Sustainability–steel and the environment

Abstract

A two-dimensional heat and fluid flow model was used to simulate the plasma arc furnace, where the flow is governed by the steady state incompressible Navier–Stokes equations. The flow has been taken as turbulent and the standard k-epsilon model was used to simulate the turbulence in the flow. The coupled non-linear differential equations were solved with suitable boundary conditions and temperature dependent plasma properties at atmospheric pressure by employing an efficient finite volume method. The calculations and heat transfer to various parts of the furnace were calculated for argon, nitrogen and hydrogen plasmas. The voltage–current characteristic for the different types of plasma and the effect of other process parameters on heat transfer are discussed.     

ARCHIV FÜR DAS EISENHÜTTENWESEN

Mathematical model of fluid flow and temperature distribution in the slag during electroslag remelting. Maxwell's equations, Navier-Stokes-equations, heat transport equation. Application of Spalding's k-W-model of turbulence. Consideration of natural and forced convection. Numerical calculations for certain operating conditions.     

Two-fluid simulation on the mixed convection flow pattern in a nonisothermal water model of continuous casting tundish

A transient two-fluid model is applied to simulate fluid flow and heat transfer in a nonisothermal water model of continuous casting (CC) tundish. The original liquid in the bath is defined as the first fluid, and the inlet stream, with the temperature variation, is defined as the second fluid. The flow patterns and heat transfer are predicted by solving the three-dimensional (3-D) transient transport equations for each fluid. The results predicted by the two-fluid model make the effect of natural convection more clear compared with the generally used single fluid model k-ɛ turbulence model.     

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.     

Optimal configuration of blast furnace slag runner to reduce fluid flow stresses at wall using mathematical modelling

Abstract

A three-dimensional mathematical model was developed to predict the wall shear stresses due to flow of liquid slag in slag runner of 'G' blast furnace of Tata Steel under different conditions. The liquid slag flow in the slag runner was considered to be turbulent and incompressible. The model was developed for single phase, steady state and isothermal conditions. To this end, the Navier Stokes equations along with continuity and turbulence equations (standard k–? model) were simultaneously solved with appropriate boundary conditions at the associated physical boundaries of the calculation domain. Several configurations were numerically assessed with respect to reduced shear stresses on the wall of the slag runner to select the best one. Due to accelerating flow the operating heights of liquid slag (density 2800 kg m^–3 at 1500°C) within the slag runner for different configurations were estimated with the help of Bernoulli's and continuity equations and fixed before the computation. The different configurations comprised of three segments with different parameters of either elevation or radius of curvature. Relatively high shear stresses were numerically predicted at the joint area of second and third segments of the slag runner for all the configurations. The radius of curvature was found as the dominant factor to reduce the shear stress at the joint region.     

Development of a mathematical model for multihearth roasters

A simultaneous heat and mass transfer model has been developed for the multiheart roasters, considering dead roasting of chalcopyrite as a typical roasting reaction. Various mass and energy balances have been worked out during the development of this model yielding coupled nonlinear partial differential equations with highly complex boundary conditions. These equations have been solved numerically using a line-by-line finite difference approach to obtain profiles of gas temperature, solid temperature, oxygen concentration, and solid fraction reacted in the roaster. The trend of the computed results appears to be realistic and can be easily explained from simple physical considerations. The effects of gas preheating and the heat transfer coefficient between the solid and the gas upon the roasting process are examined. The results show that gas preheating is beneficial for the roasting process, and the process parameters, such as particle size, gas flow rate,etc., must be adjusted so as to give the desirable value of the heat transfer coefficient needed for proper roasting.     

Mathematical modelling of electroslag remelting P91 hollow ingots process with multi-electrodes

Abstract

Electroslag remelting (ESR) hollow ingot process with T-shape current supplying mould is a new metallurgical technology. A mathematical model was developed to describe the interaction of multiple physical fields of this process for studying the process technology. Maxwell, Navier-Stokes and heat transfer equations have been adopted in the model to analyse the electromagnetic field, magnetic driven fluid flow, buoyancy driven flow and heat transfer using finite element software ANSYS. Moreover, the model has been verified through the metal pool depth measurements, which were obtained during remelting of 10 electrodes into Φ900/500 mm hollow ingots of P91 steel, with a slag composition of 50–60 wt-% CaF₂, 10–20 wt-% CaO, 20–30 wt-% Al₂O₃, ≤8 wt-% SiO₂. There was a good agreement between the calculated results and the measured results. The calculated results show that the distribution of current density, magnetic induction intensity, electromagnetic force, Joule heating, fluid flow and temperature are symmetric but not uniform due to the multi-electrode arrangement in two symmetric groups. Simulation of the ESR hollow ingot process will help to understand the new technology process and optimise operating parameters.     

Fluid Flow and Heat Transfer Modeling of AC Arc in Ferrosilicon Submerged Arc Furnace

 arc has been developed and used to predict heat transfer from the arc to the molten bath in ferrosilicon AC submerged-arc furnace. In this model the time-dependent conservation equations for mass, momentum and energy in the specified domain of plasma zone have been solved numerically coupled with the Maxwell and Laplace equations for magnetic filed and electric potential respectively. A control volume based finite difference method was used to solve the governing equations in cylindrical coordinates. The reliability of the developed model was tested by comparison with the data available in the literature. The present model showed a better consistency with the data given in the literature because of solving the Maxwell and Laplace equations simultaneously for calculation of current density. Parametric studies were carried out to evaluate the effect of electrical current and arc length on flow field and temperature distribution within the arc. According to computed results, a lower power input lead to the higher arc efficiency.     

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.     

Coupled turbulent flow,heat, and solute transport in continuous casting processes

A fully coupled fluid flow, heat, and solute transport model was developed to analyze turbulent flow, solidification, and evolution of macrosegregation in a continuous billet caster. Transport equations of total mass, momentum, energy, and species for a binary iron-carbon alloy system were solved using a continuum model, wherein the equations are valid for the solid, liquid, and mushy zones in the casting. A modified version of the low-Reynolds numberk-ε model was adopted to incorporate turbulence effects on transport processes in the system. A control-volume-based finite-difference procedure was employed to solve the conservation equations associated with appropriate boundary conditions. Because of high nonlinearity in the system of equations, a number of techniques were used to accelerate the convergence process. The effects of the parameters such as casting speed, steel grade, nozzle configuration on flow pattern, solidification profile, and carbon segregation were investigated. From the computed flow pattern, the trajectory of inclusion particles, as well as the density distribution of the particles, was calculated. Some of the computed results were compared with available experimental measurements, and reasonable agreements were obtained.     

A Unified Mechanism for the Formation of Oscillation Marks

Oscillation marks (OMs) are regular, transverse indentations formed on the surface of continuously cast (CC) steel products. OMs are widely considered defects because these are associated with segregation and transverse cracking. A variety of mechanisms for their formation has been proposed (e.g., overflow, folding, and meniscus freezing), whereas different mark types have also been described (e.g., folded, hooks, and depressions). The current work uses numerical modeling to formulate a unified theory for the onset of OMs. The initial formation mechanism is demonstrated to be caused by fluctuations in the metal and slag flow near the meniscus, which in turn causes thermal fluctuations and successive thickening and thinning of the shell, matching the thermal fluctuations observed experimentally in a mold simulator. This multiphysics modeling of the transient shell growth and explicit prediction of OMs morphology was possible for the first time through a model for heat transfer, fluid flow, and solidification coupled with mold oscillation, including the slag phase. Strategies for reducing OMs in the industrial practice fit with the proposed mechanism. Furthermore, the model provides quantitative results regarding the influence of slag infiltration on shell solidification and OM morphology. Control of the precise moment when infiltration occurs during the cycle could lead to enhanced mold powder consumption and decreased OM depth, thereby reducing the probability for transverse cracking and related casting problems.     

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.     

Flame formation and post-combustion at blowing of oxygen into a carbon monoxide containing slag foam

A combined post-combustion model (CPM) for smelting reduction was developed in a multi-national research project supported by the European Coal and Steel Community. The project partners were CSM, Rome, Hoogovens, Ijmuiden, MPI, Düsseldorf, and TUB, Berlin. This paper is a report about a flame model developed by TUB, Berlin. An oxygen jet is blown into a carbon monoxide containing slag foam. The jet entrains carbon monoxide and slag droplets. Carbon monoxide is combusted by oxygen to carbon dioxide and the developed heat is transferred by radiation from the gas to the surrounding slag and by radiation and convection to the entrained droplets. The droplets are mixed with the slag at the flame end so that also their heat content is finally transferred to the bulk slag. The model consists of a detailed treatment of the entrainment processes, the combustion reaction taking into account the carbon dioxide dissociation equilibrium, the enthalpy changes, and the heat transfer processes. One obtains two ordinary differential equations describing the temperature and composition of the flame gas as functions of the flame pass-way. They are solved numerically by the Runge-Kutta method. As the results, the main flame properties, namely the flame velocity, the diameter and the upwards angle of the flame, the amount of gas and slag entrained from the surroundings to the flame, the oxygen utilisation, from which the post-combustion degree is calculated, the flame temperature along the flame pass-way, and the total heat transfer from the flame gas to the slag, are described as functions of various internal and external parameters. The presented flame model is part of a general post-combustion and heat transfer model of a smelting reduction process with post-combustion in the slag.     

Post-combustion and heat transfer at blowing of oxygen into a carbon monoxide containing slag foam

A combined post-combustion model (CPM) for smelting reduction processes was developed in a multi-national research project supported by the European Coal and Steel Commission. The project partners were CSM, Rome, Hoogovens, Ijmuiden, MPI, Düsseldorf, and TUB, Berlin. This paper reports about a heat transfer model developed by TU Berlin within this project. The batch-type smelting reduction reactor has a two-layered slag: an upper foamy and a lower less foamy slag. A bubble stream of (CO+H₂) gas originating from the iron oxide reduction reaction with coal in the lower slag flows upwards. The rising (CO+H₂) gas is post-combusted by three oxygen jets blown horizontally into the upper part of the slag. A flame zone, and above the flame a mixing and a bubble zone form, in which post-combustion reaction and transfer of the post-combustion heat to the slag take place. The modelling of the flame zone was the subject of a previous paper. The present report describes models of the mixing and the bubble zone and of the occurrences in the gas space above the slag. The macro-kinetics of the overall heat transfer process including slag recirculation and heat transfer from the upper foamy to the lower dense slag are presented further. The model calculations provide information about the distribution of the post-combustion and the heat transfer processes over the single zones as functions of the important internal process parameters. Further, the oxygen utilisation, the heat efficiency and the temperatures at various locations of the process are described as functions of the ratio of post-combustion oxygen flow rate to (CO+H₂) evolution rate. In all the calculations a specific gas through-put of carbon monoxide of 3 mol/t?s is assumed. This value corresponds to 510 mol/s for the assumed melt of 170 t. The model shows that heat transfer efficiencies of more than 90 % and slag temperatures of less than 1700°C are possible, if the slag circulation rate is 300 kg/s. Lower circulation rates lead to higher slag temperatures and worse heat transfer efficiencies. Controlled slag circulation is thus an important process tool.     

Modeling mean flow and turbulence characteristics in gas-agitated bath with top layer

A numerical study is presented of the flow characteristics in a gas-agitated water bath in the presence of a top layer of dissimilar fluid. Two systems are considered, comprised separately of silicon and normal pentane as the top layer, to simulate slag cover in a real steelmaking process. The mathematical model involves solution of transport equations for the variables of each phase, with allowance for interphase transfer of momentum. Turbulence is assumed to be a property of the carrier (liquid) phase and represented through solution of additional transport equations for the turbulence kinetic energy, k, and its rate of dissipation, ɛ. The model also accounts for turbulence modulation by the bubbles through enhancement of the source terms in the equations for k and ɛ. The predicted mean and fluctuating velocities, stresses, and turbulence production are generally in the consensus of the experimental data. Both mean flow and turbulence characteristics are found to be suppressed in the water/silicon system of smaller density ratio, indicating enhanced re-entrainment of the top layer, than the water/normal pentane system.     

Heat transfer and fluid flow phenomena in electroslag refining

A mathematical formulation has been developed to represent the electromagnetic force field, fluid flow and heat transfer in ESR units. In the formulation, allowance has been made for both electromagnetically driven flows and natural convection; furthermore, in considering heat transfer the effect of the moving droplets has been taken into account. The computed results have shown that the electromagnetic force field appears to be the more important driving force for fluid motion, although natural convection does affect the circulation pattern. The movement of the liquid droplets through the slag plays an important role in transporting thermal energy from the slag to the molten metal pool, although the droplets are unlikely to contribute appreciably to slag-metal mass transfer The for-formulation presented here enables the prediction of thermal and fluid flow phenomena in ESR units and may be used to calculate the electrode melting rates from first principles. While a detailed comparison has not yet been made between the predictions based on the model and actual plant scale measurements, it is thought that the theoretical predictions are consistent with the plant-scale data that are available.     

Numerical study of dc arc plasma and molten bath in dc electric arc furnace

Abstract

A numerical study of the arc plasma and molten bath in a dc electric arc furnace (EAF) is useful for understanding and improving the production process of the dc EAF. In the present paper, a mathematical model based on conservation equations of mass, momentum and energy along with Maxwell's equations is developed to describe the flow field and heat transfer in the arc and molten bath regions of a dc EAF simultaneously. The governing equations are solved using the PHOENICS software package. The calculated results show good agreement with those of previous studies, giving a useful insight into the factors of arc heat transfer and bath circulation.     

A two-dimensional heat and fluid-flow model of single-roll continuous-sheet casting process

Single-roll continuous-sheet casting process has been simulated using a mathematical model based on considerations of fluid flow, heat transfer, and solidification. The principal model equations include momentum and energy balances which are written for various zones comprising the process. The flow of liquid metal in the pool is taken to be a two-dimensional recirculatory flow. The concepts of vorticity and stream function are used to reduce the number of equations and number of unknowns, respectively. Model equations and boundary conditions are written in terms of dimensionless variables and are solved, using an implicit finite difference technique, to give stream functions and velocity fields in the metal pool, temperature fields in the metal pool, sheet, and caster drum, and the final sheet thickness for various operating parameters. The parameters examined are: (1) rotational speed of the caster drum, (2) liquid metal head in the tundish, (3) superheat of the melt, (4) caster drum material, and (5) cooling conditions prevailing at the inner surface of the caster drum. The final sheet thickness decreases with increasing rotational speed of the caster drum and melt superheat, but it increases with increasing standoff distance and metal head in the tundish.     

A mathematical model for the solution mining of primary copper ore: Part I. leaching by oxygen-saturated solution containing no gas bubbles

An unsteady-state, one-dimensional model which simulates the solution mining of a rubblized copper ore body deeply buried below the water table has been developed. Leaching is accomplished by pumping water saturated with oxygen into the bottom of the flooded rubble chimney. The physical processes incorporated in the present model include the axial convective transport of mass and heat, axial dispersion of mass, mass transfer between the bulk fluid and solid surface, and pore diffusion within the ore fragments. The solution withdrawn from the top of the chimney is recycled through the bottom of the chimney, and the temperature of the chimney is allowed to build up by means of the heat generated during leaching. The coupled model equations are solved numerically by an implicit finite-difference method. Model calculations for the leaching process are made for two different modes of operation: (1) constant flow-rate and (2) variable flow-rate of the leach solution during leaching. The calculated results from both modes of operation indicate that thefractional recovery of copper increases with decreasing ore particle size, ore grade, pyrite/chalcopyrite molar ratio, and shape factor. Copper recovery is rather insensitive to the chimney porosity under typical operating conditions.