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Densities and volume expansion coefficients of water and liquid steel. 10)
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A mathematical model was developed using ANSYS 12.0 in order to simulate non-isothermal melt flows in a delta shaped four strand billet caster tundish. The fluid inside the tundish considered was water, so that the CFD model could later be validated against water model experiments. The buoyancy term was included in the momentum equation using Bouss...
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... schematic diagram of the experimental set up is given in Fig. 1(b). Table 1 shows the properties of water and liquid steel. The value of the step increase in water temperature was selected by maintaining a similarity criterion, called the Tundish Richardson number (Tu) 3 , similar for the model and the prototype. ...
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... Because of that, in recent years, more researchers have considered the temperature variable in their simulations versus most previous works, which ignore their effects [27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45]. Both approaches have generated debate about the importance of temperature on flow patterns among researchers [19][20][21][22][23][24][25][26]. Some assure that temperature effects strongly impact the flow patterns inside the tundish. ...
... Still, the flow behaves similarly to an isothermal state after a short period. Using a four-strand tundish, Chattopadhyay et al. [25] found a strong influence of the natural convection if the tundish is empty; however, using an impact pad, the temperature effects on the fluid dynamics and removal rates vanish. Sousa Rocha et al. [26], using a two-strand tundish with different configurations for the flow control devices, did not find substantial differences between the isothermal and non-isothermal cases. ...
The continuous casting tundish is non-isothermal due to heat losses and temperature variation from the inlet stream, which generate relevant convection forces. This condition is commonly avoided through qualitative fluid dynamic analysis only. This work searches to establish the conditions for which non-isothermal simulations are mandatory or for which isothermal simulations are enough to accurately describe the fluid dynamics inside the tundish by quantifying the buoyant and inertial forces. The mathematical model, simulated by CFD software, considers the Navier-Stokes equations, the realizable k-ε model for solving the turbulence, and the Lagrangian discrete phase to track the inclusion trajectories. The results show that temperature does not significantly impact the volume fraction percentages or the mean residence time results; nevertheless, bigger velocity magnitudes under non-isothermal conditions than in isothermal conditions and noticeable changes in the fluid dynamics between isothermal and non-isothermal cases in all the zones where buoyancy forces dominate over inertial forces were observed. Because of the results, it is concluded that isothermal simulations can accurately describe the flow behavior in tundishes when the flow control devices control the fluid dynamics, but simulations without control devices or with a weak fluid dynamic dependence on the control devices require non-isothermal simulations.
... Whereas the tundish is a flow reactor, a unique thermo-hydrodynamic system forms inside its working space, as a function of the tundish's shape, capacity, number of outlets, and installation of flow control devices or non-standard equipment, e.g., a vacuum chamber, annular porous permeable brick with a swirl block, swirling chamber, or multi-port ladle shroud [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]. In addition, the hydrodynamic system in the tundish is modified by the temperature gradient generated by the cooling of molten steel during the casting process, the inflow of a hotter or colder batch of steel into the tundish from the ladle, or the steel-reheating zones in the tundish [31][32][33][34][35][36][37][38][39][40]. The impact of natural convection is particularly observable in tundishes with acapacity of over 50 tons, fitted with turbulence inhibitors or fed via an advanced ladle shroud, which slow down the momentum of the supply stream. ...
... drodynamic system in the tundish is modified by the temperature gradient generated by the cooling of molten steel during the casting process, the inflow of a hotter or colder batch of steel into the tundish from the ladle, or the steel-reheating zones in the tundish [31][32][33][34][35][36][37][38][39][40]. The impact of natural convection is particularly observable in tundishes with acapacity of over 50 tons, fitted with turbulence inhibitors or fed via an advanced ladle shroud, which slow down the momentum of the supply stream. ...
... Water was flowing into the model at the rate of 20.1 LPM. For the temperature gradients under consideration, according to Equation (4) [35], water temperature values were calculated, amounting to 5, 10, and 15 K for the values of 12, 23, and 35 K applied in the computer simulations, respectively. ...
This paper presents the results of studies on the occurrence of transient disturbances in the hydrodynamic system of a tundish feeding area and their effect on the casting process. In addition, the effect of changes in the level of superheating of the molten steel fed to the tundish on the evolution of the hydrodynamic system was analyzed. The studies were conducted with the use of a physical model of the tundish and a numerical model, representing the industrial conditions of the process of the continuous casting of steel. When a tundish is fed through a modified ladle shroud that slows down the momentum of the stream, this creates favorable conditions for the emergence of asymmetrical flow within the working tundish volume. The higher the degree of molten steel reheating in the ladle furnace, the stronger the evolution of the hydrodynamic structures in the tundish during the casting process.
... For this reason, although this work is not related to tundishes, the non-isothermal operating conditions of the tundish have been studied with interest, [7][8][9][10][11][12][13] where it is clear, that the tundish performance depends on the steel being delivered by the ladle. ...
In this work, the Planar Laser-Induced Fluorescence (PLIF) technique is applied to study the effect of the number of nozzles, their radial position and the gas flow rate on the thermal mixing during the secondary steel refining under non-isothermal conditions in a water model. In the physical model, three burners have been used to simulate the arc heating during the liquid metal processing.
The results suggest that an increase in the gas flow rate and injection nozzles located at the bottom of the model, in the same radial and angular positions as the heat sources affecting the liquid surface, improve the system’s heating efficiency.
The use of PLIF proved to be a relevant tool to analyze the heat transfer phenomena and increase the thermal performance of the ladle, opening the possibility of carrying out experiments in non-isothermal physical models of steelmaking reactors, which are currently scarce.
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... Kumar et al. [12] established that the submerged entry nozzles (SENs) closest to the ladle nozzle have the shortest transition billet, whereas the SEN farthest from the ladle nozzle receives mixed steel flowing from the vicinity of the SEN closest to the ladle nozzle, thus increasing the transition billet. In addition, the length of the transition billet can be reduced by optimizing the tundish furniture [1,[13][14][15][16][17][18][19][20] or making the temperature of the new grade higher than that of the old grade [16,[21][22][23]. ...
This study aims to investigate the effect of tundish level control on the change in element content and inclusion amount in molten steel during the low tundish-level steel grade transition. Based on multiphase flow, mass transfer, and discrete phase, a three-dimensional transient numerical simulation of the tundish was established in Ansys Fluent. The model uses moving mesh refinement technology to obtain clear steel and slag interface with a small number of meshes. The numerical simulation results were verified through industrial experiments and physical simulations. The results indicate that when the tundish is at a low level, strand 3 becomes a short-circuit flow, and the number of inclusions in strand 3 is approximately four times that in strand 1. If the old grade density is higher than that of the new grade, the unqualified length of the element content in the transition billet is 10.2 m shorter than that in the opposite order. When the filling speed of the tundish is three times the normal flow rate, the length of the transition billet with an unqualified number of inclusions is 7.1 m less than that when the filling speed is 2 times the normal flow rate. In addition, at the initial stage of the low tundish level steel grade transition, the minimum amount of inclusions in the transition billet can be reduced to 40% of the average amount of inclusions in the old grade; however, the maximum number of inclusions in the transition billet increase by a factor of 2.5 times the average number of inclusions in the new grade at the end stage of the low tundish-level steel grade transition. It can be observed that the inclusions in the initial stage of the low tundish-level steel grade transition have less effect on the quality of the old grades; however, they have a greater effect on the new grades in the final stage of the low tundish-level steel grade transition.
... where k is the kinetic energy of turbulence per unit mass; ε F is the turbulent energy dissipation rate; µ is the molecular viscosity; µ t is the turbulent viscosity; G k is the turbulent kinetic energy generated by the laminar velocity gradient; G b is the turbulent kinetic energy generated by buoyancy [19]; γ M is the fluctuation generated by the transition diffusion in compressible turbulence; σ k and σ ε are the turbulent Prandtl numbers of k and ε, respectively; C 1 , C 2 , and C 3 are the constants; and S K and S ε are the source term of the turbulent kinetic energy(k) and its dissipation rate (ε F ). As mentioned by Launder and Spalding [18], the other values for model constants in this study were C 1 = 1.44, ...
For the collapse of the working layer of dry vibrating material during preheating, the four-strand tundish of a steel plant was taken as a prototype for numerical simulation. The software ANSYS was used to calculate the temperature field and stress and strain field on the working layer under three preheating stages through the indirect coupling method. The results show that during the preheating process, the temperature field distribution on the hot surface of the working layer gradually develops toward uniformity with the increase in preheating temperature. However, the temperature gradient between the cold and hot surfaces increases subsequently, and the highest temperature between the cold and hot surfaces reaches 145.31 °C in the big fire stage. The stress on the top of the working layer is much larger than in other areas, and the maximum tensile stress on the top reaches 39.06 MPa in the third stage of preheating. Therefore, the damage to the working layer starts from the top of the tundish. In addition, the strain of the area near the sidewall burner nozzle in the casting area is much larger than that in the middle burner area with the increase in preheating temperature. Thus, the working layer near the sidewall burner nozzle is more prone to damage and collapse compared with the middle burner nozzle.
... Cwudzinski et al. [19] simulated the RTD curves and the flow patterns in a six-strand tundish for both isothermal and non-isothermal conditions by a numerical model. Chattopadhyay et al. [20] studied the flow phenomena of molten steel for a four-strand billet tundish using water and mathematical models in non-isothermal conditions. The results showed that while the step-up conditions facilitated the flotation of inclusions because of upward buoyancy-driven flows, the step-down conditions generated catastrophic results in terms of molten metal quality. ...
In the continuous casting process, the fluid flow of molten steel in the tundish is in a non-isothermal state. Because of the geometric shape and process parameters of a multi-strand tundish, the fluid flow behavior of each strand is quite inhomogeneous, and the difference in temperature, composition and inclusion content between each strand is great, which directly affects the quality of the steel products. In this paper, the fluid flow, heat transfer phenomena and inclusion trajectories in a four-strand tundish with and without flow-control devices (FCDs) are investigated using a water model and numerical simulation in isothermal and non-isothermal conditions. The results show that natural convection has a significant influence on the flow pattern and temperature distributions of molten steel in the tundish. Without FCDs, the average residence times of the molten steel in the tundish obtained by the isothermal water model, non-isothermal water model and non-isothermal mathematical model were 251.2 s, 263.3 s and 266.0 s, respectively, and the dead zone volumes were 21.51%, 29.26% and 28.21%, respectively. With FCDs, the average residence times of the molten steel obtained by the isothermal water model, non-isothermal water model and non-isothermal mathematical model were 293.0 s, 304.0 s and 305.2 s, respectively, and the dead zone volumes were 43.98%, 50.23% and 52.78%, respectively. The flow characteristics of the molten steel in the tundish were different between the isothermal and non-isothermal conditions. Compared with isothermal conditions, the numerical simulation results were closer to the water model results in non-isothermal conditions. The trial results showed that the fluid flow in a tundish has a non-isothermal characteristic, and the results in non-isothermal conditions can better reflect the actual fluid flow and heat transfer behaviors of molten steel in a tundish.
... The change in temperature will also be reflected in the change in the nature of the flow, which will be a combination of forced convection and natural convection, as a result of which there are differences in melt densities and the resulting buoyancy forces. In this case, natural convection results in the formation of reverse flow [10,12]. ...
... Non-isothermal flow contributes to better separation of non-metallic inclusions into the cover slag. The resulting product at times of non-isothermal flow can achieve significantly higher homogeneity and purity [10,12]. ...
... The functions of the main flow control devices (shown in Figure 1) in tundish can be summarized based on the literature study. Miki (1999) [5] M, P FLUENT 1 S W, D Iso/Nonisothermal V, TP, ID, IS, TKE, TDR, IRR Palafox-Ramos (2001) [6] N, P -2 S/W TI, D Nonisothermal RTD, CS, TD Vargas-Zamora (2003) [7] N, P -1 W TI, D Nonisothermal CIT, FP, BF, TM, TOI, TD Rogler (2005) [8] P -1 W TI, G Isothermal FCD, GFR, IS, GBS, RTD, IRR Ramos-Banderas (2006) [9] N, P -1 W TI, D, G Isothermal FCD, FP, V, GVF, IS, Najera-Bastida (2007) [10] N, P -2 W TI, G Isothermal FCD, RTD, TD, V, FP, TKE Zhong (2008) [11] P -2 W TI, D, W, G Isothermal FCD, GFR, GL, RTD Seshadri (2012) [12] P -2 W TI, G Isothermal GFR, GL, IS, PM Arcos-Gutierrez (2012) [13] N FLUENT 2 S TI, G Isothermal V, IS, PS, GBS Chattopadhyay (2012) [14] N, P FLUENT 4 S/W TI Nonisothermal IRR, TC, TD, TM, FP Singh (2012) [15] N FLUENT 1 S TI, IW, B, D Iso/Nonisothermal CIT, TP, FP, TC Sun (2012) [16] N, P -1 S/W TI, W, D, SR Nonisothermal FP, V, RTD Merder (2013) [17] N, P FLUENT 2 S/W TI Isothermal V, FCD, TKE, TD, RTD He (2013) [18] N OpenFOAM 2 S TI, B Isothermal MS, RTD, FCD, V, TKE Hamid (2013) [19] N, P -4 S/W TI Nonisothermal SM, TM, RTD Chang (2015) [20] N, P FLUENT 7 S /W TI, B, G Nonisothermal V, FP, FCD, GP, RTD, TD Wang (2016) [21] N, P -7 S/W TI Nonisothermal FCD, RTD, TD, FP, TP, Neves (2017) [22] N, P CFX 2 S/W TI, W, D, SR Isothermal FP, RTD Agarwal (2019) [23] N FLUENT 6 S TI Nonisothermal FP, TP, V, TM, RTD, TT Mishra (2019) [24] N FLUENT 2 W TI Isothermal RTD, V Neumann (2020) [25] N OpenFOAM 2 S TI, F Isothermal FP, PN, IRR Wang (2020) [26] N Miki (1999) [5] M, P FLUENT 1 S W, D Iso/Nonisothermal V, TP, ID, IS, TKE, TDR, IRR Palafox-Ramos (2001) [6] N, P -2 S/W TI, D Nonisothermal RTD, CS, TD Vargas-Zamora (2003) [7] [11] P -2 W TI, D, W, G Isothermal FCD, GFR, GL, RTD Seshadri (2012) [12] P -2 W TI, G Isothermal GFR, GL, IS, PM Arcos-Gutierrez (2012) [13] N FLUENT 2 S TI, G Isothermal V, IS, PS, GBS Chattopadhyay (2012) [14] (1) Weir: It is mainly used to divide the inlet chamber and the outlet chamber. The appearance of the weir is good for controlling the turbulence in the inlet chamber, benefits the inclusion flotation and decrease the surface wave amplitude in the outlet chamber [11,16,22,26]. ...
... The functions of the main flow control devices (shown in Figure 1) in tundish can be summarized based on the literature study. Miki (1999) [5] M, P FLUENT 1 S W, D Iso/Nonisothermal V, TP, ID, IS, TKE, TDR, IRR Palafox-Ramos (2001) [6] N, P -2 S/W TI, D Nonisothermal RTD, CS, TD Vargas-Zamora (2003) [7] N, P -1 W TI, D Nonisothermal CIT, FP, BF, TM, TOI, TD Rogler (2005) [8] P -1 W TI, G Isothermal FCD, GFR, IS, GBS, RTD, IRR Ramos-Banderas (2006) [9] N, P -1 W TI, D, G Isothermal FCD, FP, V, GVF, IS, Najera-Bastida (2007) [10] N, P -2 W TI, G Isothermal FCD, RTD, TD, V, FP, TKE Zhong (2008) [11] P -2 W TI, D, W, G Isothermal FCD, GFR, GL, RTD Seshadri (2012) [12] P -2 W TI, G Isothermal GFR, GL, IS, PM Arcos-Gutierrez (2012) [13] N FLUENT 2 S TI, G Isothermal V, IS, PS, GBS Chattopadhyay (2012) [14] N, P FLUENT 4 S/W TI Nonisothermal IRR, TC, TD, TM, FP Singh (2012) [15] N FLUENT 1 S TI, IW, B, D Iso/Nonisothermal CIT, TP, FP, TC Sun (2012) [16] N, P -1 S/W TI, W, D, SR Nonisothermal FP, V, RTD Merder (2013) [17] N, P FLUENT 2 S/W TI Isothermal V, FCD, TKE, TD, RTD He (2013) [18] N OpenFOAM 2 S TI, B Isothermal MS, RTD, FCD, V, TKE Hamid (2013) [19] N, P -4 S/W TI Nonisothermal SM, TM, RTD Chang (2015) [20] N, P FLUENT 7 S /W TI, B, G Nonisothermal V, FP, FCD, GP, RTD, TD Wang (2016) [21] N, P -7 S/W TI Nonisothermal FCD, RTD, TD, FP, TP, Neves (2017) [22] N, P CFX 2 S/W TI, W, D, SR Isothermal FP, RTD Agarwal (2019) [23] N FLUENT 6 S TI Nonisothermal FP, TP, V, TM, RTD, TT Mishra (2019) [24] N FLUENT 2 W TI Isothermal RTD, V Neumann (2020) [25] N OpenFOAM 2 S TI, F Isothermal FP, PN, IRR Wang (2020) [26] N Miki (1999) [5] M, P FLUENT 1 S W, D Iso/Nonisothermal V, TP, ID, IS, TKE, TDR, IRR Palafox-Ramos (2001) [6] N, P -2 S/W TI, D Nonisothermal RTD, CS, TD Vargas-Zamora (2003) [7] [11] P -2 W TI, D, W, G Isothermal FCD, GFR, GL, RTD Seshadri (2012) [12] P -2 W TI, G Isothermal GFR, GL, IS, PM Arcos-Gutierrez (2012) [13] N FLUENT 2 S TI, G Isothermal V, IS, PS, GBS Chattopadhyay (2012) [14] (1) Weir: It is mainly used to divide the inlet chamber and the outlet chamber. The appearance of the weir is good for controlling the turbulence in the inlet chamber, benefits the inclusion flotation and decrease the surface wave amplitude in the outlet chamber [11,16,22,26]. ...
... The high turbulence of the incoming stream can spread throughout the tundish if the flow is not properly controlled. It may cause the disturbance of the steel/slag interface and thereby promote slag entrainment [10,14,15,17]. ...
The effects of flow control devices (FCD) in a single-strand tundish, including weir, dam, turbulence inhibitor and gas curtain, have been investigated using water model experiments and CFD simulations. A scaled-down water model was built up to visualize flow pattern and measure the residence-time distribution (RTD) of different tundish configurations. A CFD model was applied to calculate the fluid flow, heat transfer and RTD curves in the prototype tundish under the nonisothermal conditions. The Eulerian–Lagrangian approach was applied to investigate the bubble flow in the system. The results show that each FCD has its own unique function to control the flow. It is important to evaluate the combined effects of FCD based on their installations. The molten steel flow in the tundish could be improved if these flow control devices were arranged properly.
... where βp is the volumetric thermal expansion of liquid steel, set to 0.000127 (1/K) [12]. βm is the volumetric thermal expansion of water, set to 0.00021 (1/K) [34]. ...
Natural convection of molten steel flow in a tundish occurs due to the temperature variation of the inlet stream and heat losses through top surface and refractory walls. A computational fluid dynamics (CFD) model was applied to study the effect of thermal buoyancy on fluid flow and residence-time distribution in a single-strand tundish. The CFD model was first validated with the experimental data from a non-isothermal water model and then applied to both scale-down model and prototype. The effects of flow control devices, including weir, dam and turbulence inhibitor, were compared and analyzed. Parameter studies of different heat losses through the top surface were performed. The results show that thermal buoyancy has a significant impact on the flow pattern and temperature distributions of molten steel in the tundish. The increase of heat loss through the top surface shortens the mean residence time of molten steel in the tundish, leading to an increase in dead volume fraction and a decrease in plug flow volume fraction.
... Plant scale trials with modified tundish indicated a reduction in tundish skull by 50% without adversely affecting tundish hydrodynamics performance. Much research has been carried out for improving the steel cleanliness by the introduction of tundish furniture [2,3,6,8,[20][21][22][23][24][25][26] but only a few studies have been carried out dealing with tundish skull loss and feasible solutions to minimise the same. ...
During continuous casting, some amount of metal is left in the tundish at the end of the casting sequence to avoid slag entrapment into continuous casting mould. This tundish loss often called as skull loss. It reduces the caster yield and is directly related to the size of the tundish. JSW Steel operates with 44 T, 8 strand billet caster tundish which had ~7T tundish loss under previous operational practice. Water modelling studies were carried out using a 0.25 scale model to design a new tundish bottom to reduce tundish skull loss. Three different tundish bottom configurations were studied and the corresponding effect on tundish flow profile and vortex formation was also investigated. Based on water modelling results, the optimized tundish design was used for plant trials. A 47% reduction in skull loss was obtained with no adverse effect on steel cleanliness from different strands.
