Mathematical Model for Growth and Removal of Inclusions in Molten Steel under Gas‐stirring Conditions

A three‐dimensional mathematical model has been developed to predict growth and removal of inclusions during gas stirring through eccentric tuyeres in a ladle. In the model, the efficiency of inclusion removal is investigated under three different collision mechanisms: Brownian, turbulent and Stokes collision. The Importance of the three approaches of wall adhesion, Stokes flotation and bubble adhesion on inclusion removal is analysed and the efficiency of inclusion removal through three types of tuyeres in central, eccentric and multi‐tuyere form is studied. The results indicate that inclusion growth resulting from turbulent collision is most important and the effect of Stokes collision is remarkable with increased inclusion size, while inclusion growth resulting from Brownian collision is negligible. Removal by Stokes flotation is the main mechanism for large inclusions, while inclusion removal by wall adhesion is negligible. The smaller the bubbles are, the higher the efficiency of inclusion removal is. The type of tuyere arrangement has a great effect on inclusion removal. Inclusion removal in a 135t ladle with one eccentric tuyere is more efficient than in a ladle with central tuyere or multi‐tuyere design.     

钢液中气泡和夹杂物的去除

熔池中钢液的流动、气泡以及夹杂物的大小都影响着钢液中夹杂物的去除率.研究表明,向上流动的钢液有利于夹杂物的上浮,几乎所有的夹杂物都能在钢液上升流中上浮.向下流动的钢液对夹杂物和气泡的上浮有阻碍作用,当气泡的直径小于1mm时其在钢液中将无法上浮.在钢包精炼吹氩过程中,应使用较小的吹氩量,一方面避免产生过大的气泡而降低底吹气体的利用效率,另一方面减小熔池内的钢液流速,促进气泡和夹杂物的上浮.但吹氩量也不宜过小,必须使气泡保持一定的尺寸来保证其充分上浮.在钢包精炼过程中选择吹氩量时,应综合考虑钢液流速和气泡大小的影响.     

Numerical Simulations of Inclusion Behavior in Gas-Stirred Ladles

A computation fluid dynamics–population balance model (CFD–PBM) coupled model has been proposed to investigate the bubbly plume flow and inclusion behavior including growth, size distribution, and removal in gas-stirred ladles, and some new and important phenomena and mechanisms were presented. For the bubbly plume flow, a modified k-ε model with extra source terms to account for the bubble-induced turbulence was adopted to model the turbulence, and the bubble turbulent dispersion force was taken into account to predict gas volume fraction distribution in the turbulent gas-stirred system. For inclusion behavior, the phenomena of inclusions turbulent random motion, bubbles wake, and slag eye forming on the molten steel surface were considered. In addition, the multiple mechanisms both that promote inclusion growth due to inclusion–inclusion collision caused by turbulent random motion, shear rate in turbulent eddy, and difference inclusion Stokes velocities, and the mechanisms that promote inclusion removal due to bubble-inclusion turbulence random collision, bubble-inclusion turbulent shear collision, bubble-inclusion buoyancy collision, inclusion own floatation near slag–metal interface, bubble wake capture, and wall adhesion were investigated. The importance of different mechanisms and total inclusion removal ratio under different conditions, and the distribution of inclusion number densities in ladle, were discussed and clarified. The results show that at a low gas flow rate, the inclusion growth is mainly attributed to both turbulent shear collision and Stokes collision, which is notably affected by the Stokes collision efficiency, and the inclusion removal is mainly attributed to the bubble-inclusion buoyancy collision and inclusion own floatation near slag–metal interface. At a higher gas flow rate, the inclusions appear as turbulence random motion in bubbly plume zone, and both the inclusion–inclusion and inclusion-bubble turbulent random collisions become important for inclusion growth and removal. With the increase of the gas flow rate, the total removal ratio increases, but when the gas flow rate exceeds 200 NL/min in 150-ton ladle, the total removal ration almost does not change. For the larger size inclusions, the number density in bubbly plume zone is less than that in the sidewall recirculation zones, but for the small size inclusions, the distribution of number density shows the opposite trend.     

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.     

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The phenomenon of inclusion removal by fine and uniform heterophases in the molten steel in the ladle was simulated in the water model. The movement behavior of small bubbles and inclusions was analyzed by using of high-speed video camera and image processing technology. Furthermore, the experiment in inclusion simulant removal by purifying agent in three ball-making modes was also carried out in the water model. The effects and causes of inclusion removal under different bubble generation method were analyzed to improve the cleanliness of molten steel. The results show that the purifying agent promotes the removal of inclusions. There is the phenomenon of the bubble capturing multiple inclusion simulants. The rate of inclusion removal by the heterophases at different time is higher than the rate of inclusion removal without small bubbles and the average number raises 13.66%. The composite sphere produced outer layer of purifying agent and the kernel of simulants is most likely to produce fine bubbles and to remove inclusions 100% in three ball-making modes. Because the bubbles are generated, the bubbles impact on the core material to promote cracking of the purifying agent, so more bubbles are generated.     

Physical Modelling of Inclusion Behaviour in Secondary Refining with Argon Blowing

The effects of gas blowing time and flow rate on inclusion removal in a ladle were quantitatively investigated. A physical model was developed where emulsion drops simulate the collision and aggregation of inclusions in steel. The results show that most of the inclusions can be removed within eight minutes at lower gas flow rates, whereas sixteen minutes are needed with larger gas flow rates. All the inclusions which had the possibility to be removed almost disappeared from the system in twenty‐eight minutes. Both the high and the low gas flow rates seemed to be efficient for inclusion removal, which was explained based on discussing the mechanism of inclusion removal by bubbles. In addition, it was found that the inclusion removal was in exponential relationship with gas blowing time.     

Numerical modelling of the transport and removal of inclusions in an industrial gas-stirred ladle

A full-scale, three-dimensional, transient CFD modelling approach capable of predicting the three-phase fluid flow characteristics and the inclusion removal in a gas-stirred ladle was developed. The comparison with experimental data indicates that this model can accurately predict the multiphase fluid flow and slag eye behaviour. The transport and removal of the inclusions in the gas-stirred ladle were predicted by tracing the movement of individual inclusions through computing their particle trajectories and considering a fluctuant top slag layer. The effects of inclusion size, gas flow rates, and injected bubble diameters as well as various removal mechanisms including slag capture, bubble attachment, and ladle wall adhesion on the removal of inclusions were investigated. It is shown that the slag capture is the prevailing mechanism for inclusion removal and the gas flow rate is the most important parameter for enhancing the inclusion removal efficiency.     

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.     

Numerical Simulation of Nonmetallic Inclusions Behaviour in Gas‐Stirred Ladles

The secondary refining of molten steel in gas‐stirred ladle has played a more and more important role in the production of high quality steel. In the present work, a mathematical model of the fluid flow and inclusions behaviour in a 150t gas‐stirred ladle was presented, and the variations in concentration, size and density for non‐metallic inclusions in the ladle during the refining process were predicted. The results show that during the refining process, the variations in the number density of the inclusions differed depending on size. The inclusions with a diameter less than 25 μm decrease during the whole period, while inclusions with diameter larger than 25 μm increase in the first stage of the treatment and gradually decrease during the later stage. After 15 minutes, all inclusions show a tendency to decrease, but the removal rate for inclusions of smaller size becomes slower. After treatment in the ladle, inclusions with a diameter larger than 50 μm were removed, the number of inclusions with a size between 30‐40 μm was not high, while inclusions that were smaller than 25 μm still remained in the molten steel. Two‐jet bubbling demonstrated an advantage over one‐jet for inclusion removal. The practice of bubbling argon with a higher gas flowrate initially, followed by a lower flowrate in the ladle was found to be beneficial for inclusions removal.     

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.     

Fundamental of Inclusion Removal from Molten Steel by Rising Bubble

The mechanism of inclusion removal by attachment to rising bubble was analyzed, and the movement behavior of inclusion, the mechanism of bubbles/inclusion interaction, collision probability and adhesion probability were discussed. A mathematical model of inclusion removal from molten steel by attachment to fine bubble was developed. The results of theoretical analysis and mathematical model showed that the optimum bubble diameter for inclusion removal is 1 to 2mm. A new method that argon is injected into the shroud from ladle to tundish during continuous casting has been proposed to produce fine bubble. It provides theoretical guides for production of super clean steel.     

长水口吹氩生成微小气泡工业实验研究

在连铸生产中采用大流量长水口吹氩,并采用“冷钢片沾钢法”沾取中间包钢液试样,成功沾取了中间包钢液中微小氩气泡。冷钢片沾样表面气泡为中间包上部钢/渣界面和炉渣中氩气泡,尺寸主要位于1.0~3.0 mm,但该尺寸不能反映中间包钢液内部长水口吹氩生成气泡,冷钢片沾样内部气泡为钢液内部长水口吹氩生成的气泡。结合扫描电镜和共聚焦显微镜对沾取试样内部气泡形貌、尺寸和数量进行了分析,结果表明大部分气泡为独立圆形气泡,偶见少量粘连和聚合气泡;钢液内部氩气泡尺寸主要位于100~1000 μm,平均尺寸为500 μm左右;气泡在长水口出口及其下方较为弥散,气泡数量可达15.2 cm?2。采用扫描电镜结合能谱分析,发现部分气泡内粘附有夹杂物,有些气泡粘附多个夹杂物;气泡粘附Al₂O₃夹杂物的几率高于粘附CaO(?MgO)?Al₂O₃?SiO₂复合夹杂物的几率。      

Coupling of CFD and PBE Calculations to Simulate the Behavior of an Inclusion Population in a Gas-Stirring Ladle

Gas-stirring ladle treatment of liquid metal has been pointed out for a long time as the processing stage is mainly responsible for the inclusion population of specialty steels. A steel ladle is a complex three-phase reactor, where strongly dispersed inclusions are transported by the turbulent liquid metal/bubbles flow. We have coupled a population balance model with CFD in order to simulate the mechanisms of transport, aggregation, flotation, and surface entrapment of inclusions. The simulation results, when applied to an industrial gas-stirring ladle operation, show the efficiency of this modeling approach and allow us to compare the respective roles of these mechanisms on the inclusion removal rate. The comparison with literature reporting data emphasizes the good prediction of deoxidating rate of the ladle. On parallel, a simplified zero-dimensional model has been set-up incorporating the same kinetics law for the aggregation rate and all the removal mechanisms. A particular attention has been paid on the averaging method of the hydrodynamics parameters introduced in the flotation and kinetics kernels.     

偏心底吹氩钢包内夹杂物行为的物理模拟

 选择乳状液滴作为模拟夹杂物,利用物理模型研究了偏心底吹氩钢包内夹杂物的物理行为,考察了时间、吹气量对夹杂物去除行为的影响规律。结果表明,较小气量在8 min内可将绝大部分的模拟夹杂物去除,而较大气量则需要16 min才能去除绝大部分的模拟夹杂物,所有气量在28 min内可将能够去除的模拟夹杂物几乎全部去除。在相对较短的吹气处理时间内,较小气量的去夹杂效果要优于较大气量。总体上看,存在一个获得去夹杂较佳效果的气量范围。     

吹氩精炼钢包内非金属夹杂物去除机理

 通过物理模拟试验,研究分析了底吹氩精炼钢包内夹杂物去除机理以及吹氩量对其的影响规律。结果表明：钢包中夹杂物的上浮主要是通过上升的钢液流携带,底吹氩量对夹杂物在钢包表面的钢-渣界面去除行为存在重要影响。吹氩量较小时,钢-渣界面稳定,夹杂物在浮力、毛细作用力等共同作用下穿过平坦的钢-渣界面而被吸收;吹氩量较大时,钢-渣界面波动大,渣眼周围发生卷渣,夹杂物被卷入的液滴吸收,随液滴进入渣层;吹氩量大,渣眼周围形成渣泡,夹杂物被渣泡吸收,随渣泡进入渣层。吹氩量达到一定时,夹杂物被钢-渣界面的吸收成为其被去除的限制性环节,且吹氩量较大时夹杂物去除效果最差,为实际吹氩精炼过程吹气量的控制提供了指导。     

钢包内气泡的形成与运动过程的数值模拟

 以钢包精炼底吹氩气过程中氩气泡为研究对象,运用VOF模型追踪氩气与钢液的界面,在层流条件下三维数值模拟了氩气泡的生成和运动过程。采用Tecplot进行模拟结果的后处理,研究了不同气体流量条件对气泡脱离直径的影响以及气泡的运动特性。模拟结果显示,氩气泡的形成历经膨胀、脱离两个阶段,气泡脱离直径随着气体流量的增加而增加,针对2 mm直径的孔口,其鼓泡流量上限为1.325 L/min。气泡从孔口脱离后历经近似球形、扁平的椭球形、规则的椭球形和不规则的球帽形的形状变化;气体流量越大,气泡的变形程度越剧烈,气泡位于钢包高度中上部位置时,全部呈现近似规则的球形,不随流量的改变而改变。     

Modelling Effect of Circulation Flow Rate on Inclusion Removal in RH Degasser

Based on the similarity principles,a 1∶ 7 scale physical model was established to study the behavior of molten steel flow and inclusion removal in a 145 t Rheinsahl-Heraeus( RH) degasser.On the basis of the quantitative measurements of the circulation flow rate and inclusion removal under various lifting gas flow rates,the effect of circulation flow rate on inclusion removal was investigated in the RH degasser.The inclusion removal rate shows the trend of first increase and then decrease twice with increasing the circulation flow rate when the circulation flow rates are smaller than 104.7 L/min.Whereas,the inclusion removal rate increases again with the further increase in circulation flow rate when the circulation flow rate is larger than 104.7 L/min.At lower circulation flow rates,inclusions are mainly removed by Stokes flotation to the slag/steel interface after inclusions are transferred near the slag/steel interface by the circulation flow.At higher circulation flow rates,the collision and aggregation of inclusions improves the inclusion removal efficiency.With the further increase in the circulation flow rate,inclusions are mainly removed by following the turbulent fluctuation( turbulent diffusion)to the slag/steel interface after inclusions are transferred near the slag/steel interface by the circulation flow.     

Regimes of Micro-bubble Formation Using Gas Injection into Ladle Shroud

Gas injection into a ladle shroud is a practical approach to produce micro-bubbles in tundishes, to promote inclusion removal from liquid steel. A semi-empirical model was established to characterize the bubble formation considering the effect of shearing action combined with the non-fully bubble break-up by turbulence. The model shows a good accuracy in predicting the size of bubbles formed in complex flow within the ladle shroud.     

板坯连铸中间包气幕挡墙夹杂物去除的研究

分析了中间包不加气幕挡墙和加气幕挡墙吹氩时夹杂物上浮速度与气泡直径、夹杂物直径和密度的关系。气泡尺寸对夹杂物的上浮速度影响比较明显,夹杂物的密度对上浮速度的影响不大。进行了中间包气幕挡墙的工业试验,试验表明:中间包底吹气对钢液中小夹杂物的去除作用不明显,而对大型的夹杂物去除效果显著。     

RH装置内夹杂物聚合与去除的三维数值模拟

 摘 要：基于RH精炼装置内流场,建立了一个研究夹杂物聚合与去除行为的三维数学模型。数值结果表明,夹杂物在钢包内上升管左侧存在一个侧“V”分布,上升管下方及下降管右侧均存在大的环状分布;夹杂物浓度和数量密度具有相似的空间分布;钢包内夹杂物的平均数量密度及浓度大于真空室内的平均值;夹杂物在气液两相区浓度较低;整个过程前400秒夹杂物去除最快,900秒后可去除大部分夹杂物,在处理后期,夹杂物平均特征尺寸有减小的趋势。