Decarburization of Levitated Fe-Cr-C Droplets by Carbon Dioxide

Experiments have been conducted at 1873 K (1600 °C) to study the kinetics of decarburization of Fe-Cr-C levitated droplets containing 10, 17, and 20 wt pct Cr using argon–carbon dioxide gas mixtures containing up to 30 pct CO₂, at flow rates of 100, 1000, 3000 and 12200 mL min^?1. It was found that chromium did not have a strong influence on the kinetics of decarburization while showing only minor effects on the extent of carbon removal. The results indicate that, for high carbon concentrations in the melt, the decarburization rates were controlled by mass transfer in the gas phase. Conventional formulation of governing mass transport numbers did not adequately describe the experimental observations made in this work. The observed rates are consistently higher than the values predicted using either the Ranz–Marshall correlation or the Steinberger–Treybal equation. A new correlation has been proposed to express the decarburization kinetics of levitated droplets for gas-flows in the range of Reynolds numbers between 2 and 100. The experimentally-derived model was found to be in excellent agreement with rate data derived from studies conducted by other researchers using levitated droplets.     

Magnetohydrodynamic Modeling and Experimental Validation of Convection Inside Electromagnetically Levitated Co-Cu Droplets

A magnetohydrodynamic model of internal convection of a molten Co-Cu droplet processed by the ground-based electromagnetic levitation (EML) was developed. For the calculation of the electromagnetic field generated by the copper coils, the simplified Maxwell’s equations were solved. The calculated Lorentz force per volume was used as a momentum source in the Navier–Stokes equations, which were solved by using a commercial computational fluid dynamics package. The RNG k-ε model was adopted for the prediction of turbulent flow. For the validation of the developed model, a Co₁₆Cu₈₄ sample was tested using the EML facility in the German Aerospace Center, Cologne, Germany. The sample was subjected to a full melt cycle, during which the surface of the sample was captured by a high-speed camera. With a sufficient undercooling, the liquid phase separation occurred and the Co-rich liquid phase particles could be observed as they were floating on the surface along streamlines. The convection velocity was estimated by the combination of the displacement of the Co-rich particles and the temporal resolution of the high-speed camera. Both the numerical and experimental results showed an excellent agreement in the convection velocity on the surface.     

铁碳金属颗粒与熔渣的反应

对ＣａＯ－ＳｉＯ２－Ａｌ２Ｏ３－ＦｅＯ熔渣体系与铁碳金属颗粒反应的脱碳反应速率及脱碳反应限度进行了研究。在实验条件下,脱碳反应速率随金属颗粒初始碳含量及熔渣中氧化亚铁含量的增加而增大。金属颗粒终点碳含量随熔渣中氧化亚铁含量的增加而降低,但反应最终远未达到平衡状态。当反应坩埚内壁衬有金属钼片时,金属颗粒的终点碳含量可以降到极低的水平。因而推断：在低碳含量范围内,熔渣中电子的传递能力对反应起着非常重要的作用     

The Decarburization Kinetics of Metal Droplets in Emulsion Zone

Metallurgical and Materials Transactions B - A mathematical model has been developed to predict the decarburization rate within individual droplets in the emulsion zone. All the chronological...     

Dephosphorization of Levitated Silicon-Iron Droplets for Production of Solar-Grade Silicon

The treatment of relatively inexpensive silicon-iron alloys is a potential refining route in order to generate solar-grade silicon. Phosphorus is one of the more difficult impurity elements to remove by conventional processing. In this study, electromagnetic levitation was used to investigate phosphorus behavior in silicon-iron alloy droplets exposed to H₂-Ar gas mixtures under various experimental conditions including, refining time, temperature (1723 K to 1993 K), gas flow rate, iron content, and initial phosphorus concentration in the alloy. Thermodynamic modeling of the dephosphorization reaction permitted prediction of the various gaseous products and indicated that diatomic phosphorus is the dominant species formed.     

RH MFB精炼过程脱碳数学模型及工艺研究

 为研究RH MFB精炼工艺对脱碳过程的影响，将脱碳机理确定为钢液本体脱碳与CO克服静压力上浮、氩气泡表面脱碳和飞溅液滴脱碳，根据脱碳反应动力学和质量守恒原理建立了RH MFB脱碳数学模型。计算结果表明：降低初始碳含量、增大初始氧含量可使脱碳终点碳含量降低；提高压降速率和吹氩流量、增大浸渍管内径使得脱碳速率增大；在固定氧气流量下，随着吹氧时间的延长，脱碳终点碳含量降低，但脱碳终点氧含量升高。     

数学建模思想融入《数学分析》教学

数学素质和创新能力是现代数学教育的目标,将数学建模的思想方法融入<数学分析>教学,从教学的主要环节提出了渗透数学建模思想方法的一些方法和实践.     

旋转磁场作用下真空精炼超低碳钢脱碳过程的模拟分析

建立RH装置内钢液流动与脱碳过程耦合的数学模型,采用均相流模型提出一种新的流场计算方法,避免了先前的一些不具推广性的模型与方法,如简化计算区域或者预先规定含气率分布等.应用该模型对有、无旋转磁场作用时的RH系统进行了模拟计算,模拟结果表明:流场和脱碳过程与文献中实验结果相符合;有旋转磁场作用时,脱碳速度比无磁场作用时明显增加.造成这一现象的主要原因是:①旋转磁场作用下,RH系统的循环流量得到了提升,循环流量是影响脱碳速度的最主要因素;②旋转磁场增加了RH系统内的搅拌能,即增加了碳的容积传质系数,从而增加了脱碳速度.     

Mathematical Modelling of Non‐equilibrium Decarburization Process during Vacuum Circulation Refining of Molten Steel: Mathematical Model of the Process

The characteristics of the non‐equilibrium decarburization process during the vacuum circulation (RH) refining of molten steel have been considered and analysed. On the basis of the fundamentals of metallurgical reaction engineering and non‐equilibrium thermodynamics, as well as the two‐fluid model for gas‐liquid two‐phase flow and a modified k‐? model for turbulent flow, a novel three‐dimensional mathematical model for the process has been proposed and developed. The details of the model, including the establishment of the governing equations and the especially modified two‐equation k‐? model, the determination of the appropriate source terms and boundary conditions and others, have been presented. The related parameters of the model have been discussed and determined for the decarburization refining process of molten steel in a 90‐t multifunction RH degasser under RH and RH‐KTB operating conditions.     

Mathematical Modeling of Lake Tap Flows

A lake tap is the submerged piercing of a tunnel at the intake to connect the reservoir to the tunnel system. It is referred to as a dry lake tap if the tunnel is dry before the blasting of the last rock plug at the tunnel entrance. Transient state conditions in the tunnel following a dry lake tap are modeled using the lumped and distributed-system approaches. Fourth-order Runge-Kutta method and the method of characteristics are used in the lumped-system model and distributed-system models, respectively. The results computed by the lumped and distributed-system approaches agree with one another. Pressures computed by using distributed-system and lumped-system models are compared with the experimental results available in literature for rapid filling of a pipeline with closed end. The rate of dissipation of pressure oscillations in the measured air pressure during prototype lake tap at Crater Lake Snettisham project in Alaska, and in the experiments reported in the literature is higher than that computed by the mathematical models using steady state friction and constant wave velocity.     

高碳钢65Mn脱碳研究

文章对高碳钢65Mn脱碳行为进行研究讨论,从加热温度、保温时间、炉内气氛等各方面分析了高碳钢加热过程中脱碳层变化规律,为高碳钢加热制度提供理论研究依据。     

Modelling Decarburization in Electrical Steels

A model is presented to predict the decarburization rate of electrical steels during reactive annealing. In a first step, the warm annealing atmosphere composition is calculated as function of the composition of the cold gas containing N₂‐H₂‐H₂O‐CO‐CO₂‐CH₄‐O₂. In a second step, the decarburization kinetics, which is controlled both by the surface reaction and by the diffusion of carbon towards the surface, is calculated. The model is then used to study the balance between surface reaction and the diffusion control of the decarburization process. We could conclude that for low sheet thickness and/or low H₂O/H₂ ratio in the annealing atmosphere, the decarburization is surface reaction controlled, while for commercial thicknesses and industrially applied dew points, the process is diffusion controlled. Furthermore, we looked at the difference in decarburization between complex N₂‐H₂‐H₂O‐CO‐CO₂ atmospheres used in industrial application, and N₂‐H₂‐H₂O atmospheres typically used in lab annealing. We could conclude that the decarburization rate is influenced by the addition of CO and CO₂ and that the final carbon level is increased if CO and CO₂ are added to the gas.     

数学建模方法在图书采购管理的应用

文章利用横向的数学建模和纵向的条件分类方法,对现今的采购管理进行了一定的分析,给出了相应的解决方法。在横向给出了同一类图书的几个重要的比较要点。通过两个方面的比较,使有限的资金得到最大的使用。     

Mathematical Modeling of VOD Oxygen Nozzle Jets

This study has focused on numerically exploring the oxygen flow in the convergent‐divergent De Laval nozzle. The De Laval nozzle has been commonly used as oxygen outlet at the lance tip in the vacuum oxygen decarburization (VOD) process. The nozzle geometry used in an active VOD plant was investigated by isentropic nozzle theory as well as by numerical modeling. Since an optimal nozzle design is only valid for a certain ambient pressure, one VOD nozzle will be less efficient for a large part of the pressure cycle. Different ambient pressures were used in the calculations that were based on the De Laval nozzle theory. Flow patterns of the oxygen jet under different ambient pressures were studied and the flow information at different positions from the nozzle was analyzed. In addition, the study compared the effects of different ambient temperatures on jet velocity and dynamic pressure. The predictions revealed that the modeling results obtained with the CFD modeling showed incorrect flow expansion, which agreed well with the results from the De Laval theory. Moreover, a little under‐expansion is somewhat helpful to improve the dynamic pressure. The jet dynamic pressure and its width for the specific nozzle geometry have also been studied. It has been observed that an altering ambient pressure can influence the jet momentum and its width. In addition, a high ambient temperature has a positive effect on the improvement of the jet dynamic pressure.     

Thermodynamics of the carbides in the system Fe-Cr-C

Phase relations in the Fe-Cr-C system in the temperature range 900 to 1150°C have been studied using metallographic and X-ray methods and the electron microprobe. An isothermal section of the phase diagram at 1000°C is shown. Lattice dimensions of the three carbides were determined for several values of the ratio Cr:(Fe +Cr). The solubilities of the carbides at each temperature were determined by metallographic study of quenched specimens. The distribution of Cr between austenite (γ) and the several carbides was determined by use of the electron microprobe. Data of Wada et al on the activity of carbon were used to calculate activities at the y-phase boundary and the free energy of the several carbides as a function of their chromium content. The data are treated thermodynamically on the basis of assumed random mixing of Cr and Fe atoms in each carbide. While this randomness was not definitely proved, the assumption was shown to be reasonable and the results useful. Extrapolation to 0 and 100 pct Cr gives values for the standard free energy of Cr₇C₃ and the hypothetical carbides Cr₃₆C, and Fe₇C₃. Formerly with the Research Staff, Massachusetts Institute Technology     

Mathematical Modeling and Simulation of Dissolvable Hydrogels

Hydrogels have a large number of potential applications in microelectromechanical technology as sensors and actuators. In this paper we try to understand the physics of dissolvable hydrogels and investigate the various parameters controlling the dissolution process. Hydrogels, crosslinked via disulfide bonds, when immersed in a solution containing the disulfide cleaving agent can break covalent cross links causing the hydrogel to dissolve and thereby indicating the presence of the cleaving agent. Such a concept can be used to develop biochemical sensors, sacrificial structures in microfluidic systems, and other applications. The mechanism of the hydrogel dissolution process has been studied in detail and a mathematical model has been developed. From the vanishing time of the dissolvable hydrogel, a significant amount of qualitative and quantitative information about the solution can be obtained. A large number of factors governing the hydrogel dissolution process were investigated by simulations and experiments.