Industrial application of a numerical model to simulate lubrication, mould oscillation, solidification and defect formation during continuous casting

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1 IOP Confeence Seies: Mateials Science and Engineeing Industial application of a numeical model to simulate lubication, mould oscillation, solidification and defect fomation duing continuous casting To cite this aticle: Pavel E Ramiez Lopez et al 2012 IOP Conf. Se.: Mate. Sci. Eng Related content - Simulation of tansient fluid flow in mold egion duing steel continuous casting R Liu, B G Thomas and J Sengupta - Modelling of hoizontal centifugal casting of wok oll Zhian Xu, Nannan Song, Rob Val Tol et al. - Simulation study on continuous casting pocess of Al/Al bimetal ound billet unde multi-electomagnetic Li Wu, Tongmin Wang, Ying Fu et al. View the aticle online fo updates and enhancements. This content was downloaded fom IP addess on 09/11/2018 at 16:39

2 IOP Conf. Seies: Mateials Science and Engineeing 33 (2012) Industial application of a numeical model to simulate lubication, mould oscillation, solidification and defect fomation duing continuous casting Pavel E Ramiez Lopez 1, Ulf Sjöstöm 1, Thomas Jonsson 1, Pete D Lee 2, Kenneth C Mills 3, Mako Petäjäjävi 4 and Jano Piinen 5. 1 Casting and Flow Simulation Goup, Sweea MEFOS, Aonstopsvägen 1, SE Luleå, SWEDEN 2 School of Mateials, The Univesity of Mancheste, Ruthefod Appleton Laboatoy, Didcot, Oxon, OX11 OFA, UNITED KINGDOM 3 Depatment of Mateials, Impeial College London, Pince Consot Road, SW7 2AZ, London, UNITED KINGDOM 4 Reseach Enginee, TRC / Melt Metallugy, Outokumpu Tonio Woks, FIN Tonio, FINLAND 5 Development Enginee, Continuous Casting, Rautauukki Oyj, Tevaaitti 4 B 26, Oulu, FINLAND pl@mefos.se Abstact. In ecent yeas, the addition of the phase to numeical models of the Continuous Casting (CC) pocess has opened the doo to a whole new ange of pedictions. These include the estimation of infiltation and powde consumption (lubication), heat tansfe and cooling though the coope mould (solidification) and investigating the effect of opeational paametes such as mould oscillation and powde composition on suface quality / defect fomation. This wok pesents 2D and 3D CC models capable of descibing the dynamic behaviou of the liquid/solid in both the shell mould-gap and bed as well as its effects on heat extaction and shell fomation. The pesent pape also illustates the application of the model to a vaiety of castes and the challenges faced duing its implementation. The model attained good ageement on the pediction of mould tempeatues and shell thicknesses as well as film fomation and heat flux vaiations duing the casting sequence. The effect of diffeent oscillation stategies (sinusoidal and non-sinusoidal) was exploed in ode to enhance powde consumption and suface quality. Futhemoe, the modelling appoach allows one to pedict the conditions leading to iegula shell gowth and uneven lubication; these ae esponsible fo defects such as, stickes, cacking and, in the wost case scenaio, to beakouts. Possible mechanisms fo defect fomation ae pesented togethe with stategies to enhance pocess stability and poductivity of the CC machine. 1. Intoduction The behaviou of the casting powde and the way it influences heat tansfe and solidification ae amongst the most complex, but impotant, phenomena occuing in Continuous Casting. This behaviou includes a vaiety of themo-chemical eactions, such as phase tansfomations, fluid flow and heat tansfe mechanisms. Fo instance, pactically all the heat tansfe modes (convection, Published unde licence by Ltd 1

3 MCWASP XIII IOP Conf. Seies: Mateials Science and Engineeing 33 (2012) conduction and adiation) and combustion occu within the mould duing casting. Fistly, convection cuents and heat dissipation appea in the metal and the liquid pool in esponse to density changes duing phase tansfomation and cooling. Secondly, conduction takes place though the shell, solid film, sinteed bed and coppe mould duing solidification. Finally, adiation accounts fo ~10-15% of the total heat extacted fom the melt1). The vaiety of phases and heat tansfe mechanisms occuing at the meniscus and bed ae depicted in Figue 1. Figue 1: Heat tansfe mechanisms at the meniscus. The dynamic behaviou of the needs to be included in the simulations to povide a moe ealistic epesentation of the pocess. Howeve, it is often teated sepaately because of its complexity and the computational effot equied to solve it. In most of the pevious modelling studies the incopoation of into the calculations is avoided and limited to the use of measued heat fluxes (fom themal monitoing systems) as bounday conditions which define the heat extaction ate to the mould 2, 3). To a lesse extent, the -film has been epesented though an equivalent themal esistance system which gives a bette idea of the effect of popeties on heat tansfe and solidification, but is usually based on abitay definitions of the film thickness4-6). Thus, these models ovelook the dynamic behaviou of the, which includes the effect of powde composition changes duing the heat, the tansient influence of mould oscillation on powde consumption and the ole of infiltation on defects such as oscillation maks, stickes, entapment, etc. Only the investigations epoted by Meng et al. 7) and the cuent authos 8) have addessed the modelling of the tansient film behaviou and its impact on infiltation. The cuent eseach addesses the poblem of adding to the top of the steel in the mould, and its implications on numeical simulations. This includes the ceation of a model that couples the metal flow, heat tansfe, mould oscillation and solidification within the mould. Pevious publications by the authos have descibed the theoy behind this model9) as well as its validation with industial obsevations10). Futhemoe, the tansient appoach used in the simulations allows one to pedict defects such as oscillation maks 8) and to deduct a unified mechanism fo thei fomation 11). In this manuscipt the challenges faced duing the industial application of the model ae detailed and specific cases aising fom its implementation and some selected esults ae pesented. 2. Fully-integated multi-phase appoach The modelling methodology ecently intoduced by the authos9, 10) couples the flow dynamics in metal, and gas phases (if pesent) to the heat flux and solidification duing mould oscillation. The fluid model is based on the Navie-Stokes equations fo compessible viscous flow coupled with the Volume of Fluid (VOF) method. This allows one to pedict the /metal inteface and makes no assumptions egading the shape of the meniscus (i.e. avoiding a pe-fixed Bikeman pofile o 2

4 IOP Conf. Seies: Mateials Science and Engineeing 33 (2012) sepaating the fom the metal domain). The VOF scheme pedicts the inteface steel/ by solving a single set of continuity and momentum equations fo a phase tue (othewise, the scheme is educed to a typical single-phase Navie-Stokes appoach) 12). Since steel is the pimay phase, the continuity equation fo the volume faction is given by: t ( α steelρsteel) + ( α steelρsteelv) = ( m& steel m& steel ) Whee (α) is the phase faction, ( ) is the density, (v ) is the oveall velocity vecto and m& is the mass tansfe between the phases. The effective density ( ρ ) and the effective viscosity ( µ ) fo the tue phase ae given as: Thus, the momentum equation becomes: t ρ = α ρ + ( 1 α ) ρ steel steel µ = + ( 1 ) αsteelµ steel α µ ( ρ v) + ( ρ vv) = P+ µ ( v+ vi + ρ g S Sγ s+ 2 3 Whee ( P ) is the pessue, ( g ) is the gavitational foce vecto and the last two tems ae the momentum sinks due to solidification and intefacial tension. ( S γ ); the latte esults fom the intefacial tension between steel and and is calculated though the CSF model poposed by Backbill et al. 13) : Whee ( γ metal S γ = γ metal metal (1) (2) (3) (4) ρκ α 1 (5) ( ρsteel + ρ) 2 ) is the -metal intefacial tension as calculated by Chung and Camb 14) as a function of the powde and metal compositions, and (κ ) is the local suface cuvatue as defined by Backbill et al. 13). The appoach fo solving heat tansfe in the liquid phases is compaable to the multiphase appoach, with the continuity and momentum equations shaing the enegy Equation 15) : t ( ) = ( K T + ( τ v ) ( ρ E) + v( ρ E+ P) whee ( E ) is the enthalpy and ( K eff eff ) denotes the effective themal conductivity fo the phase tue. An impovement fom pio wok 9, 10) includes a coection to K eff afte each iteation to account fo the bluing effects (gadient at the inteface) inheent to VOF 12). The additional steps consist of locating the -metal inteface and updating the aveaged value of Keff fo α steel 0. 5 to the appopiate value of K as a function of tempeatue. Although adiation conduction in the ( K ) has not been explicitly included in the model, its effects on heat tansfe ad have been added by enhancing K though: ( K = Kcond + Kad ), whee: Kad is ~3-5% of the conductivity ( K cond ) as demonstated by Wang et al. 16). Unfotunately, this method does not fully epesent the effects of cystallization in the film, which ae time and composition dependent. Howeve, Mills et al. 1, 17) concluded that adiation accounts fo ~15% of the total heat tansfe in the eff (6) 3

5 IOP Conf. Seies: Mateials Science and Engineeing 33 (2012) mould, which makes ( K K 0.05) a easonable assumption. Finally, the solid wide and = cond naow faces ae included in the analysis by solving the heat conduction equation fo solids: Whee ( h ) is the sensible enthalpy and ( K ( h) = ( K T) ρ coppe coppe t (7) coppe ) is the themal conductivity of the coppe mould (~400 W/m-K). The solidification outine is based on the leve ule as detailed elsewhee 18). Additionally, an enthalpy-poosity technique that teats the mushy zone as a poous medium is used to include the velocity sink due to solidification. This sink tem ( S s ) is intoduced in Equation (4) and depends on the solid faction at each cell though: whee S s = ( 1 f ) 2 l 2 ( f ) 8 A mush = 1 10, is the pulling velocity and l l A mush ( v v ) pull (8) f is the liquid faction of steel. Tubulence effects ae added though the k -ε model which has poven fast and obust in pio woks 19, 20) and is descibed elsewhee 15). Finally, solidification effects on tubulence ae included by adding a sink tem to the k (tubulent kinetic enegy) and ε (tubulent enegy dissipation ate) expessions 18). 3. Model Paticulaities Industial application of the model led to a vaiety of changes in ode to account fo the conditions on the casting floo; these have often been ovelooked in moe fundamental studies, but ae extemely impotant to the pocess. These include specific details of the mould geomety (e.g. mould tape, coating, etc), powde feeding pocedues, oscillation stategies, as well as pefeed pactices fom opeatos. These paticulaities ae descibed in the following sections. A summay of the standad bounday conditions to un the model and solution pocedues has been pesented elsewhee 9) Intefacial themal esistance and mould coating The heat tansfe between shell and mould (i.e. acoss the film) is extemely impotant since excessive heat emoval leads to thicke shells that cack when the slab is withdawn. In contast, insufficient heat emoval can lead to thin shells that cause beakouts and mould level changes. Heat tansfe in the -film is a complex pocess involving lattice conduction and adiation and is also affected by both the thickness and degee of cystallisation of the 16, 21). Since the cystalline phase has a highe density than the glassy phase within the film, cystallisation is accompanied by shinkage. This poduces ugosity and loss of contact with the mould, ceating an additional themal esistance denominated intefacial themal esistance ( int ) as noted by Spitze et al. 21) (Figue 2). Pevious studies have linked int to the total film esistance and solved algebaically the heat tansfe as a system of electical esistances as pesented in Figue 4 22, 23). The pesent model avoids this by solving the actual infiltation of liquid- into the gap and using its themal popeties to diffeentiate between the phases. These popeties include the vaiation of themal conductivity and C p as a function of tempeatue as shown in Figue 3. Consequently, the themal esistances in the -film ( film ) ae educed to: int solid film d cy d glassy d liquid K cy K glassy K liquid solid liquid = int d + K film eff (9) 4

6 themal conductivity, Kcond (W/m-K) MCWASP XIII IOP Conf. Seies: Mateials Science and Engineeing 33 (2012) Figue 2: Suface ugosity on sample quenched against a coppe mould. Afte Holzhause et al.24) Tempeatue ( C) 1000 Figue 3: Example of themal conductivity popeties as a function of tempeatue (implemented in the model). Figue 4: Themal esistances between liquid steel and cooling wate on CC. Whee d film is the thickness of the film (a esult of the calculations) and K eff is the coected themal conductivity fo the when α steel 0.5 o the themal conductivity of steel if α steel > 0.5. The magnitude of int is citical on the simulations and depends on the basicity as descibed on pio wok 10): int = (CaO/SiO 2 ) 4.19 (10) Modelling of the Nickel o Chomium coating that is often applied to the mould hot face was done accoding to the specifications of each caste. Fo some cases, the thickness is constant along the mould length, whilst fo othes the thickness vaies fom top to bottom in a simila way as the tape. Both cases wee implemented as an additional esistance ( coating ) in the gap, (Equation 11). gap = d film K eff + int + 6coating 78 d coating K coating (11) 3.2. Powde viscosity The behaviou of afte infiltation depends on its beak tempeatue ( ), cystallisation ate and viscosity ( ) as it tavels downwads and feezes (solidifies) against the mould. This behaviou was included in the simulations though an exponential incease of viscosity below as intoduced by Meng et al. 25). Nevetheless, this appoach is not sufficient to account fo the events occuing on the bed. Theefoe, additional viscosity popeties wee used to model the evolution fom oom tempeatue to the melting point (Figue 5). A natual esult of this implementation is the pediction of a im and powdeed-sinteed layes in the bed without the aid of any special function to descibe thei pofile 8). 5

7 IOP Conf. Seies: Mateials Science and Engineeing 33 (2012) Figue 5: Slag viscosity used in the simulations vs evolution of duing heating. Lowe potion of the diagam afte Mills 17) Powde feeding and bed tempeatue A pessue inlet condition was applied to the top of the mould to simulate the effects of a system open to the atmosphee. The is supplied at this bounday (as in the eal pocess) by adding powde to maintain the desied bed thickness. Hee, citical diffeences in casting pactices have deep implications on modelling. Fo some castes, the casting powde is added until it fills completely the mould cavity, which ceates a thick powde bed. In contast, othe opeational pactices maintain only a powde laye of seveal mm (30-60 mm) above the metal level. In modelling tems, the thin powde bed case epesents the use of a thid phase (ai on top of the bed), and the supply of a cetain volume faction of powde though this bounday. The thick bed case equies only a 2-phase model whee only is supplied at the bounday. In both cases, the tempeatue at the top of the bed is a citical bounday condition which can be measued using pyometes o an infaed camea. Figue 6: Example of CAD models and computational gid used on the simulations 6

8 IOP Conf. Seies: Mateials Science and Engineeing 33 (2012) Geomety In ode to povide a ealistic epesentation of the caste, full CAD models based on the exact dimensions of the SEN and mould wee ceated. These CAD s wee late used to poduce detailed 2D and 3D gids fom the eal components including wate channels layout, bolt systems, fillets and SEN design featues. Finally, the machine adius (fo cuved moulds) and tape (fo staight moulds) ae also included in the simulations (Figue 6). 4. Industial Application: Selected esults Afte validation, the modelling methodology has been applied to vaious conventional and thin-slab caste configuations. Selected esults fo both a 3D, ¼ model and some 2D models ae pesented next Metal flow Metal flow pedictions shown in Figue 7 descibe the fomation of a standing wave esulting fom a paticula SEN design which causes most of the metal leaving the pots to flow hoizontally. This ceates a stong dischaging jet which beaks into a small uppe oll and a lage lowe oll. The pedictions wee compaed with nail bed measuements (fo a simila configuation) and a good ageement on standing wave height and extension (Figue 8) was found. Figue 7: Jet angle pedictions on 3D vs 2D Figue 8: Standing wave pedictions on 3D vs 2D Thee dimensional simulations ae time consuming, but must be pefomed to veify the applicability of 2D models to a flow patten that is inheently 3-dimensional (e.g. CC mould). Dischaging jet angles and pedicted metal levels ae compaed, fo identical configuations, in 2D and 3D in Figue 9. The maximum standing wave height is less ponounced fo the 2D model than fo the 3D case (11 mm vs 9 mm) but pesents a bette ageement with the nail boad measuements. Moeove, the diffeences in jet axis wee only 1.5 degees, which demonstates the viability of using 2D calculations to study caste pefomance (e.g oscillation settings, steel gades and powde composition) (Figue 10). Nevetheless, 2D calculations cannot descibe the entie shape of the wave, which is equied to addess issues such as cone cacking, iegula infiltation, longitudinal cacking, etc. Figue 9: Jet angle pedictions on 3D vs 2D Figue 10: Standing wave pedictions on 3D vs 2D 7

9 IOP Conf. Seies: Mateials Science and Engineeing 33 (2012) Heat tansfe Mould tempeatue calculations fo a diffeent slab caste ae pesented in Figue 11. These pedictions fo the shell and mould show a typical pofile with the highest tempeatues occuing between 40 to 50 millimetes below the metal level followed by a gadual decease along the casting diection. The simulations clealy show tempeatue fluctuations, due to mould oscillation, which esult late in intenal iegulaities in shell gowth as seen in the casting pactice 26). This esult depats adically fom pevious modelling woks whee smooth paabolic shells wee pedicted 6, 27). Moeove, inceases of tempeatue in the mould cooling wate ( T) ageed well with pedictions (Figue 12 ). Figue 11: Pedicted shell and mould tempeatues measued fom the mould top. Figue 12: Pedicted T in cooling wate vs measuements Futhemoe, diffeent oscillation modes wee implemented in the model accoding to paticula caste settings. Heat fluxes fo sinusoidal modes wee pesented at MCWASP XII 8) including validation by compaing pedictions with a lab-based mould simulato intoduced by Badi et al. 28, 29). An impoved model vesion includes non-sinusoidal modes as pesented in Figue 13, which shows the pedicted heat flux evolution fo 2 cases unde identical casting conditions but diffeent oscillation modes. The vaiation between maximum and minimum heat-fluxes ove the cycle vaies consideably with oscillation mode; the vaiations fo the non-sinusoidal mode ae moe abupt, eaching up to 1.5 MW/m 2 -K, c.f. the sinusoidal mode with vaiations of ~0.5 MW/m 2 -K. A cucial diffeence between modes is the time spent on the high heat flux egion. Fo the non-sinusoidal mode, the peaks tend to be extemely fast which leaves most of the cycle in the low heat-flux aea. In contast, the sinusoidal mode emains longe in the high heat flux egion. This stong vaiability of heat tansfe poduces iegula cycles of shell gowth and thinning duing solidification, as descibed in the next section. a) b) Figue 13: Pedicted heat flux vaiations ove 6 seconds fo 2 uns with identical casting conditions but diffeent oscillation modes, a) Sinusoidal b) Non-sinusoidal 8

10 IOP Conf. Seies: Mateials Science and Engineeing 33 (2012) Solidification and powde consumption The shell thickness ( ) is easily measued by tacking points along the solidification font and the liquid film thicknesses ( ). Pio wok has demonstated the model s validity to pedict tends obseved in the industial pactice fo sinusoidal modes unde a vaiety of oscillation settings 9, 10). This motivated the authos to compae powde consumption pedictions fo the 2 oscillation modes shown in Section 4.2 (Figue 13) on Figues 14 and 15. Figue 14: Shell and liquid film thicknesses fo sinusoidal oscillation mode Figue 15: Shell and liquid film thicknesses fo non-sinusoidal oscillation mode (α=0.65) The non-sinusoidal mode appeas to be moe beneficial in tems of a smoothe shell by avoiding the long tem heat flux vaiations and eplacing them with a fast that affects the gowth only duing steep changes in mould velocity ( ), (Figue 15). Howeve, the non-sinusoidal mode also poduces a slightly thinne and weake shell which may be moe pone to cacking and may also esult in mould level vaiations. Nevetheless, the majo benefit of non-sinusoidal oscillation is to incease the powde consumption as eflected by the liquid -film thickness ( ), which goes fom 200 µm fo the non-sinusoidal case to less than 100 µm fo the sinusoidal mode. These pedictions ae in 30, 31) line with industial obsevations including the decease in oveall heat flux and mould tempeatue fo non-sinusoidal oscillation as noted by Suzuki 30). Pactical application of these esults includes the calculation of mould fiction and oveall powde consumption to poduce impoved oscillation stategies fo specific SEN-mould combinations. These stategies ae beyond the scope of this manuscipt. 5. Summay and conclusions A numeical model of the CC pocess, (which explicitly incopoates the pesence of ) has been successfully implemented into the industial pactice. The model includes specific infomation about the castes modelled (including mould-sen geomety, powde and steel compositions, oscillation settings) and opeato s pactices which ae vey elevant to the pocess but ae often ovelooked in numeical simulations. Addition of these pactical constaints to the model bing it close to eality and make possible the pediction of phenomena which ae still difficult to obseve in the plant (such as heat flux evolution duing the oscillation cycle and changes in shell intenal quality). A seies of conclusions wee dawn fom the diect industial implementation of the model. These include: 1. Addition of the bed and powde popeties to simulations is necessay fo an accuate epesentation of the meniscus. The fact that the model is able to pedict infiltation as a diect esult of the calculations (without a pedefined -film o meniscus cuvatue) is enough eason to add into simulations. This makes possible not only the calculation of the film but also pedicting vaiations on its thickness fo diffeent oscillation modes. 2. The implementation of geometically ealistic models fo the mould and SEN, plus the calculation of the -metal suface povides a good epesentation of the flow patten in the mould as eflected by the metal level (standing wave) pedictions. 3. A pecise implementation of opeatos pactices such as powde feeding elates fo the fist time the heat tansfe on the bed (including calculation of the liquid pool) to the amount of 9

11 IOP Conf. Seies: Mateials Science and Engineeing 33 (2012) consumption and tansient gap shape that makes possible to pedict changes on heat flux and shell thickness duing an oscillation cycle fo diffeent oscillation modes. 4. Implementation of diffeent oscillation modes makes possible to explain phenomena obseved on the casting floo, such as, the decease in oveall tempeatue, intenal quality enhancement and incease in powde consumption fo non-sinusoidal vs sinusoidal modes. Refeences [1] S. S. Ozawa, M. M. Susa, T. T. Goto and R. Endo: ISIJ Intenational, 46 (2006), 413. [2] B. G. Thomas: Metall. Mate. Tans. B, 33 (2002), [3] A. C. Mapelli, A. W. Nicodemi and A. A. Macandalli: Ionmak. Steelmak., 30 (2003), [4] R. Saaswat, A. B. Fox, K. C. Mills, P. D. Lee and B. Deo: Scand. J. Metall., 33 (2004), [5] J. W. Cho, T. Emi, H. Shibata and M. Suzuki: ISIJ Intenational, 38 (1998), 834. [6] Y. Meng and B. G. Thomas: Metall. Mate. Tans. B, 34 (2003), [7] X. Meng and B. G. Thomas: Metall. Mate. Tans. B, 34B (2003), [8] P. E. Ramiez-Lopez, P. D. Lee and K. C. Mills: Modeling of Casting, Welding and Advanced Solidification Pocesses XII, 12 (2009), Vancouve, CA. [9] P. E. Ramiez Lopez, P. D. Lee and K. C. Mills: ISIJ Intenational, 50 (2010), [10] P. E. Ramiez-Lopez, P. D. Lee, K. C. Mills and B. Santillana: ISIJ Intenational, 50 (2010), [11] P. E. Ramiez Lopez, K. C. Mills, P. D. Lee and B. Santillana: Metall. Mate. Tans. B, 43B (2012), [12] J. L. Liow, M. Rudman and P. Liovic: ISIJ Intenational, 41 (2001), [13] J. U. Backbill, D. B. Kothe and C. Zemach: J. Comput. Phys., 100 (1992), [14] Y. Chung and A. W. Camb: Metall. Mate. Tans. B, 31B (2000), 957. [15] B. E. Launde and D. B. Spalding: Lectues in Mathematical Models of Tubulence, Cambidge Univesity Pess, (1972). [16] W. Wang, K. Gu, L. Zhou, F. Ma, I. Sohn, D.-J. Min, H. Mastsuua and F. Tsukihashi: ISIJ Intenational, 51 (2011), [17] K. C. Mills: Mould Powdes fo Continuous Casting, Impeial College London, (2003), 211. [18] ANSYS Fluent Use's Guide: ANSYS Inc. ( ), [19] Q. Yuan, S. Sivaamakishnan, S. P. Vanka and B. G. Thomas: Metallugical and Mateials Tansactions; B; Pocess Metallugy and Mateials Pocessing Science, 35B (2004), [20] P. E. Ramiez-Lopez, R. D. Moales, R. Sanchez-Peez, L. G. Demedices and P. O. Davila: Metall. Mate. Tans. B, 36 (2005), [21] K. Spitze, K. Schwedtfege and J. Holzhause: Steel eseach, 70 (1999), [22] B. B. G. Thomas and B. B. G. Ya Meng: Metall. Mate. Tans. B, 34B (2003), [23] K. Soimachi, T. Yamauchi and A. Yamauchi: Ionmak. Steelmak., 29 (2002), [24] J. Holzhause, K. Spitze and K. Schwedtfege: Steel Reseach, 70 (1999), [25] B. Bououga and J. Gilles: Int J Mate Fom, 3 (2010), [26] B. Santillana, B. G. Thomas, G. Botman and E. Dekke: 7th Euopean Continuous Casting Confeence, (2011), Dusseldof, Gemany. [27] M. Hasan and S. H. Seyedein: Can. Metall. Q., 37 (1998), [28] A. Badi, T. T. Nataajan, C. C. Snyde, K. D. Powes, F. J. Mannion and A. W. Camb: Metall. Mate. Tans. B, 36B (2005), [29] A. Badi, T. T. Nataajan, C. C. Snyde, K. D. Powes, F. J. Mannion and A. W. Camb: Metall. Mate. Tans. B, 36B (2005), 355. [30] M. Suzuki, S. Miyahaa, T. Kitagawa, S. Uchida, T. Moi and K. Okimoto: Tetsu-to-Hagane, 78 (1992), [31] T. Aaki and M. Ikeda: Canadian Metallugical Quately,, 38 (1999),