Effect of submerged entry port structure on fluid flow, solidification and inclusions motion in Ф800 mm large section round billets continuous casting

In the present study, a two-dimensional phase field model coupled with Lattice Boltzmann method (PF-LBM) is proposed to predict the dendritic growth and motion in the melt of Fe-C binary alloy, where the phase field method (PF) is used to calculate the dendritic growth, including the phase field and the concentration field, and the lattice Boltzmann method (LBM) is used to calculate the flow field. The dendrite motion is determined by Newton’s Second Law and tracked by Lagrangian point in a Cartesian coordinate system. Later, the model validations were performed with the benchmark of a solid particle settlement in a stagnant fluid and particle motion in a shear flow, and the results show that the present model is capable of predicting the solid particle motion in the fluid flow. Finally, the model is adopted to investigate the dendritic growth and motion in a forced fluid flow (laminar flow or rotational flow), and the dendrite settlement in a terrestrial environment. The results show that when the forced fluid flow is a laminar flow, the free dendrite would be driven to translate, and the relative velocity between the dendrite and flow fluid decreases, resulting in weak influence of fluid flow on the dendritic growth. When the forced fluid flow is a rotational fluid flow, the dendrite would centrifugally rotate on the domain center with a counterclockwise self-spinning, and the rotation radius becomes larger and larger. For the case of dendrite settlement in a terrestrial environment, the relative movement between the dendrite and melt promotes the downward branch growth, but inhibits the upward branch growth, and two vortices form at the wake region of dendrite. Therefore, the settling dendrite shows a significant asymmetrical morphology.

Inclusions in the steel in a four‐strand continuous casting tundish, billet and wire products are firstly investigated with industrial trials, and the fraction of inclusions removed in terms of total oxygen in the tundish is measured. Then the 3‐dimenional fluid flow, heat transfer and inclusion motion in the tundish are numerically simulated. The κ‐∊ two‐equation model is used to model turbulence. Inclusion motion and trajectories are calculated by considering drag force and buoyancy force, coupling the effect of turbulent fluctuation (Random Walk Model). The effect of strands‐blocking on the fluid flow, heat transfer and inclusion removal is studied. A new design of tundish is proposed focusing on removing more inclusions from the molten steel.

Effect of mold corner structures on the fluid flow, heat transfer and inclusion motion in slab continuous casting molds

In the current study, the fluid flow and thermal stratification during the holding period are numerically simulated. The standard k–e two-equation turbulence model is adopted to describe the turbulence. The trajectories of inclusions are calculated by the discrete phase model (DPM) considering the stochastic effect of turbulence. Two different initial conditions for the flow field are compared: the quiescent state of flow and the fluid flow induced by gas stirring. Significant differences are observed between these cases. In practice, the holding period starts from the shut-off of the gas blowing. Thus, it is proposed that the flow field at the terminal of gas stirring should be considered for the simulation of the fluid flow, heat transfer, and inclusion motion during the holding period.

Mathematic Model of SEN Clogging During Continuous Casting of Steel

PurposeThe purpose of this article is to numerically investigate the effect of casting speed on the fluid flow, solidification and inclusion motion under the influence of electromagnetic stirring (EMS) in the bloom caster mold with bifurcated submerged entry nozzle (SEN).Design/methodology/approachThe electromagnetic field obtained by solving Maxwell’s equation is coupled with the fluid flow, solidification and discrete phase model using the in-house user-defined functions. An enthalpy porosity approach and Lagrangian approach are applied for the solidification analysis and non-metallic inclusions motion tracking, respectively.FindingsInvestigation shows that the casting speed and EMS significantly affect the steel flow, solidification and inclusion behavior inside the mold. Investigations are being conducted into the complex interplay between the induced flow and the SEN’s inertial impinging jet. In low and medium casting speeds, the application of EMS significantly increases the inclusion removal rate. Inclusion removal is studied for its different size and density and further effect of EMS is also reported on cluster formation and distribution of inclusion in the domain.Practical implicationsThe model may be used to optimize the process parameter (casting speed and EMS) to improve the casting quality of steel by removing the impurities.Originality/valueThe effect of casting speed on the solidification and inclusion behavior under the influence of time-varying EMS in bloom caster mold with bifurcated nozzle has not been investigated yet. The findings may assist the steelmakers in improving the casting quality.

In the current study, the three-dimensional fluid flow, heat transfer, and solidification in steel centrifugal continuous casting strands were simulated. The volume of fluid model was used to solve the multiphase phenomena between the molten steel and the air. The entrapment and final distribution of inclusions in the solidified shell were studied with the discussion on the effect of rotation behavior of the caster system. Main results indicate that after applying the rotation of the shell, the fluid flow transformed from a recirculation flow to a rotation flow in the mold region and was driven to flow around in the casting direction. As the distance below the meniscus increased, the distribution of the tangential speed of the flow and the centrifugal force along one diameter of the strand became symmetrical gradually. The jet flow from the nozzle hardly impinged on the same location on the shell due to the rotation of the shell during solidification. Thus, the shell thickness on the same height was uniform around, and the thinning shell and a hot spot on the surface of shell were avoided. Both of the measurement and the calculation about the distribution of oxide inclusions along the radial direction indicated the number of inclusions at the side and the center was more than that at the quarter on the cross section of billet. With a larger diameter, inclusions tended to be entrapped toward the center area of the billet.

Continuous casting of slab caster of Tata Steel has been simulated using a three dimensional mathematical model based on considerations of fluid flow, heat transfer and solidification for better understanding of the process. Liquid metal comes in the mould by bifurcated nozzle. The principal model equations are momentum and heat balances. In various zones, different standard boundary conditions have been used. In the mould region, Savage and Prichard expression for heat flux has been used. In the spray cooling zone, heat transfer coefficient for surface cooling of the slab has been calculated by knowing the water flow rate and nozzle configuration of plant. The turbulence in the molten metal has been modelled by the Realizable k–ε model. CFD software (Fluent) has been used for the solution of equations to predict the velocities in the molten pool of the slab, temperature of the entire volume of the slab, heat transfer coefficient in the mould region, heat flux in the spray and radiation region and shell thickness. The variables studied are different casting speed.

The tundish in the current study was for a five-strand billet continuous caster. The effect of closing different outlets on the fluid flow, temperature and inclusion removal was investigated. The top surface level fluctuations at the inlet zone isolated by the tall turbulence inhibitor weir was very severe and caused slag entrainment. The simulation shows that the highest level fluctuation was 0.87 mm while the lowest one was -0.389 mm. The fraction of inclusions entering the outlet far away from the inlet was much higher than entering other outlets. Closing any strand had a certain effect on the removal of inclusions to the top and on the fraction of inclusions to different strands. The temperature difference between inlet and outlet of tundish was increased by closing outlets for the current tundish and the increase of maximal temperature difference was 1~2 K.

Clogging of the submerged entry nozzle (SEN) is a serious problem during the continuous casting of steel, due to its influence on the casting operations and product quality. Fluid-flow-related phenomena in the continuous casting mold region with the SEN clogging are investigated in the current article, including the quantitative evaluation of inclusion removal, slag entrainment, heat transfer, and the prediction of breakouts. The calculations indicate that, in order to accurately simulate the fluid flow in the mold region, the SEN should be connected with the mold region and the two should be calculated together. In addition, the whole mold region has to be calculated. Clogging at the SEN at one side induces asymmetrical jets from the two outports; thus, the fluid flow in the mold is asymmetrical. In addition, more inclusions are carried by the flow to the top surface of the nonclogged side, and the slab at the nonclogged side has a lower quality. With SEN one-sided clogging, inclusions travel a much larger distance, on average, before they escape from the top or move to the bottom. The overall inclusion entrainment fraction from the entire top surface for inclusions of any size is less than 10 pct. A higher turbulence energy and a larger surface velocity induce more inclusion entrainment from the top surface. Smaller inclusions are more easily entrained into the steel than are larger ones. More >200-μm inclusions can be entrained into the molten steel from the top slag with SEN clogging than without clogging. The SEN one-sided clogging generates an asymmetrical temperature distribution in the mold; it also generates temperatures higher than the liquidus temperature at some locations of the solidified shell, which increases the risk of breakouts. The SEN clogging should be minimized in order to achieve a uniform steel cleanliness, a cleaner steel, and a safe continuous casting operation.

In the current study, a three-dimensinal (3D) numerical model is built to investigate the effect of a local-type electromagnetic brake (EMBr) on the fluid flow, heat transfer, and inclusion motion in slab continuous casting strands. The results indicate that the magnetic force affects the jet characteristics, including jet angle, turbulent kinetic energy, and its dissipation rate. To reduce the top surface velocity and stabilize the top surface, the magnetic flux intensity should be larger than a critical value. With a 0.39 T magnetic flux intensity, the top surface velocity and its fluctuation can be well controlled, and less slag is entrained. The motion of argon bubbles is also studied. More bubbles, especially >2.0-mm bubbles, escape from the top surface between the mold submerged entry nozzle (SEN) and \( \frac{1}{4} \) width for the case with a 0.39 T EMBr. This may push the top slag away and create an open “eye” on the top slag. Small bubbles (≤1 mm) tend to escape from one side of wide face no matter with or without EMBr, which is induced by the swirl flow from the SEN outport. EMBr has a little effect on the overall removal fraction of inclusions; however, it affects the local distribution of inclusion in the slab. With EMBr, more inclusions accumulate the region just below the surface, thus a worse subsurface quality, whereas the inner quality of the slab is better than that without EMBr. For heat transfer in the mold, the heat flux on the narrow face and the area of possible break-out zones can be reduced by using EMBr. Prevention of bias flow and/or asymmetrical flow in mold by EMBr is also concluded.

In the present work, a coupled three-dimensional numerical model of fluid flow, heat transfer, and inclusion motion during the solidification of molten steel in slab continuous casting mold has been developed. Based on the model, this paper has studied the inclusion capture during the process. The influence of the primary dendrite arm spacing on inclusion capture has been considered. The inclusion distributions, total masses, and average diameters at different depth from the slab surface have been given out in the present paper. The simulation results revealed the inclusion concentration existed in the solidification process, and the inclusion capturing area varies with the depth from the slab surface.

In this article, a combination of Lattice-Boltzmann method (LBM) and smoothed profile method (SPM) are used in simulation of one, two, and many particles’ motion in fluid flow. SPM is used as the simulation method for particles motion. A shear flow is produced using a) solid walls for which standard bounce-back (SBB) boundary condition is applied and b) Lees-Edwards boundary conditions (LEBC). Simulation of Couette flow problem of fluid-only system reveals the accuracy of both methods. LBM-SPM coupled with LEBC is applied for flow geometries of one and two particles in a shear flow. Comparison of results obtained from simulation of one and two interacting particles using moving walls with SBB with those in the literature shows good correspondence. In addition, for the case of many particles, the effective viscosity of a suspension of circular particles which are placed randomly between two parallel walls is investigated from dilute to dense regimes. Relative bulk viscosity is compared with theoretical and semi-empirical results of other investigators and satisfactory agreement is found. Finally, a combination of SPM-LBM is examined for sedimentation of one, two and many particles. Numerical results show suitability of LBM-SPM with LEBC for simulation of particles suspended in flow.

An analysis of mould, spray and radiation zones of a continuous billet caster has been done by a three‐dimensional turbulent fluid flow and heat transfer mathematical model. The aim was to reduce crack susceptibility of the billets and enhance productivity of the billet caster. Enthalpy‐porosity technique is used for the solidification. Turbulence is modelled by a realizable k‐ε model. The three‐dimensional mesh of the billet is generated by Gambit software, and Fluent software is used for the solution of equations. In various zones, different standard boundary conditions are applied. Enhanced wall treatment is used for the turbulence near the wall. In the mould region, Savage and Prichard expression for heat flux is applied. In the spray cooling zone, the heat transfer coefficient for surface cooling of the billet is calculated by knowing the water flow rate and the nozzle configuration of the plant. The model predicts the velocities in the molten pool of a billet, the temperature in the entire volume of billet, the heat transfer coefficient in the mould region, the heat flux in the cooling zone and radiation cooling zone, and the shell thickness at various zones. The model forecasts that the billet surface temperature up to the cutting region is above the austenite‐ferrite transformation temperature (which is accompanied by large volume change). The model predicts a temperature difference of maximum 700 K between the centre and surface of the billet. The entire solidification takes place at 11.0 m length at 3.0 m/min. For the same casting arrangement, increasing the casting speed up to 4.0 m/min has been explored. Based on the simulation results, recommendations to alter the spray water flow rate and spray nozzle diameter are presented to avoid a sudden change of temperature.

The study reports the influence of Caputo–Fabrizio fractional derivative and magnetic field on blood flow as an electrically conducting non-Newtonian fluid along with magnetic nanoparticles through circular cylindrical arterial segment, by assuming blood as Jeffrey fluid. The main structure of the governing fractional nonlinear partial differential equations was obtained from non-Newtonian fluid model in which convective derivative is considered instead of the time derivative which is capable of describing the phenomena of relaxation time and retardation time. The exact solutions of the governing fractional partial differential equations were obtained by the virtue of Laplace and Hankel transforms. Numerical simulations have been performed to analyze the behavior of the Jeffrey fluid flow using Mathcad software and the results are presented graphically for an explicit and detail discussion. We noticed from the graphical representation of results that the fractional derivative, particle concentration, electro-kinetic width, Jeffrey number and the applied magnetic field have profound influence on the magnitude of blood velocity along with magnetic nanoparticles. The effect of each of the influential parameters tremendously decelerates the fluid flow and thereby showing appreciable variation in the distribution of axial and radial velocities. Practically, increasing the applied magnetic field strength and the value of the Jeffrey number on the motion of fluid flow together with magnetic nanoparticles, vehemently decreases the velocities of blood along with magnetic nanoparticles, which helps to have effective control over the fluid networks. From the study, we conclude that the fractional model, Jeffrey number and the application of the external magnetic field on the fluid flow have extensive applications in the clinical and the medical sciences.