This work evaluates the performance of a novel design for a bifurcated submerged entry nozzle (SEN) used for the continuous casting of steel slabs. The proposed design incorporates fluid flow conditioners attached on SEN external wall. The fluid flow conditioners impose a pseudosymmetric pattern in the upper zone of the mold by inhibiting the fluid exchange between the zones created by conditioners. The performance of the SEN with fluid flow conditioners is analyzed through numerical simulations using the CFD technique. Numerical results were validated by means of physical simulations conducted on a scaled cold water model. Numerical and physical simulations confirmed that the performance of the proposed SEN is superior to a traditional one. Fluid flow conditioners reduce the liquid free surface fluctuations and minimize the occurrence of vortexes at the free surface.
Increasing cleanliness of the steel slabs produced in continuous casting machines remains one of the priorities of the steel industry [
Researchers from academia and industry recognize that the fluid flow pattern in the mold significantly affects the quality of the steel produced in continuous casting machines [
The many fluid flow patterns observed inside the mold could be grouped on three general types: double roll, unsteady, and single roll [
The design of the internal geometry of the SEN aims to induce a double roll fluid flow pattern inside the mold. Despite this, wrong operation conditions trigger a single roll or an unsteady fluid flow pattern. Some characteristics of an unsteady flow pattern are high mold level fluctuations, uneven molten slag layer thickness, and vortexing [
Several approaches have been used to damp fluctuations of the interface between molten slag and liquid steel in slab continuous casting. One of them is to impose an electromagnetic field across the mold to change the flow pattern [
Immersing external refractory shapes in the mold is another approach recently proposed by Kamal and Sahai [
Following Kamal and Sahai, the present work proposes a new submerged entry nozzle design. The hypothesis behind this device is that fluid flow conditioners attached to the SEN external wall reduce the oscillations of the liquid surface. The flow conditioners impose a pseudosymmetric pattern in the upper zone of the mold by inhibiting the fluid exchange between the zones created by conditioners. The performance of the SEN with fluid flow conditioners is analyzed through CFD numerical simulations conducted on the commercial software ANSYS FLUENT [
In theory, the design of the internal geometry of the SEN should produce a double roll pattern inside the mold under normal operation conditions. The former numerical simulations using the CFD technique supported this idea. For simplicity and computational limitations, 2D simulations covered only half of the mold. For the same reasons, the first 3D models used a quarter of the mold. This modeling approach forces symmetry restrictions on the numerical results. All these numerical simulations were done using a single phase, the liquid steel. The simulation of multiphase systems is relatively recent.
However, various defects in the cast steel suggested that the actual fluid flow pattern inside the mold is different from the ideal one. Physical simulations expose several phenomena contradicting the ideal pattern. These simulations used scaled models and water as the working fluid [
The source of the phenomena that modify the ideal fluid flow pattern inside the continuous casting mold is still a subject of study. According to RealRamirez and GonzalezTrejo [
The imaginary symmetry plane colored in blue inhibits the fluid exchange between mold quarters (I) and (II), as well as the exchange between mold quarters (III) and (IV).
The imaginary symmetry plane colored in green inhibits the fluid exchange between mold quarters (II) and (III), as well as the exchange between mold quarters (IV) and (I).
Upper zone of the mold. Symmetry planes define quarters (I), (II), (III), and (IV).
Asymmetry of the flow pattern allows fluid exchange between quarters in direct contact. This causes the formation of vortexes in the zone near to the liquid surface, which trap the molten slag that floats on top of the steel. Asymmetry also intensifies fluctuations of the liquid surface [
The SEN with fluid flow conditioners proposed in this work is depicted in Figure
Sketch of the SEN with fluid flow conditioners.
The aim of this design is to enhance the symmetry of the fluid flow pattern at the mold upper zone. To achieve this goal, we replace only one of the two imaginary symmetry planes by a physical barrier, named as fluid flow conditioner. A physical barrier on the other plane of symmetry could damage the formation of the solidified layer of steel in the central area of the wide walls of the mold. Our design is simple. Despite this, it has not been previously published nor patented.
This first design of the nozzle uses fluid flow conditioners of rectangular shape with constant cross section. The conditioner length and thickness values must be tuning to obtain optimal results. This analysis will be reported elsewhere. Subsequent works will report the performance of nozzles with fluid flow conditioners of trapezoidal shape with nonuniform cross section.
If we consider that the flow is incompressible, we obtain the following Navier Stokes equation, which describes the fluid dynamics of a system:
The numerical simulations used the standard
In these equations,
The model constants
These values have been determined from experiments for fundamental turbulent flows. Several works have reported that these values are adequate for numerical simulations of the steel continuous casting.
The aim of the SEN with fluid flow conditioners is to inhibit the formation of vortexes in the zone near to the liquid surface, which trap the molten slag that floats on top of the steel. Another advantage of using flow conditioners is the damping of the fluctuations of the liquid surface. Therefore, numerical simulations include two fluids with different phase. The mathematical model has a liquid that enters into the mold through the SEN and a gas that floats over the liquid free surface inside the mold. The liquid used in numerical and physical simulations is water, in order to compare the results of them. For simplicity, the molten slag phase was omitted.
The Volume of Fluid (VOF) model is a surfacetracking technique applied to a fixed Eulerian mesh. It is designed for two immiscible fluids where the position of the interface between the fluids is of interest. In the VOF model, a single set of momentum equations is shared by the fluids, and the volume fraction of each of the fluids in every computational cell is tracked throughout the domain. In order to properly model multiphase flow, both spatial and time discretization schemes were used; therefore, a general transport equation can be written as
The tracking of the interface between the air and liquidwater phases is accomplished by the solution of a continuity equation for the volume fraction of one (or more) of the phases. For the
The volume fraction equation will not be solved for primary phase; the primaryphase volume fraction will be computed based on the following constraint:
To obtain the face fluxes for all cells, the implicit scheme is used for time discretization standard finitedifference interpolation schemes and the equation is written in the following form:
Since this equation requires the volume fraction values at the current time step, a standard scalar transport equation is solved iteratively for the secondaryphase volume fraction (air) at each time step.
A single momentum equation is solved throughout the domain, and the resulting velocity field is shared among the phases. The momentum equation is dependent on the volume fractions of all phases through the properties
For timedependent VOF calculations, (
The effects of surface tension along the interface between the air and liquid water phases are included. The VOF model can be augmented by the additional specification of the contact angles between the phases. The value of the surface tension coefficient was constantly equal to 1.400.
These flows involve the existence of a free surface between the flowing fluid and air phase above it, acting as the atmosphere. In such cases, wave propagation and free surface behavior become important. Flow is governed by the forces of gravity and inertia. Open channel flows are characterized by the dimensionless Froude Number, which is defined as the ratio of inertia force and hydrostatic force:
Numerical results of the mathematical model described above will be validated with a scaled model and using cold water as working fluid. Therefore, the geometrical dimensions and boundary conditions of the mathematical model coincide with that of the scaled model, which is a rectangular prism made of acrylic plates (see Figure
Sketch of the physical model. (a) Isometric view of a half of the mold. (b) Inset showing the inner geometry of a traditional SEN. (c) Inset showing the inner geometry of the SEN with conditioners.
The primary inlet boundary condition is the liquid inlet velocity. Water enters into the mold through the inlet port at the top of the nozzle. The liquid velocity has a constant value of 1.150 m/s. This value corresponds to a nominal casting speed of 1.800 m/min.
The secondary boundary condition is the pressure inlet condition, defined at the upper wall of the mold. At this boundary, the pressure has a constant value of 101325 Pa. The total pressure
The third boundary condition corresponds to the outlet at the bottom of the mold. This wall is as an outflow boundary. The flow rate weighting value is 1.000.
The models representing the mold with a traditional SEN and the model using the SEN with fluid flow conditioners were discretized employing similar criteria. The size of the minimum element was
For illustrative purposes, exclusively, Figure
Meshing on the SEN external wall and the mold wide wall. The figure includes the SEN with fluid flow conditioners and a traditional SEN.
In this section, we present the results of transient numerical simulations using the models, boundary conditions and operating conditions as described in the previous section. The transient numerical simulations represent 60 seconds of operation of the physical model. It was observed that this process is time enough to eliminate the behaviors associated with the start of the simulation. It was also observed that both models reached a quasisteady state using 60 seconds of operation time. However, fluctuations in the free liquid surface are higher for the mold with the traditional nozzle.
Figure
Numerical simulation of the free liquid surface on the mold using the SEN with flow conditioners and a traditional SEN.
Figure
Fluid velocity field on a plane parallel to the mold wide walls using the SEN with flow conditioners and a traditional SEN. The plane is located close to onemoldwide wall.
Figure
Liquid velocity vectors on the free surface. The figure shows the results of both the SEN with flow conditioners and a traditional SEN.
The aim of the SEN fluid flow conditioners is to induce at the top of the mold a fluid flow pattern as symmetric as possible. Figure
Figure
Liquid velocity vectors on a plane perpendicular to the mold wide walls. The plane is located between the liquid free surface and the SEN outlet ports. The figure shows the results of both the SEN with flow conditioners and a traditional SEN.
Results previously presented and discussed have shown qualitatively that the fluid flow conditioners indeed improve the behavior of the SEN. Table
Analysis of the fluid flow pattern inside a volume near the liquid free surface.
Variable  Average values over the control volume  

Traditional SEN  SEN with flow conditioners  

−2.041289 × 10^{−3}  8.948284 × 10^{−5} 

−4.936211 × 10^{−2}  −8.935193 × 10^{−2} 
Velocity magnitude  6.853202 × 10^{−2}  1.006960 × 10^{−1} 
As expected, the fluid conditioners attached to the SEN increase the average fluid velocity magnitude at the mold upper zone. However, the average
In accordance with several authors, some distortions of the ideal fluid flow pattern in the mold upper zone eventually induce deviations of the ideal pattern in the mold middle zone, and vice versa [
The fluid flow pattern inside the mold using the SEN with flow conditioners and a traditional SEN is depicted through stream traces starting at the SEN inlet port.
Figure
The results of numerical simulations previously presented confirm that the fluid flow pattern inside the mold when using the nozzle with fluid flow conditioners match the expected one. This means that the performance of the proposed SEN is better than that of a traditional nozzle. In addition, the results of physical experiments discussed in the next section also support the findings with numerical simulations.
The relationship between oscillation marks on the slab surface and heat transfer is widely recognized [
Contours map of fluid velocity magnitude at the mold walls using the SEN with fluid flow conditioners and a traditional SEN.
The scaled model is a rectangular prism made of acrylic plates. The physical dimensions of the physical model were described in Section
Figure
Liquid free surface under no flow conditions.
When liquid is flowing through the mold, the free surface of the liquid oscillates permanently. Several authors have argued that the liquid free surface behaves like a standing wave [
(a) Liquid free surface generated with a traditional SEN. (b) The previous image combined with the reference free surface.
Figure
(a) Liquid free surface generated with the SEN with flow conditioners. (b) The previous image combined with the reference free surface.
Figures
Fluid flow pattern inside the mold using the nozzle with flow conditioners. Small air bubbles outline the flow pattern. The time elapsed between images (a) and (b) is 1/12 sec.
To test the versatility of the proposed design, Figure
(a) Liquid free surface generated with the SEN with flow conditioners. (b) The previous image combined with the reference free surface. The flow conditioner is a perforated plate instead of the solid one.
Figure
Fluid flow pattern inside the mold using the nozzle with flow conditioners. Small air bubbles outline the flow pattern. The time elapsed between images (a) and (b) is 1/12 sec. The flow conditioner is a perforated plate instead of the solid one.
Numerical simulations confirm that the nozzle with the fluid flow conditioners produces a fluid flow pattern as expected. At the free surface, the conditioners inhibit the flow from one of the mold wide walls to the other one. Therefore, the occurrence of vortexes at the free surface is minimized.
Numerical simulations also confirmed the anticipated increase of the fluid mean velocity at the mold upper zone. The simulations presented in this work showed that the downward angle of the nozzle jet remains almost unchanged when using the SEN with fluid flow conditioners. Apparently, the formation of the solidified layer is not degraded by using a nozzle with flow modifiers. Nevertheless, the thermal and structural effects of the fluid flow conditioners on the solidification process of the steel inside the mold must be evaluated before its implementation at industry.
Physical simulations probed that the SEN with fluid flow conditioners reduces the fluctuations of the free surface. This work also shows that the fluid flow modifiers may be replaced by a grid that interferes as little as possible to the flux, which serves to insulate the steel and to lubricate the mold.
Some additional features of the proposed design are as follows.
The nozzle with fluid flow conditioners can be easily manufactured using currently available ceramic materials.
The shape of the fluid flow conditioners can be easily changed to improve its performance.
The fluid flow conditioners can also be used for cooling purposes by circulating a coolant fluid inside them.
The authors declare that there is no conflict of interests regarding the publication of this paper.
F. RiveraPerez (F. RP) thanks Universidad Autonoma Metropolitana for Ph.D. Grant. R. HernandezSantoyo thanks Consejo Nacional de Ciencia y Technología (CONACYT) for Grant no. 284913. This work was done in partial fulfillment of F. RP’s PhD requirements. The numerical and physical simulations were done in the Laboratorio de Computo CientificoDepartamento de Sistemas at Universidad Autonoma MetropolitanaAzcapotzalco.