Research Status of Numerical Simulation of Nonmetallic Inclusions Interfacial Removal

The removal of inclusions in liquid steel has always been the focus of research, and the removal of inclusions is mainly through the process of the inclusion through the slag–steel interface. The inclusion removal process can be subdivided into inclusions in molten steel grew up rise, in steel–slag interface through separation, adsorb dissolved in molten slag 3 steps. Based on the microscopic process of three steps, this article summarizes and discusses the mathematical model, fluid mechanics model, and experimental verification method of inclusion removal process, analyzes limiting and influencing factors of inclusion removal process, and comprehensively describes the numerical simulation research progress of inclusion removal process. With the development of numerical simulation techniques and experimental equipment, some progress has been made in the study of interfacial removal of inclusions. The inclusion interface removal behavior can be analyzed semiquantitatively based on dynamic force model. The computational fluid dynamics model has advantages in studying the phenomena of the inclusion interface, and the phase-field method is often used to simulate the removal process of the inclusion interface. The combination of water model and numerical simulation, high-temperature laser confocal method, and other methods is of great help to explore the interface behavior of inclusions.     

Theoretical analysis of the interfacial phenomena during the injection of carbon particles into EAF slags

A theoretical analysis of FeO reduction through the injection of carbon fines in electric arc furnace slags, involving the interfacial phenomena at the liquid‐gas‐solid interface, has been performed using basic principles of transport phenomena and physical chemistry of steelmaking. It was found that small angle contacts between slag and carbon favour FeO reduction. Moreover, FeO in basic slags are more prone to be reduced because the interfacial liquid‐gas interface has more free reaction places. In acid slags FeO reduction is difficult because the gas‐liquid interface is partially filled by polymeric silicates. When the particle size is smaller than 100 μm the influence of slag basicity is considerably decreased. Practical applications of these results can be found in electric arc furnace shops aiming at the mastering of slag foaming practices and energy saving.     

Large-eddy simulation of laser-induced surface-tension-driven flow

The turbulent flow inside a laser-generated molten pool is investigated by an adapted large-eddy simulation (LES) model that incorporates physical considerations pertaining to the solid-liquid phase change. A single-domain, fixed-grid enthalpy-porosity approach is utilized to model the phase-change phenomena in the presence of a continuously evolving solid/liquid interface. The governing transport equations are simultaneously solved by employing a control-volume formulation, in conjunction with an appropriate enthalpy-updating closure scheme. To demonstrate the performance of the present model in the context of phase-change materials processing, simulation of a typical high-power laser melting process is carried out, where effects of turbulent transport can actually be realized. It is found that the present LES-based model is more successful in capturing the experimental trends, in comparison to the k-ε-based turbulence models often employed to solve similar problems in contemporary research investigations.     

Multiparticle interfacial drag in equiaxed solidification

A physical model is proposed for the solid/liquid interfacial drag in both globular and dendritic equiaxed solidification. By accounting for the presence of multiple particles and the nonsphericity and porosity of the individual equiaxed crystals, a drag correlation is developed, which is valid over the full range of solid volume fractions. It is shown that neither the solid liquid interfacial area concentration nor the grain size alone is adequate to characterize the interfacial drag for equiaxed dendritic crystals in both the free particle and packed bed regimes; thus, the present model is based on a multiple length scale approach. The model predictions are compared to previous analytical and numerical results as well as to experimental data available in the literature, and favorable agreement is achieved. Formerly Graduate Research Assistant, Department of Mechanical Engineering, University of Iowa     

Dynamic and equilibrium interfacial phenomena in liquid steel-slag systems

The equilibrium interfacial energy between a liquid iron alloy and a liquid slag is a key physical parameter in the design of steel-refining processes as high interfacial energies are desired to avoid emulsification of slag in steel and the creation of casting defects. During a chemical reaction between a liquid iron alloy droplet and a liquid slag, it is possible to observe by X-ray photography a number of dynamic interfacial phenomena such as droplet flattening, interfacial turbulence, and spontaneous emulsification that can potentially lead to serious processing problems. These dynamic phenomena have been studied during reactions between Fe-Al and Fe-Ti alloys and silica-containing slags, and the presence of significant interfacial disturbance has been observed during the times of high reaction rate between the slag and the metal. It is suggested that interfacial chemical reactions induce Marangoni and natural convection at the slag-metal interface. This interfacial flow gives rise to interfacial waves due to a Kelvin-Helmholtz instability. The waves grow, become unstable, and lead to spontaneous emulsification of slag in steel and steel in slag. Experiments using industrial samples and controlled laboratory tests have indicated that this phenomenon may be more common than once thought and could lead to some serious problems in the processing of steel alloys containing high quantities of aluminum and/or titanium. This article is based on a presentation made in the “Geoffrey Belton Memorial Symposium,” held in January 2000, in Sydney, Australia, under the joint sponsorship of ISS and TMS.     

100 t底吹氩钢包插入浸渍管对钢液流场影响的数值模拟

以100t单孔底吹氩钢包为原型,应用三维连续性方程、动量N-S方程及湍流κ-ε双方程模拟了底吹氩过程中钢包内的钢液流动状态。利用Mixture多相流模型对单孔吹氩（0~700 L/min）过程进行数值模拟,对比分析插入直径691.05 mm,深650 mmn浸渍管前后钢包内的流动状态和钢液表面的卷渣。结果表明,无浸渍管时,临界卷渣吹气量为102 L/min,插入浸渍管后,临界卷渣吹气量增大到217 L/min。插入浸渍圆筒可以在增加吹氩量的条件下提高钢液搅拌效果,加速钢液混匀。     

Influence of melt carbon and sulfur on the wetting of solid graphite by Fe-C-S melts

The interfacial phenomena between carbonaceous materials such as graphite, coke, coal, and char and Fe-C-S melts are important due to the extensive use of these materials in iron processing furnaces. However, the understanding of the interfacial phenomena between these kinds of carbonaceous materials and molten iron alloys is far from complete. In this study, graphite was selected as the solid carbonaceous material because its atomic structure has been well established. The sessile drop method was adopted in this investigation to measure the contact angle between solid graphite and molten iron and to study the interfacial phenomena. The influence of carbon and sulfur content in Fe-C-S melts on the wettability of solid graphite has been investigated at 1600 °C. The melt carbon content was in the range of 0.13 to 2.24 wt pct, and the melt sulfur content was in the range of 0.05 to 0.37 wt pct. X-ray energy-dispersive spectrometer (EDS) analysis was conducted on an HITACHI S-4500 scanning electron microscope to detect composition distribution at the interfacial region. It was found that contact of solid graphite with Fe-C-S melts will result in a nonequilibrium reactive wetting. It involved carbon transfer from the solid to the liquid and iron transfer from the liquid to the solid. The Fe-C-S melts exhibited relatively poor wetting when the reactions were absent. The mass transfer between solid graphite and Fe-C-S melts was observed to strongly enhance the wetting phenomena. It is proposed that the decrease of system free energy corresponding to the mass transfer reactions strongly influences the formation of the interface region and results in the progressive spreading of the wetting line. The composition and thickness of the graphite/iron interfacial layer was dependent on the intensity of mass transfer across the interface. The resulting change in the interfacial energy γ _ls is a strong function of mass transfer, and it varies in accordance with time of contact. The influence of carbon content on the wetting phenomena could only be seen at in the initial stages, whereas the influence of sulfur on the wettability was found when the system approached equilibrium. Therefore, the interfacial tension in its equilibrium condition at the graphite/Fe-C-S melt interface was determined only by the extent of sulfur adsorption at this interface.     

Pattern formation during stationary heating and zone melting recrystallization of a silicon thin film

Solid/liquid (S/L) interface patterns during stationary heating and zone melting recrystallization (ZMR) of a Si thin film were calculated by using a phase-field model. The formation of an irregular S/L interface, solid particles in an undercooled liquid, and liquid droplets in a solid Si during stationary heating of the Si thin film could be interpreted by the difference in reflectivity between the solid and liquid Si, which results in the formation of undercooled liquid in front of the interface. The effects of the heater's scanning velocity and the radiation width during ZMR on the S/L interface pattern were calculated for a given interfacial energy anisotropy constant. An irregular, zigzag-shaped interface pattern was preferred at a lower scanning velocity and wider radiation zone. A regular, cellular S/L pattern can be obtained at a certain range of processing parameters. The cellular spacing increased by increasing either the heater's scanning velocity or the radiation width.     

Pattern formation during stationary heating and zone melting recrystallization of a silicon thin film

Solid/liquid (S/L) interface patterns during stationary heating and zone melting recrystallization (ZMR) of a Si thin film were calculated by using a phase-field model. The formation of an irregular S/L interface, solid particles in an undercooled liquid, and liquid droplets in a solid Si during stationary heating of the Si thin film could be interpreted by the difference in reflectivity between the solid and liquid Si, which results in the formation of undercooled liquid in front of the interface. The effects of the heater’s scanning velocity and the radiation width during ZMR on the S/L interface pattern were calculated for a given interfacial energy anisotropy constant. An irregular, zigzag-shaped interface pattern was preferred at a lower scanning velocity and wider radiation zone. A regular, cellular S/L pattern can be obtained at a certain range of processing parameters. The cellular spacing increased by increasing either the heater’s scanning velocity or the radiation width.     

A new method for three-dimensional numerical simulation of electromagnetic and fluid-flow phenomena in electromagnetic separation of inclusions from liquid metal

The magnetohydrodynamic (MHD) flow around a suspended particle in a liquid metal subjected to electric and magnetic fields can affect the force exerted by the applied electromagnetic field on the particle. In this article, a novel approach to the computational simulation of three-dimensional nonlinear MHD flow in two-phase systems is proposed. The electromagnetic field in the conducting fluid, including the particle, is represented using the current-vector potential (T) and reduced magnetic scalar potential (Ψ) to avoid the discontinuity of the electric field at the fluid-particle interface. To avoid the solution of the electromagnetic field in free space and to account exactly for the electromagnetic field interactions with the fluid and the particle, the electric and magnetic fields are specified at the boundary of the fluid-flow domain using Ampere’s law. This formulation permits the numerical solution of the coupled electromagnetic and fluid-flow equations on a common mesh. The discretized equations are derived using a finite-element formulation, and an iterative procedure is described for the efficient solution of these equations. This method is used to investigate the electromagnetic and fluid-flow phenomena in electromagnetic separation of a nonconducting spherical particle in crossed uniform electric and magnetic fields at intermediate Hartmann numbers. The computed results show that the magnetic field has no effect on either the velocity field or the net force on the particle when the Hartmann number is less than 1. Beyond this threshold value of the Hartmann number, the velocity decreases almost linearly with increasing magnetic-field strength. The damping of the flow by the magnetic field manifests itself in a reduction of the separation force, even though it is relatively small for this system.     

上水口环形吹氩对中间包内渣眼形成的影响

 中间包上水口环形吹氩可以在塞棒周围形成清洗钢液的环形气幕,同时部分氩气泡随钢液进入上水口内,可以减少非金属夹杂物在水口内壁的黏附,起到防止水口堵塞的作用。然而,不合理的吹氩量会导致中间包内液面渣层受过强的气液羽流冲击而形成渣眼,使得钢液裸露并发生二次氧化,严重影响铸坯质量。采用标准 k ε 湍流模型研究中间包内流体流动,采用DPM模型和VOF模型耦合方法,研究上水口环形吹氩条件下渣眼的形成及演化规律。结果表明,上水口环形吹氩在塞棒周围形成较强的上升流,塞棒上部邻近区域存在多个涡流区;在钢液涡流的影响下,中间包液渣下层远离塞棒区域,上层向塞棒区域迁移;随着吹氩量的增大,平均湍动能增大,塞棒附近钢液速度逐渐增大,钢渣界面钢液速度先增大后减小,渣眼边缘钢液速度先增大后减小然后再增大,速度与垂直方向夹角逐渐减小;增大吹氩量,中间包熔池液面形成以塞棒为中心的渣眼,渣眼面积逐渐增大。试验条件下不产生渣眼的临界吹氩量为4.2 L/min,对应的钢渣界面最大速度为0.247 m/s,与垂直方向夹角为70°。     

Numerical Simulation of Dehydrogenation of Liquid Steel in the Vacuum Tank Degasser

Vacuum tank degassers are often utilized to remove hydrogen from liquid steel. A new comprehensive numerical model, which has been developed to simulate hydrogen removal in the vacuum degassers, is presented in this paper. The degassing model consists of two sub-models, which calculate the gas-steel flow field and the species transport of hydrogen. An extended k–ε turbulence model is adopted to consider the effect of gas injection on the turbulent properties and an interfacial area concentration model is introduced to compute the interfacial area density between liquid steel and the bubbles. The fluid dynamic sub-model is validated with a physical gas stirred tank, which is believed to have similar flow phenomena as the studied vacuum degasser based on the modified Froude number. Two fundamental expressions for mass transfer coefficient, which have been paid little attention by the researchers concentrating on vacuum degassing, are evaluated with a simulation case corresponding to practical operation. The effect of vacuum pressure on the dehydrogenation process is investigated and, moreover, the integrated model is verified with industrial measurements. The predicted final hydrogen contents in liquid steel show good agreement with the measured ones. The model and the main results are presented.     

Heat Flow and Solidification Modeling of Industrial Scale,Ingot Casting Operation

A model, based on the concept of effective thermal conductivity, was developed to study thermal fields and the resultant solidification behavior of large, round, industrial size ingots. In this, flow and turbulence phenomena during mold filling as well as subsequent solidification were not modeled explicitly but their influence was accounted for by artificially raising the thermal conductivity of solidifying steel. Thus, a conduction like equation embodying a conjugate approach was applied to simultaneously predict the evolution of temperature fields in the mold as well as in the solidifying ingot following teeming. Prior to comparing model predictions against industrial scale measurements, sensitivity of calculations to grid size, time step height, convergence criterion etc. were rigorously assessed. Similarly, modeling of interfacial resistance, chemical reactions and heat effects in the hot top as well as their influence on predicted results were evaluated computationally. Embodying mixed thermal boundary conditions (free convection + radiation) at the mold wall, temperature fields during solidification of two different industrial large ingots were predicted numerically. Parallely, mold wall temperature was monitored as a function of time and surface temperature of ingot was measured at the instant of mold stripping using hand held, radiation pyrometers. Incorporating relevant operating conditions (viz., mold dimensions and size, ingot and hot top dimensions and material, initial mold and liquid temperature etc.) into the calculation scheme, predictions were made via a computational procedure developed in-house and results thus obtained were compared against equivalent industrial scale measurements. Very reasonable agreement between the two was demonstrated.     

Mechanism of heterogeneous

The present article describes a novel theoretical approach to the mechanism of heterogeneous nucleation of pores in metallic systems. The proposed mechanism is based on the behavior of foreign particles at the advancing solid/liquid (S/L) interface. Foreign substrates act as a barrier to the fluid flow as well as to the diffusion field at the S/L interface, giving rise to enhanced gas segregation and viscous pressure drop. Mathematical analyses have been employed to pre- dict the gas segregation and pressure drop in the gap between the particle and the S/L interface. The equations which arise are solved using available experimental data in the literature. An order of magnitude analysis is done, and it is shown that pressures in the range of the activation barrier (fracture pressure) can be obtained in normal castings. The effect of particle properties and solidification parameters, such as wettability, density, thermal conductivity, solidification rate and morphology of S/L interface, are discussed. A complete assessment of all possible kinds of particles is not possible, since the material values and experimental parameters are not known in most of the cases. To consolidate the mechanism, therefore, further quantitative measurements of material values, interfacial energies in particular, are required on systems of interest.     

A Semianalytical Thermal Model for Fiction Stir Welding

The main difficulty in the formulation of any model for friction stir welding (FSW) is due to the high coupling between thermal and mechanical phenomena. In the analytical models present in the literature, the fundamental unknown parameter, under the assumption of sticking between the tool/matrix interface, is the yield shear stress, which is temperature dependent. For this reason, any fully analytical model is unable to predict the temperatures for conditions not supported by measurements of the heat input. In this work a semianalytical thermal model for FSW is proposed. The formulation of heat flow during the welding process is based on generic solutions of the differential equation for heat conduction in a solid body, formulated for a point heat source with constant linear velocity. The heat generation was considered as a function of the tool-matrix interface temperature, which is calculated by means of a numerical routine written in Matlab code. Comparison with the experimental measurements taken from the literature shows that the results from the present semianalytical model are in good agreement with the test data.     

底吹氩过程LF炉盖内气体流动的数值模拟

基于流体模型和湍流修正模型,借助流体工程模拟软件Fluent 6.3.26对吹氩过程中210 t LF精炼炉盖内气体的流动、混合和质量、动量传输进行了计算模拟,分析了其流动行为和分布状态。结果表明,随钢包净空高度增加,液面上部氩气回旋区扩大,"死区"减小;当氩气流量增至500 L/min时,吹氩孔位于0.68 R的盖内流动效果优于0.3 R的效果;正常工作状态下的合理抽气压力为-150 Pa;在合理的抽气压力和吹氩孔位置的情况下,300 L/min的氩气流量基本可以满足要求,强搅拌时可增至500 L/min。     

强制对流影响下Fe?C合金定向凝固微观组织的相场法研究

定向凝固技术能够获得特定柱状晶结构,对于优化合金轴向力学性能具有非常显著的效果。本文采用耦合流场的相场模型模拟了定向凝固过程中枝晶的生长过程,研究了各向异性系数、界面能对定向凝固枝晶生长的影响以及强制对流作用下枝晶的生长行为。数值求解过程中,选用基于均匀网格的有限差分方法对控制方程进行离散,实现了格子中标记点算法（MAC）和相场离散计算方法的联合求解。处理微观速度场和压力场耦合时,采用MAC算法求解Navier-Stokes方程和压力Poisson方程,采用交错网格法处理复杂的自由界面。结果表明:随着各向异性系数的增大,枝晶尖端生长速度增大,曲率半径减小,枝晶根部溶质浓度逐渐降低;随着界面能的增大,枝晶尖端曲率半径增大,当界面能为最大（0.6 J·m?2）时,凝固呈现平界面的凝固方式向前推进;强迫对流对定向凝固枝晶生长方向影响较大,上游方向定向凝固枝晶粗大且生长速度更快,其现象随流速的增大而愈加明显。      

Study of transient flow and particle transport in continuous steel caster molds: Part I. Fluid flow

Unsteady three-dimensional flow in the mold region of the liquid pool during continuous casting of steel slabs has been computed using realistic geometries starting from the submerged inlet nozzle. Three large-eddy simulations (LES) have been validated with measurements and used to compare results between full-pool and symmetric half-pool domains and between a full-scale water model and actual behavior in a thin-slab steel caster. First, time-dependent turbulent flow in the submerged nozzle is computed. The time-dependent velocities exiting the nozzle ports are then used as inlet conditions for the flow in the liquid pool. Complex time-varying flow structures are observed in the simulation results, in spite of the nominally steady casting conditions. Flow in the mold region is seen to switch between a “double-roll” recirculation zone and a complex flow pattern with multiple vortices. The computed time-averaged flow pattern agrees well with measurements obtained by hot-wire anemometry and dye injection in full-scale water models. Full-pool simulations show asymmetries between the left and right sides of the flow, especially in the lower recirculation zone. These asymmetries, caused by interactions between two halves of the liquid pool, are not present in the half-pool simulation. This work also quantifies differences between flow in the water model and the corresponding steel caster. The top-surface liquid profile and fluctuations are predicted in both systems and agree favorably with measurements. The flow field in the water model is predicted to differ from that in the steel caster in having higher upward velocities in the lower-mold region and a more uniform top-surface liquid profile. A spectral analysis of the computed velocities shows characteristics similar to previous measurements. The flow results presented here are later used (in Part II of this article) to investigate the transport of inclusion particles.     

Turbulent flow of liquid steel and argon bubbles in slide-gate tundish nozzles: Part I. model development and validation

The quality of continuous-cast steel is greatly affected by the flow pattern in the mold, which depends mainly on the jets flowing from the outlet ports in casting with submerged tundish nozzles. An Eulerian multiphase model using the finite-difference program CFX has been applied to study the three-dimensional (3-D) turbulent flow of liquid steel with argon bubbles in slide-gate tundish nozzles. Part I of this two-part article describes the model formulation, grid refinement, convergence strategies, and validation of this model. Equations to quantify average jet properties at the nozzle exit are presented. Most of the gas exits the upper portion of the nozzle port, while the main downward swirling flow contains very little gas. Particle-image velocimetry (PIV) measurements are performed on a 0.4-scale water model to determine the detailed nature of the swirling velocity profile exiting the nozzle. Predictions with the computational model agree well with the PIV measurements. The computational model is suitable for simulating dispersed bubbly flows, which exist for a wide range of practical gas injection rates. The model is used for extensive parametric studies of the effects of casting operation conditions and nozzle design, which are reported in Part II of this two-part article.     

Dissipation of Turbulent Kinetic Energy in a Tundish by Inhibitors with Different Designs

Turbulent flow of liquid steel and its control is studied using different geometries of turbulence inhibitors. Four designs of turbulence inhibitors were characterized through experiments of tracer injection in a water model and mathematical simulations using the Reynolds Stress Model (RSM) of turbulence. Inhibitor geometries included octagonal‐regular, octagonal‐irregular, pentagonal and squared. A layer of silicon oil was used to model the behaviour of tundish flux during steel flow. Fluid flows in a tundish using these geometries were compared with that in a bare tundish. Experimental and simulation results indicate that the flow in a bare tundish and a tundish using turbulence inhibitors open large areas of oil close to the ladle shroud due to strong shear stresses at the water‐oil interface with the exception of the squared inhibitor. Oil layer opening phenomena are explained by the high gradient of the dissipation rate of turbulent kinetic energy. Using the squared inhibitor the kinetic energy reports a high gradient from the tundish floor to the free bath surface as compared with other geometries.