Mixing characteristics of a submerged jet measured using an isokinetic sampling probe

The flow properties and mixing characteristics of a submerged gas jet near the injection point were measured using an isokinetic sampling probe in a water model. The radial and axial profiles of gas velocity, water velocity, and void fraction were measured. Since the gas velocity was always larger than that of the water, the existence of a slip velocity between gas and water was confirmed. A one-dimensional mathematical model was developed using the dimensionless slip velocity as a parameter. The dimensionless slip velocity (S) was estimated to be 0.3 to 0.6 for the nitrogen-water system. TheS of the He-water system was slightly larger than that of the nitrogen-water system. When the model was applied to calculate the gas fraction in the jet for the nitrogen-mercury system,S was estimated to be 0.95 to 0.97. A large slip velocity between gas and liquid is expected for gas-metal systems. Formerly Research Associate, the Research Institute of Mineral Dressing and Metallurgy, Tohoku University     

Steel dissolution in quiescent and gas stirred Fe/C melts

The dissolution rates of commercial black iron rods in iron/carbon melts under isothermal conditions were measured. The effect of melt carbon content, temperature, natural convection, and gas stirred forced convection conditions were investigated. The experimental data under natural convection conditions (no external stirring) were fitted with a dimensionless correlation for vertical cylinders: Sh = 0.13(Gr . Sc)^0.34, representing mass transport control dominated by turbulent natural convection. Under bottom injection gas stirring conditions, it was found that the kinetic power input had little effect on the rod dissolution rates which were controlled by the total gas flow rate. Derived mass transport coefficients under gas stirring conditions were found to have the following dependence on the gas injection rates:k _m ∝Q ^0.21, wherek _m = mass transport coefficient andQ = gas flow rate. A comparison of the experimental results with previously measured mass transfer coefficients under forced convection conditions gave a plume velocity flow rate dependence ofU ∝Q ^0.3. A general discussion of gas stirring fluid dynamics and resulting mass transport effects is presented.     

Mixing models for gas stirred metallurgical reactors

The mixing of liquids in ladles, (0.5 ≦L/D ≦ 2.0), agitated by a centrally rising bubble plume, has been analyzed both theoretically and experimentally. An exhaustive review of previous metallurgical literature on mixing in ladles and furnaces demonstrates that the majority of previous investigators in the field consider mixing to be brought about primarily by turbulent diffusion phenomena. The present study clearly shows that mixing is a combination of both convection and eddy diffusion processes, neither of which can be disregarded for gas stirred systems. For predicting mixing times during such gas injection procedures, a simple empirical equation is proposed for axisymmetric systems:τ _mαε_m ^−1/3L⁻¹R^5/3. Hereτ _m is the 95 pct mixing time,ε _m is the specific energy input rate,R is the vessel radius, andL is the depth of liquid. On the basis of physical and mathematical modeling, the rate of liquid mixing in conventional gas injection ladle metallurgy operations is compared with those observed in C.A.S. (composition adjustment by sealed argon bubbling) systems. It was found that mixing in C.A.S. operations is relatively slow and highly insensitive to gas flowrates(i.e., specific energy input rates).     

Hydrodynamics of gas stirred melts: Part I. Gas/liquid coupling

A hydrodynamic model of submerged gas injection systems and their effects on liquid metal stirring is presented. It is argued that hydrodynamic conditions at the nozzle, tuyere, or plug are not critical to flow recirculation produced in large cylindrical vessels(i.e., furnaces or ladles). An analysis of a buoyancy driven plume generated through gas injection shows that gas voidages are usually quite low (less than 10 pct). By equating the energy supplied by rising bubbles to turbulent energy losses within the bath, it is shown that mean plume velocities can be predicted using the relationship,U _p α (Q ^1/3 L ^1/3)/R^1/3 whereU _p equals mean plume velocity,Q is gas flow rate (at mean height and temperature),L is depth of liquid, andR is radius of the vessel. Associated rates of liquid turnover as a function of vessel dimensions and gas flow rate can also be predicted and these are similarly presented.     

A two-dimensional transient model for convection in laser melted pool

A two-dimensional transient model for convective heat transfer and surface tension driven fluid flow is developed. The model describes the transient behavior of the heat transfer process of a stationary band source. Semi-quantitative understanding of scanning is obtained by a coordinate transformation. The non-dimensional forms of the equations are derived and four dimensionless parameters are identified, namely, Peclet number (Pe), Prandtl number (Pr), surface tension number(S), and dimensionless melting temperature(@#@ T_m ^* @#@). Their governing characteristics and their effects on pool shape, cooling rate, velocity field, and solute redistribution are discussed. A numerical solution is obtained and presented. Quantitative effects of Prandtl number and surface tension number on surface velocity, surface temperature, pool shape, and cooling rate are presented graphically. This paper is based on a presentation made at the symposium “Fluid Flow at Solid-Liquid Interfaces” held at the fall meeting of the TMS-AIME in Philadelphia, PA on October 5, 1983 under the TMS-AIME Solidification Committee.     

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     

Modelling study of slag foaming phenomenon

A one‐dimensional model based on mass and momentum conservations has been developed to predict the heights of foams caused by gas injection. In the development of the model, a dimensionless number, N_foam = u_s.[(3C_d)/(4d_bg)]^1/2, has been deduced to characterise the foaming behaviour. According to the model, an increase in this dimensionless number results in an increase in foaming height. The validity of the model has been experimentally examined using silicon oils. The experiments have also shown that foamings can be classified into two types, namely one‐layer foaming and two‐layer foaming. The former type results in much larger height than the latter.     

Numerical modelling of gas stirred ladles

Abstract

A finite element analysis of the flow in a gas stirred vessel is presented. Turbulence is modelled using the two equation k–L predictor/ε corrector scheme algorithm; two alternative studies are compared, with and without flotation in k and ε transport equations. The biphasic zone is considered as an homogeneous fluid with a reduced density – the quasi-single phase approach. This reduced density is estimated taking into account the slip velocity between the rising bubbles and the liquid according to correlations from the literature. The numerical results are compared with experimental water model data and then used to predict the flow in two industrial liquid steel ladles with twin eccentric Ar injectors.     

Modelling criteria for flow simulation in gas stirred ladles: experimental study

Abstract

Criteria for modelling isothermal flows encountered in typical gas stirred ladles have been investigated both theoretically and experimentally. To this end, the phenomena of fluid mixing in ladles have been investigated in order to deduce the relationship between model and full scale gas flowrates, needed for maintaining dynamic similarity between the two. Starting with the governing equation for material transport, mixing times in geometrically and dynamically similar gas stirred systems were first correlated theoretically. On the basis of this, it is shown that, in the Froude dominated flow regime (typical of industrial ladle refining operations), the ratio of mixing times in geometrically and dynamically similar gas stirred systems can be represented in terms of the geometrical scale factor λ(=L _mod /L _fs ) according to τ_m,mod /τ_{m,fs = λ}^1/2. To assess the adequacy and appropriateness of various scaling equations reported in the literature (namely Q_{mod /Q fs} =λⁿ, proposed values of nbeing 1·5, 2·5, and 2·75, respectively), extensive experimental measurements of mixing times were carried out in three differently sized water model ladles. To measure mixing times, the conventional conductivity measurement technique was adopted. Comparisons of experimental ratios of mixing times with the corresponding theoretical ratio (=λ^1/2 ) confirm that, in the Froude dominated flow regime, the most appropriate criterion for dynamic similarity between model and full scale ladles is Q _mod /Q _fs = λ^2·5. Such findings were also corroborated through consideration of empirical mixing time correlations reported for Froude dominated ladle flows.     

Degassing of static melts by insoluble purge gases

A model has been developed to describe the degassing of static melts by insoluble purge gases. In this treatment, both the diffusion of dissolved hydrogen through the melt to the purge gas bubbles and the chemical kinetics of the adsorption of hydrogen at the bubble surfaces are considered. The process is modeled as one in which a small diameter column of purge gas bubbles rises in the center of a large diameter cylindrical static melt. Three dimensionless groups appear in the analysis, and they determine the melt gas content as a function of time. The first dimensionless group,β, is defined as the ratio of the diameter of the bubble column to that of the melt. The second,N _D, is the ratio of the kinetic rate of incorporation of hydrogen into the bubble column to the rate of diffusion of hydrogen through the melt to the bubble column. The third, α, is determined by the equilibrium concentration of hydrogen in the melt, and is normally wholly determineda priori. The model has been used to analyze the degassing of liquid aluminum. The degassing rates predicted by this model are shown to be in good agreement with experimental observations in melts of greatly different sizes and using various gas flow rates.     

Numerical studies of the motion of spheroidal particles flowing with liquid metals through an electric sensing zone

A mathematical model has been developed to describe the motion of variously shaped and oriented spheroids entrained in liquid metals passing through a cylindrical electric sensing zone (ESZ) developed for liquid metals cleanliness analyzer (LiMCA) systems. The fluid velocity field within the ESZ was obtained by solving the Navier-Stokes equations, while the trajectories of particles within the ESZ were calculated using the equations of motion for particles. These incorporate forces resulting from drag, added mass, history, and electromagnetic and fluid acceleration balanced against the time rate of changes in a particle momentum. The effects of particle or inclusion shape and orientation were taken into account by including correction factors for drag (R ^D), added mass (M ^A), history (B), and electromagnetic force (E ^M). The numerical results show that particle trajectories are affected by the magnetic pressure number (R _H), the Reynolds number (Re), the blockage ratio (k), and the particle-fluid density ratio (γ). In the axial direction, spheroidal particles travel further axially before hitting the wall as the fluid velocity (Re) increases. In the radial direction, the outwardly directed electromagnetic force on nonconducting spheroids increases with radial distance from the axis, with increasing electric current (R _H) and with increasing size (k) of the particle. At low electric currents (low R _H), the competition between the electromagnetic force and the radial fluid acceleration force in the entrance region is predicted to result in particle movements first toward the central axis, before outward motion toward the wall, but directly toward the wall at large currents (high R _H). Spheroidal particles with symmetric axes perpendicular to the transverse axis of the ESZ move faster toward the sidewall as the particle aspect ratio (E) increases. The dominating increase in the added mass force over the increase in the electromagnetic force with decreasing E makes this effect much stronger for oblates (E<1) than for prolates (E>1). The stronger drag force on a prolate with its symmetric axis parallel to the axis of the ESZ makes it move slower toward the wall than a prolate with its axis of symmetry perpendicular to the axis of the ESZ. Low-inertia (low-γ) spheroidal particles move faster toward the sidewall than do heavier particles. This effect of γ is stronger for prolates than for oblates traversing with their symmetric axes perpendicular to the axis of the ESZ, owing to the decreased added mass effect as E increases, while the effect of γ becomes much stronger for a prolate traversing with its symmetric axis perpendicular rather than parallel to the axis of the ESZ, owing to its smaller added mass. The radial particle velocity when approaching the wall is predicted to decrease due to the wall effects. This model has been applied to the movement of spheroidal inclusions within the ESZ of a LiMCA system in molten aluminum, and it was proven from the theoretical point of view that LiMCA systems could be used in aluminum industries.     

Mixing time and correlation for ladles stirred with dual porous plugs

Bulk mixing times up to a degree of 95 pct were measured in three different, cylindrical-shaped water model ladles (D=0.60 m, 0.45 m, and 0.30 m, respectively) in which, water was agitated by air introduced through two tuyeres/nozzles placed diametrically opposite at the base of the vessels at ±1/2 R positions. To this end, the electrical conductivity measurement technique was applied. A range of gas flow rates and liquid depths were investigated (viz. 0.7≤L/D≤1.2 and 0.002≤ɛ _m (watt/kg)≤0.01) and these were so chosen to conform to the practical ladle refining conditions. In the beginning, extensive experimental trials were carried out to assess the reliability of the measurement technique. In addition, some experiments were carried out to determine the location of the probe in the vessel such that measured mixing times could be interpreted as the bulk mixing times. It was observed that for smaller gas flow rates (or specific energy input rates), 95 pct bulk mixing times tend to decrease appreciably with increasing gas flow rates (e.g., τ _mix∞Q ^−0.58. However, for relatively higher flow rates, the dependence was found to be less pronounced, mixing times decreasing nearly in proportion to a third power of gas flow rates. Similarly, it was found that there exists a critical gas flow rate for any given vessel beyond which mixing times in dual plug stirred configuration are somewhat shorter than those in equivalent axi-symmetrical systems. A dimensional analysis followed by multiple regression of the experimental data (for ɛ _m ≥0.07 W/kg) indicated that mixing times in ladles fitted with dual plugs located diametrically opposite at ±R/2 locations could be reasonably described via τ _{mix, 95 pct}=15Q ^−0.38 L ^−0.56 R ^2.0 in which L is the depth of liquid (m), R is the vessel radius (m), and Q is the ambient flow rate (referenced to mean height and temperature of the liquid). Finally, the adequacy and appropriateness of the correlation was demonstrated with reference to the experimental data derived from a 0.20 scale, tapered cylindrical-shaped water model of a 140 T industrial ladle as well as scaling equations and modeling criteria reported in the literature.     

Mass transfer between solid and liquid in vessels agitated by bubble plume

Mass transfer from solid benzoic acid cylinders to a gas-stirred aqueous bath has been investigated both theoretically and experimentally. Two typical gas injection configurations, the conventional central injection and the C.A.S. (C omposition A djustment by S ealed Argon Bubbling) were employed and the rates of dissolution of the acid compacts at various locations in the bath were measured at different gas-flow rates. These demonstrated that the mass-transfer rates are the highest in the two-phase region, while elsewhere in the bath, these were found to be practically identical. Furthermore, mass-transfer rates at the corresponding locations were found to be relatively greater for the conventional central injection than those for the C.A.S. configuration. Distribution of velocity and turbulence intensity in the vessel were computed theoretically using a previously reported calculation procedure. Based on these, values of various relevant dimensionless numbers were estimated so as to assess the adequacy and effectiveness of heat and mass-transfer correlations reported in the literature. These, however, did not fit with the present experimental observations. For this reason, a new correlation has, therefore, been proposed and it is shown that the experimental data can be described reasonably well by the equation Sh = 0.73 (Re_loc,r)^0.57 (T_i)^0.32 (Sc)^0.3. This correlation also embodies more plausible definitions of Reynolds number (Re_loc,r) and the turbulence intensity (Ti) in contrast to those reported in literature, since it has been derived using the local resultant mean velocity and the local fluctuating velocity in the fluid.     

Effect of interphase lift force on fluid flow in air stirred cylindrical vessel

Abstract

In the present paper, based on the two-phase model (Eulerian model), the two-dimensional fluid flow in air stirred water systems is simulated, and the effect of interphase lift force on the fluid flow is specially discussed. In the Eulerian two-phase model, the gas and liquid phases are considered to be two different continuous fluids interacting with each other through the finite interphase areas. The exchange between the phases is represented by source terms in conservation equations. Turbulence is assumed to be a property of the liquid phase. The k–? model is used to describe the behaviour of the liquid phase. The dispersion of phases due to turbulence is represented by introducing a diffusion term into the mass conservation equation. The contribution of bubble movement to the turbulent energy and its dissipation rate are taken into account by adding extra volumetric source terms to the equations of turbulent energy and its dissipation rate. Comparison between the mathematical simulation and experimental data indicates that the interphase lift force has a strong effect on flow behaviour, and considering both drag force and lift force as interphase forces is important to accurately simulate the gas–water two-phase fluid flow in air stirred systems. The interphase lift force makes bubbles move away from the centreline; the gas concentration decreases near the centreline, and increases near the wall. The lift force is smaller than the drag force at the same place, especially far away from the centreline.     

Numerical Investigation of the Inner Profiles in Ironmaking Blast Furnace: Effect of the Ratio of Belly Diameter to Effective Height

The elaborate and appropriate design of blast furnace (BF) inner profile is indispensable. In practice, in this work, dumpiness, quantified by the ratio of belly diameter to effective height (R_D–H), primarily determines the inner profile and significantly affects the BF performance. However, the effects of R_D–H on BF operation are not investigated thoroughly, and an optimal range of R_D–H is not yet proposed. In this work, a numerical study on this topic is presented to recommend an R_D–H range for BF designers. This is achieved by using a recently developed 3D multi-fluid BF process model based on a 380 m³ industrial BF. In the results, it is shown that both too slender and too dumpy BFs do not favor BF production. Excessively slender BF leads to a dramatic increase in gas pressure drop; however, the saving of coke or the improvement of productivity is insignificant. In contrast, excessively dumpy BF leads to a dramatic increase in coke rate and a significant decrease in productivity. Under the current conditions, the recommended dumpiness exists in the value of R_D–H at around 0.35, where a low coke rate, low gas pressure drop, high productivity, and high thermal energy utilization are all ensured.     

Order-of-magnitude scaling of the cathode region in an axisymmetric transferred electric arc

A new technique of order-of-magnitude scaling (OMS) has been applied to the mathematical modeling of the cathode region of a long gas tungsten arc (GTA). The estimations obtained are combined with numerical calculations; thus, important features of both techniques are considered simultaneously: the high precision of numerical modeling and the generality and simplicity of algebraic expressions. Power-law expressions for the estimations of characteristic unknowns such as maximum pressure in the cathode spot and maximum plasma velocity are obtained and are consistent with previous analytical or asymptotic work. Dimensional analysis is used to identify dimensionless groups governing the system, and asymptotic considerations are used to identify two dimensionless groups (the Reynolds number and the dimensionless arc length) as the most significant ones governing momentum transfer in the cathode region. The estimations obtained are calibrated with functions that depend only on these two most significant dimensionless groups. It is suggested that the numerical results for different cases can be reduced to a single general map.     

Submerged liquid slag injection in steel melt: scaleup study using cold model and dimensional analysis

Abstract

Submerged injection of solid flux powder is used in the steel industry to eliminate impurities in an economical way. The efficiency of such an injection process is limited by the fact that only a fraction of the injected particles penetrate into the liquid melt, while the majority remain as bubble encapsulated solids, causing poor heat and mass transfer. Therefore, liquid slag injection can be considered a potential alternative technique in the refining of steel to improve the efficacy of mass transfer in such a process. In the present work, liquid slag injection in a steel melt has been simulated by means of laboratory scale cold model experiments in which, water, paraffin oil and benzoic acid have been used as low temperature analogues for liquid steel, slag and impurities, respectively. Through dimensional analysis it is observed that the modified Froude number can be considered as a criterion for scaling up such a process from a bench scale to a full scale system. A regression analysis has also been carried out to correlate the dimensionless mass transfer rate constant with the relevant dimensionless numbers, namely, dimensionless gas velocity, Froude number, aspect ratio and non-dimensional lance depth.     

Mass transfer in a bottom blowing cold model converter

In a model converter containing oil and water the volumetric mass transfer of caprylic acid was determined in dependence of the gas flow rate. Several other parameters were varied such as the number and configuration of nozzles, gas velocity, oil viscosity and volume and model size. Partially the results could be described by dimensionless equations. Visual observations of the bath surface with special regard to the wave formation complete the results of the measurements. By knowledge of the drop size spectrum independently determined, the mass transfer coefficient under dispersion conditions could be evaluated. These values were compared with mass transfer coefficients which had been directly measured by the single rising drop technique as well as the bubble stirred interface without dispersion. It seems that turbulence in dispersed systems does not enlarge the mass transfer coefficient.     

Effect of Salt Tracer Amount on the Mixing Time Measurement in a Hydrodynamic Model of Gas‐Stirred Ladle System

The hydrodynamic modeling method in gas‐stirred ladle system that widely used to measure the mixing time was reconsidered and discussed in this paper. The effect of injected salt tracer amount on the mixing time measurement was investigated. For the mixing time curve, the final concentration increased with the tracer amount increased; also this curve exhibited occasional sharp increasing tendency when a larger amount of tracer was injected. Besides, the obtained mixing time decreased with the tracer amount increased. The error of mixing time measurement was mainly from the tracer concentration fluctuation beyond the criterion range when a much smaller amount of tracer was injected. While the criterion range increased with the tracer amount increased for a certain criterion of mixing. Finally, the tracer selection should be considered combined with the criterion of the definition of mixing. In the present study, the dimensionless tracer amount (defined as the ratio of tracer amount to the water volume in hydrodynamic model) of KCl solution should be larger than 0.2692 × 10^?3 or 0.6731 × 10^?3 when 5 or 1% criterion was used.     

Non-isothermal finite diffusion-controlled growth in ternary systems

A mathematical model has been developed for diffusion controlled phase growth in ternary systems. Local equilibrium at phase boundaries and one dimensional diffusion controlled growth is assumed. The model includes a method of determining phase growth velocity and interface compositions consistent with the diffusion rate of both solute elements. This method also accounts for the effects of overlapping diffusion fields and nonisothermal growth. Initial conditions can be any curvilinear composition gradients and boundary conditions can be fixed or vary with time and/or temperature. The Crank-Nicolson finite difference equations are used to provide numerical stability and flexibility. Other capabilities of the model include treatment of finite systems, of nonisothermal phase growth and of off-diagonal ternary coefficients (D ₂₁ ³,D ₁₂ ³). Several sample simulations of the constant cooling of a 2.1 wt pct P, 4.1 wt pct Ni, 93.8 wt pct Fe alloy are presented. Three cooling rates are used: 5×10⁻³, 5×l0⁻⁴, and 5×l0⁻⁵ °C/s. An Fe-Ni-P alloy of this same composition was cooled in the laboratory for five days at 5×lo⁻⁴ °C/s from 900 to 685°C. Excellent agreement was found for the predicted and measured composition gradients and precipitate sizes.