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.     

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.     

超音速射流流场中湍流模型

为了确定适用于超音速射流流场数值模拟的湍流模型,首先从理论上分析常用的五种湍流模型之间的差异及其适用范围;其次,采用五种湍流模型,分别对不同马赫数下超音速射流流场进行数值模拟,将数值模拟结果与实测值和理论值进行对比分析.结果表明:剪切压力传输k-ω模型与其他模型相比,通过对输运方程的修正,保证其在计算射流流场时具有较高的准确性;在喷管内部和外部射流流场的模拟中,剪切压力传输k-ω模型的计算结果与理论值和实测值具有较高的吻合度,在五种湍流模型中最适合于超音速射流流场的数值模拟研究.      

Simulation of fluid flow inside a continuous slab-casting machine

A finite element model has been developed and applied to compute the fluid flow distribution inside the shell in the mold region of a continuous, steel slab-casting machine. The model was produced with the commercial program FIDAP, which allows this nonlinear, highly turbulent problem to be simulated using the K- ε turbulence model. It consists of separate two-dimensional (2-D) models of the nozzle and a section through the mold, facing the broad face. The predicted flow patterns and velocity fields show reasonable agreement with experimental observations and measurements conducted using a transparent plastic water model. The effects of nozzle angle, casting speed, mold width, and turbulence simulation parameters on the flow pattern have been investigated. The overall flow field is relatively insensitive to process parameters. Formerly Graduate Student, Department of Mechanical and Industrial Engineering, University of Illinois-Urbana     

Numerical Study of the Transition Regime between the Skimming and Wake Interference Flows in a Water Flume by Using the Lattice-Model Approach

A numerical study to describe the transition regime between the skimming and wake interference flows due to the influence of an idealized bed roughness in a water flume was carried out here using the lattice model approach. The model reproduced the skimming, transition, and wake interference regimes for different aspect ratios that determine the bed roughness geometry. The simulated turbulent structures were visualized by drawing the trajectories of a large number of passive tracer particles released in the computational domain, and the results agreed with those reported by the research works. The dimensionless streamwise and vertical turbulent intensities were calculated at five test sections. The results obtained supported the visualized flow patterns permitting us to detect the presence of a shear layer developed at the top of the roughness element, whose strength varied according to the flow regime simulated.     

A numerical and experimental study of the solidification rate in a twin-belt caster

A numerical and experimental study was carried out to investigate the solidification process in a twin-belt (Hazelett) caster. The numerical model considers a generalized energy equation that is valid for the solid, liquid, and mushy zones in the cast. Ak-ε turbulence model is used to calculate the turbulent viscosity in the melt pool. The process variables considered are the belt speed, strip thickness, nozzle width, and heat removal rates at the belt-cast interface. From the computed flow and temperature fields, the local cooling rates in the cast and trajectories of inclusions were computed. The cooling rate calculations were used to predict the dendrite arm spacing in the cast. The inclusion trajectories agree with earlier findings on the distribution of inclusion particles for near horizontally cast surfaces. This article also reports the results of an experimental study of the measurement of heat flux values at the belt-cast interface during the solidification of steel and aluminum on a water-cooled surface. High heat fluxes encountered during the solidification process warranted the use of a custom-made heat flux gage. The heat flux data for the belt surface were used as a boundary condition for the numerical model. Objectives of the measurements also included obtaining an estimate of the heat-transfer coefficient distribution at the water-cooled side of the caster belt. Y.G. KIM, formerly Graduate Student, Materials Engineering Department, Drexel University.     

Melt flow control in a multistrand tundish using a turbulence inhibitor

Water modeling and mathematical simulation techniques were used to study the melt flow under the influence of turbulence inhibitors in a multistrand bloom caster tundish. Three different cases were studied: a bare tundish (BT), a tundish with two pairs of baffles and a waved impact pad (BWIP), and a tundish equipped with turbulence inhibitor and a pair of dams (TI&D). Chemical mixing of tracer turbulence diffusion was also simulated and compared with actual experimental results. The TI&D arrangement showed an improvement of the fluid flow characteristics, yielding better tracer distribution among the outlets, lower values of back mixing flow, and higher values of plug flow. A mass transfer model coupled with k-ɛ turbulence model predicted acceptably well the experimental chemical mixing of the tracer in the water model. The water modeling and the numerical simulation indicated that the TI&D arrangement retains the tracer inside the vessel for longer times, increasing the minimum residence time. These results encourage the use of turbulence-inhibiting devices in bloom and billet casters, which pursue excellence in product quality.     

CFD Modeling of Swirl and Nonswirl Gas Injections into Liquid Baths Using Top Submerged Lances

Fluid flow phenomena in a cylindrical bath stirred by a top submerged lance (TSL) gas injection was investigated by using the computational fluid dynamic (CFD) modeling technique for an isothermal air–water system. The multiphase flow simulation, based on the Euler–Euler approach, elucidated the effect of swirl and nonswirl flow inside the bath. The effects of the lance submergence level and the air flow rate also were investigated. The simulation results for the velocity fields and the generation of turbulence in the bath were validated against existing experimental data from the previous water model experimental study by Morsi et al.[1] The model was extended to measure the degree of the splash generation for different liquid densities at certain heights above the free surface. The simulation results showed that the two-thirds lance submergence level provided better mixing and high liquid velocities for the generation of turbulence inside the water bath. However, it is also responsible for generating more splashes in the bath compared with the one-third lance submergence level. An approach generally used by heating, ventilation, and air conditioning (HVAC) system simulations was applied to predict the convective mixing phenomena. The simulation results for the air–water system showed that mean convective mixing for swirl flow is more than twice than that of nonswirl in close proximity to the lance. A semiempirical equation was proposed from the results of the present simulation to measure the vertical penetration distance of the air jet injected through the annulus of the lance in the cylindrical vessel of the model, which can be expressed as L_va = 0.275( d_o - d_i )Fr_m^0.4745 . L_{va} = 0.275\left( {d_{o} - d_{i} } \right)Fr_{m}^{0.4745} . More work still needs to be done to predict the detail process kinetics in a real furnace by considering nonisothermal high-temperature systems with chemical reactions.     

Flow fields in electromagnetic stirring of rectangular strands with linear inductors: Part I. theory and experiments with cold models

A model is presented to compute the electromagnetic force fields and fluid flow fields in electromagnetic stirring of continuously cast strands with rectangular cross-section. The model involves the solution of the Maxwell equations, the Navier-Stokes equations, and the transport equations for the turbulence characteristicsk and e. The procedure of depth-averaging is applied in the treatment of several three-dimensional flows. Experiments were performed to check the computations using mercury as fluid. The spatial distribution of the magnetic induction and of the force density was determined for the laboratory inductor used in the stirring experiments. The flow velocity was measured photographically or with a drag probe, respectively. The agreement between experimental and theoretical data was found to be within 25 pct. It is concluded that the theory is sufficiently reliable to predict the flow fields in electromagnetic stirring of steel strands. In Part II of this paper the model is applied to analyze stirring situations in continuous casting of steel. Formerly with Institut für Allgemeine Metallurgie, Technische Universit?t Clausthal     

The mathematical and physical modeling of turbulent recirculating flows

A physical model has been constructed to represent turbulent recirculating flows that occur in argon-stirred ladles. By using a mechanically driven circulating system including a moving tube it was possible to generate flow fields such that all the boundary conditions could be defined unambiguously. The velocity fields developed in the system and the spatial distribution of the turbulent kinetic energy were measured experimentally using a laserdoppler anemometer. The experimental measurements were found to be in good agreement with predictions based on theK-W model for turbulent recirculating flows, provided appropriate wall functions were used. A simplified model was also described in the paper, for representing the transient decay of turbulence in teemed systems or in bubble stirred vessels after the agitation had been terminated. This model, which in essence involved the use of a simple algebraic relationship, gave semiquantitative agreement with measurements. R.METZ, formerly Graduate Student Department of Chemical Engineering, State University of New York at Buffalo,     

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.     

Mathematical modeling of flows in large tundish systems in steelmaking

Numerical solutions of the three-dimensional turbulent Navier-Stokes equations, incorporating thek-ε turbulence model, are presented for the turbulent flow of liquid within a tundish of high aspect ratio. Experimental results, obtainedvia Laser-Doppler anemometry and flow visualization techniques, are also reported. Calculated flow fields were shown to be similar to corresponding experimental flow fields. Such results can provide useful technological information regarding the design of tundishes in the steel industry for optimization of steel cleanliness.     

Transient steel quality under non-isothermal conditions in a multi-strand billet caster tundish: part I. Analysis of fluid flow,thermal behaviour and inclusion behaviour

A numerical model based on computational fluid dynamics was used to simulate the effect of non-isothermal conditions on melt flows in a multi-strand billet caster tundish. To start with, water was used as the operating fluid in a one-third scale tundish to calculate the fluid flow and temperature fields under isothermal and non-isothermal conditions. The model was then extended to the full-scale tundish with molten steel as the operating liquid in order to simulate the conditions in a real plant. It was observed that using step inputs of 10° and 23° for water and steel cases, respectively, changed the fluid flow patterns significantly, more so at locations far from the inlet, due to stronger buoyancy-driven natural convective flows. The temperature distribution and inclusion trajectories within the tundish were also affected due to the presence of non-isothermal conditions.     

Numerical and Physical Modeling of Steel Flow in a Two-Strand Tundish for Different Casting Conditions

This article presents computational and water model studies of the three-dimensional turbulent fluid flow in a two-strand tundish for steady-state and transient casting conditions. First, it presents the flow field measurements obtained at a 1:3-scale water model of the tundish with the particle-image velocimetry (PIV) method during steady-state casting. The PIV measurements were performed using the Reynolds-similarity criterion. Thereafter, numerical simulation is carried out with the computational fluid dynamic software, FLUENT, using the realizable k-ε turbulence model. The numerical model is validated using the measurement results obtained with the water model. The results of the numerical calculations are in good agreement with the PIV measurements. On this basis, the validated numerical model is adapted to simulate the 1:1-scale steel flow with boundary conditions that are derived from the real casting process. The nonisothermal, unsteady numerical calculations concerning the cooling process of steel melt inside the tundish are done for a 1:1-scale industrial facility—a 69-t two-strand tundish with a 380-t ladle. The influence of transient boundary conditions at the outlet of the tundish (one blocked strand) on the flow structure and mixing process of fluid during the casting process are investigated. The evaluation of the flow structure is performed using a zonal method, which relates the fluid flow with the mixing processes.     

Simulations of the Ladle Teeming Process and Verification With Pilot Experiment

The ladle teeming process was investigated by 2D axis‐symmetrical mathematical models and a pilot‐plant experiment. Different turbulence models, including the low Reynolds number k–ε model and the realizable k–ε model both with an enhanced wall treatment (EWT) and a standard wall function (SWF), were used to simulate this process. All of these turbulence model predictions generally agreed well with the experimental results. The velocity distributions in the nozzle were also predicted by these turbulence models. At the late stage of the teeming process, the drain sink flow phenomenon was studied. The combination of an inclined ladle bottom and a gradually expanding nozzle was found to be an effective way to alleviate a drain sink flow.     

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.     

Application of Several Depth-Averaged Turbulence Models to Simulate Flow in Vertical Slot Fishways

Vertical slot fishways are hydraulic structures which allow the upstream migration of fish through obstructions in rivers. The velocity, water depth, and turbulence fields are of great importance in order to allow the fish swimming through the fishway, and therefore must be considered for design purposes. The aim of this paper is to assess the possibility of using a two-dimensional shallow water model coupled with a suitable turbulence model to compute the flow pattern and turbulence field in vertical slot fishways. Three depth-averaged turbulence models of different complexity are used in the numerical simulations: a mixing length model, a k?ε model, and an algebraic stress model. The numerical results for the velocity, water depth, turbulent kinetic energy, and Reynolds stresses are compared with comprehensive experimental data for three different discharges covering the usual working conditions of vertical slot fishways. The agreement between experimental and numerical data is very satisfactory. The results show the importance of the turbulence model in the numerical simulations, and can be considered as a useful complementary tool for practical design purposes.     

Fluid Flow,Heat Transfer and Inclusion Motion in a Four‐Strand Billet Continuous Casting Tundish

Inclusions in the steel in a four‐strand continuous casting tundish, billet and wire products are firstly investigated with industrial trials, and the fraction of inclusions removed in terms of total oxygen in the tundish is measured. Then the 3‐dimenional fluid flow, heat transfer and inclusion motion in the tundish are numerically simulated. The κ‐? two‐equation model is used to model turbulence. Inclusion motion and trajectories are calculated by considering drag force and buoyancy force, coupling the effect of turbulent fluctuation (Random Walk Model). The effect of strands‐blocking on the fluid flow, heat transfer and inclusion removal is studied. A new design of tundish is proposed focusing on removing more inclusions from the molten steel.     

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.     

3D Numerical Simulation of Turbulent Buoyant Flow and Heat Transport in a Curved Open Channel

A three-dimensional buoyancy-extended version of k–ε turbulence model was developed for simulating the turbulent flow and heat transport in a curved open channel. The density-induced buoyant force was included in the model, and the influence of temperature stratification on flow field was considered. The flow and temperature fields were simulated simultaneously. The model was validated by comparison with laboratory measurements, and the simulated fields were generally in good agreement with experimental data. A comparison of velocity fields in thermal and isothermal flow in curved open channel is presented and the effects of channel curvature and buoyant force on the velocity fields are also discussed.