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* Corresponding author: E-mail: pavel.ramirez.lopez@swerea.seDOI: http://dx.doi.org/10.2355/isijinternational.ISIJINT-2017-482

1. Introduction

Continuous Casting (CC) is the most widespread method for casting in the world. As such, CC is a critical step in steelmaking where liquid steel is transformed into a usable solid shape (e.g. slabs, blooms, billets, bars, etc.), but also where most surface defects are born which diminish the overall yield and productivity in steel plants. As a conse-quence, considerable efforts have been made on casting research in the past 40 years to understand defect forma-tion within the mould and the various process variables to control these issues.1–4) However, the introduction of new grades, wider/thicker formats, increased casting speeds, and a diverse product mix has pushed the caster outside its typical operational limits; thus, bringing back problems such as cracking, inclusions, micro/macro-segregation and in the worst case scenario; breakouts. Numerical modelling was

Key Lubrication Concepts to Understand the Role of Flow, Heat Transfer and Solidification for Modelling Defect Formation during Continuous Casting

Pavel Ernesto RAMIREZ LOPEZ,1)* Pooria Nazem JALALI,1,2) Ulf SJÖSTRÖM,1) Pär Goran JÖNSSON,2) Kenneth C. MILLS3) and Il SOHN4)

1) Casting and Flow Simulation Group, Process Metallurgy Department, Swerea MEFOS, Aronstorpsvägen 1, SE 974 37 Luleå, Sweden.2) Department of Materials Science and Engineering, KTH Royal Institute of Technology, Brinellvägen 23, S-100 44 Stockholm, Sweden.3) Department of Materials, Imperial College London, London, SW7 2AZ, United Kingdom.4) Materials Science and Engineering Department, Yonsei University, Seoul, 120-749 South Korea.

(Received on August 10, 2017; accepted on October 5, 2017; J-STAGE Advance published date: December 21, 2017)

Surface defects are recurrent problems during Continuous Casting of steel due to the introduction of new grades that are often difficult to cast, as well as the everlasting pursuit for higher quality and improved yield. Accordingly, numerical modelling has become a ubiquitous tool to analyse the formation mechanisms of such defects. However, industrial application of simulations is often hampered by oversim-plifications and omissions of important process details such as variations in material properties, specific casting practices or shortcomings regarding fundamental metallurgical concepts. The present manuscript seeks to create awareness on these issues by visiting key notions such as slag infiltration, interfacial resistance and Lubrication Index. This is done from a conceptual point of view based on industrial obser-vations and numerical modelling experiences. The latter allows a re-formulation of outdated concepts and misconceptions regarding the influence of fluid flow, heat transfer and solidification on lubrication and defect formation. Additionally, the manuscript addresses common challenges and constraints that occur during industrial implementation of numerical models such as the lack of high-temperature material data for slags. Finally, the manuscript provides examples of improvements on product quality and process sta-bility that can be achieved through a holistic approach which combines modelling with laboratory tests, experiences from operators and direct plant measurements.

KEY WORDS: numerical modelling; Continuous Casting; defects; lubrication; powder consumption.

introduced as an alternative to study such issues in a more cost-efficient way than using traditional trial-error tests in the plant. Starting in the late 70’s and 80’s with the advent of personal computers, the first generation of models man-aged to predict the overall behaviour of the caster based on empirical data.5–7) Subsequently, models in the 90’s added Computational Fluid Dynamics (CFD) and solidification to casting simulations.8–10) Faster computers and improved codes allowed huge progress regarding multi-phase appli-cations (e.g. bubbles and inclusions) combined with cal-culations of flow and solidification in the past decade.11–14) Currently, a wide variety of commercial and in-house codes are available for CC modelling such as PROCAST, COMSOL, TEMPSIMU, CON1D/2D, etc.15–17) Moreover, a recent trend is the development of thermo-mechanical models coupled to flow dynamics for solving the combined problem of flow, solidification and stress-strain during casting.18,19) Of all these, PHYSICA and THERCAST are two of the most promising approaches; which allow: a) 3D unstructured - mesh, multi-physics model using a combina-

Review

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tion of volume and finite element techniques (PHYSICA)20) and b) a fully-coupled, thermal-metallurgical-mechanical, finite- element analysis coupled to a Navier-Stokes solver to calculate the stress-strain during solidification through FEM (THERCAST).21) Finally, significant efforts have been made by Beckerman et al.,22) Gandin et al.,23) Senk et al.24) and others to bring microstructural modelling to usable scales for industrial application in CC. However; despite all the advances described, the prediction of some particular problems (e.g. localized cracking and irregular oscillation marks) have remained elusive. In many cases, this is due to the use of statistical averages as inputs for the analysis. For instance, it is common practice to use thermo-couple readings as input data for heat transfer calculations in the mould (i.e. heat-flux boundary conditions). As expected, such models predict the “typical” behaviour during casting well, but fail to capture specific problems arising from sin-gularities in the process. Another key issue is the absence of slag in most models since this would require a multi-phase approach that is complex and time consuming. Hence, slag effects are often included as a set of thermal resistances.25–28) Unfortunately, real slag behaviour is not so simple and important knowledge gaps persist in areas such as crystal-lization, radiation properties, wettability and lubrication extent in the mould.29,30) Last but not least, CC deals with liquid- metal- flows that are inherently turbulent, since cast-ing conditions are constantly changing. This is due to the fact that liquid metal available for casting relies on prior steelmaking processes, such as, ladle refining, degassing, alloying etc. Thus, the casting machine must adapt to both these conditions in one end; and customer demands (such as format and order size) in the other. This often turns caster schedules into a real puzzle. Essentially, all these conditions create a process, far from “stable or steady state”, where casting speed, nozzle immersion depth, product size, pour-ing temperature, etc. are always changing to fit production demands. Evidently, “steady state” models are unable to simulate these issues. The authors have addressed some of these shortcomings by introducing models able to deal with: a) flow dynamics in transient state, b) explicit slag infiltration, c) mould oscillation, d) argon injection and e) advanced turbulence modelling (e.g. LES).31–36) However, a variety of multiphase and multi-phenomena interactions

are yet to be included in modern CC models to move away from average predictions that enable simulations tailored to specific caster problems. The present manuscript seeks to redefine essential notions required for a more realistic modelling of CC processes as well as to enumerate the chal-lenges for its industrial implementation.

2. CC Process Overview

Prior to casting, liquid steel is poured from the ladle into the tundish which serves as a reservoir or intermediate ves-sel during the casting sequence. Casting begins when the stopper is lifted to let steel flow through the Submerged Entry Nozzle (SEN) into the water-cooled copper mould. A dummy bar is used as temporary bottom to allow filling of the mould and initial formation of a solidified skin known as “shell”. Once the desired metal level in the mould is reached (ca.100 mm from the top), the dummy bar is withdrawn downwards, while the strand is guided through the rolls and into the secondary cooling area consisting of a series of water sprays (Fig. 1). The typical length of a conventional slab mould is approximately 900 mm. Solidification of the remaining liquid core is completed after straightening. Whereupon, the products are cut to a given length (typically between 6–12 m. for billets, blooms and slabs) by means of a gas-flame torch. A rapidly- melting, starting powder is typically added to the top of the melt to accelerate formation of a slag layer to protect steel from oxidation and provide enhanced lubrication at the beginning of casting; this is later replaced by a conventional casting powder for the rest of the sequence. Considering the differences on solidification behaviour between different steel grades; the selection of an appropriate powder is critical to obtain a good internal/surface quality on the final products. These include thermo-physical properties such as crystallization, viscosity and break temperature. However, powder performance is also closely linked to casting conditions such as pouring tem-perature and casting speed. These are, in turn, a function of both steel grade and product format (e.g. slab, billet or bloom) to be cast as well as the specifications of each caster (e.g. vertical or curved, nozzle and mould design, spray loops performance, soft reduction, hydraulic vs mechanical oscillation, etc.). These topics are discussed in the follow-

Fig. 1. Caster layout and typical defects in continuously cast products.

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ing sections to highlight their effects on the casting process.

3. Composition and Thermo-physical Properties of Slags

Casting powder transforms into liquid slag as it melts in contact with steel at high temperatures. This liquid provides lubrication by infiltrating between the recently- formed shell and mould. As expected, the amount of lubrication is strongly dependent on the thermo-physical properties of the powder (now slag). Slags consist of calcium-silicate’s based compounds to which fluxes are added to reduce its melting temperature and viscosity depending on the composition requirements for the steel to be cast. The properties of these slags are strongly dependent on their structure, which is defined by the degree of polymerisation, cation effects and physical state (e.g. liquid or solid, glassy or crystalline, granules or powder, etc.). Polymerisation chains are com-posed of network formers such as SiO2 and Al2O3, whereas CaO and MgO act as network breakers. Fluxes reducing the melting point include Na2O, K2O, Li2O, CaF2, and MnO, while impurities (e.g. FeO and TiO2) are also present to some extent. The degree of polymerisation can be directly linked to basicity (i.e. %CaO/%SiO2), which varies between 0.6 and 1.5 for CC slags. A considerable amount of research has been focused on the properties of slags and the pres-ent manuscript is not an attempt to review such properties. Instead, the reader is referred to Mills’ et al.29,30,37–39) and Sohn’s et al.40,41) work which provide further information on slag properties. However, the main role of these properties will be discussed below in relative terms to distinguish their influence on the casting process.

3.1. Viscosity and Break TemperatureViscosity is a critical property since it affects lubrication

and changes strongly with temperature and composition dur-ing casting. It can also be directly associated to the degree of polymerisation; where high viscosity slags are typically more glassy (e.g. high SiO2 content= low basicity), while low viscosity slags tend to be more crystalline (e.g. high CaO content=high basicity). This crystallization tendency assumes that the primary crystalline phase formed is cus-pidine (3CaO·2SiO2·CaF2) and that kinetics of crystalliza-tion are accelerated with the depolymerised structural units of the slag. Typically, CC slag viscosities range from 0.5 dPa-s (high speed casting) to 30 dPa-s (billet casting).30) “Process-wise”, low- viscosity slags are able to infiltrate more easily into the shell-mould channel. However, this behaviour is strongly affected by the melting behaviour (i.e. break temperature and melting rate) as well as casting conditions for any given steel grade. The break temperature (Tbr) is closely related to viscosity, since it is the point at which solid crystals are precipitated in the liquid slag.42) At this point, the viscosity increases rapidly as the temperature decreases. In many cases, Tbr does not coincide with the initial crystallization temperature; where the latter is the temperature at which initial crystallization is observed. This has profound effects on infiltration; for instance, assuming two slags have a similar viscosity at a given temperature, the one with a lower Tbr will provide an extended lubrication within the mould. This occurs since more heat is available

to remain liquid before solidifying:

�T T Tbreak pouring br� �

Effectively, ΔTbreak represents the amount of heat avail-able to convert casting powder into liquid slag. A similar phenomenon occurs with the pouring temperature and steel composition, where a steel grade with a higher Tliquidus will require a higher pouring temperature (Tpouring = Tliquidus + superheat). Consequently, if the same powder is used to cast 2 different grades, the one with higher Tpouring will produce more lubrication. In addition, the extent of the difference between the solidus temperature (Tsolidus) and Tbr indicates the lubrication range of the casting powder within the mould. Mills et al.42) have mapped the viscosity and break temperature for a variety of commercial slags in Fig. 2. Here, the boundaries of crack and sticker sensitive grades provide the operational window for viscosity of CC slags with regards to casting speed.

Within the mould, lubrication is accomplished by both the liquid and solid-liquid slag. Nevertheless, these rela-tionships are not entirely straightforward since viscosity also affects the extent of lubrication in the mould (i.e. Lubrication Index). Moreover, local thermal gradients due to metal flow from the SEN or mould geometry (e.g. size, corners, funnel shape, cooling slots design, etc.) may affect infiltration locally by changing the viscosity and break tem-perature as the slag travels downwards in the casting direc-tion, but also along the perimeter of the mould.

3.2. Thermal Conductivity, Crystallization and Radia-tion

At the beginning of casting, the infiltrated slag forms a solid glassy (i.e. amorphous) rim due to fast cooling by direct contact with the water-cooled copper mould; later, the rim may crystallise depending on time, temperature and composition. The meniscus region provides the lowest thermal resistance (i.e. highest heat flux some millimetres below the meniscus) which allows solidification of the shell tip. Thereafter, slag infiltrates and solidifies to form a slag film that once again; depending on time, temperature and composition; will be glassy, partially crystalline or fully

Fig. 2. Typical operational window for break temperature and viscosity of CC powders.

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crystalline (Fig. 3).The thermal conductivity of CC slags is linked to their

structure; where glassy types tend to have lower conductivi-ties similar to the liquid phase (ca. 1 W/m·°K). However, the conductivity of crystalline and partially crystalline slags is around double the value for the glassy phase due to increased long range ordering.30) Figure 4 shows the typi-cal behaviour of thermal conductivity as a function of the temperature and cooling/heating history.43)

Crystalline slags typically have higher thermal conduc-tivities since conduction is dependent on the transport of phonons through lattice vibrations;44) however, this is coun-ter intuitive to current industrial practices where crystalline slags are used to decrease the overall heat transfer to the mould. Nevertheless, the insulating effect of crystalline slags may be explained by the larger grain boundaries on crystals that can act as scattering sites and lower the total radiative heat transfer, which may counteract the effect of thermal conductivity. In either case, the cooling rate (i.e. heat flow from steel to mould) controls the formation of crystalline phases and the residence time in the mould by affecting the viscosity. Thus, the slag film resistance is a result of slag infiltration including both liquid and solid slag formation. The heat transfer from the molten metal to the mould is mainly controlled by the solid slag film (i.e. glassy/

crystalline); while the thin liquid slag layer performs a sig-nificant role in lubrication of the newly formed shell.45) In addition, the formation of crystalline phases is a function of the local composition and thermal history within the mould as the slag travels from the slag bed to the shell-mould gap. Thus, the control of crystallization to balance the conductive and radiative heat transfer is imperative for a uniform shell formation. Hence, the role of thermal conductivity should be carefully reviewed when assessing the performance of crystalline slags. Furthermore, it is the author’s contention that one of the main components of the thermal resistance provided by crystalline slags is related to changes not only to the radiative and conductive properties, but also to the increase of the interfacial contact resistance between solid slag and mould (i.e. surface roughness) during crystalliza-tion.

3.3. Interfacial Contact Resistance and Cooling RateCrystallization is accompanied by the formation of a

surface roughness between the mould and solid slag as described by Tsutsumi et al.46) and Spitzer et al.47) This roughness originates from the transformation of glassy into crystalline slag which is accompanied by densifica-tion and contraction. The thermal contraction during phase transformation increases the surface roughness and results in the formation of a thermal resistance between the solid slag and mould walls.47–49) This roughness (ca. 5–40 μm) is often named “air-gap” since the contact between the solid slag and mould is not perfect and the free space is filled with gas (not necessarily air). However, it should not be confused with the lack of contact between the shell and slag film/mould that is caused by strand shrinkage or a lack of taper, which is also often termed “air-gap”. For the sake of clarity, the term surface roughness (arising from the flux contraction/crystallization) will be maintained and its influ-ence on the heat transfer will be defined via the interfacial contact resistance, (rint). The surface roughness has been found to be a function of crystallinity and cooling rate;46) where crystalline powders are more tortuous while glassy films have a smoother surface and result on a better con-tact with the mould as seen on industrial slag film samples obtained by Mills, Li and Becerra50) (Figs. 5(a) and 5(b)). Recent work with a copper disc mould simulator by Park et al. have shown that varying flux compositions result in different degrees of crystallization, which is accompanied by contraction during crystallization and less cracking (Figs. 5(c) and 5(d)).

Industrial slag film samples and laboratory disc samples bear a close resemblance with a smooth surface on glassy slags, while crystalline samples exhibit a more tortuous pro-file, plagued with cracks due to contraction and cooling, dur-ing crystallization. This is especially evident for industrial samples subjected to ferrostatic pressure and force imbal-ances during cooling. The resulting interfacial resistance has always been associated to the film thickness in laboratory experiments.25,51) This creates a problem where the magni-tude of thermal resistance is linked to a specific total film thickness; and although this may hold true for a given set of casting conditions resulting in a similar film thickness, it is not applicable to any other situation. Furthermore, the values obtained in experiments do not include the effect of

Fig. 3. Evolution of crystallization in the slag film within the mould.

Fig. 4. Typical thermal conductivity behaviour for CC slags.

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ferro-static pressure that pushes the shell against the mould and “compresses” the slag film. This results in a huge disparity between interfacial resistance values measured in experiments (0.5 × 10−4 −1.4 × 10−3 m2·°K/W,25,27,46,52–54)), the plant measurements available by Hanao and Kawamoto (0.1−0.5 × 10 −4 m2·°K/W,55,56)), and those used in numeri-cal models (5 × 10 −9– 1.8 × 10 −3,18,26,36)). Regardless of these particularities, the experimental versus industrial measurements differ by at least 2 orders of magnitude, while the input data spreading in modelling is of 6 orders of magnitude. This makes comparison and evaluation of model accuracy very difficult. Yamamura et al.57) have pre-sented recent research results to clarify this issue by using a contact resistance simulator; while Hanao, Kawamoto and Yamanaka58) have evaluated the interfacial resistance on a pilot caster compared to a parallel-plates simulator, which shows clearly that the total resistance of the film and rint increase with solidification temperature whereas the increase of thermal resistance by crystallization of the film decreases the cooling rate in the mould. Nevertheless, it is clear that improved characterization techniques for rint are necessary since its values must be independent of the film thickness and probably be a function of crystallization/basicity and cooling rate (as presented by Hanao et al.58)) in order to clarify this factor which has great influence on the overall heat transfer in the mould. Likewise, mapping of a wider variety of powders is necessary to complete a suitable database for numerical modelling (Fig. 6).

Furthermore, it must be noted that formation of a homo-geneous slag film and a fixed ratio of the crystalline and glassy layers in such film in the whole mould is an idealized concept. This is because actual slag films are highly hetero-geneous and constantly change during casting. For instance, crystals in the film grow when exposed to high temperatures during prolonged periods within the mould (e.g. casting sequence). Moreover, they often do not show a clear bound-ary between phases. A closer look reveals that islands with crystals appear in glassy areas and vice-versa. Slag films retrieved from a mould simulator by Park et al.59) shown in

Figs. 7(a)–7(b) indicate separate islands of cuspidine crys-tals which are formed within glassy regions. Additionally, gas porosity may form throughout the film creating voids that affect heat transfer to the mould. Rigorous splitting between liquid and solid slag layers occurs only within the framework of modelling concepts to assign properties and simplify calculations. However, it is the author’s conten-tion that the structure of the film changes dynamically as it grows, it is exposed to diverse temperature gradients (e.g. cooling rates) and travels down the mould during casting. This results in varying grain sizes within the crystalline layer as well as drastic changes in radiative properties (i.e. thermal diffusivity, scattering, etc.) as shown in Fig. 8 for a slag film simulator sample along the whole mould length.60)

3.4. Interfacial TensionThe interfacial tension between metal and slag (γm− s) is

another important factor during casting since it affects the curvature of the meniscus. Typical values for γm− s are in the range of 0.8–1.4 N/m, but these values are heavily affected by the content of surface active elements such as S, N and O in the steel. Theoretically, a higher interfacial tension would increase the meniscus radius; thereby increasing the occur-

Fig. 5. Surface roughness on slag films recovered after casting, a) Crystalline and b) Glassy slag (after50)) and slag from cop-per disc mould simulator c) crystalline slag and d) glassy slag.

Fig. 6. Interfacial contact resistance ranges obtained by labora-tory tests and industrial sampling as well as used in numerical models (dotted boxes: experimental/plant; grey boxes: numerical modelling).

Fig. 7. a) SE-SEM image of the slag film, b) BSE-SEM image of an enlarged crystalline region in the slag film retrieved from mould simulator experiments60) for medium carbon steels and c) Gas porosity on slag films obtained directly from caster (after50)).

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rence of deep oscillation marks. On the contrary, a lower interfacial tension would produce a shorter radius and lower propensity to marks. In terms of hook formation, a shorter radius (i.e. low γm− s) might initially imply lower propensity to hooks because marks are shallower. However, the smaller radius reduces slag infiltration, bringing the shell closer to the mould and enhancing cooling of the tip; thus, bringing back the risk of hook formation. In contrast, a larger radius (i.e. high γm− s) would decrease heat transfer due to the lon-ger distance between shell-tip and mould; thus decreasing the hook risks. Some industrial evidence has been found to support this speculation, based on the effect of sulphur con-tent on the formation of hooks by Miyake et al.61) Yet, an increased radius might also favour solidification along the curved meniscus into the melt, increasing hook formation frequency. Observations in the plant show a high variability and the results are often contradictory. Takeuchi found an inverse correlation between the oscillation mark depth and hooks;62) whilst Shin et al.63) found the opposite. Elfsberg64) could not find a clear correlation between oscillation marks and hooks. Consequently, the effect of γm− s on surface qual-ity is still under debate.

4. Key Lubrication Concepts

Lubrication (a.k.a. slag infiltration and powder consump-tion) requires that liquid slag infiltrates between the mould and solidified shell to avoid direct contact between molten steel and the copper mould which has a significantly lower melting point. As described previously, casting powder is added continuously to the mould to form an insulating layer (i.e. slag bed) that melts in contact with the steel (e.g. slag pool). This supplies fresh slag to the lubrication film as it is dragged downwards by the shell in the casting direc-tion. The main driving forces for powder infiltration are the dragging of liquid slag by the shell and the oscillation of the mould, where infiltration is at the highest during the second half of negative strip time and first half of positive strip time, Qc = 1/2tn + 1/2tp).36,65) This also explains the contradictory observations during plant trials increasing/

decreasing negative strip time. In fact, extending either tn or tp would increase powder consumption to some extent; but the increase is more evident if it occurs in the middle of the cycle. Thus, the overall consumption is mostly made of liquid slag fed from the liquid pool. Nevertheless, there is also a minor contribution from solid slag travelling down-wards at a much lower speed than the liquid slag. This has been documented on sequential trials with 2 different casting powders, where it takes approximately 30 minutes for the thermocouple mould readings to stabilize after a change in powder type, so the second powder replaces the initial solid film (casting speed=1 m/min).66) A similar phenomenon is observed when using a starting powder.

Figure 9 shows a schematic diagram of the slag infiltra-tion and formation of fully lubricated, intermittent contact and air-gap regions. The fully-lubricated region is defined by the powder’s break temperature, (since slag at tem-peratures higher than Tbreak remains liquid; thus, enhancing convective and conductive heat transfer even if significant strand shrinkage occurs (as long as there is molten slag to fill in the gap). On the contrary, heat transfer will drop due to air gap formation in the absence of liquid slag for temperatures below Tbreak combined with strand shrinkage. Finally, an intermittent contact zone is possible due to fluc-tuations on heat transfer during the oscillation cycle, local flow dynamics and changes in conditions during casting. The Lubrication Index is defined as the mould length above Tbreak divided by the effective mould length (e.g. measured from the metal level to the mould bottom).

L Ifully lubricated region

effective mould length. . =

A Lubrication Index equal to 1 would mean that the slag film remains liquid along the whole mould length. Recent trials by Jung et al.41) using Al2O3 as substitute for SiO2 showed that it was possible to extend such lubrication range in casting powders for high Al and Mn steels. The aim of such “wet mould” practice is to provide a smoother and continuous heat extraction; but in some cases, it is also used

Fig. 8. Cross-section micrograph using back-scattered scanning electron microscope of slag film on mould simulator (after60)); a) upper mould (20 mm from top of meniscus), b) middle mould and c) lower mould (20 mm from bot-tom of mould).

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to minimize the interaction between casting powders and the melt by decreasing the slag’s residence time in the mould (Fig. 10(a)). Typical CC machines operate on a semi-dry level of lubrication (e.g. L.I.<<1), where the solid slag film breaks apart from the mould bottom and the temperature in the second half of the mould drops unless the taper is optimized to maintain contact (Fig. 10(b)).

Figures 10(c)–10(e) shows the effect of taper on the shape of the infiltration channel and air-gap. An insufficient taper produces early separation of the shell from the mould, decreased heat transfer and poor solidification. This results in thinner shells, which are prone to breakouts. In contrast, an excessive taper closes the channel and promotes mould wearing as well as possible sticker events. Kajitani et al.67) observed a strong effect of the channel shape on lubrication by means of a cold model experiment. Specifically, the experiments proved that a channel that closes towards the mould bottom (i.e. excessive taper) still allows infiltration, whereas a channel that widens towards the mould bottom (i.e. insufficient taper) eradicates infiltration. The latter could also explain why operators prefer an excessive taper rather than a lack of contact, since an insufficient taper not only affects the heat transfer and shell thickness but actively counteracts powder consumption.

5.  Effect of Flow Dynamics, Heat Transfer and Solidifi-cation

Flow dynamics occurring inside the mould during Contin-uous Casting have been extensively investigated in the past. This includes water and numerical models to understand the formation of typical flow structures such as double/single rolls, discharging jets, impingement point, standing waves, etc.35,68–72) (Fig. 11) as well characterizing the unsteadiness of metal flows in the mould arising from asymmetric flows (e.g. nozzle misalignment), control valves (e.g. stoppers and sliding gates) and gas injection.73–76) Nevertheless, the effect of flow dynamics on heat transfer has been analysed considerably less,8,77–79) while their combined influence on solidification is a relatively new topic.8,80,81) Despite the extensive research on these phenomena, their effects on lubrication have been rarely addressed or even analysed in the context of defect formation during casting. This is possibly due to the fact that the slag phase has not been included in the calculations. Instead, its effects have been mostly modelled through imposed heat flow conditions as discussed in previous sections. However, the advent of more powerful computers and improved multi-phase mod-elling techniques has made possible the treatment of the slag phase on multi-physics models which have opened the door to understand their combined influence on lubrication. The most evident effect of flow and heat transfer during casting is their influence on the temperature distribution

Fig. 9. Key lubrication concepts in CC.

Fig. 10. Schematics of lubrication in the CC mould: a) wet practice, b) normal practice, c) insufficient taper, d)ideal taper & e) excessive taper.

Fig. 11. Typical flow structures in CC and resultant heat distribu-tion in the mould (darker shades represent higher tem-peratures).

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in the mould. This is difficult to capture through standard monitoring systems, which are limited by the number of thermocouples. However, it is evident in higher resolution systems (e.g. fibre optics) as well as numerical models (Fig. 11).79) This thermal map is a natural consequence of hav-ing the liquid steel transported from the SEN to the mould as the main source of heat in the process. Therefore, the flow of steel within the mould affects the heat distribution and extraction through the mould as well as the infiltration pattern and Lubrication Index. Contrary to the generalized perception, slag infiltration fluctuates not only in the casting direction but also along the mould width. A clear example of this behaviour is the use of inverted port SEN’s to promote heat delivery to the meniscus and ensure lubrication in the mould corners82,83) (Fig. 12). These differences in lubrica-tion are also evident when studying recovered slag films after casting, which reveal a high variability of the lubrica-tion film along the perimeter of the mould (Fig. 13).84)

The authors have previously established that differences in the flow and heat transfer affect the Lubrication Index (extent of lubrication) in the mould.85–87) This became more evident when analysing the flow and heat transfer provided by the same nozzle type at different immersion depths, casting speeds and argon flow rates (Fig. 14). An initial consequence of these changes is the possible forma-tion of prejudicial flow structures such as strong waving or excessive standing waves at shallow immersion depths, high casting speeds, narrow mould widths and upward port nozzles angles. In the worst case scenario, high standing waves decrease the pool depth at the meniscus. This in turn, may interfere with slag infiltration or cause engulfment of powder into the melt. A secondary effect is an initial shell-tip growth at different heights along the mould perimeter. This behaviour is strongly linked to the steel composition and superheat, promoting the formation of deep marks (i.e. excessive infiltration) for steel with a high solidification point. In contrast, it can delay shell tip formation to the point where dragging of slag is not possible for a low melting point grade. A possible conclusion is that the shell needs to grow at a minimum height for any given grade to produce sufficient slag infiltration, but not excessively into the melt in order to avoid hooks. Certainly, the opposite is true for deep SEN positions, low casting speed, ultra-wide moulds and downward-port nozzles angles, where the lack of flow circulation close to the metal surface may cause meniscus freezing.

The behaviour of the lubrication Index under all these circumstances is of utter importance to the formation of defects in the mould since it controls the length at which heat extraction in the mould is more effective; thereby, controlling shell growth. Consequently, solidification becomes irregular along the slab width causing differences in shell thickness which are responsible for stress accumulation and possible cracking. Moreover, the Lubrication Index is constantly changing due to normal variations in the casting conditions during the sequence (e.g. casting speed, immersion depth, pouring temperature, etc.). This causes a shifting of the heat flux curve and the amount of local heat extracted through the mould (as exemplified in Fig. 15 for different immer-sion depths). Effectively, this can shift solidification from optimal (i.e. without cracking) to a position with reduced/

increased heat transfer and lubrication, which increases the risk of forming defects. Alternatively, defects may shift from one position to another relieving cracking locally, but creating a new defect on a different location of the strand. A typical example of this is the switching between longitudinal cracks and corner cracks by changing powder composition or immersion depth.87) Suzuki et al.,88) Carmona et al. and others89) have clearly related the heat flux extracted from the strand to cracking issues for a variety of steel types. However, this variation of heat flux and solidification was considered only along the casting direction. It is the author’s contention that cracking in the strand will also change locally along the mould perimeter due to changes in lubrication as flow; heat transfer and solidification take place. Therefore, it is not possible to address these issues by changing overall casting parameters such as casting speed, oscillation settings or mould temperature since these have an effect on the whole mould, whereas lubrication variations occur at local level. In response to this, the authors foresee some possible solutions including: i) Adaptive mould cooling by changing water channel design and local water flow rates during casting, ii) Optimized nozzle design to re-direct the steel flow to modify slag infiltration and shell thickness locally, iii) Functional casting powders such as Non-Newtonian fluxes where slag properties change locally depending on lubrication require-ments90,91) and iv) Localized mould powder feeding92) which are all promising alternatives to enhance lubrication in CC to minimize defects.

Fig. 13. Slag film on the wide face recovered after casting, after Hooli.84)

Fig. 14. Effect of immersion depth on Lubrication Index (darker shades represent higher temperatures).

Fig. 12. Flow and heat distribution when using a typical SEN versus inverted ports (darker shades represent higher temperatures).

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6. Challenges for Modelling Application to Industrial Practice

The previous discussion has deep implications for applica-tion of numerical models to casting operations by demonstrat-ing that simplified models for heat transfer and lubrication are not enough to capture the transient 3-dimensional nature of some critical defects in CC. Consequently, more detailed models are required to enable more realistic predictions. These details include the followings aspects:

• Improved characterization of the dynamic behaviour of slags (e.g. TTT and CCT diagrams) which should be obtained experimentally. This allows a more precise mapping of slag properties by accounting for tempera-ture, residence time and cooling rate in the film rather than using a simplistic approach based on pre-defined layers.

• Studies of crystallization effects on slags which range from its impact on properties (e.g. thermal conductiv-ity, viscosity, optical properties) to interfacial resis-tance, mechanical resistance, shearing effects (due to mould oscillation) and wettability.

• Accounting for taper effects in calculations including shell shrinkage and taper type (e.g. linear, parabolic, curved caster, etc.). Specifically, this would require a coupled stress-strain formulation for the shell/mould interactions.

• The use of 3D transient flow calculations including detailed SEN geometries to simulate the effect of flow control valves (i.e. stopper control/sliding gate dither-ing) and argon injection.

• A comprehensive modelling of the dynamic conditions in the caster such as temperature decrease during the sequence and ladle/tundish changes, the variation of SEN immersion depth, grade changes, start and end of sequences, etc.

• A more exhaustive monitoring of the caster status and product quality, such as automatic linking of quality reports to casting logs, higher resolution of mould tem-perature monitoring (for instance, through fibre optics) and the implementation of improved friction alarms.

7. Conclusions

From the above discussion, it is evident that the model-ling of continuous casting; as advanced as it is, is still far from complete. Specifically, a variety of phenomena that have a direct impact on lubrication are yet to be included in the simulations. Thereby, the quality of the predictions and industrial applicability could be greatly improved. Increased computer power and advanced multi-physics models present casting researchers with the paradigm of which phenomena to take into account and how to include them in the simula-tions. But, as it is often the case with modelling, there must be a trade-off between speed and accuracy considering the practical issue to be solved. Regardless of this, it is evident that a huge effort on casting powder characterization must be made to provide models with reliable property data. Such characterization must go beyond the current experimental limitations to secure a more realistic description of the con-ditions in the mould during casting. These properties were not in demand before, since the effect of slags on simula-tions was simplified to cope with the available computing power. By taking these implications into account, it is pos-sible to bring simulations beyond steady-state predictions and into a new generation of models capable of predicting specific problems that arise in the caster due to the inherent variability of the process.

AcknowledgementsPNJ and PERL would like to thank the casting floor

engineers and operators at SSAB; especially, Mr. Christer Nilsson, Dr. Patrik Wikström and Dr. Erik Roos for fruitful discussions and support during this work. PRL would like to thank Prof. Zushu Li for providing slag microstructure images and Dr. Paavo Hooli for providing the slag film overview in the mould. The research leading to these results has partly received funding from the Swedish Energy Agency (Energimyndigheten) project n° 37976-1. The research leading to these results has received co-funding from the European Union’s Research Programme of the Research Fund for Coal and Steel (RFCS) under the grant agreement n° [RFSR-CT-2011-00005]. This study was also partially supported by the Brain Korea 21 PLUS (BK21 PLUS) Project at the Division of the Eco-Humantronics Information Materials.

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