a2—x=—/2a—y + In +0.3768a (4.18)2 ywhere, p the density of steel,Pf: the density of liquid mould flux,a: interfacial tension, and,a2 2a (4.19)(P5— f)gx: is the distance to mould surface in the horizontal direction.y: is the distance below the meniscus in the longitudinal direction.The vertical depth of the curved meniscus for steel is about 8 to 10 mm from equation (4.18).This number is used as the modeling length, Lmould, in the steel heat transfer model in themeniscus region.4.3.6 Removal of Latent Heat in the Solidification RangeThe precise manner in which the latent heat of fusion is released within the solidus and theliquidus temperature range is unknown due to the complex nature of solidification in the mushyzone. Owing to the fact that the latent heat of fusion is of considerable magnitude whencompared to the sensible heat and superheat of steel, the mathematical treatment of the removalof latent heat from the melt during solidification is crucial and could have a significant influenceon the model predictions. In the current model, the latent heat of fusion is incorporated byartificially increasing the value of the specific heat in the mushy zone as shown in Figure 4.12.The value of modified specific heat in the mushy zone is given by the following equation:42Cp11, = cp+ L (4.20)2iq — T01To ensure latent heat (L) was not under estimated for each node during solidification, a smallmesh size and time step was used in calculation.4.3.7 Calculation of Extraction Rate of Latent Heat and Superheat RemovalEvaluation of latent heat extraction:During casting process, a thin solid shell close to the mould is formed due to the heat extractionby mould. Also there is a mushy zone where both liquid and solid steel coexist adjacent to thesolid shell.(1) In the solid shell, latent heat is extracted totally during solidification and it equals to:Qiat = LpV0A = LpVTHsol (4.21)where: L: latent heat of steel.V: casting speed.p: density of steel.THsol: solid shell thickness.(2) In the mushy zone, only a portion of the latent heat is released for each node. The total latentheat extracted in this region is:miiqT1. —T(x)Qiat — PVC J— TLdx (4.22)iiq solwhere: THliq: solid shell thickness plus mushy thickness.Evaluation of Superheat Extracted by Mould:The superheat content at the meniscus and at the exit of the modeling domain are calculatedseparately as:Qsup_in = ATsPCPVCWm01d (4.23)43=pCpV.i;:: (T(x) — Tiiq )dx (4.24)then, superheat heat extracted by mould is:= Qs_m — Qsup_out (4.25)where: Al;: superheat temperature.Wmould: distance from mould to SEN at meniscus.4.3.8 Calculation of the Average Drop in the Superheat Temperature of SteelIn the meniscus region, the average drop in the superheat temperature of steel, AT2, is calculatedby considering the superheat extracted by the mould, Q, and the heat taken by the SEN, Q1.Q +Q1AT2 = sup (4.26)pC VL mold Wmold4.3.9 Sensitivity AnalysisIt was essential to examine the effect of the node size and the time step on accuracy and stabilityof the computed solution. Therefore, calculations were performed using various node sizes andtime steps to determine the optimum magnitude of these variables which are listed in Table 4.1.Thomas et al [101 has found that the best accuracy can be achieved when the Fourier numberdtx. . . .is roughly about 0.1. This criterion was adopted in the model.44Table 4.1: The Modeling Flow Chart.Steel Model in the MeniscusCal. Superheat Exiraction,.45Table 4.2: Variables Used in Models.U: casting speed. 0.761 rn/mm.e: emissivity of SEN body and sleeve materials. 0.6h0: convective heat transfer at SEN-air interface. 15 W/m2°CTyour: hot steel temperature inside SEN. 1550 °CT1: initial temperature of steel at meniscus. 1530 °CT11:liquidus temperature of steel. 1524 °CT0i: solidus temperature of steel. 1490 °CTa: air temperature. 27 °CL: latent heat of steel. 272 (kJ/kg)p: density of steel. 7200 kg/m3slab thickness. 240 mmL0: SEN whole length. 0.7 mW0: SEN wall thickness. 25.5 nmiR0: SEN inner diameter. 76 mmLsieeve: SEN sleeve length 120 mmD1: liquid flux pool depth. 10 mm.D0lld: solid flux depth. 20 mm.Tsmei melting temperature of mould flux. 1200 °CWrnold• distance between SEN and mould. 54.5 mm.46SEN bodySEN sleeve////Figure 4.1: A Typical SEN design used in modeling.SEN Wallyl(FFigure 4.2: Modeling domain and dimension of the SEN wall.4725Figure 4.3: Thermal conductivities of SEN materials as function of temperature.Figure 4.4: Specific heat of SEN materials as function of temperature.0 200 400 600 800 1000 1200 1400 1600Temperature (°C)18001600i: E6004002000-0 200 400 600 800 1000 1200 1400 1600Temperature (°C)48—iiiIiIItl4I1IIltII IItIIIlI11LtUt•‘IIIJiLl•1111IIiI,,,II•1IIii.,II,rriItillVelocityVectorsflenterilrieMeniscus Surface)fromFaceWallInletMeshTemperature,ContoursFig.4.5:Steelflowpatterninthemodelingplane[11].1600 T• node:8*45L) 1400 • node:15*891300node:291771200_______________-0.02 0 0.02 0.04 0.06 0.08Distance fromthe Meniscus (m)Figure 4.6: Axial surface temperature profile of SEN outer wall for different node sizes.1400 :::::1200meniscus-0.02 0 0.02 0.04 0.06 0.08Distance fromMeniscus (m)Figure 4.7: Axial surface temperature profile of SEN for different heat transfer coefficientsbetween the steel and the SEN wall outer surface.50EN wallFig. 4.8: Control volume of steel inside SEN tube.Fig. 4.9: Thermal conductivity of steel as a function of temperature [121.‘I.steel‘I,60c-)04030C2O100ThqTsol0 200 400 600 800 1000Temperature (°C)1200 1400 1600511400 TIiq1200 Mushy Zone- 1000 Tsol800600g400200a0 I I I I0 200 400 600 800 1000 1200 1400 1600Temperature (°C)Fig. 4.10: Enthalpy of steel as a function of temperature [121.SEN wallmouldS______Wmold_______meniscusdy,—dXL__ILmold steel\Fig. 4.11: Calculation domain of steel heat flow model in mould.52specific______________heatOp________ ________solidus liquidusTemperatureFig. 4.12: Assumed linear Latent heat release in the mushy zone by artificially increasingthe specific heat.250020001500100050000 0.1 0.2 0.3 0.4 0.5 0.6Distance below Top of Mould (m)Fig. 4.13: Heat flux profile along the mould broad face.53Chapter 5 Model Predictions and DiscussionsThis chapter presents the predictions of the mathematical models (discussed in the previouschapter) utilized to analyse the heat transfer in the SEN wall and in the liquid steel both insidethe SEN and outside in the meniscus region for a slab casting mould. The results and theirimplications on slab quality are discussed.5.1 Models Predictions5.1.1 Heat Transfer Characteristics of the SEN WallTemperature Profile:Figure 5.1(a) shows temperature contours in the SEN wall for the standard case, the conditionsof which are given in Table 4.2. The horizontal axis in the plot represents the distance from theouter surface of the SEN wall that is in contact with the liquid steel and the mould flux, while thevertical axis represents the distance from the steel meniscus along the longitudinal direction ofthe SEN wall and the ‘zero’ point in this axis denotes the position of the steel meniscus. Aschematic diagram of the meniscus region in the mould, Figure 5.1 (b), is also shown adjacent tothe temperature contour to help explain the plot better. In addition, the enlarged configuration oftemperature distribution in the SEN wall close to the meniscus region is presented in Figure 5.2.It is evident that, above the meniscus in the SEN wall, heat flows strongly towards theatmosphere from the inside of the tube. There are two positions around the meniscus and themould flux top surface where the SEN temperatures change quickly in the longitudinal direction.Further, the same features can also be found in Figure 5.3 which shows the axial temperatureprofiles of the SEN wall at different distances from the outer surface of the SEN.54Based on the results of the mathematical model for the SEN wall shown in Figure 5.1 and Figure5.3, the SEN wall can be divided into three zones exhibiting distinctly different patterns in thetemperature distribution: low temperature drop region, high temperature region and intermediatetemperature region.a) Region of small temperature drop (below the steel meniscus):In the region below the meniscus, both surfaces of the SEN wall are in contact with theliquid steel. Since the heat transfer coefficient between the liquid steel and the outer surface ofthe SEN wall is high (- 15000 W/m2 °C), and the depth of the SEN immersed in the liquid steelis large (175 300 mm, [281), the effect of heat loss due to radiation and convection from theSEN wall exposed to the atmosphere does not extend into this region. Therefore, the SEN walltemperature in this region remains very close to the steel temperature, i.e., around 1530°C at theoutside surface and close to 1550°C at the inner surface of the SEN.b) Region of large temperature drop (above the top surface of the mould flux):The SEN wall temperature drops quite significantly, by about 500°C, across the thickness(—1525°C to —4030°C) above the level of the mould flux. This occurs because the outer surfaceof the SEN wall is exposed to the atmosphere and loses heat by radiation and convection. Thiscauses steep gradients in the SEN wall due to the high thermal resistance offered by the SENrefractory.c) Region of intermediate temperature drop (between the meniscus and the top surface of themould flux):The SEN wall temperature changes in the through thickness direction from 1530°C1550°C at the inner surface, to about 1250°C 1525°C at the outer surface. But the temperaturedifference is not as large as in the second region (large temperature drop region).55In addition to the features described above, the material of the SEN body influences thetemperature. As shown in Figure 5.2 and Figure 5.3, in the region close to the interface betweenthe SEN sleeve and body above the meniscus, the temperature of the SEN wall close to its outersurface exhibits a slight increase (this is evident from temperature profile 1 in Figure 5.3). Thisphenomenon can be explained by the difference between the thermal conductivity of the SENbody and the sleeve: the SEN body, with higher thermal conductivity, offers a lower thermalresistance to the heat flowing from the inside of the SEN outwardly through the wall and remainsat a higher temperature.It should also be pointed out that the temperature of the outer surface of the SEN in the region ofthe meniscus is about 1510°C 1525°C and is lower than the adjacent liquid steel temperature of1530°C. This difference can be explained by heat loss from the exposed surface of the SEN wallcausing axial conduction upwardly away from the meniscus. In addition, in Figure 5.4, a Vshaped temperature well is observed in the transverse temperature profile in the SEN wall at themeniscus. The temperature well occurs because the steel temperature, used for the boundarycondition at outer surface of the SEN, does not change corresponding to the heat transfer of theSEN without considering the fluid flow. In the meniscus region, the resistance to heat flow fromthe SEN wall to the liquid steel is much lower than the resistance in the SEN material itself.Under these conditions, the steel temperature is more likely to be lower in this region and henceis less likely to form a deeper temperature well inside the SEN wall. In other words, the presenceof a deep temperature well inside the SEN wall suggests a lower temperature of steel adjacent tothe SEN wall in the meniscus region.Heat Flux Profile:The transverse and axial heat flux profiles at various locations in the SEN wall are shown inFigures 5.5 and 5.6 respectively.56It is evident from Figure 5.5 that the transverse heat flow from the SEN to the surroundingmedium is negligible over the portion of the SEN submerged in the steel. Above the meniscus,the heat loss from the SEN increases with increasing height. The highest value of the transverseheat flux, 400 kW/m2,is obtained at the inner surface of the SEN; the heat flux value at the outersurface of the SEN is about 300 kW/m2. It should also be pointed out that, in the meniscusregion, the transverse heat flux is negative and has a maximum value of about - 200 kW/m2at themeniscus. This means that in the meniscus region, instead of losing heat to its surroundings, theSEN wall is actually absorbing heat from the adjacent liquid steel. Meanwhile, the heat flux ofabout 100 kW/m2 at the mould flux/SEN interface indicates that a small amount of heat flows tothe liquid mould flux pool. Above the meniscus, there are increases of the transverse heat flux,moving from the SEN sleeve to the SEN body because of the thermal conductivity difference inthe SEN materials. This phenomenon leads to the temperature increase in the SEN body close tothe outer surface of the SEN above the meniscus, as shown in Figure 5.2.The values of axial heat flux in the SEN wall, shown in Figure 5.6, are very small below themeniscus and can be neglected. However, the heat flow becomes significant above the meniscusbecause of the nature of the boundary conditions at the outer surface of the SEN wall. The majorcomponent of heat flow in the axial direction lies in a small region, between the meniscus and thetop surface of the mould flux, very close to the outer surface of the SEN wall. Two axial heatflux peaks of 350 kW/m2and 180 kW/m2are observed at the top surface of the mould flux and atthe meniscus, respectively. The first peak corresponds to a sudden change in the boundarycondition: from being adiabatic at the interface of the SEN wall and the mould flux to stronglyradiative/convective at the outer surface of the SEN wall exposed to the atmosphere. The secondpeak in the heat flux profile also corresponds to a change in the boundary condition: the outersurface of the SEN wall changes from the liquid steel at the meniscus (-1 530°C) to the liquidmould flux of 1200°C over a short distance of 10 mm, thereby creating a large temperaturegradient in the axial direction and hence, a large driving force for heat transfer.57Under steady state, up to 95% of the total heat absorbed by the SEN wall comes from the hotsteel present inside the SEN tube while only 5% comes from the steel present outside the SEN inthe meniscus region. As far as the heat losses from the SEN wall are concerned, a notablepercentage (93%) of heat is lost to the atmosphere by radiation and convection from theexposed surface, about 5 - 6% of the heat flows into the liquid flux and only a small amount ofheat is transferred to the liquid steel outside the SEN in the region below the meniscus.5.1.2 Steel Temperature Drop from the SEN Entrance to ExitThe temperature of the liquid steel changes as it falls through the SEN tube. The model wasemployed to evaluate this temperature drop encountered between the tundish and the mould. Asshown in Table 5.1, for a SEN tube length of 0.7 m and a steel pouring temperature of 1550°C,the drop in steel temperature is about 2.4°C. This temperature change is caused by the SEN wallheat flow, losing heat to the atmosphere by convection and radiation. Also shown in Table 5.1,the influence of steel pouring temperature and of the length of the SEN tube on the steeltemperature drop was studied and will be discussed in a later section.5.1.3 Average Temperature Drop at the Meniscus RegionThe average drop in liquid steel temperature in the meniscus region was computed by assumingthat the heat absorbed by the SEN wall at the meniscus affects the entire volume (Wmold*Lmold)of steel in this meniscus region. An average temperature drop of about 0.62°C thus wascomputed and of which about 30% is the result of the heat lost to the SEN wall in the meniscusregion. It is important to note that the V-shaped temperature well which develops inside the SENwall also represents a large amount of heat absorbed by the SEN in the meniscus region. Theaverage drop in liquid steel temperature has been calculated for different SEN lengths and steelpouring temperatures, Table 5.2. As will be described in the following section, the influence ofthese two parameters is not significant.58If the liquid steel temperature drops both inside the SEN tube and in the meniscus region aresummed, the total is about 3°C in the standard case which did not count the equivalent amount ofheat loss represented by the V-shaped temperature well in the SEN. The finding of a drop in thesteel temperature at the meniscus agrees quite well with the observation of Hoffken [301, wherethe SEN wall was observed to cause cooling of the liquid steel between the mould broad face andthe SEN.5.2 Variables Affecting the Heat TransferSince the SEN has an influence on steel temperature which can affect slab surface quality, anyvariable that influences heat flow in the SEN may be critical from the standpoint of productquality. To establish a clear understanding of the effects of different critical variables, ananalysis of heat flow resistances has been attempted in this section.Under steady state conditions, the heat flux in the transverse and axial directions can be writtenas:q=4 (5.1)The total resistance to heat flow in the transverse direction, R, from the inner surface of the SENwall to its outer surface is given by:R=--+1+ (5.2)In snwhere, the terms refer respectively to the thermal resistance offered by the SEN wall, theconvective resistance at the inner surface and the outer surface.It can be seen that, in the lower part of the SEN, submerged in liquid steel, the thermal resistanceto convective heat transfer at both surfaces is very small ( 0.15 mm°C/W ) and amounts toabout 8% of the total thermal resistance. Thus, the thermal resistance offered by the SEN wall59(up to 92%) is rate controlling. For the portion of the SEN exposed to the atmosphere, thethermal resistance offered by the SEN wall is about 40% of the total and has a strong influenceon the SEN heat transfer.In the axial direction, the resistance to heat flow in the SEN wall can be written as follows:R=— (5.3)Kwhere, D is the distance between the two positions concerned.The model predictions indicate that the heat transfer in the SEN wall influences the steeltemperature by absorbing heat from the liquid steel in the meniscus region; this is likely to affectthe initial solidification of steel in the mould and the generation of surface defects on the slabwhen the superheat of steel is low according to the investigation of Yoshida et al [621. There area number of mould related factors that can influence the heat transfer in the SEN wall and theliquid steel. In the following cases, the calculations were based on the standard conditionsdescribed in Chapter 4, and only one factor was varied in each case. The factors tested in themodel are shown in Table 5.4.As pointed out earlier, because the depth of the V-shaped temperature well, developed in theSEN wall close to its outer surface and the meniscus region, represents an amount of heatabsorbed from the steel, it was evaluated and compared for different conditions. In addition, thetemperature drops in the longitudinal planes of the SEN wall as well as the drop in liquid steeltemperature inside the SEN tube were also used to compare the affect of various operatingconditions listed in Table 5.4. For the convenience of comparison, the calculated value of heatloss of the liquid steel to the SEN in the meniscus region and the drop in liquid steel temperatureinside the SEN, for cases of 1 to 12, are presented in Figure 5.7 and Figure 5.8 respectively andwill be discussed in the following sections.605.2.1 Thermal Conductivity of the SEN WallThe materials from which the SEN (body and sleeve) are manufactured have thermalconductivity values in the range of 4 to 25 WIm°C. To determine the significance of thermalconductivity, the model was run with two limiting values of 5 W/m°C and 20 W/m°C, indifferent combinations for the sleeve and body as shown in Table 5.3.Figure 5.9 shows the influence of varying thermal conductivity of the SEN body and sleevematerials on the transverse temperature profile in the SEN wall at the meniscus. The V-shapedtemperature well is the deepest (33°C) for cases 2 and 4 where a low thermal conductivity of5 W/m°C was employed for the SEN sleeve material. Case 3 (Ksieeve=2OW/m°C,KbOdY=5W/m°C) has the shallowest well (about 10°C), while case 1 (Ksieeve=l2W/m°C,KbOdY=l 7.5 W/m°C) has a slightly deeper well of about 15°C. Figure 5.9 illustrates that the SENsleeve has a greater influence on the heat absorbed by the SEN from steel in the meniscus regionas compared to the SEN body. This is quite logical since the SEN body is located further awayfrom the meniscus as compared to the sleeve, and thus, it is less likely to have a significantimpact on the heat transfer in the meniscus region. Whereas, the SEN sleeve is located at themeniscus and hence affects this region directly. The temperature well depth is stronglyinfluenced by the thermal resistance through the wall; thus with a higher thermal conductivity ofthe SEN sleeve material, more heat flows from the inner surface of the SEN to the meniscusregion and causes the SEN temperature to rise and yield a shallower temperature well.Increasing the thermal conductivity of the SEN body from 5 W/m°C to 20 W/m°C causes a slightincrease in the temperature of the inner surface of the SEN wall. As will be described later, thisis also related to the heat flow from the liquid steel inside the SEN.61Figure 5.10 shows the axial temperature profiles at the outer surface of the SEN wall for differentthermal conductivities, while Figures 5.11 and 5.12 show axial temperature profiles at mid-thickness and at the inner surface of the SEN wall, for the same conditions. In case 2(Ksieeve=S W/m°C, KbOdY=5W/m°C) and case 4 (Ksieeve=S W/m°C, KbOdY=2W/m°C), thetemperatures are roughly the same in the sleeves while in the SEN body, the temperatures aresensitive to the four-fold change in thermal conductivity; at the outer surface (Figure 5.10), theSEN temperature for case 2 well above the meniscus is low, approximately 600°C, while it isabout 1000°C for case 4. However, the temperature difference between the inner and the outersurface of the SEN, not surprisingly, is small. As shown in Figure 5.11, the highest predictedtemperature difference between cases 2 and 4 is about 200°C at mid-thickness of the SEN. Atthe inner surface (Figure 5.12), a high temperature is computed when the thermal conductivitiesof both the body and the sleeve are low (as in case 2). In case 3, a large axial temperaturegradient is observed: the temperature is high in the SEN body and low in the sleeve because thelatter has a four-fold higher thermal conductivity which results in a lower thermal resistance anda greater heat loss. The experimental study conducted by Hoffken [30] showed a reducedseverity of longitudinal cracking problem with increasing the thermal conductivity of the SENmaterial. In addition, Yoshida et al [621 also found a relationship between the low superheat ofthe liquid steel and the occurrence of the longitudinal cracks. Therefore, the linkage between theSEN and the longitudinal cracking may be suggested as: the SEN absorbs heat from the liquidsteel and causes a lower superheat of the liquid steel in the meniscus than expected and when theSEN sleeve, which is in contact with the steel in the meniscus region, has low thermalconductivity, the SEN outer surface tends to be cooler and then absorbs more heat from the steel.According to this suggestion, many observations of the longitudinal cracking problems inpractice can be explained. Moreover, in the current model, it is found that the SEN bodymaterial also influences the temperature of steel flowing inside the SEN: the temperature drop inthe liquid steel inside the SEN increases from 1.27°C to 3.19°C when the thermal conductivity of62the SEN body is increased from 5 to 20 W/m°C, as seen in Figure 5.8. Thus, both the SENsleeve and the SEN body materials are the influencing factors.5.2.2 Thickness of the SEN WallThe wall thickness of the SEN used for slab casting is in the range of 11 40 mm [81, 82]. Tostudy the influence of SEN wall thickness on heat transfer, two cases namely, case 6 ( wallthickness, 10 mm) and case 5 (wall thickness, 40 mm) have been examined and the results werecompared with the standard case where the SEN wall thickness is 25.5 mm. The transversetemperature profiles, at the meniscus plane for the three cases, can be seen in Figure 5.13. Thus,for the thinnest SEN wall, the temperature well is the shallowest and the temperature of the SENwall close to the outer surface is the highest. In the standard case, the well depth is about 15°Cand the temperature of the outer wall of the SEN at the meniscus is 1515°C. However, when thewall thickness is reduced to 10 mm, the depth of the temperature well reduces dramatically to2°C, and the temperature at the meniscus increases by 10°C. On the other hand, when the wallthickness is increased to 40 mm, the temperature well depth increases considerably to about 38°Cwhile the temperature of the SEN wall at the meniscus reduces to 1505°C. These predictionsreveals that the thin walled SEN tends to absorb less heat from the surrounding steel in themeniscus region. The same trend can also be seen in Figure 5.7; the heat loss from the liquidsteel to the SEN increases from 162 W to 1630 W when the SEN wall thickness is increasedfrom 10 mm (case 6) to 40 mm (case 5).Figure 5.14 shows the axial temperature profile at the outer surface, mid-thickness and innersurface of the SEN wall for the three cases described above. For thinner walls, the temperaturedrop across the wall is lower: 280°C for a 10 mm thick wall, 550°C for the 25.5 mm thick walland 680°C for the 40 mm thick wall. As far as the liquid steel inside the SEN is concerned, the63predicted temperature drop increases slightly with decreasing wall thickness, as shown in Figure5.8.The explanation for the temperature variation across the wall, as expected, is quite similar to theeffect of the thermal conductivity of the SEN material. For a thinner SEN wall, the thermalresistance to heat flow is lower; thus, the temperature gradient across the SEN wall is smaller andthe temperature of the SEN wall is higher than the case of the thick walled SEN.5.2.3 SEN Sleeve LengthThe SEN sleeve length is expected to affect the heat transfer because the SEN sleeve has adifferent (lower) thermal conductivity than that of the SEN body commonly in slab casting, thelength of the SEN sleeve is 0 - 200 mm [821. Thus, the effect of three sleeve lengths, 120 mm(standard case), 60 mm (case 7) and 160 mm (case 8), have been studiedThe predictions of transverse temperature profile in the SEN wall can be seen in Figure 5.15.Thus, the depth of the temperature well at the meniscus decreases by a small amount (less than5°C) when the sleeve length is reduced from 120 mm to 60 mm. However, when the sleevelength is increased form 120 nm to 160 mm, there is no obvious change in the depth of thetemperature well. Also seen in Figure 5.7, the heat loss from liquid steel in the meniscus regionincreases slightly because of the longer sleeve which has a lower thermal conductivity and higherresistance to heat flow. In addition, as can be seen in Figure 5.16 which shows the axialtemperature profiles of the SEN wall (at inner surface, mid-thickness and outer surface) forvarious sleeve lengths, a change in the sleeve length only affects the temperature of the SENbody; the SEN wall temperature in the meniscus region remains nearly unchanged for all cases.Further, the effect of sleeve length on the temperature drop of the liquid steel passing through theSEN is very small and can be neglected, Figure 5.8.64The shallower temperature well and the slightly higher temperatures observed in the SEN wallfor shorter sleeves result from the heat flow in the SEN body which has higher thermalconductivity. It should also be noted that for sleeve lengths in the range of 60 mm to 120 mm,heat transfer in the SEN wall, especially in the meniscus region, changes only slightly.Therefore, reducing the sleeve length will have little effect on the heat absorbed by the SEN fromthe liquid steel in the meniscus.5.2.4 Unmelted Mould Flux DepthAs mentioned in the literature [16, 28], the unmelted mould flux zone above the liquid mouldflux layer serves as an insulating medium. Also, the depth of the unmelted layer influences thearea of the exposed surface of the SEN and then changes the thermal resistance in the SEN wallin the axial direction from the meniscus to the top surface of the unmelted mould flux. Thereported depth of this layer varies between 10 35 mm [48]. In order to check the importance ofthis factor, the depth of the unmelted flux layer was examined for 20 mm (case 1, standard), anextremely large depth of 40 mm (case 9) and an extremely small depth of 5 mm (case 10).Once again, the magnitude of the heat absorbed by the SEN wall from the liquid steel at themeniscus is reflected in the depth of the transverse temperature well at the meniscus plane asshown in Figure 5.17. As described in this figure, a smaller layer of the unmelted mould fluxyields a deeper temperature well while the temperature of the SEN wall in the meniscus is lower.When the unmelted flux depth was lowered from 40 mm to 20 mm, an increase of 7°C wasobserved in the depth of the well. When the urimelted mould flux layer was further reduced to5 mm, an additional drop of 19°C is seen. Also as seen in Figure 5.7, the calculated heat lossfrom the liquid steel to the SEN increases by about 900 W with a decrease in the depth of theunmelted mould flux. This can be explained, again, by considering the resistance encounteredduring heat transfer. For a large distance between the top surface of the mould flux and themeniscus, the thermal resistance is also expected to be larger and less heat is lost to the65atmosphere; this will result in a shallower temperature well and higher wall temperature at themeniscus.As far as the overall temperature profile of the SEN wall is concerned, the wall temperatureincreases with increasing depth of the mould flux, and the general pattern remains the same forall three cases. The temperature of the outer surface of the SEN wall is the lowest (less than1000°C) for case 10 with a mould flux depth of 5 mm, while it is the highest (greater than1100°C) for case 9 where the unmelted mould flux depth is 40 mm. The SEN temperatureincreases with the deeper unmelted mould flux layer because the surface area of the SEN wallexposed to the atmosphere is reduced; thus the heat loss by radiation is smaller. It can beconcluded that, by operating with a sufficiently deep layer of the unmelted mould flux around theSEN wall, the cooling of the liquid steel in the meniscus region can be minimized and thus theheat loss from the exposed portion of the SEN wall can be reduced. Further, the drop in theliquid steel temperature inside the SEN also decreases with a deeper mould flux layer, as shownin Figure 5.8.5.2.5 Depth of the Liquid Mould FluxThe effect of the liquid mould flux layer on heat transfer around the SEN is similar to that ofunmelted mould flux. The transverse temperature profiles of the SEN wall at the meniscus fordifferent cases are plotted in Figure 5.19. When the depth of the liquid mould flux pool ischanged from 5 mm (case 12) to 10 mm (case 1) and 20 mm (case 11), the depth of thetemperature well changes by 10 15°C for the three cases and it implies that the SEN absorbsmore heat from the liquid steel in the meniscus region under the condition of lower liquid fluxdepth. But the wall temperature at the meniscus increases by about 5°C for every 5 mm increasein pool depth. This is reflected as a decrease in the heat loss from the liquid steel at the meniscusclose to the SEN, Figure 5.7. As shown in Figure 5.20, the effect of the depth of the liquidmould flux pool does not extend much beyond the mould flux insulation region. When66compared with the unmelted mould flux layer, the liquid mould flux has a smaller effect on theheat transfer in the SEN wall. The mechanism by which the liquid pooi depth affects the heatflow in the SEN wall is the same as that for the unmelted mould flux: variation in depth changesthe exposed surface area of the SEN and hence the heat flow by radiation and convection. With ashallower liquid pool, not only does the SEN wall have greater surface area exposed to theatmosphere, but also the distance between the top of the insulation layer and the meniscus issmaller, leading to a lower thermal resistance and a higher heat loss. The liquid steel flowinginside the SEN also shows a decrease in the heat loss when the pool depth is increased, Figure5.8.5.2.6 Steel Pouring TemperatureIn order to determine if the pouring temperature of the liquid steel plays any role in the heat lossfrom the liquid steel inside the SEN, a calculation was performed for a pouring temperature of1535°C (1550°C in standard case). The predicted effect was insignificant because, inside theSEN, the steel remains at a high temperature and the physical properties of steel do not changemuch. Therefore, the drop in the steel temperature caused by the SEN wall also does not showany significant change. But the heat, absorbed by the SEN from the liquid steel in the meniscusregion, decreases by about 20% from 760 W to 914 W, as shown in Table 5.2, when the pouringtemperature is decreased from 1550°C to 1535°C.5.2.7 The SEN Tube LengthVariation in the SEN tube length will affect the heat transfer in the liquid steel inside the SENtube but has no influence on the heat transfer in the SEN wall. In addition to the standard lengthof 0.7 m, a longer SEN of 1.0 m was employed in the calculation to elucidate its effect on thetemperature change of liquid steel. As shown in Table 5.1, the drop in liquid steel temperature isincreased from 2.4°C to 3.62°C by the increase in the SEN length. This is quite understandableas a longer SEN increases the area of the SEN wall exposed to the atmosphere and therefore the67heat loss. However, there is no significant affect to the SEN wall itself and the steel at themeniscus.5.2.8 Distance Between the Mould Plate and the SENThe distance between the mould plate and the SEN wall, Wmojd, is proportional to the bulkvolume of the steel present in the meniscus region, and affects the drop in the averagetemperature of steel owing to the heat transfer in the SEN in the meniscus region. The distance,Wmold, can be altered by changing the SEN tube size or the slab section. The drop in the averagetemperature of steel in the meniscus region, A7, for different values of WmO1d are tabulated inTable 5.2. Decreasing Wmold from 56 mm (standard, case 1) to 10 mm, the /J increasesquickly, due to the decrease in the bulk volume of the liquid steel in the meniscus region, from0.62°C to 3.5°C at the steel pouring temperature of 1550°C, while it increases from 0.66°C to3.7°C at the steel pouring temperature of 1535°C. It has also been found that the amount of heatabsorbed by the SEN wall from the liquid steel at the meniscus accounts for about 30% of thetotal superheat removed in this region at the pouring temperature of 1550°C, and about 34% atthe pouring temperature of 1535°C.The above findings indicate that, for large values of Wmo1d the influence of heat transfer in theSEN on the steel initial solidification at the meniscus is not very significant. However, when theSEN is closer to the mould plate (smaller Wmold), the influence of the SEN becomes greater.Since the superheat temperature in the meniscus, in the slab casting mould, is usually only 35°C, withdrawal of heat from the liquid steel by the SEN which locally depresses the steeltemperature by, say 5°C (as in the case of 10 mm distance between mould plate and the SENwall), may produce thick and irregular shells. The results may be surface quality problems, suchas longitudinal cracks and deep oscillation marks. As discussed in the literature, this mechanismhas been widely studied and reported by a number of investigators. Japanese researchers [621have studied the relationship between the severity of longitudinal cracks in the slab and the68difference between the temperature of the liquid steel in tundish and near the meniscus in themould. The results from their investigation are shown in Figures 2.16 and 2.17; thus, when thetemperature difference is less than about 27°C, the index of the longitudinal cracks is less than0.1, whereas for a larger temperature difference of about 33°C, the index rises to 1. Thus theirwork reveals an important effect of steel superheat level in the meniscus region on the formationof slab surface defects in slabs; when the steel superheat in the mould is low, a small decrease inits value will deteriorate the quality problem quite significantly [621. On the other hand, assuggested by Bommaraju [481, the local melting rate of the mould flux can be influenced by theSEN, the uneven flow of the liquid flux between the strand/mould may cause the longitudinalsurface cracks. Thus, with shorter value of Wmold, the influence of the SEN on the melting of themould flux is stronger and it is more prone for the slab to have surface cracking problems.69Table 5.1: Steel Temperature Drop Inside the SEN Under Different Conditions.SEN Length, SEN Inner Steel Flow Tpour TemperatureL110 (m) Radius, R0 (m) Speed (mis) (°C) Drop, AT (°C)0.7 0.038 1 1535 2.41.0 0.038 1 1535 3.50.7 0.038 1 1550 2.41.0 0.038 1 1550 3.670Table 5.2: Average Temperature Drop of Steel in the Meniscus Region with Different Distancesbetween the SEN Wall and the Mould Plate.SEN Wall Steel_SolidificationKsleeve Kbody Qi Tm T Wmould Qsup QrQsup AT1(WIm°C) (W/m°C) (W) (°C) (m) (W) (W) (°C)0.056 1740 2654 0.66914 Tm: 1530 0.025 1709 2623 1.4612 17.5 T: 1535 0.010 1770 2684 3.74(at 800 (at800 0.056 1739 2499 0.621400 °C) 1400 °C) (standard)760 Tm: 1530 0.025 1709 2469 1.37T: 1550 0.010 1770 2530 3.52Q1 Heat loss to SEN wallQ Superheat loss to mouldTable 5.3: Thermal Conductivity of the SEN Materials Used in Calculations.case Sleeve thermal conductivity (W/°C) Body thermal conductivity (W/m °C)1 (standard) 12 (at 800 1400°C) 17.5 (at 800 1400°C)2 5 53 20 54 5 2071Table 5.4: Variables tested in the model:Case Conditions1 (standard) as in Table 4.2, Figure 4.3 and Figure 4.42 thermal conductivity of the SEN body (5 W/m°C), sleeve (5 W/m°C)3 thermal conductivity of the SEN body (5 W/m°C), sleeve (20 W/m°C)4 thermal conductivity of the SEN body (20 W/m°C), sleeve (5 W/m°C)5 the SEN wall thickness, 40 mm6 the SEN wall thickness, 10 mm7 the SEN sleeve length, 60 mm8 the SEN sleeve length, 160 mm9 unmelted mould flux depth, 40 mm10 unmelted mould flux depth, 5 mm11 liquid mould flux depth, 20 mm12 liquid mould flux depth, 5 mm13 steel pouring temperature, 1 53 5°C14 mould plate to the SEN wall distance, 56 mm15 mould plate to the SEN wall distance, 25 mm16 mould plate to the SEN wall distance, 10 mm72TheSENWallTemperatureContour0.0750.0500.0250.000-0.025-0.050-0.075 0.0000.025DistancefromtheSENWallouterSurface(m)(a)(b)SENWallE (0 0 (0 a) a) E 0 a) C) C (0a) 11Figure5.1:TemperaturecontouroftheSENwall (standardcase).t7LDistancefromtheMeniscus(m)cScSooo00000—.3CT)I\)0[‘3CT)out:ac:i—C’) CDtI*I*1111i’*’’.’‘I..r..ICDiIi*I*t*l*i*t***‘5’I*IIii*I*ltI*I*I’’‘JZoIjI1lIl*i**I*S0IIIII*III’’’’’b\ .0i‘I‘.\‘\—CD.,•j IIjiI*I*I*’sCIIIIIIIII1*‘SI1\1V*v1\\-._3 *sCDD00—s— ——I’_I.II\I\%’5-.‘—.5Cr1....—51)16001500 “1400meniscus_I/ sleeve body900-0.02 0 0.02 0.04 0.06 0.08Distance from the Meniscus (m)—0———— Omm —+——— 7.28mm —h--——— 12.75mm —<>-——-- 18.21mm —)(——- 25.5mmFigure 5.3: Predicted axial profiles of the SEN wall temperature at different depths from the SENouter surface (standard case).1550l510 I0 0.005 0.01 0.015 0.02 0.025 0.03Distance from the outer surface of the SEN wall (m)Figure 5.4: Transverse temperature profile in the SEN wall at the meniscus (standard case).75c’J 2.x D LL.TheSENWallHeatFlux400300200100 0-100-200Figure5.5:AxialprofilesoftransverseheatfluxintheSENwallatdifferentdepthsfromthe-50050DistancefromtheMeniscus(mm)outersurfaceoftheSEN(standardcase).300200x U100IIII0510152025DepthfromtheSENouterSurface(mm)—a-80.0mm300-60.0mm300-40.0mm.20.0mm00mmDepthbelowtheMenlscus200ofeachTransversePlane200\xx\.2\U100“—-100I‘-I0---0051015202505101525DepthfromtheSENouterSurface(mm)DepthfromtheSENOuterSurface(mm)Figure5.6:AxialheatfluxprofilesintheSENwall at different axiallocationsfromthemeniscus-20.0mm-10.9mm-6.5mm-1.8mm0.0mmDepthbelowtheMeniscusofeachTransversePlane\\\ \E ‘C U Ca a) IDepthfromtheSENouterSurface(mm)20(standardcase).Figure 5.7: Calculated heat loss of steel to the SEN wall at the meniscus in different cases.Figure 5.8: Steel temperature drop inside the SEN tube in different cases.1630W18001600140012001000•S 800600‘ 4002000 I iii1 2 3 4 5 6 7 8 9Case Number10 11 123.5U 302.51.50.53.19°C1.27°CIi, I,’,”9 10 111 2 3 4 5 6 7 8Case Number781550Figure 5.9: Transverse temperature profiles at the meniscus with different thermal conductivitiesof the SEN sleeve and body.Figure 5.10: Axial temperature profiles at the outer surface of thethermal conductivities for the sleeve and body.SEN wall with different0I1540153015201510150014901480—G-———— case 1——---—case 2—4——-—— case 3—A—---— case 40 0.005 0.01 0.015 0.02Distance from the SEN wall outer Surface (m)0.025 0.03• easel• case2155014501350,_ 1250U______0‘— 11501050950f- 850750650550-0.02 0I case3A case4meniscus0.02 0.04 0.06Distance from the Meniscus (m)0.08791600Figure 5.11: Axial temperature profiles at mid-thickness of the SEN wallconductivities for the sleeve and body.Figure 5.12: Axial temperature profiles at the inner surface of the SENthermal conductivities for the sleeve and body.with different thermalwall with differentU0I150014001300120011001000-0.02—4-----— ease 2—s——--— ease 30 0.02 0.04 0.06Distance from the Meniscus (m)0.08C)0I—0————— ease 1——---— ease 215501545154015351530152515201515-0.02—El---——— case 3—&----— case 4meniscus0 0.02 0.04 0.06Distance from the Meniscus (m)0.0880Figure 5.13: The SEN wall transverse temperature profiles at the meniscus plane with differentwall thicknesses (‘men’- meniscus plane).Figure 5.14: Axial temperature profiles at the outer surface (o), mid-thickness (m) and innersurface (i) with different wall thicknesses.1600150014001300(-)0I 120011001000900• case 1_o—4)--—-—— case 1_rn—O------ case 1_i• case 5_o—4---——— case 5_rn—O-------- case 5_iA case 6_o—h--—-—— case 6_rn———-——case 6_i800meniscus-0.02 0 0.02 0.04 0.06Distance from the Meniscus (m)0.0881Figure 5.15: Transverse temperature profiles in the SEN wall at the meniscus for different sleevelengths.Figure 5.16: Axial temperature profiles at outer surface (o), mid-thickness (m) and inner surface(i) of the SEN for different sleeve lengths.155015401530fr. 15201510F’15001490148014701545.5 °C•—•--—--— ease Icase 7—a————— case 80 0.005 0.01 0.015 0.02 0.025 0.03Distance from the outer surface of the SEN wall (m)160015001400L)01300120011001000900-0.02• ease 1_o—0------— case 1_rn—0------— case 1_i• case 7_o—4-——— case 7_rn—0------- case 7_iA case 8_o————--—— case 8_rn—--——case 8_i0 0.02 0.04 0.06 0.08Distance from the Meniscus (m)821550 1547 °CFigure 5.17: Transverse temperature profiles in the SEN wall at the meniscus for different depthsof the unmelted mould flux.Figure 5.18: Axial temperature profiles at the outer surface (o), mid-thickness (m) and innersurface (i) of the SEN for different depths of the unmelted mould flux.1514.415401530152015101500149014801470—O——------ case 1—(>—-—-- case 9—---——h-———— case 100 0.005 0.01 0.015 0.02 0.025 0.03Distance from the outer surface of the SEN wall (m)160015001400L)13001200E- 11001000900• case 9_o—G-———— case 9_rn—o--—-- case 9_i—•-—---case lo—Q--——-— case 1_rn—-—O---———— case 1_i—A--—-— case 10_o—&----— case 10_rn—---&———— case 10_i-0.02 0 0.02 0.04 0.06 0.08Distance from the Meniscus (m)831550 1546 °CFigure 5.19:depths.Transverse temperature profiles at the meniscus for different liquid mould flux• caseil_o—‘—-——— case li_rn——0-———— case 11_i—•------— case i_o—0—--—— case 1_rn—0--—— case 1_i—A-—-— case 12_oz2c— case 12_rn—&—— case 12_i15401530152015101500149014801470—0------- case I—G--——— case II—&-—-— case 120 0.005 0.01 0.015 0.02 0.025Distance from the outer surface of the SEN wall (m)0.031600150014001300120011001000900nniscus-0.02 0 0.02 0.04 0.06Distance from the Meniscus (m)0.08Figure 5.20: Axial temperature profiles at the outer surface (o), mid-thickness (m) and innersurface (i) of the SEN for different liquid mould flux depths.84Chapter 6 Conclusions and RecommendationsA steady-state two-dimensional heat flow mathematical model has been developed to elucidatethe influence of the SEN on the liquid steel temperature in the meniscus region in a slab castingmould. The model was utilized to calculated the heat flux profiles and temperature distributionin the SEN wall. Further, the change in steel temperature, which is influenced by the heattransfer in the SEN wall, was also computed both inside the SEN and in the meniscus region;mould heat flux profiles calculated from measurements made in an earlier plant trial [281 wereemployed as the boundary condition in the mould for the solidification of steel. The effect ofvarious operating factors was examined with the help of the model and the impact of eachparameter on the liquid steel temperatures was studied.The model results have revealed that the heat flow in the SEN wall is mainly concentrated in itsupper part which is above the meniscus and it absorbs heat from the liquid steel at both insideand outside surfaces, losing heat mainly to the atmosphere through radiation and convection; asmall fraction of the heat goes into the liquid mould flux pooi. The heat absorbed by the SENwall from the liquid steel causes a drop in temperature of the steel and hence is likely toinfluence the initial solidification of steel in the meniscus; this is clearly known to influence theformation of the longitudinal surface cracks and deep oscillation marks in slabs.6.1 Conclusions from the Present ModelThe following important conclusions can be drawn from the study; recognizing the evaluation ofthe boundary condition used in the model, predictions should be considered to besemiquantitative.851) Below the meniscus, the transverse and axial heat flux profiles exhibit a small temperaturegradient in the portion of the SEN wall submerged in the liquid steel. Above the meniscus, thetransverse heat flux increases in the axial direction and a negative peak occurs in the heat flux inthe meniscus region indicating heat flowing from the liquid steel to the SEN wall; a maximum inthe axial heat flux profile is observed at the top surface of the mould flux, where a large drivingforce for heat flow exists.2) The temperature distribution in the SEN wall also reveals a strong heat flow toward theexposed surface of the SEN wall in the upper portion and large temperature gradients at themeniscus as well as the mould flux top surface.3) Among the factors examined, the thickness of the SEN wall has the most significantinfluence on the heat absorbed by the SEN from the liquid steel at the meniscus. When the wallthickness is decreased from 40 mm to 10 mm, the heat loss from the liquid steel to the SEN at themeniscus drops significantly from 1630W to 162W. Other influencing factors are the mould fluxdepth (both unmelted and liquid) and the thermal conductivity of the SEN sleeve.4) The heat loss from liquid steel during its flow through the SEN. and the drop in liquidsteel temperature inside the SEN tube are affected greatly by the thermal conductivity of the SENbody. The temperature drop increases from 1.27°C to 3.19°C by increasing the thermalconductivity of the SEN body from 5 to 20 WIm°C while the superheat temperature at themeniscus is about 5°C. The next important factor is the depth of the mould flux layer. However,the thickness of the SEN wall and the length of the SEN sleeve have very small effect.5) With a higher steel pouring temperature, the overall temperature profile of the SEN wallshifts to a higher temperature level with a small change in the temperature drop in the liquidinside the SEN.866) The SEN tube length also has an effect on the drop in liquid steel temperature inside theSEN, but has no influence on the heat transfer in the meniscus region. With a longer SEN tube,the steel at the exit gets colder.7) The distance between the SEN and the mould plate is also important from the standpointof heat transfer in the SEN wall. The cooling effect caused by the SEN is more pronounced forthe case when the distance is smaller.The predictions from the mathematical model have shown that the heat transfer in the SENinfluences the variation in steel temperature, especially at the meniscus. A number of otherfactors, such as poor insulation of the SEN and the meniscus, improper physical properties of theSEN sleeve and body ,can also indirectly have impact on the steel temperature by influencing theheat transfer in the SEN wall. The following is the summary of the major findings in the currentwork.1) The SEN wall may influence the steel initial solidification at the meniscus by taking heatfrom it to the atmosphere and cooling the steel. This cooling effect is the biggest in the midplaneof broad face because there is the shortest distance between the mould and the SEN.2) The SEN thermal conductivity and the mould flux layer depth are the most influencingfactors to the SEN heat transfer. Thicker mould flux layer and higher SEN sleeve thermalconductivity will benefit the meniscus steel with less heat flow through the SEN wall to theambient, while lower thermal conductivity of the SEN body can reduce the heat loss andtemperature drop of steel inside the SEN tube.873) The larger cooling effect, at the midplane of the broad face, will cause uneven heat flowacross the broad face and irregular and thicker solid shell of steel. In addition, the SEN may alsocause the nonuniform melting and flowing of the mould flux, then give rise to the nonuniformheat transfer in the flux channel between the mould and the strand. Therefore, it is very prone tothe formation of surface problems, such as the longitudinal midface cracks and deep oscillationmarks, by influencing the mould flux in the meniscus.6.2 Suggestions for Future WorkThe findings, in the present study, have demonstrated the significance of the SEN wall on theheat transfer of steel in the meniscus and also on the formation of surface defects and deeposcillation marks in slabs. However, because of the limitation of the current model and the lackof sufficient experimental data, it is very difficult to predict the precise drop in the liquid steeltemperature due to the SEN wall in the meniscus region for various slab sections. A clear insightinto the slag rim formation, which is important from the standpoint of slab surface quality, couldnot be established due to the lack of accurate knowledge on the melting and flow behavior of themould flux above the meniscus.Hence, it is very essential to examine the heat flux data in the mould for a wide range of slabsections. Also the behavior of mould flux and its properties in the liquid pool need to be clarifiedfurther in order to check the influence of the SEN wall on the slag rim. Furthermore, a threedimensional mathematical model involving not only the heat transfer, but also the fluid flow inthe mould is required to establish a more flexible and actual boundary condition at the SENwall/steel interface in the meniscus region, and a changing temperature of steel in the meniscusas well. It is also necessary in the further work to investigate the influence of the SEN heattransfer on the melting behavior of the mould flux to have a better understanding about the SENheat transfer, mould flux performance and the slab surface quality.88However, in addition to the factors considered in the present study, it will also be important toexamine the influence of the other variables, such as the different types of mould flux anddifferent SEN designs, on the slab surface quality.89Appendix I1. Correlations for Liquid Metal Convective Heat Transfer1.1 Liquid Metal Flow Over Plane Surface ---Dissipation Neglected1) Low Pr number Kays & Crawford [1]:Nu = 0.565(Re Pr)1 (1)NUL =1.13(ReL Pr)1 (2)where, Pr <0.05, Re <5 x i0,properties are evaluated at mean film temperature.2) Entire range of Pr number Churchill & Ozoe [2]:0.3387Re+ Pr1Nu= 2 (3)(1 + (0. 0468/Pr)1)0.6774ReL+ PrNuL= 2 1 (4)(1 + (0. 0468/Pr)1 )where, RePr > 100,properties are evaluated at mean film temperature.1.2 Liquid Metal Flow Through Tube and Pipe1) Constant wall temperature Seban & Shimazaki [3]:NuD = 5+0.O25PeD°8 (5)where, Pe>100, L/D>60,properties are evaluated at fluid bulk temperature.902) Constant wall temperature Azer & Chao [4j:NuD 5 + 0.O5PeD°77Pr°25 (6)where, PeD >15,000, Pr <0.1,properties are evaluated at fluid bulk temperature.3) Constant wall temperature Sleicher, Awad & Notter [5]:NuD =4.8+0.O156PeD°8 Pr°°8 (7)where, 0.004 <Pr <0.1, ReD <5 x i0,properties are evaluated at fluid bulk temperature.4) Constant heat flux at the wall Skupinshi Tortel & Vautrey[7]Nu = 4.82 +0.0185Pe°’827 (8)where, 3.6x10 <Re<9.05x105,l00<Pe<10000,properties are evaluated at fluid bulk temperature.2. Heat Transfer Coefficient at Steel - SEN Interface h,1,Liquid steel properties:p=7020 (kg/rn3), density of hot steel.Cp=787 (J/kg°C), specific heat of hot steel. (data from [11])K=43 (W/rn°C) , thermal conductivity of hot steel. (data from [11])KefT(5l0)K (W/rn°C), effective thermal conductivity of hot steel accountingfor both conductive and convective heat transfer.= 5.55 x 103(kg/rn s), laminar viscosity of steel. (data from [11])2.1 Outer SEN Surface ---SteelLSUb=l 70 -- 300 (rnrn),Submerge depth of SEN. (data from [28])91Table 1:V=O.1 (m/s), velocity of steel flow over SEN wall. (data from [11])h: heat transfer coefficient.LSUb K (Keff) Re Pr Pe Nu Equation h(mm) (W/m °C) VLSUbP (J.) (Re Pr) ( (W/m2°c)K K170 43 21503 0.101 2171.8 41.1388 (4) 10405.7300 43 37946 0.101 3832.5 54.65 (4) 7833Steel flow over the SEN wall surface can be simulated as flow over flat plate. Because of thelow Reynolds number of steel flow, the flow of steel over SEN would be laminar flow. Thecorrelation for laminar flow over flat plate was chosen according to Re, Pr, and Pe numbers. It’sassumed that the properties of liquid steel are constant. The calculated heat transfer coefficientsare in Table 1.2.2 Inner SEN Surface ---SteelL0=520 (mm) , length of SEN.D—76 (mm), hydrodynamic diameter of SEN.V=0.76 1 (rn/mm.), casting speed.=LnozmWm V, steel flow velocity inside SEN tube.itRwhere, Lm1580 mm, mould broad face width.Wm=240 mm , mould narrow face width.V8=1.061 (rn/s)h: heat transfer coefficient.92Table 2:LQ/D K (Kefi Re Pr Pe Nu Equation h(W/m °C) VSDP (Re Pr) hD (W/m2°c)K K6.84 43 101994 0.101 10301.39 38.25 (7) 21641.45Steel flow inside the SEN is simulated as fluid flowing through tube, constant wall temperaturewas assumed and the correlation for heat transfer coefficient calculation was selected bychecking the Re, Pr and Pe numbers. Results of the inner SEN surface-- steel heat transfercoefficients are in Table 2.93Appendix IIEffective Heat Transfer CoefficientThe total heat loss Q from SEN to ambient is caused by convection and radiation heat transfer.Q Qconv += (7—Qrad 6a( 7’—= hrad ( —Q = (h + hrad) * (7, — ;,oz) = heff ( 7, — ioz)so, heff = + hradcY(T4— 4) . .where, hrad = a noz , it is calculated by iteration process.a noz94Appendix III1. Heat Transfer Coefficient at Liquid Flux--- SEN Outer Wall InterfaceBecause of low consumption rate of liquid flux, the liquid flux pool is very stagnant and naturalconvection mechanism is used to represent the heat transfer between SEN outer wall surface andliquid flux.the working correlation [8] is:Nu = 0.68 + O.67RY4(l +(0.492 / Pr)6)where, O<Ra <10By using liquid flux properties as following:Density 3040 (kg/rn3)Specific heat Cp 1025.7 (J/kg °C)Thermal conductivity K 2 (W/m °C)Dynamic. Viscosity 0.2 (kg/rn s)Kinematics viscosity 6.58E-05 (m2/s)Expansion. Coefficient 0.00002 (1/K)Characteristic length (liquid flux pooi depth), L=0.01 (m),Gravitational acceleration g=9. 8 (kg/m s2),natural convection heat transfer coefficients are calculated in different AT (AT = Twaii_ Tsiag) valuesas shown in the following table (assuming that liquid flux properties are constant).AT(°C) Pr Gr Ra Nu h (W/m2 °C)10 102.57 0.453 46.45 2.392 478.37420 102.57 0.906 92.89 2.716 543.1549530 102.57 1.358 139.34 2.933 586.58940 102.57 1.811 185.79 3.101 620.19050 102.57 2.264 232.24 3.240 647.968100 102.57 4.528 464.48 3.724 744.836150 102.57 6.793 696.71 4.049 809.788200 102.57 9.057 928.95 4.300 860.033250 102.57 11.321 1161.191 4.508 901.571300 102.57 13.585 1393.429 4.687 937.274In the modeling program, heat transfer coefficient is calculated based on the temperature of SENwall in the previous time step; after certain times steps (iterations) the steady state heat transfercoefficient can be obtained.96References[1] Kays,W.M., & M.E.Crawford, ‘Convective Heat & Mass Transfer’, 2nd. ed., New York,McGraw-Hill, 1980.[2] Churchill,S.W., & H.Ozoe, ‘Correlations for Laminar Forced Convection in Flow over anIsothermal Flat Plate and in Developing and Fully Developed Flows in an IsothermalTube’, J. 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