The steel flow, heat transfer, and inclusion removal behaviors in a five-strand bloom tundish for five baffles and two types of turbulence inhibitors (TIs) were investigated by a multiphysical model to enhance the consistency among the strands and the purity of molten steel. Water model experiments were conducted to verify the simulated results of flow and residence time distribution (RTD). The results showed that the simulated steel flow and RTD curves were basically consistent with those of the experiments. Compared to original conditions, the total residence time reaches 595.0 s, and the volume of the plug region increases by 4.8%, while the volume of dead zone decreases by 0.2% when applying the optimized baffle and TI. In addition, the response and residence times at the 3rd strand increase by 42.5 s and 264.6 s, the total average standard deviation decreases to 0.0057. Meanwhile, the maximum temperature drop decreases from 28.6 K to 22.8 K, and the temperature difference among strands decreases from 3.7 K to 1.4 K. The inclusions removal rate increases by 0.9% to 8.3% with diameters ranging from 10 μm to 100 μm and reaches 94.4% at 100 μm. Furthermore, the qualification rates of flaw detection and nonmetallic inclusions in high rails after optimization increase from 97.94% to 98.73% and from 97.3% to 99.1%, respectively, and the consistency among the strands is apparently enhanced.

turbulence kinetic energy (m2/s2)

turbulence eddy dissipation (m2/s3)

pressure (Pa)

density of steel (kg/m3)

density of the particle (kg/m3)

constant for k–ε turbulence model

constant for k–ε turbulence model

turbulent viscosity (Pa∙s)

effective viscosity (Pa∙s)

effective thermal conductivity (W/(m K))

total average standard deviation at each strand

variance

total average residence time (s)

average residence time at each strand (s)

time interval (s)

sampling time (s)

concentration of tracer at ti

Reynolds number of inclusions

apparent wall roughness (m)

gravitational acceleration (m/s2)

fluid velocity at i direction (m/s)

constant for k–ε turbulence model

constant for k–ε turbulence model

constant for k–ε turbulence model

local temperature (K)

specific heat at constant pressure (J/(kg K))

effective diffusivity, (m2/s)

particle velocity at i direction (m/s)

relaxation time (s)

shear force (Pa)

critical fluid shear force (Pa)

probability of inclusion adsorption

random number

Hamaker number

stable spacing of Van der Waals force (nm)

response time (t)

peak time (t)

volume ratios of the plug zone

volume ratios of the plug zone at the ith strand

volume ratios of the dead zone

volume ratios of the dead zone at the ith strand

volume ratios of the well-mixed zone

volume ratios of the well-mixed zone at the ith strand

The tundish is the final metallurgical element reactor, in which both autonomous and coupled processes are realized. The flow, heat transfer and inclusion movements in the tundish have significant effects on the purity level of cast steel and, consequently, the final products [1–4]. Many factors affect the metallurgical behavior in the tundish, such as the quantity of steel residing in the tundish and the casting speed, and the tundish structure. The most commonly used procedure to improve the working efficiency and optimize the metallurgical behavior of the tundish is to use kinds of flow control devices (FCDs) that significantly determine the directions of the molten steel flow stream and heat diffusion and the behavior of nonmetallic inclusions, such as turbulence inhibitors (TIs) and baffles, in the tundish [5–9]. Merder et al. [5,6] studied the effect of TIs on the flow behavior in a two-strand tundish and found that the use of an FCD caused a decrease in the transition zone and an increase in the active flow volume in the tundish. The TI and baffles in a multistrand tundish were researched by Pieprzyca et al. [7] and Zheng et al. [9], and they found that FCDs can influence the generation of the transition zone and active flow. Moreover, the residence time distribution (RTD) curve is the plot of the tracer concentration at the outlets against time, and this curve is widely used to assess the consistency of flow characteristics among outlets and measure the reasonability of the flow field in a multistrand tundish [10–14]. Additionally, heat loss and its associated effects on the steel flow, residence time and temperature stratification in tundish systems have been investigated in a large number of publications [8,15–17], along with inclusion removal behavior [17–20].

Most of the above studies focused on metallurgical behaviors of single-strand or even multistrand tundishes, in which the consistencies of the flow, heat and inclusions among the strands can be easily controlled, usually at a high level, during the casting process. When dealing with an odd number of multistrands, the flow field, temperature distribution and inclusions near the middle strand are much different from those of the other strands, and the consistencies among the strands are usually at a relatively low level. The disqualification rate of steel produced through the middle strand is much higher than that of the other strands. Delgado-Ramirez et al. [21] performed a multiphase mathematical simulation to optimize the fluid flow and homogenization temperature in an asymmetric delta-type five-strand tundish and reported that the proposed dam design could improve the flow pattern and inclusion removal rate and avoid reoxidation and loss of steel temperature. He et al. [22] investigated the flow and temperature fields in a T-type five-strand tundish under different FCDs and found that a U-type baffle with deflector holes and a round TI could improve the flow characteristics and reduce the differences among multiple strands, while the movement of inclusions was not mentioned. In addition, most of the above mathematical outcomes about FCD optimization lack application effects from steelmaking plants. Zhang et al. [23,24] optimized the multiphase flow behavior in a five-strand bloom tundish during ladle changeover by a ladle shroud and TI, while the temperature distribution and inclusion movement were ignored. Since over 90% of the tundish casting period is in the steady-state casting process, it is necessary to improve the metallurgical behavior of the flow field and heat transfer in the tundish before optimization of ladle changeover conditions.

In this paper, a T-type five-strand high rail bloom casting tundish in a specific steelmaking plant is chosen as the research subject to investigate the influences of FCDs on the fluid flow, heat transfer and inclusion movement in an odd multistrand bloom casting tundish, improve the consistencies of flow, temperature and inclusion fields among strands, and reduce the disqualification rates of flaw detection (FD) and nonmetallic inclusions in produced high rail steel. Originally, the disqualification rates of FD and nonmetallic inclusions in the high rails poured by the five-strand tundish were relatively high and apparently more serious in steel produced through the 3rd strand, by which the FD disqualification rate in the 3rd strand reached 34.2%, and the consistency among strands was poor. To solve this problem, the molten steel flow, heat transfer and inclusion removal behaviors in the five-strand bloom casting tundish under five types of baffles and two kinds of TIs (including the original structure) are numerically investigated and compared by a multiphysical model. Water model experiments under different FCD designs are conducted and compared to the simulated results to validate the flow pattern and RTD curves. Furthermore, the optimized structure of a baffle and TI are installed and applied in the tundish in industrial trials for four months, and the results of FD and nonmetallic inclusions in the steel rails produced before and after modification by the baffle and TI are analyzed and compared.

2Model descriptions2.1Basic assumptionsThe basic assumptions on modeling of flow, heat transfer and inclusion removal in a five-strand bloom tundish are presented as follows:

- (1)
The effect of the slag layer at the top of the bloom tundish is ignored.

- (2)
The impact of the temperature field on the fluid flow is ignored, and the liquid steel is assumed to be an incompressible Newtonian fluid.

- (3)
The heat transfer process is assumed to be a steady-state transport phenomenon.

- (4)
As the percentage of inclusion in molten steel of tundish is relatively slow, the effect of nonmetallic inclusions on the steel flow is ignored, and the collision growth behavior of inclusions is not considered in this simulations.

- (5)
Inclusions are simplified as rigid spheres and are absorbed immediately when they float to the bloom top.

The three-dimensional continuity and Navier-Stokes equations are shown as follows:

where ui is the fluid velocity; ρ and μeff are the density and effective viscosity of the fluid, respectively; and P is the pressure.The turbulence is expressed by the following standard k-ε model [25,26]:

where the turbulent viscosity μt is calculated by :where the constant values of C1ε, C2εcμ, σk and σε are 1.43, 1.92, 0.09, 1.0 and 1.3, respectively.2.2.2Heat transferThe enthalpy equation is employed as follows:

where Cp and keff are the specific heat capacity and effective thermal conductively of liquid steel; T is the steel temperature.2.2.3Tracer diffusionThe conservation equation for diffusion behavior of tracer is described as follows:

where Deff is the effective diffusivity and ct is the concentration of the tracer.2.2.4Movements of inclusionsThe movement of non-metallic inclusions can be described by Lagrangian stochastic trajectory model, which is expressed by solving the BBO equation, without considering the Basset force [27]:

where the terms on the tight-hand side are inertia force, fluid resistance, pressure gradient force, gravitational force and saffman force, respectively; τp=2ρRp29μ and Rep=2ρRpui-upiμ are the relaxation time and Reynolds number of inclusions, respectively; f=Cm1+0.15Rep0.687; ui and upi are the transient velocities of steel and inclusions; ut and upt are the wall tangential velocities of the steel and inclusions, respectively; R is the radius of inclusion. Meanwhile, the displacement of inclusion can be expressed as:In order to simulate the effect of the turbulent fluctuations on the inclusion motion, the random walk model [28] can be applied. The continuous-phase velocity can be described as:

where ui¯ is the time-averaged velocity; ξ is the random number that obeys Gauss distribution, the value is ranged from zero to one; k is the turbulent kinetic energy.Inclusions can be adhered to the tundish wall when crashing on the refractories at inner walls of the tundish, and the absorption stability depends on the Van der Waals force, shear force (τw), inclusion size and surface roughness, etc. The probability of inclusion adsorption can be expressed as:

The critical fluid shear force (τcrit) can be obtained by:

where A=2.3×10-20J is the Hamaker number [29], which is the parameter reflects the adsorption strength of particles and plates; h=4 nm is the stable spacing of Van der Waals force [30]; R is the radius of the inclusions; to simplify the simulation process, the wall roughness Δ is assumed to be equal to the radius of inclusions, by which the optimum absorption effect can be obtained [31].2.3Analytical method of RTD curves2.3.1Average residence timeRTD curves are the most common way to quantitatively analyze the flow field and flow consistency among strands in a multistrand tundish, and the residence time of the steel is the main index to evaluate the metallurgical improvement in the tundish under different turbulence control devices.

The average residence time of each strand (Ta) can be calculated by:

Correspondingly, the total average residence time of an N-strand tundish (T¯a) is calculated by:

where Δti is the time interval; ti is the sampling time; and ci is the concentration of KCl resolution at ti.2.3.2Calculation of flow patternThe steel flow in the tundish includes plug flow, well-mixed and dead zones, and the dead zone is not beneficial to the floating removal of inclusions and can reduce the working capacity of the tundish. The well-mixed zone is good for the uniformity of the temperature field but is not beneficial to inclusion removal, while the ability of the plug zone is contrary to that of the well-mixed zone. The volume ratios of these three zones can be obtained by analyzing the RTD curves through a tundish flow characteristic analysis model. In this paper, the analysis method proposed by Pan et al. [32,33] is applied to investigate the RTD curves.

The variance is used to describe the deviation between the real flow pattern and ideal plug flow as follows:

where σ2 ranges from 0 to 1, 0 represents full plug flow and 1 represents well-mixed flow. As the back-mixing area increases, the RTD curves become flat, as does the value of σ2.The residence time of the dead zone (Vd) is defined as over twice the average residence time in the tundish as follows:

Then, the volume fraction of the well-mixed zone (Vm) can be calculated by:

Therefore, the volume fraction of the plug zone (Vp) can be obtained after calculating that of the dead and well-mixed zones as follows:

where di, Vmi and Vpi are the volume fraction of dead, well-mixed and plug zones at the ith strand, respectively; V is the working volume of tundish.2.3.3Judgment of consistency among strandsFor an odd multistrand tundish, the consistencies of flow, temperature and inclusion removal among the strands should be guaranteed on the basis of proper flow behavior. The total average standard deviation of the tracer concentration at each strand is applied in the calculations to judge the consistency among strands as follows:

For a multistrand tundish, a smaller value of S¯N means higher consistency among strands.

2.4Computational conditionsThe flow pattern, temperature distribution and inclusion removal behaviors in a five-strand bloom tundish are chosen as the subjects in this contribution. The boundary conditions for the calculations can be set as follows:

- (1)
The velocity inlet boundary condition is applied for the computational inlet, in which k=0.01uinlet2 and ε=2k1.5/dinlet;

- (2)
Considering a constant casting speed during the casting process, the velocities of the computational outlets are set to a constant value;

- (3)
The horizontal gradients of all variables at the symmetry plane are set to zero;

- (4)
For the free surface, the normal derivatives of all variables are set to zero, and the adiabatic condition is applied;

- (5)
For the tundish walls, a no-slip wall boundary condition is applied, the near-wall surface is treated as a standard wall function, and the normal gradients are set to zero.

A schematic view and the dimensions of the original tundish are shown in Fig. 1(a). Half of the real tundish is taken as the computational domain considering the symmetry of the tundish. The mesh distribution of the computational model is presented in Fig. 1(b), and the number of meshed cells is approximately 1,200,000. The mathematical model is solved by FLUENT, and the SIMPLE algorithm was used to resolve the pressure-velocity coupled in the momentum equation, and the criterions for convergence for continuity, momentum, energy and turbulence equations are below 10−4. After obtaining the stable steady-state flow and temperature fields, the tracer is injected to the tundish for one second, and the three-dimensional-turbulent diffusion process is subsequently calculated, then, the RTD curves of tracer concentration in each strand can be obtained.

Table 1 shows the thermophysical parameters of molten steel, and the main industrial conditions of the tundish applied in calculations are presented in Table 2.

Main industrial parameters applied in the calculations.

Casting condition | Value |
---|---|

Working capacity of tundish, t | 35 |

Bloom cross section, mm2 | 280×380 |

Casting speed, m/min | 0.63 |

Steel level, mm | 800 |

Inner diameter of shroud, mm | 81 |

Submergence depth of shroud, mm | 310 |

Velocity of outlets, m/s | 0.569 |

Original baffle | Fig. 1(a) |

Heat flux density, kW/m2 | Free surface: 15.0, Vertical sidewalls: 3.2, Horizontal sidewalls: 3.8, Bottom wall: 1.4 |

The baffle structure has a decisive effect on the metallurgical behavior in an odd multistrand tundish. To improve the flow pattern and optimize the consistency in the tundish, four kinds of baffles are designed and investigated based on the currently applied baffle (Fig. 1a). In addition, a TI is also a key FCD to alleviate the impact effect of injection flow on the tundish bottom, reduce the turbulence intensity in the impact zone and avoid slag entrapment and steel exposure. Therefore, the effects of two kinds of typical TIs on flow, heat transfer and inclusion removal behaviors are also discussed in this paper, and these kinds of TIs are rectangular without eave (A-type) and circular with eave (B-type). The designed three-dimensional structures of baffles and TIs are shown in Fig. 2.

According to the above designs of baffles and TIs, the arrangement of investigation projects to discuss the metallurgical effects of different baffles and TIs on the turbulent flow, heat transfer and inclusion removal behaviors in the five-strand bloom casting tundish are shown in Table 3, in which A0 represents the case of the original TI and baffle.

3.2Model validationThe simulation results of the flow field are verified by 1:3 water model experiments. In these experiments, the ratios of injection velocity and flow rate between real liquid metal and the water experiments can be calculated based on their equal Froude numbers (Fr) as follows:

where Frp and Frm, vp and vm, and Lp and Lm are the Froude numbers, velocities and characteristic lengths in the real tundish and water model, respectively, and the scale factor λ=13. Then, the conversion relationships among velocity, flow rate, and residence time between the real tundish and water model are vm=λ0.5vp, Qm=λ2.5Qp, and t¯m=λ0.5tp.During the experiments, 20% KCl solution is chosen to be the tracer, which is dyed by methyl blue and injected into the model through the ladle shroud after the flow field reaches stability for 3min. The behavior and distribution of the tracer are completely recorded by a camera, and the changes in electrical conductivity at the strand outlets are detected and analyzed by the electrodes. The results of conductivity are magnified, converted into dimensionless concentration, and imported into a computer; then, the dimensionless concentration versus dimensionless time curves, known as RTD curves were derived. Therefore, the response time (Tr), peak time (Tp), and average residence time of each strand and the whole tundish, as well as the volume ratios of the plug, well-mixed and dead regions, are obtained. Considering the symmetry of the tundish, the RTD curves at the 3rd, 4th and 5th strands are taken into account on behalf of the whole tundish. A schematic diagram of the water model experimental device is presented in Fig. 3.

A comparison of the RTD curves between the experimental and simulated results under A0 is presented in Fig. 4. The variation tendencies of the RTD curves for the 3rd, 4th, and 5th strands have good consistency, and the simulated results of response time, peak time and concentration in each strand are basically consistent with those of the experiments.

Fig. 5 shows a comparison of the average residence times of the 3rd strand and whole tundish between the experimental and simulated results under different projects. Additionally, the values and contrastive errors of the whole average residence time between the experiments and simulations under different projects are listed in Table 4, in which the experimental times are converted to those of the real tundish according to the principle of similarity. Good consistency of the average residence times in both the 3rd strand and whole tundish between experiments and simulations can be obtained under all the different projects, and the average residence time is relatively enhanced under A1 to B4. The errors in average residence times between experiments and simulations under different projects are generally controlled within 5%, and the largest error is only 6.5% under A0; thus, the errors are within a reasonable range.

Values and contrastive errors of whole average residence time between experiments and simulations.

Project ID | A0 | A1 | A2 | A3 | A4 | B1 | B2 | B3 | B4 |
---|---|---|---|---|---|---|---|---|---|

Converted experimental results, s | 603.8 | 617.7 | 616.3 | 613.2 | 627.0 | 610.4 | 618.5 | 618.9 | 621.7 |

Numerical results, s | 564.7 | 594.6 | 591.6 | 592.8 | 596.5 | 591.2 | 594.2 | 595.1 | 595.0 |

Relative errors, % | 6.5 | 3.7 | 4.0 | 3.3 | 4.8 | 3.1 | 3.9 | 3.8 | 4.3 |

A comparison of the dyed tracer distribution and movement at diffusion times of 20s, 40s, 80s, and 150s between experiments and simulations under A0 is shown in Fig. 6. The simulated tracer diffusion behavior is basically consistent with that of the experimental results; these two methods are reliable and accurate for intuitively simulating the real flow behaviors in the bloom tundish.

3.3Flow field3.3.1Flow field before optimizationFig. 7 presents the simulated velocity vectors at the center plane of the longitudinal section (a), streamlines (b) and RTD curves (c) in the tundish under A0. A strong flow is observed around the 3rd strand, the streamlines are extremely intensive, and the process is relatively short. In addition, two flow regions with high velocity form near the middle wall of the baffle, and this finding means adequate distribution of liquid steel and fast speed of steel update. However, some of the molten steel flows into the casting zone through the lower diversion holes in the middle wall of the baffle and flows straight out into the mold at the 3rd strand. The short circuit flow can cause a decrease in the floating removal rate of nonmetallic inclusions and seriously deteriorate the quality of the bloom produced by the 3rd strand. Moreover, the steel flow near the edges of the casting zone (the 5th strand) is very weak, and this flow is apparently slower and weaker than the velocity near the 3rd strand. Additionally, the streamlines are obviously sparse, and the distance of the flow path is much longer, which means that there is not enough fresh liquid steel replenishing at the edge zone and that a dead zone forms with a relatively larger volume. In addition, the distribution of the streamlines in the whole tundish is chaotic under A0, and this distribution is not beneficial to the development of plug flow. Furthermore, the differences in peak concentration and peak and response times among the 3rd, 4th and 5th strands are relatively large, and the fresh steel supplement at the 5th strand lags badly behind the other two, which leads to the uneven distribution of liquid steel in the whole tundish and causes poor consistency among strands.

The heterogeneities of the steel distribution and flow field mainly result from the improper design of the baffle. The original baffle has four diversion holes on the middle wall that are near the casting zone of the 3rd strand, while only two holes are arranged on each sidewall of the baffle. This kind of baffle is bound to an excessively adequate supply of fresh steel and leads to short circuit flow near the 3rd strand supplement and a large dead zone near the 5th strand, causing uneven distributions of steel composition and temperature among the strands. Therefore, the structure of the baffle for the five-strand bloom tundish should be optimized to solve the problem mentioned above.

3.3.2Flow field after baffle optimizationTo improve the flow field in the casting zone and ensure the uniform distribution of molten steel among the strands, the basic idea of baffle optimization is to control the steel supplement at the 3rd strand, eliminate the short circuit flow, and enhance the steel supply at the 5th strand, reducing the volume of the dead zone. Then, four kinds of baffles are proposed and discussed, and the characteristics of the baffles are shown in Fig. 1. Fig. 8 presents the streamlines in the tundish and the velocity vectors at the center planes of the longitudinal section (y=0) for the four baffles with the A-type TI. The flow field is apparently changed after the change in baffle structure, and the molten steel flows upward into the casting zone through upward diversion holes and forms the surface flow when it reaches the top surface. Then, most of the molten steel flows toward the two sides of the bloom tundish and generates a large circulation flow along the tundish wall after a certain distance, while a relatively small circulation flow is formed in the region between the baffle and tundish wall by partial liquid steel, which generally flows to the 3rd and 4th strands. Compared to the streamlines in the tundish with the original baffle (Fig. 7b), the flow field can be obviously improved when the lower diversion holes in the middle wall of the baffle are canceled and two large holes are arranged at each sidewall of the baffle. The steel supplement near the 3rd strand can be reduced and the flow path prolonged so that the response time and residence time of the 3rd strand are effectively extended to avoid the appearance of short circuit flow and offer enough floating removal time for the nonmetallic inclusions. Additionally, the large holes in the baffle sidewalls can enhance the steel supply at the far end of the tundish, and the steel velocity near the 5th stand is increased so that the volume of the dead zone can be shrunk and the steel composition and temperature uniformities in the tundish are improved. Moreover, the formation of two circulation flows can promote plug flow and enhance the rate of inclusion removal.

The velocity vectors in Fig. 8 show that the flow behavior is more uniform and stable in the whole casting zone among the strands after optimization of the baffle, and the steel velocity near the 3rd strand and the remarkable surface layer flow between the 3rd and 4th strands decrease. The surface layer flow is relatively stronger under A2 and A4, and the impact pressure of steel flow on the middle wall of the baffle can be decreased through this type of baffle, which will guarantee the maintenance of the structure and shape of the baffle under the long-term and high-temperature casting environment and is beneficial to sequence continuous casting.

3.3.3Effect of TI on the flowThe baffle separates the tundish into two parts, the casting and impact zones, and the TI is installed directly below the ladle shroud at the bottom of the impact zone. Therefore, the study of the metallurgical effect of the TI is mainly focused on the flow pattern in the impact zone. Fig. 9 shows the velocity vectors in the planes of symmetry under A0 (a), A4 (b) and B4 (c). The velocity vectors in the impact zone under A0 are basically the same as those under A4, as these two projects have the same TI and different baffles, which means that the structure of the baffle has little effect on the flow behavior in the impact zone. While the flow pattern exhibits a large difference between A4 and B4, the structure of the TI has a significant effect on the steel flow behavior in the impact zone of the tundish.

When applying the A-type TI, the high-speed injection flow impinges on the inner wall of the TI and forms two upward flow strands at the front and back of the ladle shroud due to the constraint of the TI around walls. Then, these flows gradually reach the free surface and flow around the wall in the impact zone, subsequently forming the downward circulation flow along the refractories. In addition, there is basically no collision between the rising steel and the downward flow. This kind of flow in the tundish can lead to high turbulent kinetic energy (TKE) and steel velocity near the free surface with a low turbulent dissipation rate, which can cause a remarkable level fluctuation at the free surface and may increase the chance of slag entrapment and secondary oxidation due to steel exposure. When applying the B-type TI, the circulation flow in the internal area of the TI after the injection flow impinges on the TI bottom and is controlled by this area, and this effect can generate a relatively strong turbulent dissipation rate when the steel flows upward. The rebounding upward flow collides with the downward steel and effectively counteracts part of the velocity and TKE, and this process can obtain a relatively stable free surface and avoid the appearance of slag entrapment.

The distribution of TKE (a) in the impact zone and velocity vectors (b) at the free surface under the #4 baffle with A-type (a) and B-type (b) TIs are shown in Fig. 10. The B-type TI can decrease the turbulence intensity in the impact zone, especially the maximum TKE at the free surface, which decreases from 2.5×10−3m2/s2 to 5×10-4m2/s2. Such a decrease can significantly reduce the chance of slag entrapment in the impact zone. Furthermore, the velocity at the free surface of the impact zone is nonuniformly distributed when using the original TI. In this case, the maximum velocity is approximately 0.085m/s and is distributed at two sides of the shroud, and this velocity may readily cause severe slag entrapment there. When the B-type TI is applied, a relatively uniform velocity distribution can be obtained at the free surface in the impact zone, and the maximum velocity decreases to 0.049m/s, which is only 57.6% of that of the A-type TI. The structure of the TI can clearly decrease the turbulence intensity in the impact zone, reduce the velocity at the free surface, lessen the opportunity for slag entrapment and avoid the occurrence of steel exposure.

3.4Analysis of RTD curvesThe main methods to improve the flow behavior in an odd multistrand bloom tundish is to eliminate the short circuit flow, prolong the response and residence times of the tundish, improve the consistency among the strands, increase the volume of the plug zone and decrease the area of the dead zone. The simulated RTD curves under different projects are presented in Fig. 11. Table 5 lists the analysis of the RTD curves under all the projects, in which Tr, Tp, Ta, and T¯a represent the response time, peak time, and residence times of each strand and the whole tundish, respectively; Vp, Vd and Vm are the volume ratios of the plug, dead and complete mixing flow zones; and S¯N is the whole mean standard deviation of the tracer concentration at each strand.

Analysis of the RTD curves under all the research projects.

Project ID | Strand | Tr/s | Tp/s | Ta/s | T¯a/s | Tm/s | Vp/% | Vd/% | Vm/% | S¯N |
---|---|---|---|---|---|---|---|---|---|---|

A0 | 3rd | 21.0 | 162.5 | 367.7 | 561.7 | 759.8 | 49.2 | 14.0 | 36.8 | 0.0226 |

4th | 42.5 | 134.0 | 492.5 | |||||||

5th | 199.0 | 389.0 | 728.0 | |||||||

A1 | 3rd | 83.5 | 214.5 | 678.6 | 594.6 | 760.5 | 53.3 | 13.7 | 33.0 | 0.0078 |

4th | 48.0 | 142.5 | 576.3 | |||||||

5th | 81.5 | 204.5 | 570.8 | |||||||

A2 | 3rd | 67.0 | 213.0 | 626.3 | 591.6 | 760.6 | 53.1 | 13.6 | 33.3 | 0.0053 |

4th | 48.0 | 133.0 | 589.4 | |||||||

5th | 86.5 | 194.0 | 576.5 | |||||||

A3 | 3rd | 84.5 | 201.5 | 658.8 | 592.8 | 760.6 | 53.2 | 13.6 | 33.2 | 0.0074 |

4th | 48.5 | 138.5 | 579.4 | |||||||

5th | 86.0 | 216.5 | 573.2 | |||||||

A4 | 3rd | 73.5 | 326.0 | 688.2 | 596.5 | 760.3 | 53.8 | 13.6 | 32.6 | 0.0077 |

4th | 51.0 | 124.0 | 557.4 | |||||||

5th | 95.0 | 197.0 | 589.9 | |||||||

B1 | 3rd | 78.5 | 177.0 | 620.8 | 591.2 | 762.3 | 54.7 | 13.0 | 32.3 | 0.0063 |

4th | 51.0 | 152.5 | 585.2 | |||||||

5th | 94.0 | 213.5 | 582.4 | |||||||

B2 | 3rd | 68.5 | 208.5 | 609.8 | 594.2 | 761.6 | 54.9 | 12.9 | 32.2 | 0.0066 |

4th | 50.5 | 243.5 | 593.6 | |||||||

5th | 99.0 | 244.0 | 587.0 | |||||||

B3 | 3rd | 78.5 | 188.5 | 629.7 | 595.1 | 762.3 | 52.5 | 13.4 | 34.1 | 0.0075 |

4th | 49.5 | 151.0 | 583.9 | |||||||

5th | 102.0 | 257.0 | 589.1 | |||||||

B4 | 3rd | 63.5 | 372 | 632.3 | 595.0 | 762.4 | 54.0 | 13.8 | 32.2 | 0.0057 |

4th | 53.0 | 122.5 | 570.1 | |||||||

5th | 99.0 | 205.0 | 601.3 |

Fig. 4(c) and Table 5 show that the response and peak times at the 3rd strand are very short under A0 and are only 21.0s and 162.5s, respectively, and the peak concentration of the tracer is much higher than that at the other stands. While the peak and response times at the 5th strand are far behind those of the 3rd and 4th strands, the average residence time of the whole tundish is 561.7s, and the differences in residence time among the strands are very large; these values are 367.7s, 492s and 728s, respectively. The average residence time of the 3rd strand is only approximately half that of the 5th strand, and this difference leads to the difficulty of inclusion floating removal. The coincidence of the RTD curves (for the 3rd, 4th and 5th strands) under A0 is poor, and the whole mean standard deviation of the tracer concentration among the strands (S¯N) reaches 0.0226, which means that there are remarkable differences in the flow patterns among the strands. The overall liquid steel flow field in the tundish is improper. In addition, the uniformities of the composition and temperature can hardly be reached, which will affect the smooth casting and quality of the bloom.

As shown in Table 5 and Fig. 11, the response and average residence times of the 3rd and 4th strands are obviously prolonged after optimization of the baffle structure, and the response time at the 3rd strand all increase to three times that of the original project. The average residence time increases from 367.7s to over 609.8s, especially increasing to 682.2s under A4, and this increase can efficiently eliminate the short circuit flow, is beneficial for the floating removal of inclusions, and avoids the FD disqualification of the steel produced through the 3rd strand due to the short response and residence times. Additionally, the whole residence time increases by approximately 30s, and the volume rate of the plug zone increases by approximately 3.2% to 5.7%, while the volume rate of the dead zone decreases by approximately 0.2% to 1.1%; these results mean that the flow behavior in the tundish has improved, and the metallurgical functions of the tundish can fully come into play. Moreover, the total mean standard deviation among the strands decreases from 0.0226 to under 0.0078, and the flow differences among the strands obviously decrease, which is good for the uniform distributions of the steel temperature and compositions. The RTD data under different optimization proposals (A1∼A4 and B1∼B4) are similar to each other, while the response and average residence times at the 3rd strand are much longer than those of the other stands when applying the #1 and #3 baffles, and this finding is not beneficial to the consistency of the strands. When applying the #2 and #4 baffles, the steel flow can be properly distributed, the differences in the response time and average residence time among the strands are decreased, and the consistency of the strands can be further improved.

Therefore, relatively proper steel flow behavior in the tundish can be obtained when applying the optimized A4, B4, and B2 projects from only the point of view of the flow field. The whole residence time reaches 595.0s, and the volume rate of the plug area increases by approximately 4.8% under B4 compared to that of A0, while the volume rate of the dead zone decreases by approximately 0.2%. The response time increases to 63.5s and 53.0s at the 3rd and 4th strands, respectively, and the response time decreases from 199.0s to 99.0s at the 5th strand. Additionally, the total average standard deviation is only 0.0057, which decreases by approximately 75% compared to that of A0, and the consistency of the flow pattern among the strands exhibits a significant improvement.

From the above, the optimum project for improving the flow field in the tundish is B4, in which the #4 baffle and B-type TI are applied. The second-best project is B2.

3.5Temperature distributionThe inhomogeneity of the molten steel temperature distribution in the tundish can deteriorate the uniform growth of the solidifying shell in the mold, is not beneficial to the floating removal of inclusions in the steel, and can lead to pull leakage in severe cases. Based on the results of the flow fields under the different projects discussed above, the temperature fields in the tundish under A0, A4, B4 and B2 are taken into account in this section. Fig. 12 shows the temperature distributions in the whole tundish and at the vertical center planes of the outlets under A0, A4, B2 and B4.

Fig. 12(a) shows that the area of low temperature in the casting zone is very large, most of which is concentrated on the top surface upon the 4th and 5th strands, especially the region near the far edges of the tundish, in which a remarkable volume of the dead zone exists and the lowest temperature value is approximately 1744K. The largest temperature drop reaches 28.6K. Additionally, the temperature differences among the strands are large, and an apparent temperature drop along the x-direction can be observed, by which the steel temperature near the 3rd strand is much higher than that near the other strands due to the short circuit flow, while this temperature is much lower near the 5th strand due to the insufficient supplement of steel with high temperature. The phenomena of nonuniform temperature distribution among the strands and the obvious temperature drop under A0 match the results of the flow behaviors analyzed above; inconformity of the flow field can lead to uneven distribution of steel temperature among the strands.

When applying the optimized baffles and TIs, the temperature field in the tundish can be significantly improved, by which the low-temperature area near the top surfaces of the 4th and 5th strands and the temperature gradient along the x-direction are decreased, the lowest temperature and steel temperature near the 5th strand are enhanced, and there is no evident high-temperature zone near the 3rd strand. The temperature distribution is more reasonable with a lower temperature drop and difference among the strands.

Fig. 13 shows the maximum temperature drop and temperature difference among the strands under different projects. Under the original condition, the maximum temperature drop is 28.6K and the temperature difference among the strands reaches 3.7K. The temperature drop decreases to 24.2K for A4, 25.1K for B2 and 22.8K for B4, and the largest temperature difference among the strands decreases by 1.3K for A4, 1.8K for B2 and 1.4K for B4, respectively. A relatively proper temperature field can be obtained on the basis of the reasonable flow pattern in the tundish when applying the #4 baffle with the B-type TI, by which the temperature at each strand is more uniform and smooth production can be guaranteed.

Thus, it is essential to improve the structures of the tundish turbulence control devices to enhance the uniformity of steel temperature and improve the flow field on the basis of strengthening the thermal insulation in the production process.

3.6Inclusion removal3.6.1Effect of inclusion sizeThe movement loci of nonmetallic inclusions with diameters of 10μm, 30μm, 50μm, 80μm and 100μm are calculated by the Lagrangian stochastic trajectory model, and the movement in each case is repetitively calculated to ensure the accuracy of the calculations. The statistical removal rates of inclusions with different sizes under different projects are presented in Fig. 14. The removal rate increases as the inclusion size increases; the removal rate of inclusions with a diameter of 10μm is between 41.9% and 54.3%, while this rate is approximately 90% for the inclusion size of 100μm. Fig. 15 shows the movement loci of inclusions with different sizes under B4. Most of the inclusions with relatively small diameters (10μm–30μm) escape from the tundish to the mold, and the movement trajectories are basically consistent with those of molten steel. The removal rate is relatively low due to the small buoyancy and strong effect of steel flow on inclusion removal. Because the buoyancy of inclusions increases as the inclusion size increases, the removal rate increases approximately 20% when the inclusion diameter is 50μm compared to the removal rate of smaller inclusions, and the movement trajectories of inclusions with diameters of 100μm are relatively shorter; these inclusions can almost be removed during the casting process, and the removal rate can reach 94.44%.

Fig. 16 shows the movement loci of inclusions under A0, A4, B2 and B4. The movement trajectories of inclusions are mainly gathered between the 3rd and 4th strands, most of which escape into the submerged entry nozzle of the 3rd strand and rarely move to the 5th strand. When applying the proposed turbulence control device, the proportion of inclusions that escape to the 3rd strand decreases, and the differences in inclusion removal behavior among the strands are reduced. In addition, the upward flow of the molten steel is beneficial to the floating movement of inclusions after the optimization of the turbulence control device, and this effect can improve the upward ability of inclusions and enhance the chance of inclusion adsorption by the slag layer. The floating ability of inclusions with small diameters is relatively weak and flows with the molten steel so that the removal rate can hardly be enhanced. Comparatively, the Stokes floating speed is relatively higher when the inclusion diameter is greater than 50μm, and the movement trajectory is short, so the obvious removal effect can be obtained.

By comprehensively considering the above results, the optimum project for inclusion removal is B4, and the removal rates of nonmetallic inclusions with different diameters under B4 are increased by 0.9% for 10μm, 1.2% for 30μm, 5.1% for 50μm, 5.8% for 80μm and 8.3% for 100μm compared to those of A0.

3.6.3Effect of wall adsorptionFig. 17 presents the removal rates of inclusions with different sizes by wall adsorption under different projects. The main removal method for inclusions in the tundish is Stokes floating, which accounts for more than 80% of the removed inclusions. The contribution of wall adsorption to the inclusion removal rate is relatively small, and the inclusion removal caused by wall absorption gradually decreases as the inclusion diameter increases. The removal rate induced by the wall absorption under B2 is 8.6% when the inclusion size is 10μm, while the rate decreases to only 5.4% and 1.1% when the diameter is 50μm and 100μm, respectively. As the inclusion diameter increases, the buoyancy force is enhanced, and the chances of inclusions crashing into the wall decrease. In addition, inclusions with large diameters are easily exposed to the shear flow near the tundish wall, and the adsorption instability increases, which leads to a decrease in wall absorption rate.

By comprehensively considering the flow, heat transfer and inclusion removal behaviors under different baffles and TIs, the optimum design for improving the metallurgical behaviors in the bloom casting tundish and enhancing the consistency among the strands is B4.

4Application effectsBased on the above investigations and results, the optimum design should be the #4 baffle with the B-type TI. To validate the application effects of the optimized baffle and TI, the conditions of B4 are applied in industrial trials, and the qualification rates of FD in the produced steel rails are measured and compared to those of the original project. A comparison of the FD qualification rates in the steel rails between the original conditions and four months of application of the optimized baffle and TI in the industrial trials is listed in Table 6.

Comparison of FD qualification rates before and after optimization.

Conditions | Number of steel rails | Disqualification numbers of FD | Qualification rate of FD, % | FD disqualification rate from the 3rd strand, % | |||||
---|---|---|---|---|---|---|---|---|---|

1st | 2nd | 3rd | 4th | 5th | Total | ||||

Original | 63774 | 291 | 180 | 447 | 139 | 250 | 1307 | 97.94 | 34.20 |

Optimized | 28850 | 63 | 78 | 70 | 91 | 65 | 367 | 98.73 | 19.07 |

Table 6 shows that the total qualification rate of FD in the steel rails increases from 97.94% to 98.73% after applying the optimized baffle and TI, and the FD disqualification rate from the 3rd strand decreases from 34.20% to 19.07% of the total disqualified steel rails. Moreover, the disqualification numbers of FD from each strand are much closer, as the FD disqualification rates from the 1st, 2nd, 3rd, 4th and 5th strands are 22.27%, 13.77%, 34.20%, 10.64% and 19.13% under the original conditions while changing to 17.17%, 21.25%, 19.07%, 27.48% and 17.71% when applying the optimized turbulence control device, respectively. The consistency of each strand in the five-strand bloom tundish is apparently enhanced.

The inclusions in numerous products produced before and after optimization are measured using the ISO 4967 international standard. According to the production standards, the inclusion appraisal for high rail steel should be A) (sulfide type) ≤2.0, B) (alumina type) ≤1.0, C) (silicate type) ≤1.0 and D) (globular oxide) ≤1.0. Table 7 lists the statistical results of inclusion disqualification rates in the high rails produced under the original and optimized conditions. As shown in this Table, 31, 45 and 36 of 3962samples are below the qualified standards of the sulfide, alumina and silicate types of inclusions, respectively, detected using the original structures of the baffle and TI, and 5samples meet the disqualification rates of two inclusion types. Only 6, 3 and 9 of 2001 samples, respectively, are below the qualified standards when detected by applying the optimized conditions. The qualification rate of nonmetallic inclusions in high rails increases from 97.3% to 99.1% after optimization.

5ConclusionsThe flow patterns, temperature distributions and inclusion movements in a five-strand bloom tundish under different baffles and TIs are numerically and experimentally investigated, and the optimum conditions are proposed and applied in a plant. The conclusions of this contribution are summarized as follows:

- (1)
The simulated results of the flow field and RTD curves under different baffles and TIs are basically consistent with the experimental results, and the largest error is 6.5% under A0, while the others are controlled within 5%. Additionally, unevenly distributed molten steel, an improper flow field and inferior consistency among the strands can be observed when applying the original conditions.

- (2)
When applying the baffle without lower diversion holes in the middle walls, the flow and temperature fields are apparently improved, by which the volume of the plug zone and the consistency among the strands are enhanced, the short circuit flow is eliminated, and the response and residence times are prolonged at the 3rd strand. Moreover, the turbulence intensity in the impact zone and the maximum velocity near the free surface decrease from 0.085m/s to 0.049m/s when using the B-type TI.

- (3)
The optimum project is B4, by which the total residence time reaches 595.0s and the volume of the plug zone increases approximately 4.8%, while the volume of the dead zone decreases 0.2%. Additionally, the response and residence times of the 3rd strand increase by 42.5s and 264.6s compared to those of A0, respectively, and the total average standard deviation among the strands decreases to 0.0057. The consistency among the strands is apparently improved as well.

- (4)
After optimization, the maximum temperature drop decreases from 28.6K to between 22.8K and 25.1K, and the temperature difference among the strands decreases from 3.7K to between 1.4K and 1.8K. The removal rate of small inclusions exhibits little increase after optimization, and Stokes floating plays an essential role in inclusion removal. The removal rates of inclusions with diameters from 10μm to 100μm increase by 0.9% to 8.3% and reach 94.4% when the diameter is 100μm under B4.

- (5)
After applying B4 for a period of industrial trials, the qualification rate of FD in the produced high rails increases from 97.94% to 98.73%, the consistency of the strands in the five-strand bloom tundish are apparently enhanced, and the qualification rate of inclusions increases from 97.3% to 99.1%.

The authors declare no conflicts of interest.

The authors would like to express their gratitude for the financial support provided by the National Natural Science Foundation of China (51774217).

*et al*.

*et al*.