Prediction of gas‐liquid two‐phase mixture flow in a vertical pipe with a sudden expansion in diameter

The principle of gas‐lift pumps is applied to vacuum‐decarburization with the RH (Ruhrstahl Heraeus) process to circulate molten steel. Gas‐lift pumps are also applicable to the transportation of molten iron/steel between different refining processes. This paper treats theoretical analysis of steady‐state flow characteristics of gas‐liquid two‐phase mixtures rising in a vertical pipe with an abrupt expansion of its diameter. The system of governing equations is based upon a one‐dimensional multi‐fluid model. Flow pattern transitions are taken into consideration. A new numerical procedure to predict the flow characteristics at the sudden expansion has been proposed. Experiments have also been performed for several conditions to confirm the applicability as well as the validity of the present numerical model. It has been found that the predictions agree reasonably well with the experimental data. Next, the effect of the sudden expansion of pipe diameter on the pump performance was investigated numerically. As a result, it has been confirmed that the sudden expansion of pipe diameter contributes to improve the pump efficiency.     

Physical and mathematical models of steel flow and heat transfer in a tundish heated by plasma

Temperature control of liquid steel by plasma heating is physically and mathematically modeled. A dimensionless plasma heating number is employed for scaling up of heating operations between a steam jet for water model and a plasma prototype. Overall responses of step-input temperatures in steel are fairly well predicted by the physical model. Fluid-flow structure and thermal fields, in terms of dimensionless temperatures, of steel are different from those of water. Two positions of plasma in a tundish were studied, centered and off-centered. The second position decreased the heating response of a plasma, although a more homogeneous thermal field was obtained in regard to the first position. Consequently, a centered position offered a faster thermal response than the off-centered one. Flow controllers decreased the efficiency of plasma due to the formation of stagnant zones located in their proximity, which were not active enough to exchange momentum and heat with the bulk flow.     

Physical and mathematical modelling of tundish flows using digital particle image velocimetry and CFD‐methods

The flow in continuous casting tundishes is considerably responsible for the flotation of non‐metallic inclusions and the quality of steel. Because tests in liquid steel can hardly be performed, water model testing considering the geometric and dynamic similarity laws is often used. Here, quantitative investigations with time and cost expensive laser measurement techniques are possible. The digital particle image velocimetry (DPIV) can be seen as a completion and is an effective method to obtain reliable results.     

The investigations of gas‐powder two phase flow in packed bed

Gas‐powder two‐phase flow in packed beds was investigated and the results are presented in this paper. The experimental system, in which the glass powder and air gas were injected into the lower part of the packed bed allowed the estimation of the influence of gas velocity, powder feed rate, powder and packed particles diameter on pressure loss and total hold up of powder in the packed bed. On the base of the experimental results, a one‐dimensional mathematical model for gas‐powder two‐phase flow in the packed bed was developed. This model allows satisfactory prediction of the pressure loss and the hold ups of powders. The maximum deviation between calculated and measured values was less than ±15%. Futhermore, the conditions when the blockade of the flow occurs were defined. The additional pressure loss (expressed by F_k) due to the gravitional force of powders and the collision and the friction between powders and packed particles, was correlated with Froude number as: for the void fraction in the packed bed ?₀ of between 0.36 to 0.41 or .     

Review of mathematical models of fluid flow,heat transfer,and mass transfer in electroslag remelting process

Abstract

The electroslag remelting (ESR) process has been used effectively to produce large ingots of high quality based on the controlled solidification and chemical refining that can be achieved. Despite the widespread application of industrial facilities, there are still issues that prevent an effective control of the process. This is particularly critical considering the large ingots produced industrially which makes the traditional trial and error approach prohibitively expensive. Thus, mathematical models of the process are a good alternative as a process control tool. To predict the relationship between operating parameters such as power input and type, fill ratio, depth of electrode immersion, and slag chemistry and the casting rate, microstructural features, and ingot chemical composition, it is then necessary to develop mathematical models based on differential equations describing the fluid flow, heat transfer, and mass transfer phenomena that take place during the process. In the present paper, mathematical models of the transport phenomena occurring during ESR are reviewed. Although the models have evolved to a point where several features of the process can be predicted and the dominant transport mechanisms have been elucidated, more effort is required before the models can be applied to define actual operating conditions.     

薄带连铸熔池波动特性的物理数值模拟研究

薄带连铸生产铸带过程中,熔池波动大小对铸带质量影响较大,而引起波动的主要因素来自浇铸本身的工艺特性及外部设备影响。针对宝钢的薄带连铸机组,按照相似准数建立了1∶1水模型装置,测定了吐出孔位置的液面波动情况。与此同时,采用湍流双方程模型及VOF方程建立了配套水模型的液面波动模型,利用该模型研究了结晶辊静止时,布流器吐出孔位置的熔池液面波动情况。结果表明,不考虑结晶辊转动时,波动主要由吐出孔流出的钢水引起,波动形式比较单一。此外,该研究考虑了铸带拉速、吐出孔浸入深度、吐出孔倾斜角度等因素对熔池液面波动的影响,并将计算模拟结果与水模型结果进行了对比,两者吻合较好。     

Manganese and silicon activities in liquid carbon‐saturated Mn‐Si‐C alloys

The vapour pressure and activity of manganese were determined by a transportation method for carbon‐saturated Mn‐Si‐C alloys with different Si contents. 108 individual experiments were carried out in a vertical graphite tube furnace, normally at 1500 °C. Modified Gibbs‐Duhem relations were proposed to calculate the corresponding silicon activities. The present results agree well with similar studies for carbon‐saturated Mn‐Si‐C alloys.     

Simplified mathematical models of heat transfer in continuous fuel-fired furnaces

Introduction of the model based on the equations of radiative and convective heat transfer connected with equation of heat conduction in stock. Walking beam, roller-hearth and pusher furnaces. Radiative transport coefficients, mean beam lengths and configuration factors computation. Examples of furnace calculation. Use of the generalized temperature response charts.     

Physical and mathematical modelling of flow and residence time distributions in different tundish designs

A steady state, three‐dimensional, turbulent flow model has been developed in‐house for analysis of melt flow and residence time distribution phenomena in steelmaking tundish system. The governing equations of flow, turbulence and tracer dispersion were derived in terms of the Cartesian co‐ordinate systems and solved numerically with their associated boundary conditions adapting a control volume based finite difference procedure. In the numerical solution scheme, the pressure‐velocity coupling was treated via the popular Simple (semi implicit method for pressure linked equations) algorithm. Prior to carrying out elaborate numerical predictions for tundish geometry, the model was applied to several standard test problems and evaluated against corresponding bench mark results. Thus, several typical test problems such as, flows in a cubic cavity, flows in ducts of rectangular cross‐section, flow over flat plate and so on were simulated numerically to assess the adequacy and appropriateness of the computational procedure developed. Results thus obtained together with the bench mark solutions indicated that the mathematical model is internally consistent and sufficiently robust. Accordingly, the turbulent flow model was applied to simulate flow and Residence Time Distributions (RTD) in four different tundish designs . These included, a single strand and a two strand slab casting tundish systems, a six strand rectangular shaped tundish and a six strand delta shaped billet casting tundish. Various RTD parameters (e.g., minimum break through time, t_min, time at which peak concentration occurs, t_peak and average residence time, t_av) were computed numerically in the four tundish systems and these were subsequently compared with corresponding experimental measurements derived from equivalent water model tundish systems. Except for the single strand tundish system, large differences between measurements and prediction (particularly on t_min and t_peak) were noted for the other three tundish geometries. Furthermore, the extent of such discrepancy was found to be relatively more pronounced for the multi‐strand tundish system. The possible reasons for such discrepancy is discussed in the text and it was shown computationally that relatively better agreement between theory and measurement can be achieved if, instead of the high Reynolds number k‐ε turbulence model, a low Reynolds number turbulence model is applied in the computational procedure.     

Physical modeling of liquid/liquid mass transfer in gas stirred ladles

Several of the metallurgical reactions occurring in gas stirred steel ladles are controlled by liquid phase mass transfer between the metal and slag. In order to calculate the rate of these reactions, information about the two phase mass transfer parameter is necessary. The mass transfer between two immiscible liquids, oil and water simulating slag and steel, respectively, was measured in a scale model of a ladle. The mass transferred species was thymol which has an equilibrium partition ratio between oil and water similar to that for sulfur between slag and metal. The mass transfer rate was measured as a function of gas flow rate, tuyere position and size, method of injection, oil viscosity, and oil/water volume ratio. In addition, mixing times in the presence of the oil layer and mass transfer coefficient for the dissolution of solid benzoic acid rods were measured. The results show that there are three gas flow rate regimes in which the dependence of mass transfer on gas flow rate is different. At a critical gas flow rate, the oil layer breaks into droplets which are entrained into the water, resulting in an increase in the two phase interfacial area. This critical gas flow rate was found to be a function of tuyere position, oil volume, densities of two phases, and interfacial tension. Two phase mass transfer for a lance and a tuyere was found to be the same for the same stirring energy in low energy regions regardless of lance depth. Mass transfer is faster for a center tuyere as compared to an offcenter tuyere, but mixing times are smaller for the offcenter tuyere. From the results obtained, the optimum stirring conditions for metallurgical reactions are qualitatively discussed. SEON-HYO Kim, formerly Graduate Student in the Department of Metallurgical Engineering and Materials Science, Carnegie Mellon University.     

八流大方坯连铸中间包结构优化的物理和数值模拟

结合某钢厂八流大方坯连铸中间包生产现状,基于物理模拟与数值模拟方法,对中间包内钢水流动特性及温度场进行了研究.物理模拟结果表明:原中间包因各流水口距长水口冲击点距离不等,导致各流响应时间及停留时间差别增大,各流钢水温差扩大,死区体积分率偏高,影响了铸坯质量和生产顺行.此外,原中间包稳流器因内腔体积小,注流过程中存在包壁冲刷严重等问题.采用优化控流方式后,死区体积比率由优化前的37.5%减小至19.0%,各流响应时间标准差由58降至15,各流停留时间标准差由185降至68,流动一致性得到显著改善.同时,中间包内最大温差降低至4 K,各水口间最大温差降至1 K,包内温度分布更趋均匀.此外,扩大稳流器内腔容积减小了对包壁的冲刷.     

A mathematical model of the dynamics of scrapie in a sheep flock

A mathematical model is developed for the dynamics of an outbreak of scrapie in a single sheep flock with the aim of assisting the interpretation of field data. The model incorporates age structure of the sheep population, both horizontal and vertical transmission, genetic predisposition to infection, variable initial load of the infectious agent, and increasing infection load during an incubation period of the same order as sheep life expectancy. This leads to system of partial differential equations with respect to time, age and infection load. Numerical analyses using this model demonstrate that a scrapie outbreak is likely to be of long duration (several decades), will lead to reduction of scrapie susceptible allele frequency (but not to zero), and has different dynamics in homozygous and heterozygous susceptible sheep, even if these genotypes are equally susceptible, due to the different contributions of vertical infection to transmission to genotypes.     

Influence of the Stirring Gas in a 170‐t Ladle on Mixing Phenomena – Formation and On‐line Control of Open‐Eye at an Industrial LD Steel Plant

3D calculations with Computational Fluid Dynamics were carried out to evaluate the flow pattern under industrial conditions with different gas flow rates at the steel plant of Saarstahl AG. The generated flow pattern consists of a circulating loop characterised by an upward flow driven by the argon gas and a downward flow close to the wall on the opposite side of the porous plug in the case of a gas flow rate of 27 STP m³/h. When this high gas flow rate is used, the gas bubbles are taking a straight way from the inlet, but further up the momentum from the circulating steel is affecting the path of the gas bubbles followed by a breakthrough zone at the top surface. Intensive experiments with the 170‐t ladle of Saarstahl AG revealed typical open‐eyes. Large open‐eyes coupled with turbulences in the surface were generated in the case of gas flow rates between 20 and 30 STP m³/h. Intensive turbulences and even smoke formation were identified when a gas flow rate of > 30 STP m³/h was applied. For the investigation of the influence of gas stirring processes on the mixing phenomena samples were taken from the melt immediately after alloying. It could be seen that the analyses of Al, C, Mn and Si increased to the target analyses due to alloying and introduction of Ar through the porous plug. The total time for complete alloying depended on the elements within these experiments. It seemed to be that the alloying time increased in the order of Al, C, Mn and Si. For on‐line control and analysis of open‐eyes in the melt surface during ladle stirring, a BFI image processing system was installed at the steel plant of Saarstahl. It consisted of a conventional digital camera equipped with an infrared filter and coupled to an image processing software. Primary tests showed a slight influence of the open‐eye diameter at the end of the ladle treatment on inclusion densities in the liquid steel and oxidic K0 values of the finished wire rod. Additional experiments were performed but only a small correlation existed between the stirring energy at the end of ladle treatment and the inclusion length index of the applied blue brittle tests. But as soon as an open‐eye came into existence, the inclusion length was higher compared to those heats produced under a closed top slag.     

Thermodynamic study on phase equilibria in the liquid Fe‐S‐O system

The phase equilibria and thermodynamic properties of the Fe‐S‐O melt at 1273 – 1573 K were investigated by employing thermochemical equilibration technique. The γ‐Fe+liquid region was extended to higher sulphur content region than that of literature. The solubility of FeS in slags decreased with increasing the activity of FeO and the solubility slightly decreased with increasing temperature. The activity of FeO exhibited a negative deviation from ideality in the composition with a molar mass fraction of less than about 60 % FeO, while a positive deviation was observed at X_FeO > 0.6. However, the activity of FeS exhibited a positive deviation from ideality at 1273 K, and a nearly ideal behaviour at 1573 K, respectively. The enthalpy changes of mixing were calculated to be some positive value. The sulfur content in reduced solid iron decreased from about 110 to 70 ppm at 1273 K as the ratio FeO/FeS in slag increased up to the composition doubly saturated by Fe/FeO, while the sulfur content decreased from about 400 to 150 ppm at 1573 K. The oxygen content in reduced solid iron increased to about 3 ppm at 1273 K with increasing FeO/FeS ratio up to the composition saturated by FeO.