Numerical Simulation of Fluid Flow and Interfacial Behavior in Three-phase Argon-Stirred Ladles with One Plug and Dual Plugs

Transcription

1 DOI: /srin steel research int. 82 (2011) No. 4 Numerical Simulation of Fluid Flow and Interfacial Behavior in Three-phase Argon-Stirred Ladles with One Plug and Dual Plugs Heping Liu 1) *, Zhenya Qi 2), and Mianguang Xu 1) 1) Central Iron & Steel Research Institute, No. 76 Xueyuan Nanlu, Haidian district, Beijing, , P. R. China 2) Beijing MingCheng Technology Development Co., Ltd., No.11 Laoshan Lu, Shijingshan district, Beijing, , P. R. China * Corresponding author; liuhp07@gmail.com A numerical investigation is performed to describe the quasi-steady fluid flow and interfacial behavior in a three-phase argon gas-stirred ladle with off-centered bottom Ar injection through a plug and two plugs placed in 1808 and 908configurations, respectively. The flow of the fluid phase is solved in an Eulerian frame of reference together with the motion of every individually injected Ar bubble, tracked in its own Lagrangian frame. Volume of fluid (VOF) model is used to track any interface between two or more immiscible phases, which include slag/metal, slag/gas and metal/ gas. The characteristics of fluid flow in a gas-stirred ladle with one plug or two plugs configuration are described when the slag layer and the top gas are presented. The slag layer deformation and slag open-eye formation at different Ar gas flow rates for three types of plug arrangements are given. The comparison of the mixing time, the deformation of slag layer and the behavior of slag/steel interface between one-plug and twoplug system is made. Several implications for ladle operational issues during a gas-stirred ladle refining cycle are discussed. It is found that the proper selection of Ar gas flow rate and plug arrangements during a ladle refining cycle is required for different refining purposes considering the mixing and metallurgical reaction in a three-phase ladle system. Keywords: Ladle furnace, gas injection, mixing time, open-eye formation, numerical model, slag layer Submitted on 26 July 2010, accepted on 22 November 2010 Introduction Gas stirred ladle is widely used in secondary steelmaking to homogenize chemical composition of alloy elements and temperature, and to remove inclusions. As a refining process, it also is responsible for the process of deoxidation and desulphurization. The buoyant plume created by gas bubbles from porous plugs generates the recirculation flow pattern in the ladle, which enhances turbulent mixing to homogenize the chemical composition and temperature, and helps to accumulate and transport the inclusions to the top slag layer and then to be removed. In addition, at a high gas flow, the rising gas bubbles may break through the slag layer, strengthen the interfacial reaction, cause the exposure of molten metal to atmosphere and form a large spout eye to serve the desulphurization. Depending on the refining purpose in a gas-stirred ladle refining cycle, the proper features of fluid flow and interfacial behavior corresponding to a different gas flow rate are required for the production of high quality steel. For example, for the mixing and inclusions removal, the mixing behavior is important because it determines the operation time to ensure homogeneity. A relatively calm flow without a broken slag layer is good for the inclusion floatation. However, for the desulphurization process, where surface turbulence and strong interaction between slag and steel at a high gas flow rate are needed to promote the efficiency of desulphurization, an appropriate spout eye area is required for the addition of desulfurizer and the enhancement of slag/steel intermixing. Very large open-eye areas is undesirable in order to avoid the possible pick-up of oxygen and nitrogen from atmosphere, the entrainment of slag caused by the instability of slag-metal interface, and the generation of exogenous inclusions resulting from refractory wear. Therefore, knowledge of the flow features of the molten steel during a ladle refining cycle corresponding to the different gas flow rate under a given ladle geometry, particularly the interfacial behavior in the region where molten steel is in contact with the slag, helps to understand the comprehension of various phenomena such as mixing, slag emulsification and desulphurization reactions between phases in a gas-stirred ladle system. Over the past three decades, the flow and mixing phenomena in a gas stirred ladle system have received wide investigation by cold physical model [1 7] and numerical simulation [8 24]. A comprehensive review of these methods can be found from the work of Mazumdar et al. [25 27]. Several previous works were mostly focused on the hydrodynamics of gas plumes, fluid flow and mixing behavior in single-phase molten steel. With increasing demands on steel cleanliness, the phenomena of slag/steel interaction and slag eye formation in a three-phase system have been the subject of some recent work. For example, Yonezawa et al. [3] measured the spout eye formation with a video technique using mercury and silicone oil. It was found that the eye geometry is highly dynamic. The time-averaged open eye area can be represented with dimensionless correlations. Others empirical correlations for the spout size also have been proposed [4 5] and critically evaluated in the work of Krishnapisharody et al. [6]. The eye sizes were measured in room-temperature under a variety of experimental conditions and a non-dimensional eye area was 440 ß 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

2 Full Paper steel research int. 82 (2011) No. 4 derived [6 7]. Recently, Valentin et al. [28] carried out an intensive experiment to evaluate the flow pattern of the ladle under industrial conditions and observed the formation of the open eye at different gas flow rates in a 170-t ladle. It was found that the shape and size of the open-eyes are influenced very strongly by the gas flow rate and the empirical correlations might not fully describe the dynamic flow behavior in a real gas-stirred ladle. Numerical simulation plays an important role in understanding the gas plume behavior, slag/metal interface and melt mixing, etc. due to the high temperature and a lack of optical accessibility in an industrial ladle. Currently, three different approaches have been applied to mathematically describe the flow in a gas stirred vessel: Quasi-single phase models [8 12], Eulerian-Lagrangian models [13 20], Eulerian- Eulerian models [21 24]. A detailed comparison of two types [17 19, 21] or three types of models [27] in a single-phase melt has been reported. In these studies, a flat and frictionless free surface was usually assumed, neglecting the slag open-eyes formation and the interfacial behavior among slag/steel/gas phases. In order to make reasonable predictions about a real industrial ladle, preliminary results indicated that the consideration of a three-phase system is essential [24]. Cloete et al. [29] developed a full-scale, threedimensional, transient mathematical model for application to gas-stirred ladles by employing the Lagrangian discrete phase model (DPM) in describing the bubble plume and the Eulerian volume of fluid (VOF) model for tracking the free surface of the melt. Olsen et al. [30] applied a similar model to gas-stirred ladles with bottom injection at high gas flow rate. Their results showed that the flat surface assumption was not valid for the investigation of the mixing time and it might be necessary to include the effect of a dynamic free surface at high gas flow rate. By considering a three-phase ladle system, Li et al. [31] developed a mathematical model to analyze the transient three-dimensional and three phase flow in argon-stirred ladle with one and two off-centered porous plug. The effect of argon gas flow rate on the spout height and the area of slag eye were discussed. The slag layer behavior and the interface wave were analyzed. Sand et al. [32] investigated the fluid dynamic features of combined gas and electromagnetic stirring in ladle furnace by a transient and turbulent multiphase numerical flow model using VOF and discrete phase model. The purpose of this study is to investigate quasi-steady fluid flow and interfacial behavior in an argon-gas stirred ladle with one plug and dual plugs configurations by numerical simulation when the slag layer and top gas are presented. The Lagrangian approach as the discrete phase model (DPM) is used to simulate the gas injection by injecting a stream of argon bubbles into the continuous phase and a Volume of fluid (VOF) model in Eulerian frame to track any interface among three phases in a ladle, similar as the work of Cloete et al. [29]. The fluid flow features and quantified mixing in a gas-stirred ladle with off-centered bottom injection with a porous plug / two porous plugs arranged in 1808and 908 are presented by the developed Eulerian-Lagrangian approach. The mixing time and slag eye opening at a high gas flow rate are discussed. A theoretical comparison of fluid flow and interfacial behavior between one-plug and dual-plug system is made. It is expected that the combined model can be a attempt to provide a relative quantification and comparison of the quasi-steady flow characteristics and interfacial phenomena in a gas stirred ladle through numerical simulation when three phases (slag/metal/gas) are presented, although fully predicting the dynamic area of a spout eye is still an uncontrolled process due to the uncertainty of empirical parameters such as bubble size and drag coefficient available for various ladle geometries and complex operating parameters. Mathematical Models A set of Navier-Stokes equations is solved for the liquid phase and a discrete-phase model is used for the bubbles phase. The liquid phase equations are as follows. (1) ð iþ ¼ 0 i (2) Momentum i Þ i þ i e j þ rg i þ f s þ F b;i (2) i where u i is the fluid velocity, r is the density, p is the pressure, m e is the effective turbulent viscosity, and g i is the gravitational acceleration. (3) Turbulent equations: The standard two-equation k e model is used to model turbulence, which solves two equations for the transport of turbulent kinetic energy and its dissipation rate to obtain the effective viscosity field, k 2 m e ¼ m þ m t ¼ m þ rc m (3) e Turbulent kinetic energy, þ i m þ m þ G re i s i Where G is the generation of turbulence kinetic energy due to the mean velocity i G ¼ m t j i The rate of dissipation of turbulent kinetic energy, þ i m þ m s i þ e ð k C 1G C 2 reþ (6) ß 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim 441

3 steel research int. 82 (2011) No. 4 Full Paper where C 1, C 2, C m, s k, s e are the empirical constants, whose values are 1.38, 1.92, 0.09, 1.0 and 1.3, respectively. (4) VOF model To represent the interface behaviors of slag layer and top gas layer in the gas-stirred ladle, the fractional volume of fluid (VOF) scheme is used. In this technique, a scalar function F is introduced and it satisfies the following conservation volume fraction þ u i ¼ 0 (7) Where the subscript q stands for the different phases (air/ melt/slag) and the value of F defines the phase state of a control cell in the computational mesh: F a þ F m þ F s ¼ 1 (8) The effects of surface tension at the interface among different phases are taken into account though a body force as a function of volume fraction F. According to Continuum Surface Force (CSF) model, the curvature of the interface k can be defined in term of the divergence of a unit vector normal to the interface with the help of cell volume fraction and its gradient. The addition of surface tension to the VOF calculation results in a volume force source term f s in the momentum by using the divergence theorem. They can be expressed as: rkrf f s ¼ s 1 2 ðr k ¼ r rf (9) a þ r m Þ jrfj The thermo-physical properties appearing in the transport equations are determined by the volume fraction presented in each control volume: r ¼ r a F a þ r m F m þ r s F s (10) m ¼ m a F a þ m m F m þ m s F s (5) Discrete phase model The injected Ar gas bubbles are treated as discrete second phase. The trajectory of each bubble is calculated in each time step according to the drag force, the buoyancy force, the virtual mass force and the force stemming from the pressure gradient, given by: du bi dt ¼ F Di ðu i u bi Þþ r b r r g i þ 1 r d 2 r b dt ðu i u bi Þ þ r r b u i (11) F Di ¼ 18m C Di Re bi r b d 2 bi 24 (12) Re bi ¼ rd bju i u b j (13) m where, u bi and r b are the velocity and density of argon gas bubble respectively. F Di is the drag force. The drag coefficient C Di is a function of the Reynolds number Re bi, determined by the non-spherical particle drag model [33]. The shape of the bubble is assumed to be spherical cap, and the shape factor is specified as 0.7. This momentum exchange from the continuous phase to the gas plume is computed by examining the change in momentum of a bubble as it passes through each control volume. A momentum source is added to the continuous phase momentum by summing the local contributions from each bubble in the continuous phase flow field. F b;i ¼ XN b F Di ðu i u bi Þþ r b r g i r 1 b þ 1 r d 2 r b dt ðu i u bi Þþ i u i r r b Q bi Dt i (14) where, r b Q bi is the mass flow rate of argon as bubble and Dt is the time step. The two-way coupling is accomplished by alternating the argon gas bubble calculation with the molten steel flow computation. (5) Bubble size model When argon is injected from the plug, a Rosin-rammler bubble size distribution is considered at the argon gas injection inlet [29]. The mean bubble size is characterized by its equivalent diameter, using the empirical correlation with flow rate [14 15]: d b;i ¼ 0:35 Q b 2 0:2 (15) g In the computation domain, the density and the diameter of the bubble are calculated at each position according to the local static pressure and the temperature of the phases. A simple bubble breakup model is combined into the present model, which is assumed that when the bubble diameter is over the critical diameter of 40mm, two bubbles with equivalent mass are generated from one mother bubble. More advanced bubble expansion and breakup model [30, 34] can be considered in future work. (6) Random walk models In this study, the chaotic effect of turbulence in the molten steel on the bubble trajectories is considered using the random walk model. The fluctuating component of the bubble velocity is found according to the local level of turbulent kinetic energy using the turbulent random walk model as follows: pffiffiffiffiffiffiffiffiffiffi u i ¼ u i þ j 2k=3 (16) where z is a random number uniformly distributed between 0 and 1. (7)Species transport model: The mixing time in a bottom gas-stirred ladle is calculated by solving the following species þ D i (17) 442 ß 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

4 Full Paper steel research int. 82 (2011) No. 4 Figure 1. Computational domain and mesh system with one plug and dual plugs. (a) Single plug; (b) dual plugs with 1808; (c) dual plugs with 908. where C is the mass fraction of the species, and D e is the diffusion coefficient of the species: D e ¼ D 0 þ m eff (18) rsc t where Sc t is the turbulent Schmidt number which is set to 0.7. Geometrical Model and Computational Conditions Figure 1 shows the computational domain and mesh system of the gas-stirred ladle with three types of plug configurations. The ladle is of conical shape with a height of 3.50m, having an inner diameter 3.32m at the top and 3.07m at the bottom. The ladle bath is filled with molten steel up to a height of 2.647m from the bottom wall. The initial slag layer thickness is 80mm, corresponding to 16kg/t of the weight ratio between slag and steel. A free space of 0.773m above the slag is filled with top gas. Argon gas is injected through a porous plug or two plugs at the bottom of the ladle. The argon injection positions are located at about times of ladle bottom radius for every plug. Three types of porous plug configurations including single plug, two plugs with 1808 (diametrically opposed) and dual plugs with 908are simulated. The local mesh refinement is employed at the phase interface and the bubble plume zone. The detailed computational conditions and model parameters are given in Table 1. For the simulation of fluid flow, no-slip boundary condition is used at the bottom wall and side wall, with standard wall functions in order to capture the steep gradients with reasonable accuracy on a coarse grid. The Ar bubbles are assumed to escape at the surface of top gas, and be reflected at other walls. For the species transport for the tracer tracking, the zero flux boundary condition is used at walls and top surface. For the multi-phase flow field calculation, a transient flow field calculation is performed together with steady state trajectory simulations of bubbles by a finite-volume software FLUENT 1. Volume fraction equation is solved using an explicit time-marching geo-reconstruct scheme. This two-way coupling is accomplished by alternately solving the discrete and continuous phase equations. This discrete phase are updated every tenth continuous phase iteration until the solutions in both phases has little change in two successive calculation sets. The convergence criteria are set to 10 3 for the residuals of all dependent variables. A typical convergence history of volume-averaged velocity and turbulent kinetic energy are plotted in Figure 2. Results and Discussions Fluid flow and Interfacial behavior in One-Plug System. Figure 3 show the 3D streamlines distribution in a gas-stirred ladle with one plug at a gas flow rate of 100L/min when the slag layer is presented. The classic recirculation fluid-flow pattern is generated by argon injection from the ladle bottom The flow pattern of the molten steel in one-plug system consists of a large circulation, characterized by an upward flow driven by the argon gas and a downward flow close to the wall on the opposite side of the porous plug. Figure 4 shows velocity distribution of molten steel at various XY sections for different gas flow rates. The velocity distributions show the rising jet due to the bubble injection forms a plume that expands as it rises. The shape of rising bubble plume is not a strictly vertical cone and it turns towards the wall with an increase of the ladle height. The predicted flow features are consistent with available experimental observation [8]. A high gas flow rate has an intensive bubble plume with large velocity value of the upward flow. Consequently, the strong upward flow may generate the open-eyes on the surface of the slag. Figure 5 shows the comparison of the flow pattern for different gas flow rates when the slag is covered on the surface of molten steel. With the increase of the gas flow rate, it is observed that the vortice center of the flow changes and the flow pattern is more turbulent in the ladle. When the gas flow rate is less than 300L/min, there is a dead zone near the bottom corner region of the ladle. However, when the gas flow rate of 500L/min is injected, the intensified flow in the metal/slag interface impinges toward the bottom-side corner ß 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim 443

5 steel research int. 82 (2011) No. 4 Full Paper Table 1. Computational conditions. Thermal physical properties Property Symbol Value Unit Density of molten steel r m 7020 kg/m 3 Viscosity of molten steel m m Pas Density of slag r s 3500 kg/m 3 Viscosity of slag m s 0.06 Pas Density of top gas r a 0.5 kg/m 3 Viscosity of top gas m a Pas Surface tension of metal/gas s m=a 1.82 N/m Surface tension of slag/gas s s=a 0.58 N/m Surface tension of metal/slag s m=s 1.15 N/m Density of argon at 298K r b kg/m 3 Diffusion coefficient of the species D o m 2 /s Gravitational acceleration g 9.81 m/s 2 Temperature of molten steel T 1873 K Geometry Parameters of the ladle model Slag layer thickness (slag weight: 16kg/t steel) 0.08 m Diameter of the bottom of the ladle 3.07 m Diameter of the top of the ladle 3.32 m Height of the ladle 3.5 m Effective Height filled with molten steel m Height of top gas m Note: The symbol indicates that top gas has a lower density due to high temperature in a real industrial ladle system region of the ladle, which leads to the change of flow pattern and the disappearance of the dead zone. The change of flow pattern at a high gas flow rate can t be predicted when the slag layer is not taken into consideration. Figure 2. Typical convergence history of volume-averaged velocity and turbulent kinetic energy in the molten steel. Figure 6 indicates velocity distribution at main section in one plug system. It can be seen that at a low gas flow rate of 50L/min, the bubble plume can t break through the slag layer, but a part of the bubbles can be escaped from the slag layer and the top gas, causing the flow of the top gas. With the increase of Ar gas flow rate, the open-eye of the slag layer forms and the flow pattern changes. For the gas flow rate of 400L/min, the circulation loop of the flow at main section of the plug is largely constrained near the slag/metal interface around the open-eyes. The fluid flow of top gas also obviously intensifies, which can generate the intensive turbulences and the appearance of smoke around the open-eyes at high gas flow rate, as suggested by Valentine et al. [28]. Figure 7 shows the effect of different argon gas flow rate on the deformation of slag layer shape at main section of the plug. It can be observed that at a lower gas flow rate (100L/min), the slag open-eye formation can t appear in the present case. A smaller slag eye opening occurs when the flow rate of 150L/min is used. It means that if we want to reduce the index of the inclusions, it is necessary to control a lower Ar gas flow rate (100L/min) to prevent from the open-eye formation, because, according to the study of 444 ß 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

6 Full Paper steel research int. 82 (2011) No. 4 Figure 3. 3D streamlines distribution in a gas-stirred ladle with one plug (Q b ¼ 100L/min). Figure 4. Velocity field of molten steel at various X-Y sections in one plug system(z ¼ 0.5m, 1.0m,1.5m, 2.0m, and 2.5m). (a) Q b ¼ 100L/min; (b) Q b ¼ 300L/min. Figure 5. 3D Streamlines distribution in a gas-stirred ladle with one plug. (a) Q b ¼ 100L/min; (b) Q b ¼ 300L/min; (c) Q b ¼ 500L/min. Valentin et al. [28], as soon as an open-eye comes into existence, the inclusion content is higher compared to those heats produced under a closed top slag. With increasing gas flow rates, the size of the open-eyes on the slag is enlarged. At higher gas flow rate of 500L/min, the thickness of slag layer becomes very thin near the side wall of the ladle. This indicates that there is a strong flow in the molten steel, which may wear off the refractory of ladle wall and reduce the ladle life. The efficiency of desulphurization in ladle refining depends strongly on the interaction behavior between slag and steel created by argon stirring, thus it is important to examine the effect of Ar flow rate on slag eyes opening. Figure 8 shows the quasi-steady slag opening-eye size and ß 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim 445

7 steel research int. 82 (2011) No. 4 Full Paper can generate a slag eye in diameter of about 0.69m while the open-eye diameter is about 0.87m when Ar flow is set at 500L/min. High gas flow rate leads to the formation of a larger slag eye and its shape variations from a circular one to an oval one. The predicted tendency is in agreement with the observation under industrial conditions [28]. A quantitative comparison of the predicted non-dimensional eye area ratio with the available experimental results is shown in Figure 9. The experimental data were collected by Krishnapisharody et al. and the meanings of the non-dimensional parameters in the figure can be found in Ref. [7]. It can be seen that the density ratios of the fluids in the system obviously affects eye area ratio. The result of the present work seems to capture the appropriate influences of non-dimensional parameter on the eye formation and to be comparable with the experimental data. The effect of gas flow rate on the spreading area and velocity field at the interface between slag and steel (Z ¼ 2.647m) is shown in Figure 10. The higher the gas flow rates the larger the molten steel spreading area, and the higher the interfacial velocities of the top slag are. The large spreading area and high interfacial velocity is desirable for the desulphurization process, where strong mixing and large reaction area of metal and slag are required. When the slag velocity exceeds a critical value, an emulsification of the top slag is possible. Currently it is difficult to quantify the slag emulsification process in such a high-temperature ladle system by numerical simulation [31]. A general indicator of the magnitude of the slag emulsification is related to the interfacial velocity. Although a high gas flow rate, e.g. 500L/min, can improve the slag emulsification, it causes the strong level fluctuation at slag/steel interface (shown in Figure 10d). This may be harmful for the production of clean steel compared with the efficiency of the desulphurization. Figure 6. Velocity distributions at main section of the plug in one plug system. (a) Q b ¼ 50L/min; (b) Q b ¼ 200L/min; (c) Q b ¼ 400L/min. shape at the slag/gas interface for different Ar flow rate. Note that it is regarded as the slag eye opening when the slag volume fraction is less than 0.1. High slag volume fraction indicates a thicker slag layer pushed away by the rising gas bubbles. In the present study, an Ar flow rate of 200L/min Fluid flow and Interfacial behavior in dual-plug system. The velocity distributions, streamline plots and spout height of the melt at main section of the plug for dual plug system are presented in Figure 11. The legend (100 þ 100L)/min means that 100L/min of gas flow rate is employed for every plug. Compared with that of one plug, the flow pattern of dual plugs with 1808is characterized by two large recirculation loops, which is created by the upward flow from two injection plugs. For the equal gas flow rate, the loops patterns are approximately symmetrical and their vortice centers change at a high gas flow rate. No noticeable mutual influences of both gas plumes for dual plugs with 1808can be observed. This maybe is because that the distance between the plugs in present study is relatively large. However, the dual plugs with 908presents a different flow pattern at main section relative to dual plugs with 1808, only a large flow recirculation loop is found and doesn t obviously change when the gas flow rate is increased to 300L/min per plug. It seems that there is a minor mutual influences of both plumes because the plume radius and the flow of the top gas decrease when dual plugs with 908is used. Figure 11c shows the enlarged velocity profile and spout 446 ß 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

8 Full Paper steel research int. 82 (2011) No. 4 Figure 7. Slag layer deformationsat main sectionof the plug for one-plug system at differentgas flow rates. (a) Q b ¼ 100L/min; (b) Q b ¼ 150L/min; (c) Q b ¼ 200L/min; (d) Q b ¼ 300L/min; (e) Q b ¼ 400L/min; (f) Q b ¼ 500L/min. height of melt around the open eye in dual plugs with 908. The flow of the melt drives two recirculating movement of top gas near the steel/gas interface. The predicted spout height and spout shape is different from those from Li et al., where their numerical results indicated a high spout height with a tapering shape [32]. It is not clear about how to deal with the gas plume behavior in their numerical simulation. The general features of the deformation of slag layer and interfacial fluctuation due to the Ar injection from two different plug arrangements is similar as those of single plug system (not shown here for brevity).the typical predicted flow field and the shape of the slag layer in dual-plug system at a gas flow rate of 200L/min per plug are shown in Figure 12. Figure 13 presents the slag/steel interfacial velocity and slag/ steel interface fluctuation at 300L/min per plug. ß 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim 447

9 steel research int. 82 (2011) No. 4 Full Paper Figure 8. Slag opening-eye size and shape at the slag/gas interface in one plug system (Z ¼ 2.727m). (a) Q b ¼ 200L/min; (b) Q b ¼ 300L/min; (c) Q b ¼ 400L/min; (d) Q b ¼ 500L/min. Comparisons of one-plug with dual-plug system (1) Comparisons of 95% mixing time. In this study, the mixing time is defined as the time of attaining a 95% degree of homogenization in the molten steel. The locations of the sampling points are shown in Figure 14. In order to simulate the addition of the desulfurizer, the tracer is released in a form of the cylinder with the height 0.5m and diameter 0.4m, just located above at the center of the plug with larger gas flow rate and 200mm below the slag/metal interface. Figure 15 shows typical tracer response curve of various monitoring points and the procedure adopted to estimate 95% mixing time for different plug configurations. The mixing times from several calculated cases are listed in Table 2. It can be found that from the point view of mixing time, when the slag open-eye is not formed (Argon flow rate 100L/min per plug), the dual-plug system with 1808provides a shortest mixing time and dual plugs with 908is found to be worst in the present study. The single plug system doesn t give the shortest mixing time like the study of Zhu et al. [9]. A possible reason is from both different plug configurations. In our case, Figure15a and 15b shows that there is a monitoring Point 9, which is located in the dead zone of the bottom corner of the ladle, preventing from the quick mixing in the melt (also see Figure 3a and 3b). Different from the other cases where slag layer is not considered, an interesting finding in the present study is that the mixing times don t always have diminishing correlation with the increased gas flow rate when there is a dead zone and the slag layer is presented. This can be explained by the fact that the slag layer can cause significant delay in mixing time because the breakage and deformation of the slag layer consume part of the stirring input energy [8]. However, at a higher flow rate of 400L/min and 500L/min, the mixing time significantly shortens due to the change of flow pattern and the disappearance of dead zone (also see Figure 3c). It takes about 3min for gas flow rate of 500L/min to finish the mixing process (Figure 15e). Figure 15d and 15f shows that with the increased gas flow rate, the mixing time reduces for the dualplug system with 908.However, for dual plugs with 1808, the dependence is found to be less pronounced (see Table 2). An examination from the sample points shows that the mixing 448 ß 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

10 Full Paper steel research int. 82 (2011) No. 4 Figure 9. Comparison of the predicted non-dimensional open-eye arearatiowiththeavailableexperimentaldata(k& I: Krishnapisharody and Irons[6]; Y & S: Yonezawa and Schwerdtfeger[3]; H: Han et al. [35]): (a) ða e =A P Þ vs. ðqþ 1=3 ðh=hþ 1=2 ; (b) ða e =A P Þ vs. ð1 rþ 1=2 ðqþ 1=3 ðh=hþ 1=2. times are mainly retarded by the sample points of Point 7, Point 8 and Point 9, which are located in the affected region of the rising plume flow of one plug. Thus, the predicted mixing times are sensitive to monitoring points as well as to plug configuration. The difference of mixing time among different plug configurations can be explained by Figure 16, where the velocity and turbulent viscosity distribution at half height of the melt is presented. It can be seen that the flow pattern is strongly associated with the plug arrangements. At a gas flow rate of 200L/min, the turbulent viscosity of dual-plugs with 1808has a large and uniform distribution. The dualplugs with 908has a relatively small turbulent viscosity Figure 10. Moltensteelspreadingandvelocitydistributionattheslag/ steel interface (Z ¼ 2.647m). (a) Q b ¼ 50L/min; (b) Q b ¼ 150L/min; (c) Q b ¼ 300L/min; (d) Q b ¼ 500L/min. ß 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim 449

11 steel research int. 82 (2011) No. 4 Full Paper Figure 11. Velocitydistributions, streamlineplotsandspoutheightat mainsectionoftheplugin dual-plugsystem.(a) Dualplugswith1808;(b) Dual plugs with 908(only one plug at main sections is shown); (c) Enlarged view at steel/gas interface for dual plugs with 908. value, which is even lower than that of single plug system at 100L/min. Because high turbulent viscosity means better mixing, the dual-plugs with 908is not recommended as the plug configuration for the purpose of mixing at a low gas flow rate. In one-plug system, compared with Ar flow rate of 100L/min without a slag-eye opening, 200L/min with a slag eye indicates a lower turbulent viscosity. This can be contributed to the fact that the stirring input energy from Ar injection is partly consumed in the breakage and deformation of the slag layer. 450 ß 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

12 Full Paper steel research int. 82 (2011) No. 4 Figure 13. Molten steel spreading area and velocity distribution at the slag/steel interface for dual plugs (Z ¼ 2.647m) for Q b ¼ (300L þ 300L)/min. Figure 12. Predicted flow field and slag layer shape in a gas-stirred ladle with dual plugs(q b ¼ (200 þ 200L)/min). (2) Comparison of slag eye opening formation. Figure 17 shows the slag open-eye size for two-plug system at the slag/gas interface (Z ¼ 2.727m). Compared with Figure 8, it can be seen that the slag open-eye area is larger in dual plugs than that in one plug at the same total gas flow rate while the slag open-eye diameter is smaller than that in a single plug. For example, at the same total gas flow rate of 400L/min, the two-plug system for the equal gas flow generates two slag open-eyes of about m, but the total slag open-eye area in two-plug system is larger. The open-eye sizes from two non-equal gas flow rates are presented in Figure 17b and 17c. It seems that the dual plugs for non-equal gas flow rate create a smaller slag open-eye for every plug. This suggests that the gas flow rate per plug should be set at an equal value as soon as possible in the practical ladle operation to expand the slag open-eye size and promote the slag emulsification. As a result of mutual influence of the plumes in dual plugs with 908, a minor smaller slag eye size can be observed relative to that in dual plugs with 1808, shown in Figure 17e and 17f. (3) Comparison of the slag/steel interfacial behavior. Figure 18 illustrates the interfacial velocity and the spreading area of molten steel for one plug and two plugs at the slag/steel interface (Z ¼ 2.647m). With the increase of gas flow rate, the molten steel spreading area and interfacial velocity increase. One plug stirred ladle has higher interfacial velocity and the larger spreading area of molten steel. Because the emulsification of the top slag depends on some critical velocity, the intensive gas flow rate will improve the emulsification and promote the generation of large area of open-eyes on the surface of molten steel. However, because the desulphurization reaction also is ß 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim 451

13 steel research int. 82 (2011) No. 4 Full Paper Table 2. Comparison of 95% mixing time for one plug and dual plugs in the present study with taking the slag layer into consideration. Plug numbers Argon flow rate (L/min) 95% Mixing time (sec.) One plug þ þ Dual plugs with þ Figure 14. Monitoringlocationsinsideladle. Monitoredpoints: Point1 (0,0,1.324), Point 2 (0,0, 2.347), Point 3 (0,0, 0.3) Point 4 (0.9, 0.9, 1.324), Point 5 (0.9,0.9,2.347), Point 6 (0.9,0.9,0.3) Point 7 (0.9,- 0.9,1.324), Point 8 (0.9,-0.9,2.347), Point 9 (0.9, -0.9,0.3). Dual plugs with þ þ þ þ þ associated with the interaction area between steel and slag, if the desulfurizer is added into the molten steel from one plug, it seems that the dual-plug arrangement with 908has larger slag/steel interaction area than dual-plug with More than half of slag layer area (where the slag volume fraction is less than 0.5) for 300L/min per plug can take part in the slag/ metal intermixing and help to promote desulphurization reaction. Therefore, it may be preferred to have dual plugs arrangement with 908for the desulphurization at a higher gas flow rate. Furthermore, by dividing the gas flow into two weakened plumes, the dual-plug system can yield some improvements in avoiding the slag entrapment, the refractory wearing-off and re-oxidation resulting from one-plug system with high gas flow rate. (4) Comparison of velocity distribution and the behavior of slag layer at main section plane. The comparison in the flow velocity and the deformation of slag layer at the main section plane for one plug and dual plugs with 1808is examined in Figure 19. Compared with twoplug system, the flow velocity in one plug is larger and the formation of the slag eye opening is earlier. The interfacial velocity and slag eye size also is larger. At a total gas flow rate of 400L/min, for one plug, the slag layer near the refractory wall (on the left side in Figure 19c) and near the slag/steel shear layer zone (on the right in Figure 19c) around the slag eye begins to become thin, which shows there is slag entrapped into the molten steel. In contrast, dual plugs with a gas flow rate of 200L/min per plug yields some improvements in terms of the thinning of slag layer. When the gas flow rate is increased up to 600L/min, the thinning of the slag layer is more obvious in one plug than in dual plugs with total gas flow of 600L/min (300L/min per plug), it can be concluded that although the higher gas flow may improve the slag emulsification and increase the gas-stirred intensity, it also increases the interfacial velocity at steel/slag interface, which leads to the thinning of slag layer and the entrainment of the slag. At the same time, strong flow at higher gas flow rates also limits the slag layer to have enough time to absorb into the inclusions. Therefore, it should be careful to use too high gas flow rate for the cleanness of the molten steel in the practical ladle operation. Some compromise needs to be made between the desulphurization rate and the steel cleanness when the gas flow rate is optimized for different plug arrangements. Figure 20 indicates the detailed velocity profile along the diameter direction at the main section plane at the slag/steel interface (Z ¼ 2.647m). With the increase of the gas flow rate, the axial velocity profile (or the plume) more deflects the center of the plug and is closer to the refractory wall due to the effect of the intensive flow on the plume. Because the downward axial velocity stands for the pulling for the slag layer, the higher gas flow rate with larger axial velocity value in one-plug obviously increase the possibility of the emulsification and the entrainment of the slag. When dividing the gas flow into two weakened plumes, the maximum axial velocity can be reduced by about a half in two-plug system. Furthermore, the higher axial velocity closer to the refractory wall in one-plug system easily leads to the wear-off of the refractory lining, and brings more inclusions into the molten steel and reduces the ladle life. Figure 20b shows the surface velocity along slag/steel interface increases with the increased gas flow rate. At a gas flow rate of 500L/min, the maximum surface velocity is 452 ß 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

14 Full Paper steel research int. 82 (2011) No. 4 Figure 15. Typical tracer response curve and the procedure adopted to estimate 95% mixing time for different plug configurations at different Ar gas flow rate. 0.24m/s in one plug while it is about 0.14m/s in two-plug system with 1808at 300L/min per plug. (5) Some implications for ladle operation. On the basis of the comparison of mixing time, fluid flow and interfacial behaviors in a three-phase gas stirred ladle with one plug and dual plugs, several implications from the results of this model for ladle operation can be given as follows during a ladle refining cycle under the present conditions. At an initial stage of desulphurization processes, it is appropriate to use single plug with larger gas flow rate, because under this condition the large rising axial velocity can break through the slag layer, and large slag-eye opening size is favorable for the addition of desulfurizer. Short ß 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim 453

15 steel research int. 82 (2011) No. 4 Full Paper Figure 16. Velocity profiles and turbulent viscosity distribution at Z ¼ m (Half of melt height). mixing time and strong interfacial velocity will be helpful for the desulfurizer to be melt and rapidly homogenized. Naturally, the strong interfacial velocity and large metal/ slag interfacial area may promote the desulphurization. However, too high gas flow (>500L/min) causes strong level fluctuation at the slag/steel interface. The slag slayer near the refractory wall and shear layer around the slag eye became thinner, which can leads to slag entrainment and the erosion of the ladle lining. In addition, larger slag eye size increases also the potentiality for re-oxidation. Therefore, during the middle stage of the process, it is very necessary to balance the desulphurization efficiency and the cleanness of the steel during ladle operation for one-plug system at a very high Ar gas flow rate. The dual-plug with 908can provide some improvements by dividing the gas flow into two weakened plumes. It has a large metal/slag interaction area and short mixing at a high Ar gas flow rate (300 þ 300L/min), which can increase the reaction contact area between slag and steel for the desulphurization at a high gas flow. In addition, more total gas flow rate injected from dual plugs may be suitable for the inclusion modification and its removal when compared with one-plug system. At the final stage of the desulphurization, in order to secure soft bubbling, gentle mixing and inclusion removal, the dualplug system with 1808 at the lower gas flow rates (100L/ min per plug) without an open-eye is found to be the best arrangement considering the shortest mixing time. Compared with one plug system, dual plugs also will be helpful to generate more small bubbles favoring the growth and floating-up of the inclusions during the rinsing period. Conclusions In this study, the fluid flow and interfacial behavior in a three-phase gas-stirred ladle with off-centered bottom injection with a porous plug / two porous plugs have been numerically investigated. The characteristics of fluid flow at different gas flow rates for different plug configurations are described. The slag layer deformation and slag open-eye formation are presented. The comparison of mixing time, the slag-eye formation and the behavior of slag/steel interface between one-plug and two-plug system is made. 454 ß 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

16 Full Paper steel research int. 82 (2011) No. 4 Figure 17. Slag open-eye size for two plugs system at the slag/gas interface (Z ¼ 2.727m). The following conclusions can be drawn from numerical results: (1) The flow pattern of the molten steel is dependent on the plug configurations and Ar gas flow rate. When the slag layer is presented, the flow pattern of single-plug and dual plugs with 1808can be changed at a high gas flow rate. (2) The 95% mixing times are sensitive to the locations of the sample points as well as the plug configurations. The appearance of the dead zone and the presence of ß 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim 455

17 steel research int. 82 (2011) No. 4 Full Paper Figure 18. Comparison of interface velocity and spreading area of molten steel between steel and slag for one plug and two plugs at the slag/steel interface (Z ¼ 2.647m). the slag layer significantly delay the mixing time. When the slag open-eye is not formed, the dual-plug system with 1808provides a shortest mixing time and dual plugs with 908is found to be worst in the present study. (3) The slag open-eye can t form when the gas flow rate is lower. With the increased gas flow rate, the slag openeye size, the spreading area of molten steel and the interfacial velocity between slag and steel increase. For one-plug system, although the high gas flow may 456 ß 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

18 Full Paper steel research int. 82 (2011) No. 4 Figure 19. Comparisonof the flow velocityand the deformation of slag layer at the main sectionplane of the porousplugfor oneplug and dualplugs with 1808(Total gas flow rate: 200L/min, 400L/min, 600L/min, respectively) improve the slag emulsification and promote the desulphurization rate, too high gas flow rate can cause the thinning of slag layer around the slag eye, the enlargement of the open-eye area and the deflection of the plume toward the refractory side wall, which can result in slag entrainment, re-oxidation of the melt and wearingoff the refractory wall of the ladle, respectively. Therefore, some compromise needs to be made between the desulphurization rate and the steel cleanness at a very high gas flow rate if off-centered one-plug system is used. ß 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim 457

19 steel research int. 82 (2011) No. 4 Full Paper compromise in both aspects. It is recommended that dual-plug system with 1808 at a low gas flow rate without an open-eye area is used for soft bubbling and inclusion removal. References Figure 20. Velocity profile along the diameter direction at the main section plane at the slag/steel interface (Z ¼ 2.647m) for one plug and dual plugs with (4) By dividing the gas flow into two weakened plumes, dual plugs can reduce the values of interfacial velocity and avoid the significant deformation of slag layer, thus reducing the potential slag entrainment and the contamination for the melt from the erosion of the refractory wall in one-plug system with intensive Ar gas flow rate. (5) Numerical results show that the plug arrangement at different gas flow rates has its advantage and disadvantage. Proper selection of gas flow rate and plug configurations during a ladle refining cycle is required for different refining purposes. In the present study, it is suggested that single plug at a higher gas flow rate is favorable at the initial stage of the desulphurization. During the middle stage of the process, it is very necessary to balance the desulphurization efficiency and the cleanness of the steel during ladle operation if oneplug system at a very high Ar gas flow rate is used. Dual plugs with 908at a high gas flow rate can provide some [1] Y. Xie and F. Oeters: Steel Research, 63 (1992), No. 3, 93. [2] J. Mandal, S. Patil, M. Madan and D. Mazumdar: Metall. Mater. Trans. B, 36B (2005), 479. [3] K. Yonezawa and K. Schwerdtfeger: Metall. Mater. Trans. B, 30B (1999), 413. [4] Subagyo G. A. Brooks, and G. A. Irons: Iron Steel Inst. Jpn. Int., 2003, vol. 43, 262. [5] D. Mazumdar and J. W. Evans: Metall. Mater. Trans. B, 35B (2004), 400. [6] K. Krishnapisharody and G. A. Irons: Metall. Mater. Trans. B, 37B (2006), 763. [7] K. Krishnapisharody and G. A. Irons: ISIJ International, 48 (2008), [8] S. Joo and R. I. L. Guthrie: Metall. Trans. B, 23B (1992), 765. [9] M. Y. Zhu, T. Inomoto, I. Sawada and T. C. Hsiao: ISIJ Int., 35 (1995), No. 5, 472. [10] M. Y. Zhu, I. Inomoto, N. Yamasaki and T. C. Hsiao: ISIJ Int., 36 (1996), 503. [11] S. Ganguly and S. Chakraborty: ISIJ International, 44 (2004), No. 3, 537. [12] S. Ganguly and S. Chakraborty: Ironmaking and Steelmaking, 35 (2008), No. 7, 524. [13] S. M. Pan, Y. H. Ho and W. S. Hwang: J. Mater. Eng. Perform., 6 (1997), No. 3, 311. [14] S. Johansen and F. Boysan: Metall. Mater. Trans. B, 19B (1988), 755. [15] J. Aoki, B. G. Thomas and J. Peter: AISTech 2005, Nashville, TN, Sept , 2004 Assoc. Iron Steel Technology, Warrendale, PA., p [16] M. Warzecha, J. Jowsa, P. Warzecha and H. Pfeifer: Steel Research Int., 79 (2008), No. 11, 852. [17] M. Madan, D. Satish and D. Mazumdar: ISIJ Int., 45 (2005), No. 5, 677. [18] D. Guo, L. Gu and G. Irons: Appl. Math. Model., 26 (2002), 263. [19] D. Mazumdar, R. Yadav and B. B. Mahato: ISIJ Int., 42 (2002), No. 1, 106. [20] D. Mazumdar and R. I. L. Guthrie: ISIJ Int., 34 (1994), No. 5, 384. [21] J. F. Domgin, P. Gardin and M. Brunet: Second International Conference on CFD in the Minerals and Process Industries, CSIRO, Melbourne, Australia 6-8 Dec p [22] M. R. Davidson: Appl. Math. Model., 14 (1990), 67. [23] H. Turkoglu and B. Farouk: Metall. Trans. B, 21B (1990), 771. [24] C. G. Méndez, N. Nigro and A. Cardona: J. Mater. Process. Tech., 160 (2005), 296. [25] D. Mazumdar and R. I. L. Guthrie: ISIJ Int., 35 (1995), No. 1, 1. [26] D. Mazumdar and J. W. Evans: ISIJ Int., 44 (2004), No. 3, 447. [27] D. Mazumdar and R. I. L. Guthrie: Metall. Mater. Trans. B, 25B (1994), 308. [28] P. Valentin, C. Bruch, Y. Kyrylenko, H. KÖchner and C. Dannert: Steel Research Int., 80 (2009), No. 8, 552. [29] S. W. P. Cloete, J. J. Eksteen and S. M. Bradshaw: Progress in Computational Fluid Dynamics, an International Journal, 9 (2009), No. 6-7, [30] J. E. Olsen and S. Cloete: Seventh International Conference on CFD in the Minerals and Process Industries, CSIRO, Melbourne, Australia, 9-11 December 2009 p [31] B. K. Li, H. B. Yin, C. Q. Zhou and F. Tsukihashi: ISIJ Int., 48 (2008), No. 12, [32] U. Sand, H. L. Yang, J. E. Eriksson and R. B. Fdhila: Steel Research Int, 80 (2009), No. 6, 441. [33] S. A. Morsi and A. J. Alexander: J. Fluid Mech., 55 (1972), No. 2, 193. [34] A. Alexiadis, P. Gardin and J. F. Domgin: Metall. Mater. Trans. B, 35B (2004), 949. [35] J. W. Han, S. H. Heo, D. H. Kam, B. D. You, J. J. Pak and H. S. Song: ISIJ Int., 41 (2001), ß 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim