Mixing and solid-liquid mass-transfer rates in a creusot-loire uddeholm vessel: A water model case study

The process of mixing and solid-liquid mass transfer in a one-fifth scale water model of a 100-ton Creusot-Loire Uddeholm (CLU) converter was investigated. The modified Froude number was used to relate gas flow rates between the model and its protoype. The influences of gas flow rate between 0.010 and 0.018 m³/s and bath height from 0.50 to 0.70 m on mixing time were examined. The results indicated that mixing time decreased with increasing gas flow rate and increased with increasing bath height. The mixing time results were evaluated in terms of specific energy input and the following correlation was proposed for estimating mixing times in the model CLU converter: T _mix=1.08Q ^−1.05 W ^0.35, where Q (m³/s) is the gas flow rate and W (tons) is the model bath weight. Solid-liquid mass-transfer rates from benzoic acid specimens immersed in the gas-agitated liquid phase were assessed by a weight loss measurement technique. The calculated mass-transfer coefficients were highest at the bath surface reaching a value of 6.40 × 10⁻⁵ m/s in the sprout region. Mass-transfer coefficients and turbulence parameters decreased with depth, reaching minimum values at the bottom of the vessel.     

Model study on mixing and mass transfer in ferroalloy refining processes

An experimental study has been performed to investigate the bath mixing intensity induced by a high-strength submerged gas injection in a bottom blown air-stirred one-seventh water model of Creusot-Loire Uddeholm (CLU) reactor using three different tuyere configurations. Experimental results have been discussed in terms of the mass transfer rate and mixing time. The air flow rates varied from 0.00599 to 0.01465 m³/s. The mixing time was determined at various gas flow rates, bath heights, and nozzle orientations, both in the presence and absence of a second phase. The mixing time was found to decrease with increasing gas flow rate and decreasing bath height. The influence of bath mixing intensity on mass transfer between metal (water) and slag (paraffin) was studied by measuring the transfer of benzoic acid from the gas-stirred water bath to paraffin as a function of the gas injection parameters. The bath mixing intensity was characterized by the value of the mass transfer rate constant. The rate constant of mass transfer between the metal and slag was found to increase with increasing gas injection rate and decreasing bath height.     

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.     

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).     

Characterization of two-phase axisymmetric plume in a gas stirred liquid bath—A water model study

Plume profile and plume cone angle (θ_c) were determined by still photographic technique in a cold model set-up where air was blown into a water bath through an axial nozzle located at the bottom of the vessel. Effects of various operating variables,e.g., gas flow rate(Q), bath height(H), and nozzle diameter(d _n) on the plume profile were investigated. θ_c increased with increasingQ, decreased with increasingH, but was approximately independent ofd. Based on the experimental data the following empirical correlation was developed: whereD is bath diameter, Fr_m is modified Froude number (= 16Q²/π²gd⁴ _nH⋅ _G/(p_L-p_G)), g is acceleration due to gravity, andp _L andp _G are densities of liquid and gas, respectively. G.G. KRISHNA MURTHY, formerly Graduate Student in the Department of Metallurgical Engineering at the Indian Institute of Technology, Kanpur, India.     

Mathematical modeling of mixing phenomena in a gas stirred liquid bath

A macroscopic, steady state energy balance model has been formulated to describe mixing phenom-ena in a liquid bath stirred by injecting gas through a straight nozzle fitted axially at the bottom of the vessel. This, along with experimental data on a water model previously reported, was employed to make predictions. Input energy terms considered in the model consist of buoyancy energy and empirically determined fraction of gas kinetic energy. Dissipation of energy was attributed to liquid circulation and bubble slip. The two-phase plume was assumed to be a truncated cone whose dimen-sions depended upon operating conditions. Numerical solution of model equations gave liquid velocity and gas hold-up inside the plume as well as liquid circulation rate and liquid velocity in the region outside the plume. Influence of process variables, e.g., gas flow rate, bath height, and nozzle diameter, have been predicted. Validity of the model has been established by comparing some pre-dicted entrainment ratios with those experimentally measured by other investigators. Empirical cor-relations to predict circulation time and circulation number have been proposed. Circulation number was found to vary between 2 and 12 in contrast to the existing assumption in the literature of a con-stant value of 3. Usefulness of these correlations in predicting mixing time for industrial vessels has been demonstrated. Formerly a Graduate Student in the De-partment of Metallurgical Engineering at the Indian Institute of Technol-ogy, Kanpur     

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.     

Model study of mixing and mass transfer rates of slag-metal in top and bottom blown converters

Water model experiments have been conducted to clarify mixing rates of molten steel and mass transfer rates between slag and metal in LD and Q-BOP furnaces using six different circular tuyere arrangements. Splashing and ‘spitting’ were also examined with a view to finding a quiet bath with minimum mixing time and maximum mass transfer rate. Froude’s similarity criterion was fulfilled to determine gas flow rate and bath depth. Complete mixing time of water determined by tracer technique had been 0.9 second to 1.8 seconds for Q-BOP as compared to 6 seconds to 13 seconds for LD. This shows that the stirring intensity in Q-BOP is remarkably larger than that of LD. A simple relationship τ = 5.9(Q/N) ^−0.49 was obtained with gas flow rateQ and number of tuyereN. This indicates that flow rate of gas per tuyere should be intensified to realize better mixing. Mass transfer coefficient K_Ba for bottom blowing was found to be almost double that for top blowing. Of all the tuyere configurations studied for Q-BOP’s, a half circular tuyere arrangement was found to be the best considering all aspects of mixing, mass transfer, and bath agitation.     

Symmetry-breaking transitions in equilibrium shapes of coherent precipitates: Effect of elastic anisotropy and inhomogeneity

We examine the symmetry-breaking transitions in equilibrium shapes of coherent precipitates in two-dimensional (2-D) systems under a plane-strain condition with the principal misfit strain components ε* _xx and ε* _yy . For systems with cubic elastic moduli, we first show all the shape transitions associated with different values of t=ε* _yy /ε* _xx . We also characterize each of these transitions, by studying its dependence on elastic anisotropy and inhomogeneity. For systems with dilatational misfit (t=1) and those with pure shear misfit (t=−1), the transition is from an equiaxed shape to an elongated shape, resulting in a break in rotational symmetry. For systems with nondilatational misfit (−1<t<1; t ≠ 0), the transition involves a break in mirror symmetries normal to the x- and y-axes. The transition is continuous in all cases, except when 0<t<1. For systems which allow an invariant line (−1≤t<0), the critical size increases with an increase in the particle stiffness. However, for systems which do not allow an invariant line (0<t≤1), the critical size first decreases, reaches a minimum, and then starts increasing with increasing particle stiffness; moreover, the transition is also forbidden when the particle stiffness is greater than a critical value.     

Mathematical simulation of fluid dynamics during steel draining operations from a ladle

Fluid flow dynamics during ladle drainage operations of steel under isothermal and nonisothermal conditions has been studied using the turbulence shear stress transport k-ε model (SST k-ω) and the multiphase volume of fluid (VOF) model. At high bath levels, the angular velocity of the melt, close to the ladle nozzle, is small rotating anticlockwise and intense vertical-recirculating flows are developed in most of the liquid volume due to descending steel streams along the ladle vertical wall. These streams ascend further downstream driven by buoyancy forces. At low bath levels, the melt, which is close to the nozzle, rotates clockwise with higher velocities whose magnitudes are higher for shorter ladle standstill times. These velocities are responsible for the formation and development of a vortex on the bath free surface, which entrains slag into the nozzle by shear-stress mechanisms at the metal-slag interface. The critical bath level or bath height for this phenomenon is 0.35 m (in this particular ladle design) for a ladle standstill time of 15 minutes and decreases with longer ladle standstill times. At these steps, the vertical-recirculating flows are substituted by complex horizontal-rotating flows in most of the liquid volume. Under isothermal conditions, the critical bath level for vortex formation on the melt free surface is 0.20 m, which agrees very well with that determined with a 1/3 scale water model of 0.073 m. It is concluded that buoyancy forces, originated by thermal gradients, as the ladle cools, are responsible for increasing the critical bath level for vortex formation. Understanding vortex mechanisms will be useful to design simple and efficient devices to break down the vortex flow during steel draining even at very low metal residues in the ladle.     

Measurement of physical characteristics of bubbles in gas-liquid plumes: Part II. Local properties of turbulent air-water plumes in vertically injected jets

The structural development of air-water bubble plumes during upward injection into a ladle-shaped vessel has been measured under different conditions of air flow rate, orifice diameter, and bath depth. The measured radial profiles of gas fraction at different axial positions in the plume were found to exhibit good similarity, and the distribution of the phases in the plume was correlated to the modified Froude number. Different regions of flow behavior in the plume were identified by changes in bubble frequency, bubble velocity, and bubble pierced length which occur as bubbles rise in the plume. Measurement of bubble velocity indicates that close to the nozzle the motion of the gas phase is strongly affected by the injection velocity; at injection velocities below 41 m/s, the velocity of the bubbles along the centerline exhibits an increase with height, while above, the tendency reverses. High-speed film observations suggest that this effect is related to the nature of gas discharge,i.e., whether the gas discharge produces single bubbles or short jets. In this region of developing flow, measurement of bubble frequency and pierced length indicates that break-up of the discharging bubbles occurs until a nearly constant bubble-size distribution is established in a region of fully developed flow. In this largest zone of the plume the bubbles influence the flow only through buoyancy, and the spectra of bubble pierced length and diameter can be fitted to a log-normal distribution. Close to the bath surface, a third zone of bubble motion behavior is characterized by a faster decrease in bubble velocity as liquid flows radially outward from the plume.     

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.     

Water model study of the frequency of bubble formation under reduced and elevated pressures

Air was injected vertically upward into a water bath through a bottom nozzle or a bottom orifice. The surface pressure was reduced or elevated from an atmospheric pressure in order to change the hydrostatic pressure around the nozzle and orifice. The gas delivery system was designed so that bubbles were generated in the middle and high gas flow rate regimes under a constant flow condition. The frequency of bubble formation, f _B , decreased as the surface pressure, P _s , decreased when the volumetric gas flow rate, Q _g , was kept constant. The measured f _B values were predicted satisfactorily by an empirical equation proposed previously by the present authors. This equation was derived originally to correlate the frequency of bubble formation both in aqueous and molten metal systems under an atmospheric surface pressure. The effect of surface pressure on the frequency of bubble formation was considered in terms of the density of gas, ρ _g , and the volumetric gas flow rate Q _g in the aforementioned empirical equation. These two quantities, ρ _g and Q _g , were evaluated at the nozzle exit by using the hydrostatic pressure there.     

Enthalpies of mixing of rare-earth metal-aluminum alloys: Model calculations

Integral enthalpies of mixing Δ_mix H for binary rare-earth metal (REM)-aluminum systems are calculated using the following three semiempirical approaches: an ideal solution model for interaction products, the Miedema model, and a specific calculation algorithm developed by us. Possible qualitative and, for a number of alloys, quantitative agreement of the calculation results with each other and the experimental data is demonstrated. The model parameters that allow the enthalpies of mixing to be calculated using simple relations are reported. The values of Δ_mix H are calculated for Al-REM alloys over the entire composition range.     

The application of a dislocation model to the strain and temperature dependence of the strain hardening exponentn in the Ludwik-Hollomon relation between stress and strain in mild steels

With the aid of a dislocation model for the stress-strain relationship of α-Fe, analytical expressions for the strain and temperature dependence of the exponentn in the relation, σ= K · ε ⁿ, are derived. These account quite accurately for experimental results obtained with several low alloy steels. It is shown thatn varies continuously with strain but that the theoretical and experimental log σ-log ε curve in most cases can be approximated by two straight lines in accordance with the well-known “double-n” behavior. The strain, ε₁ at which the two lines intersect is equal to the strain at which the theoretical n(ε) curve has an inflection point. With the model presented it is also possible to account for the temperature dependence ofn(ε) and of ε₁ within the temperature range −78° to 500°C.     

Assessment of service induced microstructural damage and its rejuvenation in turbine blades

Correlations between service induced microstructural degradation and creep properties in investment cast IN738LC turbine blades are discussed. Microstructural degradation in the form of γ’ coarsen-ing, MC carbide degeneration, formation of continuous networks of grain boundary M₂₃C₆ carbides, and the disappearance of serrated grain boundaries are considered in some detail. Their influence on primary (t _p ,ε _p ), secondary (t _s , ε _s ,ε _m ) and tertiary (t_t, ε_t) creep behavior is analyzed through rela-tionships of the form:

Experimental determination of the jet effect for blowing oxygen into the melting bath of electric arc furnaces

Recent practice with electric arc furnaces has been the injection of oxygen through nozzle positioned on the bottom of the furnace. This type of furnace places certain requirements on bottom injection. To enable a constant coupling of the energy over the electrodes, a calm bath surface must be guaranteed. On the other hand, a good mixing of the bath is required to avoid any thermal lamination in the bath. The latter condition in particular is prerequisite for a maximum melting capacity. When judging the effect of the jet on the bath, it must be taken into account that the oxygen disintegrates directly after entering the bath and merely transfers its impulse to the liquid melt. This jet effect is described by the calculation method introduced below which is adjusted to the actual behaviour using simulation tests. In this connection, changes in the jet consistency caused by the formation of carbon monoxide have not yet been considered. Parallel to this, the mixing of the bath was determined by conductivity measurements. In these experiments, the bath level x_f, the vessel diameter D and the blown-in water mass-flux m_w were changed. A comparison of the results for fountain height and mixing time formed the basis for the development of an optimization concept for bottom-blowing nozzles in electric arc furnaces.     

Measurements of bubble plume behaviour and flow velocity in gas stirred liquid Wood's metal with an eccentric nozzle position

The distribution of gas fraction and the flow field of gas-stirred liquid metal in steel ladles at eccentric injection of the stirring gas through the bottom of the vessel were measured in melts of 437 kg liquid Wood's metal. The melts had a temperature of 100°C. The bath height was 37 cm and the vessel diameter 40 cm. The blowing nozzle was positioned at half of the vessel radius. Gas flow rates were between 100 and 800 cm³(STP)/s. The gas fractions were measured by electrical resistance probes. The flow velocity of the liquid metal was determined by magnet-probes. The gas fraction and the velocity distribution in the plume were found to have a Gaussian shape. The cross-section of the plume is ellipsoid, as the plume width in the direction of the radius was a little smaller than the width in the direction perpendicular to it. Moreover the plume was inclined to the wall. The results which were found for the plume are mathematically described. The flow field at eccentric gas-stirring consists of one great loop, which fills almost the entire vessel. This is contrary to centric blowing, where for aspect ratios of the ladle in the order of 1, a toroid is formed in the upper and a dead zone exists in the lower part of the vessel. The consequences of this behaviour, especially for mixing in the melt, are discussed.     

Experimental evidence for electrochemical nature of the reaction between iron oxide in calcia-silica-alumina slag and carbon in liquid iron

The electrochemical nature of the reaction between iron oxide in calcia-silica-alumina slag and carbon in liquid iron has been studied by measuring the kinetics of the slag-metal reaction. A base slag (48 pct CaO-40 pct SiO₂-12 pct Al₂O₃) containing iron oxide (≤8 wt pct FeO _t ) was reduced by an Fe-C metal bath (∼4 wt pct C) at 1400 °C. The reaction rate was calculated from measurements of the total inlet gas flow rate and the CO concentration in the outlet gas stream. The slag was “internally short circuited” by dipping an iron plate through the slag layer, and this resulted in an increase in the rate of CO evolution. An external circuit was produced by dipping a graphite rod (shielded from the slag) into the metal bath and a steel or molybdenum rod into the slag layer; the open-circuit voltage and short-circuit current were measured when iron oxide was added to the base slag layer. The reaction rate was enhanced by applying a voltage across the slag layer, and an electric arc cathode was employed in some of these “electrolysis” experiments.