Mathematical modeling and computer simulation of the rotating impeller particle flotation process: Part II. Particle agglomeration and flotation

Effective removal of unwanted particles from a molten metal alloy by flotation relies on purging a gas into the melt through a rotating impeller. This device is commonly known as a rotary degasser. Unwanted particles in the melt attach to the rising gas bubbles and rise to the slag layer where they are removed from the metal bulk. In addition, the turbulence created by the rotating impeller causes the randomly distributed solid particles to agglomerate into relatively large clusters. These clusters float up or settle down due to the difference between their density and that of the melt. A mathematical model has been developed to describe the particle dynamics and particle agglomeration that occur during the rotary degassing of aluminum melts. While previous investigations addressed particle collisions in low intensity turbulent fields where the size of the colliding particles is smaller than the Kolmogorov length scale, this model is more encompassing as it considers both low intensity and high intensity turbulence. Consequently, this model is more representative of a typical industrial rotary degassing operation.     

The removal of solid particles from molten aluminum in the spinning nozzle inert flotation process

The removal of solid particles from molten aluminum by flotation was investigated based on theoretical fluid dynamics. The energy spent for stirring the melt in the SNIF process accelerates the agglomeration of small particles into larger particle aggregates which can be removed from the metal by gas bubbles during the short residence time of the melt in the refining unit. Theory suggests that supplementation of thermal agglomeration of the particles with turbulent agglomeration and small gas bubbles are the major factors which can lead to high particle collection efficiencies in molten aluminum.     

The mechanism of inclusion removal from molten steel by dissolved gas flotation

Dissolved gas flotation (DGF) is used for removing inclusions from molten steel. The supersaturated gas forms bubbles on inclusions and carry them to the melt’s surface. Inclusion removal is modelled visually by applying a water simulation system. A mathematical model is developed to simulate the removal rate of inclusions from steel melts. From the experimental results and mathematical calculation, the mechanism of the inclusion removal by DGF was discussed, and it was concluded that first the relationship between inclusion removal efficiency and dissolved gas content, second the bubble nucleation on suspended inclusion in supersaturated molten, and finally the multi-fine bubbles flotation to the surface.     

Quantitative Analysis of the Removal Ratio of Fine Particles in Water by Gas Bubbling

Removal of non-metallic inclusions in molten steel is important from the viewpoint of improvement of quality, property and yield of the products. As a removal method of inclusions from molten metal, gas bubble flotation adhering inclusions is well known. Gas bubbling is particularly effective for the removal of fine inclusions. Water model experiment is reported the quantitative analysis of the removal ratio of dispersed particles removed from water by gas bubbles.     

Modeling of molten metal flow in a continuous casting process considering the effects of argon gas injection and static magnetic-field application

A mathematical model has been developed to analyze molten metal flow, considering the effects of argon gas injection and static magnetic-field application in the continuous casting process. The k-ɛ turbulence model is used to calculate the turbulent variables. A homogeneous fluid model with variable density is employed to tackle the molten metal-argon gas flow. The electromagnetic force is incorporated into the Navier-Stokes equation, and the effects of boundary conditions of the magnetic field on the velocity distribution near the mold wall are included. A good agreement between the numerically obtained flow-field results and measurements is obtained. The argon gas injection changes the molten metal flow pattern, mainly in the upper portion of the mold. By applying the magnetic field, values of the averaged velocity field in the bulk decrease significantly, and, especially at the top free surface, they become very small, which can cause meniscus freezing. When magnetic-field application and argon gas injection are used together, the external flow field out of the gas plume is significantly suppressed; nevertheless, flotation of gas bubbles is still active and is not affected directly by the magnetic field. Although the penetrating length of the gas plume is shortened, the argon gas bubbles in molten steel still cause fluctuation at the top free surface, which prevents the occurrence of freezing.     

Separating Effect of a Novel Combined Magnetic Field on Inclusions in Molten Aluminum Alloy

The feasibility and effectiveness of a novel combined magnetic field (CMF) on the removal of inclusions with a density smaller than the surrounding melt were investigated. The experiment of the separating effect of CMF was conducted on a laboratory-scale apparatus by the simultaneous application of a rotating magnetic field (RMF) and a downward traveling magnetic field (TMF). Primary silicon particles precipitating from the solidification process of Al-Si-Cu alloy were regarded as the inclusions in a molten aluminum alloy. It was found that a CMF consisting of both a RMF and a downward TMF was able to separate silicon particles from the molten Al-Si-Cu alloy by making these particles migrate vertically toward the upper part of the samples. Compared with downward TMF or RMF, CMF improved the separating effectiveness substantially. It was proposed that this type of CMF was approved to be highly effective at eliminating the inclusions with a density smaller than the surrounding molten alloy. A tentative mechanism for the high separating effect of CMF was discussed.     

气幕挡墙中间包钢水流动的数值模拟

根据二流连铸1500mm×250mm板坯时中间包的操作工艺参数,采用欧拉两流体模型,多孔介 质模型和拉格朗日随机轨道模型,模拟计算了采用湍流控制器和气幕挡墙技术的中间包内钢液流动特性和 夹杂物的运动轨迹,并用Monte-Carlo法统计了夹杂物的总去除率。模拟结果表明,采用中间包气幕挡墙技术 可以有效改善钢液的流动特性,延长钢液停留时间,减小死区体积;当吹气量为0.90m³/h时,夹杂物去除率比 不吹气工艺增加15.6%     

Modeling of inclusion removal in a tundish

Mathematical models have been developed to predict the removal of alumina inclusions from molten steel in a continuous casting tundish, including the effects of turbulent collisions, reoxidation, flotation, and removal on the inclusion size distribution. The trajectories of inclusion particles are tracked through the three-dimensional (3-D) flow distribution, which was calculated with the K-ɛ turbulence model and includes thermal buoyancy forces based on the coupled temperature distribution. The predicted distributions are most consistent with measurements if reoxidation is assumed to increase the number of small inclusions, collision agglomeration is accounted for, and inclusion removal rates are based on particle trajectories tracked through a nonisothermal 3-D flow pattern, including Stokes flotation based on a cluster density of 5000 kg/m³ and random motion due to turbulence. Steel samples should be taken from as deep as possible in the tundish near the outlet and at several residence times after the ladle is opened, in order to best measure the Al₂O₃ concentration entering the submerged entry nozzle to the mold. Inclusion removal rates vary greatly with size and with the presence of a protective slag cover to prevent reoxidation. The random motion of inclusions due to turbulence improves the relatively slow flotation of small inclusions to the top surface flux layer. However, it also promotes collisions, which slow down the relatively fast net removal rates of large inclusions. For the conditions modeled, the flow pattern reaches steady state soon after a new ladle opens, but the temperature and inclusion distributions continue to evolve even after 1.3 residence times. The removal of inclusions does not appear to depend on the tundish aspect ratio for the conditions and assumptions modeled. It is hoped that this work will inspire future measurements and the development of more comprehensive models of inclusion removal. These validated models should serve as powerful quantitative tools to predict and optimize inclusion removal during molten steel processing, leading to higher quality steel.     

选区激光熔化工艺参数对气雾化 316L不锈钢粉末成形制品性能的影响

本研究系统考察了激光功率和扫描速度对316L不锈钢粉末选区激光熔化工艺成形熔道、制品微观组织及力学性能的影响,并分析了各类缺陷的形成原因。研究结果表明:在低激光功率和高扫描速度条件下,熔道中出现了大量球状颗粒,这些颗粒之间的空隙恶化了下一层粉末的熔化条件,这正是成形制品中熔道分布混乱以及孔洞、裂纹产生的根本原因,进而导致成形制品力学性能降低;在高激光功率和低扫描速度条件下,熔池快速升温/冷却的热应力作用增强,使得成形制品的熔道交界处也存在孔洞和裂纹等缺陷。在本研究实验条件下,激光功率为350 W,扫描速度为1750 mm/s时,SLM成形制品的力学性能最为优异,其中抗拉强度为731 MPa、屈服强度为638 MPa、断后伸长率为40.0%,致密度为96.27%。     

Vacuum Refining of Molten Silicon

Metallurgical fundamentals for vacuum refining of molten silicon and the behavior of different impurities in this process are studied. A novel mass transfer model for the removal of volatile impurities from silicon in vacuum induction refining is developed. The boundary conditions for vacuum refining system??the equilibrium partial pressures of the dissolved elements and their actual partial pressures under vacuum??are determined through thermodynamic and kinetic approaches. It is indicated that the vacuum removal kinetics of the impurities is different, and it is controlled by one, two, or all the three subsequent reaction mechanisms??mass transfer in a melt boundary layer, chemical evaporation on the melt surface, and mass transfer in the gas phase. Vacuum refining experimental results of this study and literature data are used to study the model validation. The model provides reliable results and shows correlation with the experimental data for many volatile elements. Kinetics of phosphorus removal, which is an important impurity in the production of solar grade silicon, is properly predicted by the model, and it is observed that phosphorus elimination from silicon is significantly increased with increasing process temperature.     

Numerical Simulation of Pressure Infiltration Process for Making Metal Matrix Composites Using Dual-Scale Fabrics

Correct modeling of flow and solidification of metal melt in the pressure infiltration process (PIP) is important for accurate simulation and process optimization of the mold-filling process during the making of metal matrix composites. The fiber reinforcements used in this process often consist of fiber tows or bundles that are woven, stitched, or braided to create a dual-scale preform. The physics of melt flow in the dual-scale preform is very different from that in a single-scale preform created from a random distribution of fibers. As a result, the previous PIP simulations, which treat the preform as being single scale, are inaccurate. A pseudo dual-scale approach is presented where the melt flow through such dual-scale porous media is modeled using the conventional single-scale approach using two distinctly different permeabilities in tows and gaps. A three-dimensional finite difference model is developed to model the flow of molten metal in the dual- and single-scale preforms. To track the fluid front during the mold filling and infiltration, the volume of fluid method is used. A source-based method is used to deal with transient heat transfer and phase changes. The computational code is validated against an analytical solution and a published result. Subsequent study reveals that infiltration of an idealized dual-scale preform is marked by irregular flow fronts and an unsaturated region behind the front due to the formation of gas pockets inside fiber tows. Unlike the single-scale preform characterized by sharp temperature gradients near mold walls, the dual-scale preforms are marked by surging of high-temperature melts between tows and by the presence of sharp gradients on the gap-tow interfaces. The parameters such as the (gap-tow) permeability ratio, the (gap-tow) pore volume ratio, and the inlet pressure have a strong influence on the formation of the saturated region in the dual-scale preform.     

Slag eye formation in single and dual bottom purged industrial steelmaking ladles

ABSTRACT

Argon gas is often injected from the bottom of the ladle during steel refining operations. The injected gas interacts with the liquid (metal and slag) bath and enhances the momentum, heat, and mass transfer rate in the melt. However, during these gas–liquid interactions, an opening of the slag layer called slag eye is formed, which exposes the molten metal surface to the atmosphere, which is generally undesirable. In the current work, a transient, three-dimensional mathematical model is used to study the turbulent gas–liquid interactions in single as well as dual bottom blown industrial steelmaking ladles. A Coupled Level Set Volume of Fluid (CLSVOF) model is used for tracking the steel-argon, steel-slag, and argon-slag interfaces, from which the slag-eye area has been predicted. It is found that the inlet gas purging rate, melt height, slag layer thickness, angular and radial positions of the gas inlets affect the slag opening area. Non-dimensional empirical correlations are proposed to predict the slag opening area in both single as well as dual purged ladles, using non-linear regression analysis.     

新型浮选机叶轮动力学性能及对粗颗粒浮选效果

为了进一步提高粗颗粒的浮选回收率,开发下一代浮选机叶轮是研究的重点之一.针对某钼矿粗粒级回收率低的问题,将一种新型浮选机叶轮应用到钼矿局部浮选流程中.通过开展浮选机动力学性能研究,对比分析新型浮选机叶轮的搅拌分散和分选效果.研究表明,新型浮选机叶轮提高了粗颗粒在槽体内的输送高度,从而促进了粗颗粒回收,在考查期内选厂钼总...     

利用超重力分离铝熔体中的夹杂颗粒

利用Al-17% Si-4.5% Cu熔体中密度较小的初生硅颗粒模拟金属熔体内部的夹杂物,并采用超重力场分离熔体中的夹杂颗粒,研究了不同重力系数条件下,金属熔体中夹杂物的分离规律.实验结果表明:经过超重力处理后,初生硅颗粒在试样上部区域发生明显的偏聚现象,试样内部出现无初生硅颗粒区域,且随着重力系数的增加,无初生硅颗粒的区域面积逐渐增大,说明重力系数越大,硅颗粒在试样上部区域的聚集程度越好.随着重力系数的增大,试样的净化效率逐渐升高,当重力系数（G）为500时,试样的净化率达到了84.98%.利用DPM离散相模型对超重力场下熔体内部硅颗粒的具体受力情况进行分析,并模拟研究铝熔体内部硅颗粒在不同重力场中的分离行为.数值模拟结果证明了夹杂颗粒在沿着超重力方向上的运动行为近似符合Stokes运动定律.这表明超重力场可以有效分离金属熔体中的夹杂物.      

中间包底吹氩行为的数值模拟

 根据某钢厂连铸中间包的实际操作参数，采用欧拉两相流模型，气体入口边界条件按照多孔介质进行处理，利用CFX软件模拟计算了底吹氩中间包内钢液的流场。结果表明:底吹氩气技术代替上挡墙或下挡墙2种情况下，注入区钢液混合加剧，有利于夹杂物碰撞长大。浇注区靠近液面处速度提高易引起卷渣。当采用湍流控制器、上挡墙、下挡墙、底吹氩技术时，吹氩位置对钢液流动的影响较大，当在湍流控制器和上挡墙之间吹入气体时，钢液的流动特性有利于夹杂物的上浮去除。     

Separation of Non-metallic Inclusions from a Fe-Al-O Melt Using a Super-Gravity Field

An innovative method for separating non-metallic inclusions from a high temperature melt using super gravity was systematically investigated. To explore the separation behavior of inclusion particles with densities less than that of metal liquid under a super-gravity field, a Fe-Al-O melt containing Al₂O₃ particles was treated with different gravity coefficients. Al₂O₃ particles migrated rapidly towards the reverse direction of the super gravity and gathered in the upper region of the sample. It was hard to find any inclusion particles with sizes greater than 2 μm in the middle and bottom areas. Additionally, the oxygen content in the middle region of the sample could be reduced to 0.0022 mass pct and the maximum removal rate of the oxygen content reached 61.4 pct. The convection in the melt along the direction of the super gravity was not generated by the super-gravity field, and the fluid velocity in the molten melt consisted only of the rotating tangential velocity. Moreover, the motion behavior of the Al₂O₃ particles was approximatively determined by Stokes’ law along the direction of super gravity.     

Mass transfer in intermediate ladles of continuous-casting machine

The removal of alumina particles from steel is considered for two configurations of a (90–100)-t intermediate ladle. Mass transfer is analyzed on the basis of simultaneous solution of the convective-diffusion equations of the inclusions in the melt and equations describing melt flow within the ladle, taking account of turbulence. An innovation in the assessment of the mass-transfer coefficient between the alumina particles and the refining flux is the concept of wave flow of a thin liquid-flux film as it interacts with the rough surface of the sintered slag. The removal of alumina particles (10–100 μm) from the metal is assessed.     

An improved lance design for hot metal de-sulphurisation

Hot metal de-sulphurisation is a dip-lance process involving the pneumatic injection of fine-grained de-sulphurisation reagents into the molten metal. For maximum efficiency the particles must be dispersed in the ladle as widely as possible to increase the total interfacial area which is primarily controlled by the lance design. Seven different lance configurations were modelled and simulated to determine the most efficient design using physical and mathematical modelling approach. A 0.25 scale plexi-glass model of the 100?T hot metal ladle was fabricated for the study. Residence time and mixing time studies were carried out using the electrical conductivity measurement technique through stimulus response of injected saturated salt solution. Mathematical modelling approach using momentum balance was used to simulate fluid flow profile of lance-ladle assembly under operating conditions using computational fluid dynamics package ANSYS-CFX. Based on the studies a new curved port lance has been designed which resulted in uniform and swirling flow profile inside the ladle without rotating the lance. Injection through the new lance increased the residence time of the particles and reduced the dead zones. The new design was fabricated and experimented at de-sulphurisation stations and has resulted in reduced flux consumption and treatment time.     

Computational Fluid Dynamic Modeling of Zinc Slag Fuming Process in Top-Submerged Lance Smelting Furnace

Slag fuming is a reductive treatment process for molten zinciferous slags for extracting zinc in the form of metal vapor by injecting or adding a reductant source such as pulverized coal or lump coal and natural gas. A computational fluid dynamic (CFD) model was developed to study the zinc slag fuming process from imperial smelting furnace (ISF) slag in a top-submerged lance furnace and to investigate the details of fluid flow, reaction kinetics, and heat transfer in the furnace. The model integrates combustion phenomena and chemical reactions with the heat, mass, and momentum interfacial interaction between the phases present in the system. A commercial CFD package AVL Fire 2009.2 (AVL, Graz, Austria) coupled with a number of user-defined subroutines in FORTRAN programming language were used to develop the model. The model is based on three-dimensional (3-D) Eulerian multiphase flow approach, and it predicts the velocity and temperature field of the molten slag bath, generated turbulence, and vortex and plume shape at the lance tip. The model also predicts the mass fractions of slag and gaseous components inside the furnace. The model predicted that the percent of ZnO in the slag bath decreases linearly with time and is consistent broadly with the experimental data. The zinc fuming rate from the slag bath predicted by the model was validated through macrostep validation process against the experimental study of Waladan et al. The model results predicted that the rate of ZnO reduction is controlled by the mass transfer of ZnO from the bulk slag to slag–gas interface and rate of gas-carbon reaction for the specified simulation time studied. Although the model is based on zinc slag fuming, the basic approach could be expanded or applied for the CFD analysis of analogous systems.