Fluid flow and mass transfer in an inductively stirred four-ton melt of molten steel: A comparison of measurements and predictions

Experimental measurements are reported on melt velocities and on the rate at which immersed carbon rods dissolve in a 4-ton induction furnace, holding a low carbon steel melt. These measurements are compared with theoretical predictions, based on the numerical solution of Maxwell’s equations and the turbulent Navier-Stokes equations. In general, good agreement has been obtained, both regarding the absolute values of the velocities and the mass transfer coefficients and the trends predicted by the theoretical analysis. In addition to providing further proof regarding the applicability of the mathematical modeling technique, the principal contribution of the work is that it provides an improved insight into the behavior of inductively stirred melts. In particular it was found that for an inductively stirred melt both the velocities and the rate of turbulence energy dissipation are relatively uniform spatially, in contrast to bubble stirred systems, where most of the agitation is confined to the jet plume and to the near surface region. It was found, furthermore, that the mass transfer coefficient characterizing the rate of dissolution of immersed carbon rods depends both on the absolute values of the melt velocity and on the local values of the turbulence intensity; thus significant mass transfer will occur in the region of the eye of the circulation, where the absolute value of the mean velocity is small. On leave at Massachusetts Institute of Technology     

Effect of Ar/O2 gas mixtures on heat‐transfer and fluid‐flow characteristics in AOD nozzles

A model of fluid flow and heat transfer in a nozzle used for injection of argon and oxygen in AOD converters was developed earlier. In this study the model was used to determine the effect of changes in the ratio of argon to oxygen in argon‐oxygen gas mixtures injected through the nozzle on fluid flow and heat transfer. It was found, for the studied conditions, that the temperature and laminar kinematic viscosity at the nozzle outlet were not dependent on the gas composition. However, the velocity, density, turbulent kinetic energy and dissipation of kinetic energy varied with a change in the fraction of oxygen injected. It is therefore concluded that for use as boundary‐condition input data for an AOD converter model (under development), it is important to be able to calculate reliable velocity and turbulence parameter data for gas mixtures of different argon/oxygen ratios.     

Decay of Turbulence Downstream of a Stilling Basin

Turbulence must be modeled accurately to simulate river processes, particularly transport of aqueous oxygen and nitrogen. Spillway operations affect downstream turbulence, but there has been little research on turbulence intensities downstream of stilling basins. For this study, laboratory measurements were taken on a three-dimensional, physical model of McNary Dam, Columbia River, United States to determine how the turbulence, initially generated by spillway flow, decreases with distance downstream. The experiments also examined how flow rate, tailwater depth, and the presence of spillway deflectors affect turbulence. A mathematical analysis was used to predict turbulent kinetic energy with distance, and good agreement was found between laboratory measurements and numerical predictions. Turbulence production generated by channel bed roughness was found to be small compared to turbulent energy dissipation, and the effect of flow separation related to bed irregularities on turbulence production was found to be negligible.     

Measurement and modeling of turbulence in the gas/liquid two-phase zone during gas injection

Averaged and turbulent fluctuating liquid velocities in the gas/liquid plume zone of a gas-stirred water model ladle were measured with a combined laser Doppler anemometer (LDA) and elec-trical probe technique. The measured turbulence fields, void fraction distribution, and gas and liquid velocities in the plume zone were used for evaluation of various turbulence models. It was found that, among all of the turbulence models tested, only a modified k-ε model, with extra source terms to take into account the generation and dissipation resulting from the inter-action of the bubbles with the liquid, yielded good agreement with both the mean liquid flow field and the turbulent kinetic energy distribution. However, the values of the coefficients orig-inally proposed by their authors were found inapplicable to the bubbly plume situation; more appropriate values of the coefficients were determined based on comparison with experimental measurement.     

Effect of slag cover on heat loss and liquid steel flow in ladles before and during teeming to a continuous casting tundish

Mathematical modeling of transient fluid flow and heat transfer of melt in the ladle has been carried out, both before and during teeming of the melt to a tundish. The model involves solution of the transient, two-dimensional form of the turbulent Navier-Stokes' equation along with the equations of turbulence energy, energy dissipation rate of turbulence energy, and thermal energy conservation in the cylindrical coordinate system. Two different heat loss conditions have been assumed to occur from the top free surface of the melt in the ladle. When the ladle has an insulating layer of slag, temperature stratification occurs within the melt with the coolest melt in contact with the ladle bottom. The degree of temperature stratification increases with the increase in holding time. Pouring of the melt from such a ladle to the tundish, however, results in near uniform ladle stream temperature during the 47 minutes of pouring period considered in the present study. This is especially true if the melt in the ladle is held for a period of 20 minutes prior to teeming. When the melt in the ladle loses an appreciable amount of heat from the top due to a thin layer of slag, the average temperature of the melt drops considerably during the holding period although there is no temperature stratification. Pouring from such a ladle results in a continuous decline of the ladle stream temperature, even though the pouring starts after a holding period of 5 minutes. Formerly Graduate Student, Department of Materials Science and Engineering, Ohio State University     

Turbulent recirculating flow in induction furnaces: A comparison of measurements with predictions over a range of operating conditions

Experimental measurements and theoretical predictions are presented concerning the velocity fields, the maps of the turbulent kinetic energy, and the turbulent kinetic energy dissipation in an inductively stirred mercury pool. A single coil arrangement was used, and the frequencies examined ranged from 50 to 5000 Hz. A hot film anemometer and a direction probe were employed for characterizing the velocity fields. The theoretical predictions were based on the numerical solution of the turbulent Navier-Stokes equations. The technique of mutual inductances was employed to compute the magnetic field, while thek-ε model was used for calculating the turbulent viscosity. Overall, the theoretical predictions were in reasonable agreement with the measurements both regarding the velocities and the turbulence parameters. By presenting the results in a normalized, dimensionless form these findings were given a rather broader applicability than the actual numerical range explored. Formerly of the Department of Materials Science and Engineering at MIT     

Flow pattern velocity and turbulence energy measurements and predictions in a water model of an argon-stirred ladle

Experiments were carried out using a simplified water model of an argon-stirred ladle system. The flow patterns were determined by a flow visualization technique and the velocity and turbulence energy fields were quantitatively measured using hot-film anemometry. The latter quantities were predicted by solving the turbulent Navier-Stokes equations using Spalding’sk-W model for the turbulence viscosity. There is semiquantitative agreement between predictions and measurements. Mixing lengths also were computed. This agreement between measurements and predictions provides further evidence that modeling is a promising approach for the study of recirculating turbulent flows in steel processing operations. J. SZEKELY, formerly of the State University of New York at Buffalo.     

Transient flow and heat transfer in a steelmaking ladle during the holding period

Transient, turbulent flow and heat transfer in a ladle during the holding period are numerically investigated. The ladle refractories including the working lining, safety lining, insulation layer, and steel shell have been simultaneously taken into account. No assumptions are made for the heat transfer between the liquid steel and the inside ladle walls. Both the initial ladle heating and the heat loss from the slag surface are changed to examine their effect on thermal stratification in molten steel. A simplified model for the heat loss from the molten steel to the refractory is proposed. Correlations for the history of mean steel temperature, thermal stratification, and heat loss rate are obtained, which can be easily applied for industrial operations. Predictions are compared with experimental data in an industrial ladle and a pilot plant ladle, and those from previous studies.     

A Study on the mathematical modeling of turbulent recirculating flows in gas-stirred ladles

Computed results are presented describing the velocity field and the map of the turbulent kinetic energy in a water model of an argon-stirred ladle. The theoretical predictions agree well with the measurements, when an experimentally determined void fraction distribution is used in computing the body force driving the flow. The agreement is somewhat less satisfactory, particularly regarding the maps of the turbulent kinetic energy, when the no-slip or the drift flux models are used to predict the void fraction of the gas.     

Fluid dynamics in bubble stirred ladles: Part I. experiments

Air is supplied through a porous plug placed in the center axis of a cylindrical perspex-water model of a ladle. A Laser-Doppler system is employed to measure radial and axial mean and fluctuating velocities. Velocities in the two-phase bubbly region can also be determined. Velocities are measured near the bottom, half-way up, and near the free surface. It is shown that the bubbles contribute to production of turbulence. The ladle has recirculation zones near the bottom, where the mean velocities are very low. Close to the free surface the radial mean and turbulent velocities are high, promoting mass transfer through the interface. The present measured velocity profiles cannot be reduced to a single profile by employing similarity scaling.     

Fluid dynamics in bubble stirred ladles: Part I. experiments

Air is supplied through a porous plug placed in the center axis of a cylindrical perspex-water model of a ladle. A Laser-Doppler system is employed to measure radial and axial mean and fluctuating velocities. Velocities in the two-phase bubbly region can also be determined. Velocities are measured near the bottom, half-way up, and near the free surface. It is shown that the bubbles contribute to production of turbulence. The ladle has recirculation zones near the bottom, where the mean velocities are very low. Close to the free surface the radial mean and turbulent velocities are high, promoting mass transfer through the interface. The present measured velocity profiles cannot be reduced to a single profile by employing similarity scaling. Formerly a Visiting Scientist at SINTEF Formerly Engineer at SINTEF     

Prediction of temperature in secondary steelmaking: mathematical modelling of fluid flow and heat transfer in gas purged ladle

As a first step towards prediction of temperatures in secondary steelmaking, mathematical modelling of fluid flow and heat transfer in ladle furnace was undertaken. A two‐dimensional quasi‐single phase model has been developed for turbulent recirculating flow by solving Reynolds averaged Navier‐Stokes equations along with a two‐equation k‐? model. The model was then extended to include thermal transport in a conjugate domain (i.e., molten steel + refractory shell + steel shell). The flow model was validated with water model data reported in literature by different researchers. Good agreement for velocity field and satisfactory agreement for turbulent kinetic energy field were obtained. The thermal model showed good agreement with results predicted in literature. The paper also presents findings of tests for sensitivity of flow on modelling and process parameters. By comparison with water model experiments, it has been demonstrated that the flow field in a ladle with a porous plug can be represented using a gas voidage fraction in the plume obtained from experiments with nozzles for axial gas injection from the bottom. Flow and thermal fields were insensitive to initial turbulence level at nozzle. Maximum temperature inhomogeneity in the melt was 2 °C after 1.5 min and negligible after 3 min of onset of gas purging.     

The velocity field in the molten slag region of esr systems: a comparison of measurements in a model system with theoretical predictions

A comparison is presented between the experimentally measured velocity field in a room temperature model of an ESR system and theoretical predictions, obtained from the numerical solution of Maxwell’s equations and the turbulent Navier-Stokes equations. The experimental measurements were obtained in a horizontal trough, containing mercury, through which a current was being passedvia two electrodes. The velocity fields, which were measured, using a photographic technique were thought to model the electromagnetically driven component of the velocity field in the central plane of the slag phase in ESR systems. The agreement between the experimental measurements and the theoretical predictions is excellent, both regarding the absolute values of the velocities and the dependence of the velocity on the imposed current and on the electrode diameter. The calculations have shown that by the proper choice of the linear scale, and the current,. mercury may be used to model the electromagnetically driven flow in the slag phase of ESR systems. Furthermore, some general relationships have been developed showing the effect of the current on the velocity, the turbulence energy, and on the rate of turbulence energy dissipation. This work is thought to provide definite confirmation that the electromagnetically driven component of the velocity fields in ESR systems may be properly represented through the simultaneous solution of Maxwell’s equations and the turbulent NavierStokes equations.     

Experimental measurement and numerical computation of velocity and turbulence parameters in a heated liquid metal system

Experimental measurements are reported describing the velocity field and the turbulence parameters in molten Woods metal due to the passage of a DC current between two electrodes immersed into the melt. The measurements were made using a hot film anemometer. A mathematical model has been developed to represent these measurements; in essence, this relied on the solution of Maxwell’s equations to represent the electromagnetic force field and turbulent Navier-Stokes equations to represent the fluid flow field. Three different turbulence models were examined; two were variants of thek-ε model, while the third was mixing length model type. In general, the velocities were well predicted by all three of these models, but there were significant discrepancies as far as the turbulence parameters were concerned. In the paper, a new criterion was suggested to predict the onset of turbulence in systems of this type.     

Experimental measurement and numerical computation of velocity and turbulence parameters in a heated liquid metal system

Experimental measurements are reported describing the velocity field and the turbulence parameters in molten Woods metal due to the passage of a DC current between two electrodes immersed into the melt. The measurements were made using a hot film anemometer. A mathematical model has been developed to represent these measurements; in essence, this relied on the solution of Maxwell’s equations to represent the electromagnetic force field and turbulent Navier-Stokes equations to represent the fluid flow field. Three different turbulence models were examined; two were variants of thek-ε model, while the third was mixing length model type. In general, the velocities were well predicted by all three of these models, but there were significant discrepancies as far as the turbulence parameters were concerned. In the paper, a new criterion was suggested to predict the onset of turbulence in systems of this type.     

Dissipation of Turbulent Kinetic Energy in a Tundish by Inhibitors with Different Designs

Turbulent flow of liquid steel and its control is studied using different geometries of turbulence inhibitors. Four designs of turbulence inhibitors were characterized through experiments of tracer injection in a water model and mathematical simulations using the Reynolds Stress Model (RSM) of turbulence. Inhibitor geometries included octagonal‐regular, octagonal‐irregular, pentagonal and squared. A layer of silicon oil was used to model the behaviour of tundish flux during steel flow. Fluid flows in a tundish using these geometries were compared with that in a bare tundish. Experimental and simulation results indicate that the flow in a bare tundish and a tundish using turbulence inhibitors open large areas of oil close to the ladle shroud due to strong shear stresses at the water‐oil interface with the exception of the squared inhibitor. Oil layer opening phenomena are explained by the high gradient of the dissipation rate of turbulent kinetic energy. Using the squared inhibitor the kinetic energy reports a high gradient from the tundish floor to the free bath surface as compared with other geometries.     

Particle Image Velocimetry Study of Flow near Trashrack Models

This paper provides results of an experimental study of turbulent flow near trashrack models that are comprised of an array of three rectangular bars. The bar thickness, bar depth, and center-to-center spacing were maintained constant. The flow characteristics were studied by aligning the bars with the approach flow and conducting measurements at three different approach freestream velocities. Subsequently, the freestream velocity was kept constant and detailed measurements were conducted for four different bar inclinations relative to the approach flow. For each test condition, a high-resolution particle image velocimetry (PIV) technique was used to conduct detailed velocity measurements in streamwise-spanwise planes at middepth of flow. From these measurements, isocontours and profiles of the mean velocities, turbulence intensities, Reynolds shear stress, and production term in the transport equation for the turbulent kinetic energy were obtained to study the flow characteristics around and downstream of the aligned and inclined bars. Flow characteristics near hydroelectric station trashracks are important for efficient turbine operation and reduction of fish entrainment.     

Simulation of the Filling of a Liquid Steel Sampler

Steel samples extracted from the ladle furnace in liquid state are vital to monitor the steel making process in the iron & steel industries. The main function of the steel sample is to exam whether the steel is at the aimed composition for elements that dissolve in steel. In addition, more interest is arising to determine the inclusion characteristics in steel samples, in order to monitor the development throughout the process. However, the molten steel sampling is a process involving multi‐phenomena such as a high temperature, a fast solidification, reoxidation of steel and a highly turbulent flow pattern. Therefore, mathematical simulations have been carried out to fundamentally study the sampler filling process. The Wilcox k‐ω turbulence model was employed to predict the turbulent flow. The calculated results show that flow patterns inside the sampler can be classified into three distinct flow regions: the vortex flow region close to the free surface, the lower horizontal flow region and the middle vertical flow region. From the flow and turbulence data, the inclusion particle collision volume rate was calculated to study the influence of turbulent flow on the inclusion growth in the sampler during fillings. It is shown that the collision volume in the sampler is much higher than that found in the ladle furnace, where the steel sampling normally takes place. This is due to the high turbulence energy dissipation rate in the samplers compared to the ladles.     

Mathematical Simulation of Process Parameters in the case of Rapid Solidification of Steel

Rapid solidification of steel was investigated experimentally under laboratory conditions by immersion of cold copper rods in steel baths. For a better understanding of the process parameters during rapid solidification, an explicit finite difference model was employed. In the calculation, a coefficient of heat transfer between a frozen steel shell and solid copper of α = 40 [KW/m²·K] is assumed in good agreement with experimental data derived from temperature measurements. The solidification parameters such as local time of solidification (LST), local time of the superheat reduction (LShRT), local solidification and cooling rates (LSR, LCR) and local heat flux density of solidification and superheat reduction (LSHFD, LShRHFD) can be calculated using the developed model, in dependence on the processing conditions. This influence of processing parameters, such as steel bath superheat, steel bath material, immersed body material, initial temperature of immersed body and immersed body geometry, were the subject of intensive investigations.     

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.