Mathematical model for post combustion in smelting reduction

Post combustion in the top space of iron bath smelting reduction furnaces is analysed with three-dimensional mathematical modelling. Momentum transport and continuity equations in combination with a k-? model of turbulence are numerically solved for the gas flow field. Combustion reactions are modelled by a set of transport equations based on the SCRS combustion model and its extension to the k-?-g model. A two-stage combustion scheme is formulated to include carbon transfer and combustion. Heat transfer to bath and droplets is approximated including radiation. Computation results for rectangular reactors are presented with velocity patterns and combustion fields. The complex shapes of post combustion flames are demonstrated. Process parameters are varied to study their influence on combustion and heat transfer to the bath. Effects of the injection geometry are illustrated.     

Mathematical Modeling of Fluid Flow in Bath during Combined Side and Top Blowing AOD Refining Process of Stainless Steel: Mathematical Model of the Fluid Flow

Considering that the liquid flow field under the conditions of the combined side and top blowing would be a combined result from the common action of the side blowing gas streams and a gas top blowing jet, as the first attempt, the three‐dimensional mathematical models for the flows of molten steel in an AOD converter bath during the simple side and top blowing processes have been proposed and developed, respectively. And the mathematical model of the flow in the bath during the combined blowing AOD refining process of stainless steel has been given by the composition and superposition of the two models. In the composed model, the gas‐liquid two‐phase flow is described and treated in terms of the two‐fluid (Eulerian‐Eulerian) model. The especially modified two‐equation k?ε model for the turbulence in the liquid phase is employed. And, the surface of the sunken pit formed by impact of the gas jet blown from a top lance at the central location of the bath liquid surface is regarded as a revolution paraboloid. The related details of the composed model are shown.     

On the numerical calculation and non-dimensional representation of velocity fields in bubble-stirred ladle systems

The numerical simulation of axisymmetric gas stirred ladle systems has been considered and a mathematical model based on the dimensionless form of the turbulent Navier-Stokes equations developed. Embodying a simplified turbulence model in the calculation procedure, it is demonstrated from the first principles that non-dimensional velocity components at relatively low gas flow rates, follow identical distribution patterns at equivalent dimensionless bath depths and radii, provided values of the parameters L/R and Q/R^2.5 are similar for the various gas stirred systems being considered. The theoretical analysis has been substantiated through numerical experimentations and by considering a set of five independant experimental studies on liquid velocity measurements reported in the literature.     

Decarburization of stainless steel: Part I. A mathematical model for laboratory scale results

A mathematical model is presented for describing the reaction of iron-chromium-carbon melts with pure oxygen, air and oxygen-argon mixtures. The model is based on the generalization of the Asai-Muchi model for oxygen steelmaking to systems containing chromium and where the oxygen blown is diluted by an inert gas. The predictions based on the model were compared to the experimental measurements of Barnhardt obtained with heats of about 1.2 to 1.5 kg, having carbon contents ranging from 0.3 to 0.6 wt pct and chromium contents of 0.0 to 21.0 wt pct. The agreement between measurements and predictions was quite good for a variety of blowing arrangements which included top blowing with pure oxygen or air and bottom blowing with air. The fact that this good agreement was obtained by using a single value of the adjustable parameter in the model for all runs, renders very promising the extension of the model to more complicated systems. On leave from Department of Iron and Steel Engineering, Nagoya University, Nagoya, Japan.     

60 t AOD精炼使用炉料级铬铁冶炼400系不锈钢的生产实践

成分相同的粒度为10~400mm炉料级铬铁比粒度10~60 mm高碳铬铁价格低,但是粒度较大不能通过高仓加料的形式加入AOD内完成合金化。通过分析60 t AOD精炼不锈钢脱碳模型和工业生产实践,采用将炉料级铬铁装在废钢斗内加料的方式,沿用兑铁后加料的操作模型,控制加料前熔池的温度在1550~1600℃,炉料级铬铁替换高碳铬铁加入量在200 kg/t,供氧强度在2.0~2.5 m³/（t·min）能够实现炉料级铬铁一次性加入后操作的稳定和降低成本。     

高炉内部气体流动与传热的模拟分析

分别建立了高炉内气体流动、传热的二维和一维数理模型,对高炉煤气流的流场、压力场和温度场进行了数值模拟,基于一维模拟温度结果预测了炉内气体成分变化,并分析了燃烧温度和鼓风速率对煤气流动及温度的影响。研究结果表明：简化的一维模型可适用于高炉煤气温度轴向变化的预测：鼓风速率和燃烧温度的变化影响软熔带的位置、炉内压力损失及炉顶煤气温度。在高炉实际操作中,合理的鼓风速率和燃烧温度是高炉炉况顺行的保障。     

Single-Sludge Nitrogen Removal Model: Calibration and Verification

The objective of this work was to calibrate and verify a modified version of a mathematical model of a single-sludge system for nitrification and denitrification. The new model is based on long-term experimental results, and the main modifications are related to the biological oxygen demand removal kinetics and biomass activity expressions. The model consists of 22 equations with 54 parameters, including 19 kinetic and stoichiometric coefficients. Experiments were performed on four bench-scale units and one pilot plant fed with domestic wastewater. Six sets of runs were carried out under different operational conditions. In the calibration procedure, a mathematical algorithm was implemented, in which an optimal set of coefficients was selected. Several coefficients were directly determined experimentally. Model verification was based on the comparison of experimental results with the values predicted by the mathematical model using a fixed set of model coefficients for each set of runs. From the verification results, the model is considered to be a useful one for the design of a new treatment system and operation of an existing one.     

A mathematical model of the nickel converter: Part II. Application and analysis of converter operation

In Part I[1] of this article, a mathematical model of the nickel converter was developed based on the assumption that the three phases in the converter vessel are in chemical and thermal equilibrium. In this article, a sensitivity analysis of the model is conducted to assess the uncertainties in model predictions and to delineate the critical process variables. Following from the equilibrium assumption, the rate-controlling process in the operation is the rate at which oxygen can be supplied to the matte. Routes to process improvement then lie in increased blast volumes or oxygen enrichment and improved operating procedures to reduce idle time. Temperature was not seen to exert a significant chemical effect on the process. More important to matte composition were variables such as ladle volume and cold charge composition. These variables directly affect either the matte volume or the overall bath composition and so are more important than those variables which have only an indirect effect through changing the conditions of equilibrium. An analysis of heat distribution in the furnace indicates the overwhelming fraction of heat removed by the off-gas.     

Iron ore reduction in a continuously operated multistage lab-scale fluidized bed reactor—Mathematical modeling and experimental results

Industrial-scale fluidized bed processes for iron ore reduction (e.g., FIOR and FINMET) are operated by continuous feeding of ore, while laboratory tests are mostly performed under batchwise operation. The reduction behavior under continuous operation is influenced by both the residence time of the iron ore particles and the reduction kinetics, which is obtained by batch tests. In a mathematical model for such a process, the effect of both phenomena has to be considered. The residence time distribution of iron ore particles in a laboratory fluidized bed reactor was obtained by measuring the response of a step input and described by mathematical models similar to a continuously stirred tank reactor. In the same reactor, reduction tests with continuous feeding of iron ore were performed. Based on batch tests in a fluidized bed reactor, a mathematical model was developed to describe the kinetics of iron ore reduction under fluidized bed conditions. This kinetic model was combined with the fluidized bed reactor model to describe continuous iron ore reduction. In this detailed model, the change of gas composition while rising in the fluidized bed was considered. The degree of reduction and the gas conversion for reactors in series were calculated. The results obtained by the mathematical model were compared with experimental data from the laboratory-scale reactor.     

Simulation of the Fluid Flow-Related Phenomena in the Electrolyte of an Aluminum Electrolysis Cell

A full-scale water model and mathematical simulation were used to study the fluid flow-related phenomena in a water model of an aluminum electrolysis cell. The time-dependent, multiphase fluid flow model was developed to represent the complex transient flow in the electrolysis bath. The accuracy of the mathematical model was validated by the ink dispersion and laser doppler velocimetry measurements in the water model. The shape, motion, release frequency of large-size bubbles, the fluid flow pattern, and the electrolyte–metal interface were predicted by the mathematical simulation. The design and operation of the anode were discussed, including the effect of the anode edge corner shape, the presence of a tilted bottom angle, and the magnitude of applied current density. The results indicated that coupling using a curved corner, with slot and with tilted angle at the anode, is effective for the release of bubbles and for the stability of the electrolyte–metal interface.     

电渣重熔体系渣池运动分析及数学模型发展

对电渣重熔过程中渣池运动的驱动力进行了分析，并对电渣重熔体系的数学模型进行了回顾和评价。结果表明，引起渣池运动的因素主要包括渣池中的电磁力和渣池温度不均匀分布而产生的对流运动；电极端部形状对渣池电磁场分布有一定影响，进而影响渣池的运动。最后提出了改进和渣池运动数学模型     

应用炉气分析的转炉动态模型初步研究

运用物料平衡及反应平衡原理,利用炉气连续分析的数据,建立了转炉冶炼过程的动态模型.本模型的计算结果表明:(1)通过烟气流量、成分及原料中初始碳含量可动态地确定熔池中的碳含量;(2)以动态确定的碳含量为基础,经过热力学平衡分析,可确定熔池内温度及氧含量的动态变化.     

含碳球团-铁浴熔融还原炼铁法与COREX法的能耗比较

通过计算机模拟计算,研究了含碳球团高温快速预还原＋铁浴终还原炼铁法、含碳球团竖炉预还原＋铁浴终还原炼铁法和含碳球团铁浴一步炼铁法这３种工艺流程的能耗,并与ＣＯＲＥＸ法进行比较。结果表明：含碳球团＋铁浴终还原炼铁法比ＣＯＲＥＸ法的耗煤量和耗氧量低。另外,还介绍了高含碳球团的优点,认为高含碳球团有一定的应用前景     

基于炉气分析的熔池碳含量及温度变化研究

 根据物料平衡及反应平衡原理，利用炉气分析系统在线连续检测、分析数据，建立了转炉冶炼过程中碳含量及温度变化的动态模型。该模型计算结果与检测结果吻合较好，这表明：①通过烟气流量、成分及铁水质量和初始碳含量可动态地确定熔池中的碳含量；②以动态确定的碳含量为基础，结合炉气分析数据，再经热力学平衡分析，可预测熔池温度的动态变化。     

Fundamental Mathematical Model for AOD Process. Part II: Model validation

A fundamental mathematical model for AOD process has been developed and proposed in “Fundamental Mathematical Model for AOD Process. Part I: Derivation of the Model” 1 . Validation of the model with process data, measured from full scale AOD process, is presented in this paper. A broad selection of input data for the model was exported from various types of full scale industrial AOD heats. In this study 6 different types of heats were studied and simulated. Process data was measured from two AOD converters (95 t, 150 t). Validation of the model was then done by comparing simulated and measured values for carbon and chromium content, carbon release rate, melt composition, slag composition and bath temperature during final stages of carbon removal. The validation results showed that the model was in good agreement with the measured process data, and same model parameters were valid in all of the simulated heats.     

Mathematical model for instant interface equilibrium temperature at time τ=O+ of solid additive–melt bath system

Abstract

The instant interface equilibrium temperature at time τ=0⁺ in close form is obtained from a mathematical model which has been developed for a solid additive–melt bath system. It is a function of the Stefan number S _t and the property ratio B as well as the initial temperature of the solid additive θ _i. For B→∞ 0 ≤ S _t ≤ ∞, or S _t→0, 0 ≤ B ≤ ∞, the instant interface equilibrium temperature becomes the freezing temperature of the bath material, whereas it takes the temperature θ _i of the additive before its immersion in the bath once B→0 for 0 ≤ S _t ≤ ∞. In the case of S _t→∞, 0 ≤ B ≤ ∞, it becomes θ _e = [(24B)^1/2 + 3θ _i]/[(24B)^1/2 + 3].     

Measurement of velocity in high-temperature liquid metals

There is a paucity of methods available for the measurement of velocity in high-temperature liquid metals. This is due to the hostile environmental conditions which characterize liquid metals. This article proposes and appraises a new velocity measurement technique for liquid metal flows at high temperatures. The melting rates of metallic spheres in metal baths of the same chemical composition as the spheres are studied under isothermal conditions. It is dem-onstrated that the metallic sphere can be used as a probe for measuring the average velocity in a metal flow system over a distance equivalent to the diameter of the sphere. The system that was chosen for study is the commercial purity aluminum bath. The experimental calibration setup examined three different elements: (a) it introduced a stationary sphere in a metallic bath of a given temperature and compared its melting rate with that of a moving sphere with known external velocity along the periphery of a circle in a metallic bath of the same temperature; (b) three different sphere diameters were used; and (c) a range of bath temperatures was investi-gated. By studying the effect of these three elements concurrently, it was possible to determine the interplay of these elements. Results showed that the sphere melting time was related linearly to the flow velocity for the range of velocities of 0 to 40 cm/s and for bath superheat up to 100 °C. In order to verify the accuracy of the results obtained by the proposed technique, a comparison was undertaken between mathematical predictions and experimental results of a fluid flow field obtained in an AC induction furnace with molten aluminum. These predictions were made by solving numerically the relevant differential equations under the appropriate boundary conditions. The experimental results attained using the proposed technique were in close agreement with those from the mathematical predictions. A.C. MIKROVAS, formerly Graduate Student, Department of Metallurgy and Materials Science, University of Toronto.     

Use of Genetic Algorithm in Optimization of Irrigation Pumping Stations

Energy costs constitute the largest expenditure for nearly all water utilities worldwide and can consume up to 65% of a water utility’s annual operating budget. One of the greatest potential areas for energy cost savings is in the scheduling of pump operations. This paper presents a new management model, WAPIRRA Scheduler, for the optimal design and operation of water distribution systems. The model makes use of the latest advances in genetic algorithm (GA) optimization to automatically determine annually the least cost of pumping stations while satisfying target hydraulic performance requirements. Optimal design and operation refers to selecting pump type, capacity, and number of units as well as scheduling the operation of irrigation pumps that results in minimum design and operating cost for a given set of demand curves. The optimization process consists of three main steps: (1) generating randomly an initial set of pump combinations to start the optimization process for a given demand-duration curve; (2) minimizing the total annual cost, which consists of operation and maintenance costs and depreciation cost of the initial investment, by changing the set and discharge of pump sets based on the provided model; and (3) achieving the final criterion to stop the optimization process and reporting the optimized results of the model. Computational analysis is based upon one major objective function and solving it by means of a computer program that is developed following the GA approach to find the optimized solution of generated equations. Application of the model to a real-world project shows considerable savings in cost and energy.     

Numerical computations of fluid flow and heat transfer in a gas-stirred liquid bath

The flow and temperature fields due to bottom air injection in a cylindrical vessel containing water were numerically analyzed. The Eulerian approach was used for the formulation of both the continuous and the dispersed phases. The computational domain was extended beyond the undisturbed height of the liquid in the bath to accommodate practical gas injection systems. Turbulence in the liquid phase was modeled using a two-equationk- ε model. Interphase friction and heat transfer coefficients were calculated by using correlations available in the literature. The general-purpose computer program PHOENICS was employed to predict the velocity, vol-ume fraction, and the temperature fields of each phase. Turbulent dispersion of the phases was modeled by introducing a “dispersion Prandtl number.” The predicted flow fields were com-pared with experimental measurements available in the literature. The results are of interest in the design and operation of a wide variety of material processing operations.     

Magnetohydronamic and thermal behavior of electroslag remelting slags

The paper is based on the development and use of a mathematical model that simulates the electroslag remelting (ESR) operation. The model assumes axisymmetrical geometry and steady state. Maxwell equations are first solved to determine the electromagnetic forces and Joule heating. Next, coupled fluid flow and heat transfer equations are written for the two liquids (slag and liquid metal). Thek-ε model is used to represent turbulence. The system of coupled partial differential equations is then solved, using a control volume method. Using the operating parameters as inputs, the model calculates the current density, velocity, and temperature throughout the fluids. This paper is concerned with fluid flow and heat transfer in the slag phase. After being validated by comparing its results with experimental observation, the model is used to evaluate the influence of operating variables, such as the fill ratio, and the thermophysical properties of the slag.