On Effective viscosity models for gas-stirred ladle systems

Metallurgical and Materials Transactions B -     

Numerical computation of flow phenomena in gas-stirred ladle systems

Quasi-single-phase mathematical models as applied to the ladle hydrodynamics have been analysed rigorously. It is shown that choice of convergence criteria, nodal configuration and differencing schemes all influence the computed results significantly and consequently, results independent of these numerical parameters must first be established to draw any useful conclusion. Several quasi-single-phase computational procedures reported in the literature to study the gas-injection-induced flow phenomena have been critically examined. To this end, experimentally measured bulk flow-fields, plume-rise velocity and gas voidages have been compared with those predicted numerically. Such comparisons indicate that the bottom injection phenomena (viz., bulk flow, plume-rise velocity, and gas volume fraction within the plume etc.) can be adequately represented by assuming bubble slippage and considering a constant rise velocity in the two-phase region in the numerical solution scheme.     

钢包底吹氩均混时间及临界流量水模型实验

针对钢包底吹氩工艺,通过改变透气砖数量、单透气砖吹气位置、双透气砖夹角、喷吹气体流量、渣厚等参数,对钢包的均混时间进行了水模型实验研究.提出临界流量的概念,发现吹气量超过临界流量后均混时间明显减小.结果表明:单透气砖喷吹时,相同吹气量下偏心喷吹时的均混时间比中心喷吹时短,临界流量小;双透气砖喷吹时,透气砖夹角越大,均混时间越短,临界流量越小.     

底吹钢包用圆孔透气砖冶金效果的水模型

采用水力学模型方法对钢包底吹氩工艺进行了实验研究,对比分析了圆孔型透气砖与狭缝式透气砖对冶炼效果的影响,并研究了圆孔透气砖的孔角和孔径对混匀时间、夹杂物去除率和渣眼面积的影响规律.结果表明:当吹气流量相同时,使用圆孔斜通透气砖时,钢包的混匀时间、夹杂物去除率和渣眼面积均优于狭缝式透气砖;相比于圆孔直通透气砖的钢包,使用圆孔斜通透气砖的钢包混匀时间更短,去除夹杂物效果佳,但渣眼面积略大;对于圆孔斜通透气砖,其孔径越小,钢包混匀时间越短,夹杂物去除率越高,渣眼面积越小.     

Study of the deoxidation of steel with aluminum wire injection in a gas-stirred ladle

In the present work, the deoxidation of liquid steel with aluminum wire injection in a gas-stirred ladle was studied by mathematical modeling using a computational fluid dynamics (CFD) approach. This was complemented by an industrial trial study conducted at Uddeholm Tooling AB (Hagfors, Sweden). The results of the industrial trials were found to be in accordance with the results of the model calculation. In order to study the aspect of nucleation of alumina, emphasis was given to the initial period of deoxidation, when aluminum wire was injected into the bath. The concentration distributions of aluminum and oxygen were calculated both by considering and not considering the chemical reaction. Both calculations revealed that the driving force for the nucleation fo Al₂O₃ was very high in the region near the upper surface of the bath and close to the wire injection. The estimated nucleation rate in the vicinity of the aluminum wire injection point was much higher than the recommended value for spontaneously homogeneous nucleation, 10³ nuclei/(cm³/s). The results of the model calculation also showed that the alumina nuclei generated at the vicinity of the wire injection point are transported to other regions by the flow.     

Numerical modelling of the transport and removal of inclusions in an industrial gas-stirred ladle

A full-scale, three-dimensional, transient CFD modelling approach capable of predicting the three-phase fluid flow characteristics and the inclusion removal in a gas-stirred ladle was developed. The comparison with experimental data indicates that this model can accurately predict the multiphase fluid flow and slag eye behaviour. The transport and removal of the inclusions in the gas-stirred ladle were predicted by tracing the movement of individual inclusions through computing their particle trajectories and considering a fluctuant top slag layer. The effects of inclusion size, gas flow rates, and injected bubble diameters as well as various removal mechanisms including slag capture, bubble attachment, and ladle wall adhesion on the removal of inclusions were investigated. It is shown that the slag capture is the prevailing mechanism for inclusion removal and the gas flow rate is the most important parameter for enhancing the inclusion removal efficiency.     

Spot turbulence,breakup, and coalescence of bubbles released from a porous plug injector into a gas-stirred ladle

Many metallurgical processes are connected with gas injection into liquid metals for refining purposes. For this reason, considerable effort has been made during the past 2 decades to investigate gas-injection operations in steelmaking ladles. Numerous physical and mathematical models are available in the literature as well as experiments (most of them performed in the air-water model). In theoretical works, usually, the bubble size is assumed constant, but this approximation is good just at low gas flow rates. When the gas flow rate increases, three different types of bubble dispersion patterns are observed in experiments. This situation cannot be predicted by means of the turbulence multiphase models normally implemented in commercial CFD codes. Their results predict a smooth (and wrong) bubble-size increase and not a sudden transition from a pattern to another, as in experiments. In this articles a new idea for approaching the bubble turbulence in the ladle, called “spot turbulence,” is presented and comparison with experimental data shown.     

Mass transfer between solid and liquid in a gas-stirred vessel

Mass transfer between solid and bulk liquid in an axisymmetric gas-stirred water model of a metallurgical reactor has been investigated both experimentally and theoretically. To this end, mass transfer rates from benzoic acid compacts submerged in an aqueous gas bubble driven system were measured via a weight loss technique. In conjunction with the weight loss measurements, liquid velocity and turbulence kinetic energy distributions in the bath were also mapped via laser doppler velocimetry (LDV). From the detailed LDV measurements, relevant dimensionless groups such as $\operatorname{Re} _{loc,r} \left( { = \frac{{d\rho \sqrt {u^2 + v^2 } }}{\mu }} \right)$ and $\operatorname{Re} _t \left( { = \frac{{d\rho \hat u}}{\mu }} \right)$ were estimated. Experimental measurements indicated that flow parameters varied from one location to another within the system. The corresponding variation in dissolution rates was, however, less pronounced. Such a trend was observed for all three gas flow rates studied. It was found that experimentally measured dissolution rates can be correlated with the measured flow and turbulence parameters (viz., √u ²+v ² and û) in terms of a previously reported dimensionless correlation, viz., Sh=0.73 (Re_loc,r )^0.25 (Re _t )^0.32 (Sc)^0.33. Parallel to flow measurements, a two-phase turbulent flow model was also applied to numerically compute the distributions of mean and fluctuating velocity components in the vessel. Embodying the predicted velocity components in the aforementioned correlation, mass transfer rates were recalculated. A comparison between the two sets of Sherwood numbers (estimated on the basis of the experimentally measured and theoretically predicted flow fields) suggests that solid-liquid mass transfer rates in a gas-stirred vessel can be predicted reasonably well via an axisymmetric, steady-state, two-dimensional turbulent flow model.     

Simulation on flow field and mixing phenomenon in RH degasser with ladle bottom blowing

Abstract

A numerical method has been employed to investigate the flow field and mixing characteristic in the Rheinsahl–Heraeus (RH) degasser with side–bottom blowing. The numerical results showed that stream flows in the up snorkel, the vacuum chamber, the down snorkel and the ladle form a large rectangular circulation zone in the RH degasser with side–bottom blowing, which can enhance the circulation flow rate effectively. For an RH with side–bottom blowing, when the included angle of the line between bottom blowing location and ladle centre and the line between two snorkels is zero, the circulation flow rate increases initially with increasing dimensionless distance between the bottom blowing location and the ladle centre and then decreases, while the mixing time increases with increasing dimensionless distance. On the other hand, when the dimensionless distance is 0·2, both the circulation flow rate and the mixing time decrease with the increasing included angle initially, reach their minimum value and then increase. The optimum values for the dimensionless distance and the included angle to achieve large circulation flow rate and small mixing time are 0·2 and π/4 in the present work.     

Model experiments on mixing phenomena in gas-stirred melts

Mixing experiments were performed in a water model system of a gas-stirred ladle with both an optical decolourization method and conductivity measurements at different positions within the vessel. The experimental results show that the rate by which the concentration is homogenized depends on the location of the measuring probe as well as on the used stirring conditions. Using a centric nozzle at the bottom pronounced dead zones exist. The equalization is slowest between these dead zones and the remaining volume. The mixing process in the remaining volume is characterized by a circulating concentration cloud in which mixing takes place by random turbulent diffusion. With an eccentric nozzle arrangement dead zones can be avoided and thus, mixing times decrease and become more similar for different positions.     

Critical analysis of "flip-flop" phenomenon in two-compartment pharmacokinetic model

Computer simulations were used to examine the effect of first-order absorption on the disposition of one- and two-compartment model drugs. Two-compartment systems that attain a clinically acceptable beta-phase after rapid intravenous injection were perturbed by introduction of drug via first-order absorption. The validity of perceiving such a system as a potential "flip-flop" model was tested by comparing the negative slopes of log-linear plasma-time profiles to known values for ka and beta for various values of ka, k12, k21, and k10. Although most log-linear plots showed excellent correlation coefficients (r2 greater than 0.996), their negative slopes (S) did not represent either ka or beta under various combinations. A similar consideration of the one-compartment model enabled a comparison to be made between the two systems. Maximum negative errors were observed for both one- and two-compartment drugs as ka leads to k2 or beta, respectively. The value for S provided a good estimate of the absorption rate constant, ka, when k2 greater than or equal 2ka (one compartment) or beta greater than or equal 2ka. The elimination rate constant (k2 or beta) could be obtained from S for all one-compartment and some two-compartment drugs when the value of ka was approximately twice that of k2 or beta. Large positive errors also were observed with certain two-compartment drugs where the ratio of the four rate constants apparently linearized a nonlinear plasma profile. Conditions wherein S may be expected to approach beta wherein S approaches ka are clearly defined.     

Scaling estimations of thermal and flow field in gas-stirred ladles

To obtain a better understanding of the physical process involved in gas stirring of a steelmaking vessel, a scaling analysis approach is developed that accounts for the effects of natural convection and axisymmetric bottom gas injection in the vessel. The orders of magnitude of some important quantities such as the transient velocity scale, thermal boundary layer thickness, and the critical flow rate to homogenize the thermal stratification in the molten steel are predicted successfully.     

Turbulence characteristics of a gas-stirred steel bath outside the bubble plume

In order to understand the turbulence characteristic in melts stirred with injected gas, the relations for effective diffusion coefficient, turbulent kinetic energy and mean size of energy containing eddies were derived from the energy equation with an extended flow field for the steel bath, where strong bubble plume and surface currents are present. 67 or 23% of the energy is dissipated in the bubble plume or surface flow zone. An increasing entrainment coefficient leads to higher values of energy dissipation factor, effective diffusion coefficient and mean size of energy containing eddies, but to low degrees of turbulence. With increasing bath aspect ratio the energy dissipation factor increases, but the degree of turbulence decreases. With increasing gas flow rate and bath height the effective diffusion coefficient enlarges. Increasing bath size leads to large mean size of energy containing eddies, which reaches 17% of the bath diameter at high gas flow rates.     

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.