Modeling Study of Turbulent Flow in a Continuous Casting Slab Mold Comparing Three Ports SEN Designs

ISIJ International, Vol. 59 (2019),ISIJ No. International, 1 Vol. 59 (2019), No. 1, pp. 76–85

Ismael CALDERÓN-RAMOS,1)* R. D. MORALES,2,3) Rumualdo SERVÍN-CASTAÑEDA,1) Alejandro PÉREZ-ALVARADO,1) Saúl GARCÍA-HERNÁNDEZ,4) José de Jesús BARRETO4) and Sixtos Antonio ARREOLA-VILLA1)

1) Mechanical Engineering Department, UAdeC/F.I.M.E.-U.N., Barranquilla S/N, Monclova, Coahuila, C.P. 25280 México. 2) Department of Materials Engineering and Metallurgy, I.P.N.-E.S.I.Q.I.E., Ed. 7 UPALM, Col. Zacatenco, Cd.México, C.P. 07738 México. 3) K&E Technologies, Manizales 88, Residencial Zacatenco, Del. Gustavo A. Madero, CDMX, C.P. 07369 México. 4) Metallurgy Graduate Center, Instituto Tecnológico de Morelia, Av. Tecnológico No. 1500, Morelia Michoacán, C.P. 58120 México. (Received on July 20, 2018; accepted on September 10, 2018)

Fluid flow of liquid steel in a slab mold influenced by three different submerged entry nozzles with the same bore sizes but different ports including rectangular, square, and round shape at immersion depth of 185 mm was studied. The analysis includes numerical simulations and physical modeling. The results show that the port shape has great effects over the fluid dynamics of the liquid steel inside the slab mold. The comparison among the three nozzle port designs indicates that the nozzle with square ports, (SEN-S), decrease the jets velocity, promote a symmetrical path inside the mold and decrease the bath level oscil- lations; representing the best choice to control the turbulence and decrease the quality problems.

KEY WORDS: slab mold; continuous casting; fluid flow; SEN port design.

standing the phenomena that dominate the behavior of the 1. Introduction process, which provides the basis for achieving optimization Fluid flow in continuous casting molds is important that has an impact on minimization of production costs. The because it governs production rate of the caster and qual- aim of this work was to assess the unsteady flow structures ity of the product. However, both aspects have opposite into the slab mold developed by the SEN-R (current noz- consequences. On one side, to get high production rate it is zle), SEN-S and SEN-C for the same operating conditions necessary, to increase the casting speed; on the other side, (see Table 1). The comparison among the three SEN port an increase of casting speed leads to flux entrapment to designs was carried out through physical experiments and form inclusions impairing the product quality. This oppo- numerical simulations. site relationship between production and quality has been the driving force of many research reports related to fluid 2. Presentation of the Case flow of liquid steel, particularly in slab molds.1–4) The fluid flow inside the casting mold is characterized by having a Recently, a company that produces peritectic steels, turbulent behavior, which is associated with risky possi- acquired a new SEN design with rectangular ports, with10- bilities such as shell-thinning breakout, formation of slivers degree upward ports angle, which is presented in Fig. 1(a). and inclusion entrapment.5–8) The turbulence intensity in This nozzle was designed to create greater stirring into the the mold depends on the submerged entry nozzle, (SEN), mold and send fresh steel toward the upper mold corners port design, the casting speed and the SEN immersion to cast crack sensitive steels. Nevertheless, recent reports depth. To reach both productivity and quality, it is neces- indicate that the current nozzle (SEN-R) promotes excessive sary to understand the effect that the SEN ports have on the turbulence at bath level when its maximum immersion depth unsteady flow structures in this process. Unfortunately, due is 185 mm (to use the complete zirconia band), entraining to the high temperature of steel, it is difficult to perform particles from mold flux, slivers, and even breakout prob- velocity measurements directly in molten steel.9) Physical lems.10) To solve these quality and operational problems, models and mathematical simulations are alternative ways the plant is considering two alternative SEN port designs to to study the behavior of liquid steel inside the mold. Previ- replace the actual nozzle; the first has square ports (SEN- ous approaches are of great help in diagnosing and under- S), and the second has round ports (SEN-C). The shape and dimensions of these nozzles are shown in Figs. 1(b) * Corresponding author: E-mail: [email protected] and 1(c), respectively. Both proposed designs have a port DOI: https://doi.org/10.2355/isijinternational.ISIJINT-2018-504 size greater than the actual nozzle (SEN-R), looking for jet

Table 1. Operating conditions used in the Physical experiments and computational simulations.

Parameter Value PHYSICAL MODEL Casting Speed, (m/min), (m/s) 0.9, 0.015 Equivalent flow rate, (m3/s) × 103 6.4 Slab mold size, (m3) 1.88 × 0.23 × 0.7 Air zone, (m) 0.1 Nozzle immersion*, (m) 0.185 NUMERICAL MODEL Casting Speed, (m/s) 0.015 Pressure inlet, (Pa) 101 325 Nozzle immersion*, (m) 0.185 Viscosity of the liquid steel, (Pa s) 0.0064 Kinematic viscosity of the steel, (m2/s) 1×10 −6 Density of the liquid steel, (kg/m3) 7 100 Viscosity of the air, (Pa s) 1.7894 ×10 −5 Density of the air, (kg/m3) 1.225 Interfacial tension between air and steel, (N/m) 1.6 Turbulence Model LES Interfacial model VOF Pressure-velocity couple SIMPLEC Convergence criterion Less than 10 −4 *Distance from the free surface to the upper exit port position

Fig. 1. Geometric characteristics (in mm) of the three submerged velocity reduction and consequently to decrease the turbu- entry nozzles (SEN’s) tested, a) SEN-R, port area: 2 2 lence inside the mold without compromising productivity 0.002795 mm , b) SEN-S, port area: 0.0044225 mm , and c) SEN-C, port area: 0.003848 mm2. and quality. In other words, looking for a good symmetric flows and suitable stirring conditions to melt the mold flux and maintaining small meniscus disturbances by oscillation 3.1. Particle Image Velocimetry (PIV), Dye Injection waves, and vortex flows.11) and Ultrasonic Sensors To measure flow velocities in the water model, the PIV technique was employed. The principle of PIV is to deter- 3. Water Model minate the flow velocities by measuring the displacement A full-scale water model of the slab mold was built with vector of illuminated particle images during a known time transparent plastic plates with total height of 1 700 mm. interval. In this work, particles with diameters of approxi- To recreate the fluid flow of liquid steel into the mold, mately 20 μm and density of 1 020 kg/m3 were seeded into the model was partially inserted (250 mm) into a pit full the fluid prior to the measurements.12) A 1 mm thick laser of water to represent the continuity of the strand. The pit sheet was displayed in the central plane, at half the mold contains a submergible water pump to transport water thickness. The displacements of particles were recorded through a vertical pipe, which has a flow meter and a pre- with a CCD camera (DANTEC-Double Image 700) and the cision valve embedded along the line to control the flow signals were converted to velocity magnitudes and validated rate of water fed into the model. This pipe line feeds the through a Fast Fourier Transforms algorithm. The studied tundish fixing the bath height at the same level (1 m) as in area involves the upper-half side of the mold with a size of the actual tundish in the plant. This configuration permits 880 × 660 mm2 as shown in Fig. 2(a). To reveal the flow the water to be recycled. The flow rate from the tundish to pattern as a function of the nozzle port shape, a red dye the mold was controlled through a stopper rod as the actual tracer was injected as a pulse through an orifice located in system at the plant. The physical model includes the three the upper side of the SEN, Fig. 2(b). The mixing kinematics full scale plastic prototypes of the real SEN designs used of the dye was recorded using a conventional video-camera, at the plant. A detail explanation of the experimental setup which was fixed in front of the water model. Finally, the can be found in reference 10. The experimental techniques bath level in the mold was monitored in real time using six employed to study the fluid flow in the mold are described ultrasonic sensors. Three were placed at each side of the in the next lines. SEN; one close to the narrow mold wall (1 and 6), another at the midpoint between the SEN and narrow mold wall (sen-

v i 0 ...... (1) xi

Dvi 1 p C vi v j S veff D T ...... (2) Dt xxij E x j xi U

vvefft 0 v ...... (3) Where, the subscripts i and j represent the three Cartesian directions and repeated subscripts imply summation. The symbols p and vi in Eqs. (1) and (2) represent the pressure and filtered velocities. The residual stresses, which arise from the unresolved small eddies, are modeled using an Fig. 2. Experimental techniques employed to study the fluid flow eddy viscosity (vt). The SGS kinetic energy (SGS k) model in the slab mold, a) Schematics showing the PIV measure- employed here requires solving the following additional ments region, b) Dye tracer injection and c) Ultrasonic transport equation, which includes advection, production, sensors. dissipation, and viscous diffusion.18,19)

3 sor 2 and 5) and the last one, close to the SEN body (sensor 2 ksgs ksgs 2 ksgs C ksgs S ... (4) 3 and 4). Figure 2(c) shows a schematic of the ultrasonic vi vSt  C D vv0 2 t TT t xi xi E xi U sensors location. The ultrasonic signals were converted into 13) digital data using an acquisition card. Digital data were Where Δ is the filtration volume and Δi is the size of the received by a plotter system to visualize bath level oscilla- computational cell: tions during the experimental work and were recorded for 1 further analysis...... (5) xy z 3

4. Mathematical Model 3 2 ...... (6) vCtl ksgs The developed model is based on the solution of the Navier-Stokes equations for incompressible viscous flow, where S is the magnitude of the strain-rate tensor, defined as: together with the multiphase model (Volume Of Fluid or VOF), and the turbulence model (Large Eddy Simulation SS= 2 ijS ij ...... (7) or LES), which are embedded in the CFD (Computational Fluid Dynamics) commercial software ANSYS FLUENT®. The inlet velocity is calculated to maintain the desired cast- 1 C vi v j S Sij D T ...... (8) ing speed at the outlet. To solve the mathematical model, 2 E x j xi U the next assumptions were considered:14) a) the fluid flowing into the mold was assumed to have Newtonian behavior, The parameters Cε = 1.0 and Cl = 1.0 can be treated as b) a pressure inlet condition is applied at the mold top constants.15) (p = 101 325 Pa) to model the effects of a system open to the atmosphere, c) the system was modeled considering 4.2. Multiphase Model unsteady state and isothermal conditions, consequently the To model the interface between air and steel, the Volume thermos-physical properties remain constant, d) non-slip of Fluid (VOF) model20,21) was used. This model is a conditions were applied at all solid surfaces, and e) conver- Eulerian method that uses a volume fraction indicator to gence criterion was obtained when the residuals of the out- determine the location of the interfaces of different phases put variables reached values equal or smaller than 1×10 −4. in all cells of a computational domain. In order to minimize the effects of the inaccurate interpolation for some physical 4.1. The Turbulence Model (LES) quantities, the model needs equations accounting for the In this study the LES model was employed to simulate variation of density as well as a viscosity. If it is consid- the flows. In this model the large length scale, three-dimen- ered incompressible, immiscible fluids, (no phase change sional (3D), and unsteady turbulent motion are directly between fluids), then the variable density and viscosity resolved, whereas the effects of the smaller scale motions present at each cell can be expressed on the base of their are modeled. Therefore, the large eddies are mathematically fraction as shown below: filtered and the dissipative small-scale eddies are modeled to mixq 1 ...... (9) get closure of the motion equations. The filtering is repre- sented using an SGS k model.15,16) The governing equations mixq 1 ...... (10) for the resolved flow field account for conservation of mass and momentum as:17) A unique continuity equation for the transient system is derived depending on the number of phases. Therefore, the Eq. (11) is divided by the number of phases q in the cell.

Mass exchange between phases can be modeled by introduc- flow and the turbulence intensity inside the mold, must be ing an additional source term Sαq. controlled.

1 F n V 5.1. Flow Symmetry G qq.4 qqvSqpBmmqq p W .... (11) q Ht p1 X For the first stage of this study, images from the red dye injection experiments, (two different instants) were selected The mass transfer from phase p to phase q and from to compare the performance of the three SEN port designs. phase q to phase p is given by the right side of the equation, The first image corresponds at the instant when the jet where Sαq is a source term. The volume fraction equation reaches the narrow mold face, and the second one is when for the secondary phase (air) is solved through Eq. (11); the the double roll pattern is revealed by the tracer. Figure 3(a) volume fraction of the primary phase is computed using the shows that the SEN-R yields a pair of asymmetrical jets following constraint: with different velocity and impact depth between left and right side. This behavior promotes high flow asymmetry n when the jets split at the narrow mold face into upward and B q 1 ...... (12) q1 downward streams, as can be seen in Fig. 3(b). Figure 3(c) shows that the SEN-S develop a pair of symmetrical jets The volume fraction Eq. (11) is solved through an explicit that impact at the same depth and at the same time, which time discretization method. The standard finite-difference is translated in a good behavior, Fig. 3(d). Meanwhile, the interpolation schemes are applied to the volume fraction Fig. 3(e) shows that the SEN-C develops a pair of straight values that were computed at the previous time step. jets whit tiny difference in impact depth between left and right side. Which is the cause of slightly asymmetric flow n11n n n n q q q q n n F V pattern as can be seen in Fig. 3(f). VU qfqf4 Sm qp qq m p V BG B WW The averaged values of the depth impact points of the left t f H p1 X ...... (13) and right jet for each SEN design are plotted in Fig. 4. It is clear that the SEN-R is the worst case in terms of symmetry, A single set of momentum equations is solved through- even though this nozzle has ports with an upward angle, out the domain, and the resulting velocity fields is shared aiming to send hot flow at the upper mold corners; the actual among the phases. The momentum equation, shown below, behavior is completely opposite to the objective for which is dependent on the volume fraction of all phases through it was designed; in addition, the difference between the left properties ρ and μ. and right jet is large and the flow symmetry is affected.  mixmvv.4ix vv.pm..HFix .ugXV S 5.2. General Flow Patterns t Instant velocity fields measured with the PIV technique ...... (14) The last term of this equation is a momentum source related with balance or forces arising by surface tension properties. The surface tension value was considered constant along the interface between the phases and it is treated as a source term in the momentum equation.

4.3. Numerical Procedure The governing equations were discretized using the finite volume technique and solved considering the computational segregated-iterative method. The non-linear momentum equations were linearized using the implicit approach. The discretization was performed using the Second Order Upwind scheme. The PRESTO22) scheme was used for pressure interpolation. The algorithm SIMPLEC22) was used to couple the pressure-velocity variables. To model the flow of two immiscible phases the VOF model is the most appropriated. The computational mesh consists of 1 300 000 structured cells. The total computing simulation time was of 300 s and the time step was maintained at 0.01 s.

5. Results The ideal flow pattern is called a double roll flow (DRF). Which must be permit a gentle roll flow along to meniscus, transporting steel in contact with the molten flux to provide even the ideal solidifications conditions and another down- Fig. 3. Dye injection experiments, a–b) SEN-R, c–d) SEN-S and wards roll-flow. To reach this behavior the symmetry of the e–f) SEN-C.

79 © 2019 ISIJ ISIJ International, Vol. 59 (2019), No. 1 were selected to study the flow pattern observed on the dye flows from the jet are observed (marked with the numbers injection experiments. The investigation area is the upper “4”, “5” and “6”) but with less intensity in comparison to central frontal plane in the left side of the mold. the SEN-R. The flow patterns presented in Fig. 5(g)–5(i) Figure 5, shows three consecutive transitory images corresponding to the SEN-C, are quite different from those (with a time difference of 0.25 s between each figure), for described for the SEN-R and SEN-S. The jet maintains its the three SEN port designs. The SEN-R, presented in Figs. shape from the nozzle port to the impinging point on the 5(a)–5(c), develops a jet that does not conserve an integral narrow face of the mold. The straight jet does not suffer shape; instead, yields wandering motions of the jets and detaching flows. However, the jets promote that the upper part of the jet is detached toward the bath surface marked roll flows acquire high velocity at the bath level as is indi- by numbers “1” and “2”. Other detached flow can transport cated by the numbers “7”, “8” and “9”. great volumes of fluid affecting the meniscus stability as Comparison of the experimental measurements of veloc- indicated by the number “3”. The twisting effects show the ity using the PIV and the mathematical simulations using dynamic and changing nature of the flow pattern developed the LES model are shown in Fig. 6. Instantaneous images by the current nozzle in the plant. Figures 5(d)–5(f) corre- for each nozzle were selected and then compared to cor- spond to the flow pattern developed by the SEN-S. Detached roborate with the experimental results. As shown, there is a good agreement between the measurements and simulations results. The Fig. 6(a) shows that the SEN-R yields downward meandering jets that lose the integrity of their shapes at a distance of 600 mm approximately, (market with the numbers “1” and “2”). The velocities in the center of the jet emerging from the nozzle ports are 2 m/s and 1.78 m/s from PIV measurements and from numerical approach, respectively. Although the jets emerge with a negative angle, the formation of the upper recirculation causes high velocities near the bath level zone, as indicated by the numbers “3” and “4”. The SEN-S, shown in Fig. 6(b), develops a pair of jets with output speeds of 1 m/s and 0.95 m/s from the experimental and numerical results, respectively. The jets Fig. 4. Comparison of jet depth of the impact point developed by each SEN design. lose speed along their path to the narrow mold wall, where

Fig. 5. Consecutive transitory of the general flow fields at the upper-half side of the mold computed by the PIV technique, a–c) SEN-R, d–f) SEN-S and g–i) SEN-C.

© 2019 ISIJ 80 ISIJ International, Vol. 59 (2019), No. 1 the impact velocities are 0.1 to 0.13 m/s; (marked by the than the jet of the SEN-R. Lastly, the SEN-C presented in numbers “5” and “6”) from experimental and numerical the Fig. 6(c) develops straight jets that conserve their shape results, respectively. The jet meanders with less intensity along its path to the narrow mold face, where they split in upward and downward streams, forming the double roll pattern. These jets, impact the narrow face of the mold with larger velocities (0.5 m/s and 0.65 m/s from experimental and numerical approaches, respectively) with probable shell washing effects (market by the numbers “7” and “8”) and shear flows at bath level, as is indicated by the numbers “9” and “10”. The agreement between the experimental (PIV) and numerical (LES) results is also very good. This makes possible to continue the discussion of these results using, at convenience, any of these approaches in a complementary way in the rest of this discussion. To get quantitative information about the behavior of each nozzle design, the velocity profile was plotted along a line located in the axis of the jet shown over the velocity contours computed through the mathematical model, Figs. 7(a), 7(b) and 7(c). The velocity scale at the plots was fixed at 0.7 m/s to observe a clear velocity distribution inside the mold. Obviously, the unfilled zones correspond a velocity higher than 0.7 m/s. The images presented here correspond to a computational time of 300 seconds. Figure 7(d) shows that the jet developed by the SEN-R has the highest velocity at the discharging ports (2.6 m/s) and the velocity fluctuations are visible along their path until impinging the narrow mold face with a velocity of 0.75 m/s. In contrast the SEN-S and the SEN-C have a velocity of 1.63 and 1.85 m/s at the discharging ports; respectively, their velocity profiles do not present considerable velocity fluctuations along their path until the narrow mold face are reached, where the impinging velocities were 0.12 and 0.4 m/s for SEN-S and SEN-C, Fig. 6. Comparison of the three nozzle designs using velocity vec- respectively. tors fields computed through experimental (PIV) and The high impinging velocities at the narrow mold face, numerical (LES) approaches, a) SEN-R, b) SEN-S and c) SEN-C. yielded by SEN R, can affect the solidification front and

Fig. 7. Contours of velocity computed through LES model at 300 s, a) SEN-R, b) SEN-S, c) SEN-C and d) Velocity profile along the center of the jet from the nozzle port to the narrow mold face for the three SEN designs.

81 © 2019 ISIJ ISIJ International, Vol. 59 (2019), No. 1 promote breakouts problems, also the velocity at this zone To obtain a clear comparison among the three nozzles. governs the upper roll formation and, in consequence, the The velocity profiles at the narrow mold mid face were disturbances at the bath level. plotted in Figs. 8(a)–8(c). It is evident that SEN-R has a larger area with high impinging velocity than the other two nozzles, indicating that the probability of washing the shell will be high.

Fig. 8. Velocity contours at narrow mold face, a) SEN-R, b) SEN-S and c) SEN-C and d) Velocity profile along the Fig. 9. Velocity contours at the free surface, a) SEN-R, b) SEN-S, center line of the narrow mold face comparing the three c) SEN-C and d) Velocity profile from the nozzle wall to nozzle designs. the narrow mold face.

Fig. 10. Shape of the free surface comparing numerical predictions and physical results, a) SEN-R, b) SEN-S and c) SEN- C, d) Location of the ultrasonic sensors over the slab mold and e) Heights averaged in time (120 s) for each sensor.

The velocity profiles presented in Fig. 8(d) show that the narrow mold face, Fig. 9(d), yield high standing waves at SEN-S yields the lowest magnitudes the impinging veloci- the corners of the slab mold, Fig. 10(e). The SEN-R pres- ties on the narrow mold face. Another important parameter ents the highest free surface deformations along of all the is the velocity near the bath level (at 880 mm from the free surface; meanwhile the SEN-S and SEN-C yield stable nozzle in Fig. 8(d). The SEN-R has values of 0.4 m/s, meniscus with very shallow depressions of standing waves, meanwhile the SEN-S and SEN-C present values less than qualitatively indicating, that the flow at the free surface is 0.1 m/s. These large differences give the origin to surface less turbulent in comparison with the SEN-R. instabilities, which will be discussed in the next section. 5.3.1. Vortex Formation 5.3. Free Surface Instabilities Asymmetric flows parallel the wide faces of the mold To observe the free surface behavior, velocity contours induce secondary flows that pass with high velocities and their topology at the bath level zone were analyzed to through the narrow gap between the SEN and the mold compare qualitatively in Figs. 9(a)–9(c), and quantitatively, walls causing vortices that entrain slag. The slightest asym- the performance of each SEN design in Fig. 9(d). The metry can result in the formation of vortices, but this does SEN-R, which develops a high velocity at near the narrow not guarantee the entrainment of slag.11) To get drag slag mold face (Fig. 8(d)), yields flows at the free surface with by the melt, Gutierrez and Morales23) claim that the critical velocity peaks of 0.35 and 0.4 m/s, consequently, standing vortex necessary length is about 60 mm. waves at the mold corners are formed, as can be observed To compare the influence of each nozzle design on vortex in Fig. 9(a). The SEN-C yields flows at the free surface formation, the number of vortices per minute and their size with velocities smaller than 0.2 m/s, and the standing waves were measured from video recordings during the dye injec- are present but with less intensity and size in comparison tion experiments. Figures 11(a)–11(c) shows some vortices with the SEN-R, Fig. 9(c). Meanwhile the SEN-S presents recorded and measured for each SEN design. The SEN-R a very stable free surface without standing waves, as can yields the maximum values of vortices per minute and aver- be seen in the Fig. 9(b). The Fig. 9(d), shows that the zone age vortex length in comparison with the other two nozzle of disturbance extends from the narrow mold wall to the designs as can be seen in Figs. 11(d) and 11(e), respectively. middle of the mold. To complement, qualitatively and quantitatively those 6. Closure results, video-images of the physical experiments were recorded and compared with the phase contours predicted All simulations results are in good agreement with the by the VOF model, (Figs. 10(a)–10(c)). There is a good physical experiments, confirming that increasing the dis- qualitative agreement between numerical and the physical charging port transverse area decreases the turbulence level approach. The meniscus level variations provided by the in the whole volume of the slab mold. Also, the SEN design ultrasonic sensors (with locations indicated in Fig. 10(d) definitely has a considerable influence in the dynamic of are plotted in Fig. 10(e). As seen the wave amplitudes the flow, the SEN-R and SEN-C yield more turbulent flow provided by nozzle R are the largest followed by nozzles than SEN-S. C and S. Indeed, as can be expected, high velocities at the The origin of the asymmetric flow is the turbulence level,

Fig. 11. Vortex formation during 60 s, a) SEN-R, b) SEN-S, c) SEN-C, d) Number of vortex per minute using the three SEN designs and e) Average vortex length.

83 © 2019 ISIJ ISIJ International, Vol. 59 (2019), No. 1 but the consequences at the narrow mold faces and the free SEN design to use with the current operation conditions and surface are the dissipation rate of turbulent kinetic energy. mold size, the minimum values where remarked. Figure 12 show that each nozzle dissipates kinetic energy at the discharging ports in diverse ways and intensity, and this 7. Conclusions behavior is extended to the whole flow in the mold. All the results obtained from the physical experiments Fluid flow of liquid steel in a slab mold influenced by and numerical predictions were summarized in the Table three different submerged entry nozzles with the same bore 2. The maximum values of each presented variable were sizes but different ports SEN designs through numerical and selected; and to obtain a clear conclusion about the best physical modeling was studied. From the obtained results

Fig. 12. Instantaneous contours of dissipation rate of kinetic energy (m2/s2), computed at 300 s, a–b) SEN-R, c–d) SEN-S and e–f) SEN-C.10)

Table 2. Resume of results.

VARIABLE SEN-R SEN-S SEN-C APPROACH Jet misalignment* 150 mm 0 mm 70 mm Physical Output velocity at discharging ports 2.6 m/s 1.63 m/s 1.85 m/s Numerical Impinging velocity at narrow mold face 0.7 m/s 0.3 m/s 0.6 m/s Numerical Physical and Depth of the jet impinging point** 410 mm 320 mm 410 mm Numerical Horizontal velocity at free surface 0.25 m/s 0.05 m/s 0.1 m/s Physical Surface wave height 12 mm 2 mm 6 mm Physical Number of vortex per minute 12 5 2 Physical Average vortex length 44.5 mm 16.4 mm 13.7 mm Physical Dissipation rate of kinetic energy at discharging ports 8.5 m2/s2 2 m2/s2 4.5 m2/s2 Numerical *Is the difference between the depth of the jet impinging of the left and right side. **Distance from the bath level to the jet impact point at the narrow mold face.

© 2019 ISIJ 84 ISIJ International, Vol. 59 (2019), No. 1 and their corresponding discussion, the following conclu- explains the behavior of the fluctuating jet observed at the sions can be drawn: velocity fields captured by the PIV technique. Therefore, (1) The results of the jet misalignment inside the mold the recommendation is to replace the SEN-R by the SEN-S indicate that two of the three nozzles develop asymmetrical to reduce the quality and operational problems reported in flow inside the mold, but with different intensity, position- plant. ing the SEN-S and the SEN-R as the best and worst case studied, respectively (See Table 2). Acknowledgements (2) The global asymmetric flow inside the slab mold can The authors give the thanks to CoNaCyT, PRODEP and promote a non-uniform heat transfer from the melt to the the UA de C for their continuous support to the Mechanical mold walls. In consequence, the solidification phenomena Engineering Department. it can be affected and the cracks in the final product is very likely. Also, the large jet depth impact can affect the thick- REFERENCES ness of the first solidified shell, creating possible breakout 1) R. Chaudhary, C. Ji, B. G. Thomas and S. P. Vanka: Metall. Mater. problems. Trans. B, 42 (2011), 987. 2) J. Anagnostopoulos and G. Bergeles: Metall. Mater. Trans. B, 30 (3) The velocity contours computed at the narrow mold (1999), 1095. face using the numerical approach reveals that the SEN-R 3) Y. Miki and S. Takeuchi: ISIJ Int., 43 (2003), 1548. 4) A. Ramos-Banderas, R. Sanchez-Perez, R. D. Morales, J. Palafox- and SEN-C, yields large areas affected by high velocity Ramos, L. Demedices-García and M. Díaz-Cruz: Metall. Mater. peaks (0.6 m/s using the SEN-C and greater than 0.7 m/s Trans. B, 35 (2004), 449. using the SEN-R), meanwhile the SEN-S yields impinging 5) L. Zhang and B. G. Thomas: ISIJ Int., 43 (2003), 271. 6) W. H. Emling, T. A. Waugaman, S. L. Feldbauer and A. W. Cramb: velocities of less than 0.3 m/s; thus, using this SEN design Steelmaking Conf. Proc., Vol. 77, ISS, Warrandale, PA, (1994), 371. will result in less breakout problems. 7) B. G. Thomas: The Making, Shaping and Treating of Steel, 11th ed., Casting Volume, ed. by A. W. Cramb, AISE Steel Foundation, (4) Another consequence of having asymmetric flow Pittsburgh, PA, (2003), 24. inside the mold, due to the instability of the jets, is the tur- 8) J. Herbertson, Q. L. He, P. J. Flint and R. B. Mahapatra: Steelmaking bulence in the bath level zone (meniscus). Large velocities Conf. Proc., Vol. 74, ISS, Warrandale, PA, (1991), 171. 9) B. G. Thomas, Q. Yuan, S. Sivaramakrishnan, T. Shi, S. P. Vanka at meniscus promote slag entrainment by standing waves and M. B. Assar: ISIJ Int., 41 (2001), 1262. and vortex flows, which is the origin of inclusions problems 10) I. Calderón-Ramos and R. D. Morales: Metall. Mater. Trans. B, 46 (2015), 1314. in the final product. Physical and numerical results showed 11) L. C. Hibbeler and B. G. Thomas: Iron & Steel Technology Conf. that the SEN-R develop the highest surface waves located at and Exposition (AISTech) Proc., AIST, Warrandale, PA, (2010), 17. 12) S. Sivaramakrishnan: Master’s thesis, University of Illinois at Urban- the corners of the mold. The SEN-R yield high horizontal Champaign, Urban, (2000). velocities which travels from the narrow mold faces to the 13) E. Torres-Alonso, R. D. Morales, S. García-Hernández and J. SEN body, where both flows (coming from the left and right Palafox-Ramos: Metall. Mater. Trans. B, 41 (2010), 583. 14) S. García-Hernández, R. D. Morales, J. de J. Barreto and K. Morales- side) converge and, potentiated by the surface waves, develop Higa: ISIJ Int., 53 (2013), 1794. numerous vortex flows per minute (12 vortex/min) of great 15) U. Schumann: J. Comput. Phys., 8 (1975), 376. 16) K. Horiuti: J. Phys. Soc. Jpn., 54 (1985), 2855. intensity and size (vortex average length of 44.5 mm). These 17) S. B. Pope: Turbulent Flows, Cambridge University Press, Cambridge, vortex flows can drag slag into the liquid steel and explain the London, (2000), 771. inclusions found in the final product at the plant. 18) U. Schumann: Theor. Comput. Fluid Dyn., 2 (1991), 279. 19) W. W. Kim and S. Menon: AIAA Paper 97-0210, American Institute (5) The contours of dissipation rate of kinetic energy of Aeronautics and Astronautics (AIAA), New York, (1997), 325. at the discharging ports and the whole volume inside the 20) C. W. Hirt and B. D. Nichols: J. Comput. Phys., 39 (1981), 201. 21) P. Liovic, J. L. Liow and M. Rudman: ISIJ Int., 41 (2001), 225. slab mold indicate that the SEN-R and SEN-S develop the 22) Fluent Inc.: Fluent Guides, Fluent Inc., Lebanon, NH, (2007). highest and lowest values, respectively. This last difference 23) Y. S. Gutierrez-Montiel and R. D. Morales: ISIJ Int., 53 (2013), 230.