Modeling the Interface Dynamics in Continuous Casting Molds employing ANSYS CFX

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1 Modelng the Interface Dynamcs n Contnuous Castng Molds employng ANSYS CFX K. L. Z. Gltz 1, A. F. C. Slva 1, C. R. Malska 1, R. N. Borges 2, A. B. Soprano 1, B. T. Vale 1 1 SINMEC Computatonal Flud Dynamcs Laboratory, Department of Mechancal Engneerng, Federal Unversty of Santa Catarna, Floranopols, Brazl. 2 Magnesta Refratáros S. A. Contagem-MG, Brazl. ABSTRACT: There are some mechansms n contnuous castng that could cause the entrapment of slag. One of them s the entrapment due to the hgh shear stress actng on the nterface between the molten steel and the slag. There are few works n the lterature about the behavour of the nterface between slag and steel. These works apply expermental and numercal approaches to ths problem. However, nstead of slag and steel others fluds are employed. In order to evaluate the steel-slag nterface dynamcs, smulatons of water flow n contnuous castng molds are carred out employng the software ANSYS CFX The results are compared to expermental and numercal results publshed n the lterature. ANSYS CFX results presented good agreement wth the expermental data. 1. SLAG ENTRAPMENT IN CONTINUOUS CASTING INTRODUCTION In contnuous castng molten steel s njected nto the mold through a submerged entry nozzle (SEN). The molten steel flows from the SEN, reaches the narrow face of the mold and then flows towards the SEN agan, causng shear stress on the nterface. Dependng on the superfcal velocty of the molten steel near the slag-steel nterface, slag can be entraned nto the steel bath [4]. Ths entrapment of slag results n a defect n the fnal product and must be avoded. Therefore t s of fundamental mportance to determne the crtcal value of the superfcal velocty of steel beyond whch slag s entraned. In the lterature there are few works about the behavour of the nterface between slag and steel. These works apply expermental and numercal approaches to ths problem. However, nstead of slag and steel, other fluds are employed. For the case of slcon ol and water flow, t s related that the crtcal superfcal velocty of water beyond whch slcon ol s entraned n the water bath les between 0.15 and 0.4 m/s [5,6]. One of such works employng dfferent fluds was done by Gupta and Lahr [3]. They studed expermentally the water flow nsde castng molds wth dfferent aspect ratos. Employng dfferent port dameters and angles, they analysed the effect of the castng-speed n the menscus behavour. In ther paper there are fve consecutve frames showng the nterface poston at dfferent tmes, wth an nterval of 0.04 s among them. One of these pctures shows the entrapment of a bubble. Based on the work of Gupta and Lahr, Dash and coworkers [2] performed twodmensonal numercal smulatons of the water flow n a mold. Ther objectve was to predct the shape of the free surface and the entrapment of ar bubbles. They compared ther numercal results wth those obtaned by Gupta and Lahr n ther experments, and concluded that ther results presented good agreement wth the expermental ones. In ths work, numercal smulatons of the water flow n 1:8 aspect rato mold of [3] were carred out employng the software ANSYS CFX The results obtaned n these smulatons were compared to those obtaned numercally by [2] and expermentally by [3], and wll be presented further. 2. EXPERIMENTAL MODEL In ther study, Gupta and Lahr employed a 80 mm-thckness mold and a SEN wth parallel ports. The submergence depth was kept at 150 mm. Ths mold s llustrated n Fg. 1, whch s based on the fgure presented n [2]. In ths fgure the shaded area ndcates the porton of the doman occuped by water at tme t=0.

2 Fg. 1: The mold employed n the experments by [3] and n the numercal smulatons (Dmensons n mm). In the experments the water flow rate was equal to 1.22 x 10-3 m 3 /s. 3. NUMERICAL MODEL As well as the numercal smulatons carred out by Dash and coworkers, those employng the software ANSYS CFX 11.0 also consdered two-dmensonal flow nsde the mold llustrated n Fg. 1, by employng a one element thckness-grd. Snce the outlet was placed on one sde of the mold s wall, the water flow could not be consdered symmetrc. Thus a full-scale model of the mold was employed n the smulatons. Once the water flow s turbulent and transent and the fluds (water and ar) are ncompressble, Newtonan and sothermal, the governng equatons of ths problem are: r α t + α = x ( ru) 0 whch s the equaton of contnuty appled to both fluds, ρ + = t x ( ρu ) 0 whch s the equaton of contnuty for the mxture, D( ρu ) p U U j = + μ + ρuu + ρg + F Dt x xj xj x Equaton (3) s the momentum equaton. j σ In these equatons r α s the volume fracton of flud α, ρ uu j are the Reynolds stresses and F σ s the component n drecton of the force due to surface tenson. The flud propertes are functons of the volume fractons of the fluds: ρ = r1ρ1 + (1 r1) ρ2 (4) μ = r μ + (1 r ) μ (5) (1) (2) (3)

3 where the subscrpts 1 and 2 denote water and ar, respectvely. All the numercal smulatons employed the k-ε model n order to calculate the turbulence parameters. Ths model solves two equatons: one for the turbulent knetc energy (k) and another for the rate of dsspaton of turbulent knetc energy (ε). The surface tenson effects are ncluded n the momentum equatons as a body force. Ths force s obtaned through the Contnuum Surface Force model (CSF). In ths model the effects of ths force are spread across a regon around the nterface of varable volume fracton [1]. 3.1 Propertes of the Fluds In the numercal smulatons t was employed water and ar. The physcal propertes of these two fluds are lsted n Tab. 1. Water Ar Densty (kg/m³) Vscosty (Pa s) x 10-5 Surface tenson (N/m) Tab. 1: Propertes of the fluds. 3.2 Boundary Condtons In order to smulate the water flow nsde the mold, the followng boundary condtons were employed: Inlet: prescrbed values for the normal velocty and the turbulence ntensty. Only water flows through ths boundary; Outlet: Bulk mass flow rate equal to the mass flow rate at nlet; Top of the doman: prescrbed value for the statc pressure. At ths boundary both fluds are allowed to leave the doman. The remanng boundares of the doman were consdered to be walls wth the no slp condton. In the ANSYS CFX smulatons t was employed a 2% turbulence ntensty at the nlet. It s necessary to make some remarks about the prescrbed value of the normal component of the velocty at the nlet. Dash, Mondal and Ajman [2] reported n ther work that bubble entrapment occurs at an nlet velocty of 2 m/s or more. Based on the value of the water mass flow rate mentoned by Gupta and Lahr n ther work [3], Dash et al. consdered that the average port ext velocty of the experments of [3] was equal to 1.94 m/s. Accordng to them ths value corresponds to an nlet velocty of 3 m/s n the numercal two-dmensonal computaton. Thus t was consdered an nlet velocty of 3 m/s n the numercal smulatons performed by ANSYS CFX Intal Condtons As mentoned above the ntal feld of the volume fractons s the one llustrated n Fg. 1, n whch the shaded area ndcates the porton of the doman occuped by water. The whte area between the nterface and the top of the doman s flled by ar. There s a smoothed transton of the values of the volume fractons across the nterface, n order to avod abrupt changes n the values of the varables. At tme t=0 the velocty feld s set equal to zero, except the velocty at the nlet where the normal component of the velocty s prescrbed a value equal to 3 m/s. All the turbulence parameters are also set equal to zero n the entre doman, except the value at the nlet. 3.4 Grd Sze and Tmestep Dash et al. dd not gve detaled nformaton about the grd that they employed. In ther work there s a fgure of the grd, however the only numercal nformaton about t s the sze of the cells around the nterface. In that zone the cells are refned to a sze of 2.5 x 2.5 mm. In ther work there s also a lack of nformaton about the tmestep value employed. In the smulatons performed by ANSYS CFX 11.0 t was employed four dfferent

4 grds, each one wth 43444, 85124, and nodes. Therefore a study of the dependence of the results on the grd sze could be carred out. For these grds the szes of the cells around the nterface are 5.7 x 2.0 mm (n x-drecton and y-drecton), 3.6 x 1.4 mm, 2.2 x 1.4 mm and 1.5 x 1.3 mm respectvely. Ths refnement s appled to a 100 mm-wde regon whch nvolves the nterface at ts ntal poston. After carryng out a tmestep depence study, t was concluded that the optmal value for the tmestep s 10-4 s. Ths tmestep assures a small value of the Courant number, consequently mplyng n realstc results. 4. RESULTS As mentoned above smulatons were performed wth dfferent grd szes. The results of these smulatons were compared to those obtaned numercally by [2] and expermentally by [3]. In Fg. 2 and 3 t s shown the poston of the nterface relatve to ts ntal poston at two dfferent tmes for the left half of the mold (Fg. 1) obtaned numercally. In these fgures the results obtaned n the present work employng the fner grd are compared to those obtaned by [2]. As can be observed the numercal results n each fgure do not correspond to the same tme nstant. Whle the nterface poston at t=1.04 and 1.2 s obtaned by ANSYS CFX s plotted n Fg. 2 and 3 respectvely, the results of [2] shown n these fgures correspond to t=1.2 and 1.36 s. Ths s done because n the ANSYS CFX smulatons bubble entrapment occurs earler (at approxmately t=1.2 s) than n the smulatons performed by Dash et al., whch occurs at approxmately t=1.36 s. Fg. 2: Interface poston at t=1.04 s (Present work) and at t=1.2 s (Dash et al.) Fg. 3: Interface poston at t=1.2 s (Present work) and at t=1.36 s (Dash et al.) In both fgures the poston x= mm corresponds to the mold narrow sde and x=0 mm corresponds to the SEN wall. Snce the exact tme at whch a bubble s entrapped durng the experments s not known, t s not possble to affrm whch of the entrapment tmes obtaned numercally s the correct one. Comparng the results to those obtaned by Gupta and Lahr (Fg. 4 and 5) t can be seen that the results obtaned n the present work are qualtatvely and quanttatvely better than those obtaned by [2]. Fg. 4: Interface poston obtaned by Gupta and Lahr (Fg. 7(b) of [3]). Fg. 5: Interface poston obtaned by Gupta and Lahr at 0.08 s after Fg. 4. As can be observed n Fg. 2 and 3, the wave ampltude of the nterface near the SEN

5 wall obtaned n the present work s hgher than the wave ampltude obtaned by Dash et al., dfferng from the ampltude of the experments n only a few mllmetres. Also the shape of the nterface before the breakup presented n ths paper shows good agreement to the expermental results. 4.1 Grd Independence Results Dash et al. performed a study on the nfluence of the grd sze on the numercal results for the poston of the nterface. Besdes the grd wth 2.5 x 2.5 mm cells around the nterface, they also employed a refned grd whose cells sze around the nterface was equal to 1.25 x 1.25 mm. They concluded that the coarser grd was able to reproduce satsfactorly the expermental results. In the present work four grds wth dfferent refnement levels were employed n the smulatons. The poston of the nterface at t=1.04 s obtaned employng these grds s shown n Fg. 6. Fg. 6: Interface poston along the mold wdth at t=1.04 s for four dfferent grds. As can be seen n ths fgure there s a consderable dfference between the results for the coarsest and the fnest grds. The coarser the grd employed, earler s the breakup of the nterface. Despte some lttle dfference t can be concluded that the results obtaned employng the grd wth nodes (2.2 x 1.4 mm cells around the nterface) are qute smlar to those obtaned when the fnest grd was employed. 4.2 Surface Tenson Smulatons neglectng the effects of the surface tenson were performed too. As ther results were very smlar to those obtaned consderng these effects, t can be concluded that surface tenson plays no mportant role n ths problem. 4.3 Superfcal Velocty of Water near the Interface Snce one of the most mportant parameters of flow related to the slag entrapment problem s the superfcal velocty of the molten steel near the nterface, some results for ths parameter for the water flow along the mold s wdth are presented below. The Fg. 7 and Fg. 8 llustrate the behavour of the horzontal component of the superfcal velocty of water near the nterface at t=1.16 and 1.2 s. At ths tme nstant the entrapment of a bubble s mmnent. These fgures were bult by consderng a contour of the volume fracton of water equal to 99 %. As can be seen n these fgures the superfcal velocty of water before the breakup s hgher than that observed when the nterface break-up s about to happen. At t=1.16 s the maxmum value of ths velocty s around 0.86 m/s and after 0.04 s t s equal to 0.83 m/s. The maxmum values of the superfcal velocty of water occur at the through of the wave at the nterface.

6 Thus the crtcal value of the water superfcal velocty beyond whch ar s entrapped s around 0.86 m/s. Fg. 7: Interface poston and water superfcal velocty at t=1.16 s. Fg. 8: Interface poston and water superfcal velocty at t=1.2 s. 5. CONCLUSIONS As shown n the prevous secton the numercal results obtaned by employng the software ANSYS CFX 11.0 showed better agreement to the expermental ones than those obtaned numercally by Dash and coworkers [2]. It was also concluded n ths work that surface tenson plays no mportant role n the entrapment of bubbles by water flow. An mportant contrbuton of ths work s the establshment of numercal values for the crtcal superfcal velocty of water beyond whch ar s entrapped n the water bath. 6. ACKNOWLEDGMENTS The authors would lke to express ther grattude to FINEP and to Magnesta Refratáros S.A. for sponsorng ths research project. The frst author would also lke to express her grattude to the Natonal Councl for Scentfc and Technologcal Development (CNPq) for sponsorng her doctorate study. 7. BIBLIOGRAPHIES [1] Brackbll, J.; Kothe, D.; Zemach, C.: A Contnuum Method for Modelng Surface Tenson, Journal of Computaton Physcs, v. 100 (1992), pp [2] Dash, S.; Mondal, S.; Ajman, S.: Mathematcal smulaton of surface wave created n a mold due to submerged entry nozzle, Internatonal Journal of Numercal Methods for Heat and Flud Flow, v. 14 (2004), pp [3] Gupta, D.; Lahr, A.: Water-Modelng Study of the Surface Dsturbances n Contnuous Slab Caster, Metallurgcal and Materals Transactons B, v. 25B (1994), pp [4] Iguch, M.; Yoshda, J.; Shmzu, T.; Mzuno, Y.: Model Study on the Entrapment of Mold Powder nto Molten Steel, ISIJ Internatonal, v. 40 (2000), pp [5] Suzuk, M.; Suzuk, M.; Nakada, M.: Perspectves of Research on Hgh-speed Conventonal Slab Contnuous Castng of Carbon Steels, ISIJ Internatonal, v. 41 (2001), pp [6] Thomas, B.: Flud Flow n the Mold. Makng, Shapng and Treatng of Steel, The AISE Steel Foundaton (2003).