Accretion growth on single-pipe tuyeres: Part II. Model results and discussion

A mathematical model of accretion growth on single-pipe injectors has been used to analyze the process of accretion growth during copper converting and inert gas stirring of steel. A sen-sitivity analysis of the model developed in Part I of this article revealed that the critical unknown factor controlling the growth process is the local bath velocity. It is likely that the asymmetric forms seen in accretions are due primarily to nonuniformity in bath flow around the accretion. The important factors controlling the size of accretions in copper converting are bath superheat, gas flow rate, and oxygen content. Blockage of the tuyeres in the converter is a function of wall and bath superheat and likely is a result of the freezing of matte in the pipe. The effect of gas-flow rate on accretion size is clearly shown in the case of inert gas injection into steel. The transition between the different accretion types found on single-pipe tuyeres, pipes, porous pipes, and hemispheres, depends on events at the tuyere-pipe tip. Conditions of high back-attack frequency, low superheat, and small tuyere diameters tend to lead to accretions forming over the tip. If this takes place at high injection pressures and with a relatively ductile material, a “porous plug” will form, on which a hemisphere will grow. Under other conditions, it may result in a blockage. The presence of accretions at a tuyere has a strong influence on the thermal profile in the surrounding refractory and tuyere pipe. Steep thermal gradients near the tip in both regions will likely lead to refractory deterioration and pipe distortion. Formerly Associate Professor, University of British Columbia, Vancouver.     

Macrotransport-solidification kinetics modeling of equiaxed dendritic growth: Part I. Model development and discussion

An analytical model that describes solidification of equiaxed dendrites has been developed for use in solidification kinetics-macrotransport modeling. It relaxes some of the assumptions made in previous models, such as the Dustin-Kurz, Rappaz-Thevoz, and Kanetkar-Stefanescu models. It is assumed that nuclei grow as unperturbed spheres until the radius of the sphere becomes larger than the minimum radius of instability. Then, growth of the dendrites is related to morphological instability and is calculated as a function of melt undercooling around the dendrite tips, which is controlled by the bulk temperature and the intrinsic volume average concentration of the liquid phase. When the general morphology of equiaxed dendrites is considered, the evolution of the fraction of solid is related to the interdendritic branching and dynamic coarsening (through the evolution of the specific interfacial areas) and to the topology and movement of the dendrite envelope (through the tip growth velocity and dendrite shape factor). The particular case of this model is the model for globulitic dendrite. The intrinsic volume average liquid concentration and bulk temperature are obtained from an overall solute and thermal balance around a growing equiaxed dendritic grain within a spherical closed system. Overall solute balance in the integral form is obtained by a complete analytical solution of the diffusion field in both liquid and solid phases. The bulk temperature is obtained from the solution of the macrotrasport-solidification kinetics problem.     

Cellular and dendritic growth: Part I. Experiment

An Al-4.1 mass pct Cu alloy was unidirectionally solidified under various growth rates. Features, such as tip radius of curvature, primary arm spacing, and tip concentration were measured as functions of growth rate. Dependence of tip radius on growth rate was different between cells and dendrites. Measured tip radius and primary arm spacing were maximum at the cellular-dendritic transition. Tip concentration, however, monotonously decreases with growth rate. Linear relationships between tip radius and characteristic dimensions of dendrites like core diameter, half length of tip arc, and the first secondary arm spacing are obtained to determine what affects growth rate, convection, and gravity segregation. Experimental results are compared with current theoretical models for dendrite growth under controlled solidification. It was determined that the measured tip radius is larger than that of theoretical predictions at fast growth rate, but the measured tip concentration is in good agreement with theoretical predictions.     

A mathematical model of the nickel converter: Part I. Model development and verification

A mathematical model of the nickel converter has been developed. The primary assumption of the model is that the three phases in the converter are in thermal and chemical equilibrium. All matte, slag, and gas in the converter is brought to equilibrium at the end of each of a series of short time steps throughout an entire charge. An empirical model of both the matte and slag is used to characterize the activity coefficients in each phase. Two nickel sulfide species were used to allow for the modeling of sulfur-deficient mattes. A heat balance is carried out over each time step, considering the major heat flows in the converter. The model was validated by a detailed comparison with measured data from six industrial charges. The overall predicted mass balance was shown to be close to that seen in actual practice, and the heat balance gave a good fit of converter temperature up to the last two or three blows of a charge. At this point, reactions in the converter begin to deviate strongly from “equilibrium,” probably due to the converter reactions coming under liquid-phase mass-transfer control. While the equilibrium assumption does work, it is not strictly valid, and the majority of the charge is probably under gas-phase mass-transfer control.     

Stirring and its effect on aluminum deoxidation of steel in the ASEA-SKF furnace: Part I. Plant scale measurements and preliminary analysis

Simultaneous radioactive tracer dispersion and deoxidation measurements were taken in a 50 ton, electromagnetically stirred ASEA-SKF furnace. The tracer mixing studies were interpreted in terms of a one-dimensional dispersion model, by the “peak area method” and by the observation of the mixing time. The deoxidation measurements were interpreted by deducing the “deoxidation constant.” The measured eddy diffusivities ranged from about 100 to 300 cm²/s. and the circulation rates were of the order of 50 to 150 tons/min. The measurements indicate that the mixing characteristics of the system are not very much affected by power input (within the range studied), but the actual orientation of the electromagnetic field plays a major role. No direct correlation has been found between the rate of mixing and the deoxidation rate. It is suggested that a more sophisticated interpretation of the results through the use of turbulence theory would provide the desired relationship between mixing and deoxidation. Such work is in progress.     

Fundamental Mathematical Model for AOD Process. Part I: Derivation of the Model

This paper presents a new simulation model for the AOD process that takes the local variations into account but is still computationally efficient. The new idea here was to model AOD reactor as a combination of a plug flow reactor for the plume zone and a continuously stirred tank reactor (CSTR) for the bath and surface slag. This approach adopted has many advantages compared with the previous models. At first, it offers an effective method for considering the locally varying conditions as the gas bubbles rise in the plume. The model can be built computationally very effective compared to CFD due to significantly smaller amount of variables. The validation of the model is also easier as it has features that can be experimentally determined. The model is based on the simultaneous solution of conservation equations of mass, species and energy in all the vertical cells of the plug flow reactor, and a single volume in bath and surface slag. A novel method was developed and used for solving the rates in a mass transfer controlled multi‐component reaction system. In this Part I of this paper, the model is presented and its features discussed by few illustrative examples. In the following Part II, the model is broadly validated with new full scale industrial AOD process measurements for carbon release rate, melt composition, slag composition and bath temperature rise during final stages of carbon removal.     

A Transient Thermal Model for Friction Stir Weld. Part I: The Model

Current analytical thermal models for friction stir welding (FSW) are mainly focused on the steady-state condition. To better understand the FSW process, we propose a transient thermal model for FSW, which considers all the periods of FSW. A temperature-dependent apparent friction coefficient solved by the inverse solution method (ISM) is used to estimate the heat generation rate. The physical reasonableness, self-consistency, and relative achievements of this model are discussed, and the relationships between the heat generation, friction coefficient, and temperature are established. The negative feedback mechanism and positive feedback mechanism are proposed for the first time and found to be the dominant factors in controlling the friction coefficient, heat generation, and in turn the temperature. Furthermore, the negative feedback mechanism is found to be the controller of the steady-state level of FSW. The validity of the proposed model is proved by applying it to FSW of the 6061-T651 and 6063-T5 aluminum alloys.     

Dendritic growth of undercooled nickel-tin: Part I

Solidification of undercooled Ni-25 wt pct Sn alloy was observed by high-speed cinematography and results compared with optical temperature measurements. Samples studied were rectangular in cross-section, and were encased in glass. Cinematographic measurements were carried out on samples undercooled from 68 to 146 K. These undercoolings compare with a temperature range of 199 K from the equilibrium liquidus to the extrapolated equilibrium solidus. At all undercoolings studied, the high-speed photography revealed that solidification during the period of recalescence took place with a dendrite-like front moving across the sample surface. Spacings of the apparent “dendrite” were on the order of millimeters. The growth front moved at measured velocities ranging from 0.07 meters per second at 68 K undercooling to 0.74 meters per second at 146 K undercooling. These velocities agree well with results of calculations according to the model for dendrite growth of Lipton, Kurz, and Trivedi. It is concluded that the coarse structure observed comprises an array of very much finer, solute-controlled dendrites.     

Prenatal fluoride for growth and development: Part X

Polymerase chain reaction (PCR) with degenerate primers was utilized for partial cloning of the MADS box gene family from wheat (Triticum aestivum L.). PCR products corresponding to a part of the MADS box region were cloned and sequenced. Eleven individual clones sequenced were classified into seven types on the basis of the nucleotide sequence and five types on the deduced amino acid sequence, which included two wheat-specific MADS box protein sequences. RT-PCR analysis with degenerate primers revealed preferential expression of the MADS box genes in young spikes. Furthermore, genomic Southern blot analysis with degenerate PCR products as probes indicated that wheat MADS box genes constitute a multigene family and are dispersed throughout the genome.     

Rat mandibular distraction osteogenesis: Part I. Histologic and radiographic analysis

The application of distraction osteogenesis to craniofacial surgery has altered the approach and treatment of congenital and acquired craniofacial defects. Although the histologic and ultrastructural changes associated with distraction osteogenesis have been described extensively, relatively little is known about the molecular regulation of this process. The elucidation of the molecular mechanisms of distraction osteogenesis has important clinical implications because it may facilitate the use of recombinant proteins or gene therapy to accelerate bone regeneration. Molecular analysis of distraction osteogenesis has been hindered by the use of large animal models in which only limited genetic information is available. In this study, a rat model of mandibular distraction osteogenesis is described. This report includes a pilot study (n = 50) to develop an appropriate distraction device and to determine the optimal placement of the osteotomy. The study subsequently included 80 animals, 35 of which were distracted at a rate of 0.25 mm per day for 6 days (1.5 mm total) and 35 that were distracted at a rate of 0.25 mm twice per day (3.0 mm total). These animals were killed at various time points (after latency and during the distraction and consolidation periods) and displayed histologic and radiographic findings of membranous bone distraction osteogenesis that were consistent with those in large ,animal and clinical models. In addition, five animals each were acutely lengthened 1.5 mm and 3.0 mm and demonstrated a fibrous nonunion. Furthermore, the utility of this model is demonstrated in the analysis of the molecular mechanisms of distraction osteogenesis by applying the polymerase chain reaction to total cellular RNA isolated from normal and distracted rat mandibles. In conclusion, it is believed that the rat model of distraction osteogenesis has significant advantages over traditional models, including decreased costs and facilitation of molecular analysis.     

A thermodynamic model of nickel smelting and direct high-grade nickel matte smelting processes: Part I. Model development and validation

A thermodynamic model has been developed to predict the distribution behavior of Ni, Cu, Co, Fe, S, As, Sb, and Bi in the Outokumpu flash-smelting process, the Outokumpu direct high-grade matte smelting process, and the INCO flash-smelting process. In this model, as many as 16 elements (Ni, Cu, Co, Fe, As, Sb, Bi, S, O, Al, Ca, Mg, Si, N, C, and H) are considered, and two nickel sulfide species are used to allow for modeling of sulfur-deficient mattes. The compositions of the matte, slag, and gaseous phases in equilibrium are calculated using Gibbs free energies of formation and the activity coefficients of the components derived from the experimental data. The model predictions are compared with the known industrial data from the Kalgoorlie Nickel Smelter (Kalgoorlie, Australia), the Outokumpu Harjavalta Nickel Smelter (Harjavalta, Finland), the INCO Metals Company (Sudbury, Canada), and from a number of experimental data. An excellent agreement is obtained. It was found that the distribution behaviors of Ni, Co, Cu, Fe, S, As, Sb, and Bi in the nickel smelting furnace depend on process parameters such as the smelting temperature, matte grade, and partial pressure of oxygen in the process.     

Effect of Silicon on the Desulfurization of Al-Killed Steels: Part I. Mathematical Model

Recent observations suggest that increased silicon levels improve ladle desulfurization of aluminum-killed steel. While the overall desulfurization reaction of Al-killed steels does not show a direct role of silicon in desulfurization, model calculations are presented which test the idea that silicon suppresses the reduction of silica which can consume aluminum at the slag/metal interface. Consumption of aluminum would increase the oxygen potential at the slag/metal interface and decrease the sulfur partition coefficient between slag and metal. The model considers the coupled reactions of the reduction of silica, iron oxide, and manganese oxide in the slag and desulfurization of the steel by aluminum. The results show that silicon can indeed suppress consumption of aluminum at the slag/metal interface by side reactions other than desulfurization, with silicon affecting both the kinetics and the equilibrium of desulfurization.     

Subcritical crack growth at bimaterial interfaces: Part I. flexural peel technique

A flexural peel (FP) technique was developed to study the crack growth behavior along a bimaterial interface. The technique was based on a sandwich specimen where one arm of the specimen was peeled away from the interface under a combined tensile and shear mode. An approximate linear elastic fracture mechanics solution was derived analytically from theJ integral formulation. The solution was compared to finite element calculations based on the crack closure method and experimental measurements. From the finite element analysis, ratios of the mode-I and mode-II components of the crack tip field were determined for a wide range of modulus and thickness ratios.     

Competitive growth of stable and metastable Fe- C- X eutectics: Part I. experiments

The effect of small additions of Si, P, Cr, Mn, Ti, Al, and S to pure Fe-C eutectic, upon the transi-tion velocities from grey to white and white to grey cast iron, has been measured by varying the growth rate during directional solidification. As a result, it is found that alloying elements can be classified into three types: graphitizing (Si, Al, P, and S), carburizing (Cr), and “hysteretic effect” (Mn, Ti). The well-known influence of a thermal gradient (or the superheat) has been shown to af-fect only the grey-to-white transition. Growth undercoolings were measured as a function of growth rate, while the average lamellar spacings were determined from transverse sections of directionally solidified samples. A small addition of the element studied can have a marked effect upon these parameters.     

A kinetic model of the peirce-smith converter: Part I. Model formulation and validation

A kinetics-based mathematical model of the Peirce-Smith converter has been developed. The model considers mass transfer, heat transfer, and reactions between each of the phases present in the converter. Model validation is carried out using industrial data obtained from both copper and nickel converters. The model is generally able to predict the temperature and compositional variations of the converters to within the errors of the industrial data. However, the interactions between the white metal and slag during the copper blow are not understood sufficiently to model well.     

Dendritic solidification of Cu-Ni alloys: Part I. Initial growth of dendrite structure

Small Cu-Ni melts were furnace cooled at different rates and with different "nucleation" temperatures. Thermal analysis showed that the thermal arrests associated with the formation of the dendrite skeletons showed a significant supercooling below the liquidus temperatures. This supercooling increased with increased rates of heat extraction,i.e. higher cooling rates and lower "nucleation" temperatures; and was associated with higher dendrite growth velocities. The solute content of the dendrites measured on samples quenched during the thermal arrest quantitatively supported these observations. The magnitude of the supercooling for a given rate of heat extraction varied directly with the freezing range of the alloy but remained finite (although small) for unalloyed copper. The approximate measurements of dendrite growth velocities for one alloy (40 wt pet Ni) at different supercoolings agreed well with the predictions of Trivedi’s theory of dendrite growth. E. A. FEEST, formerly Graduate Student, University of Sussex K. HOLM, formerly Visiting Research Student, University of Susses     

Cyclic Turbulent Instabilities in a Thin Slab Mold. Part I: Physical Model

A water-physical model of a funnel-type thin slab mold fed by a two-port submerged entry nozzle (SEN) was employed to characterize the flow of liquid steel using dye tracer, particle image velocimetry, and video recording experiments. The overflow fluid flow pattern was the typical double-roll flow. A cyclic, low-frequency (≈0.01 s⁻¹), and energetic flow distortion of a short-lived (8 to 12 seconds) inducing high meniscus oscillation was identified. Its intensity grew with high casting speeds (5 and 7 m/min) and with a shallow SEN immersion position (200 mm from the meniscus level to the SEN tip). This distortion originated from the apparent existence of vortex flows located below the two discharging jets, which are formed by shear stresses in their ends that act on the surrounding fluid. These vortexes exert momentum transfer upward through a cascade mechanism from the lowest part of the discharging jets until reaching the region close to the SEN tip. This cascade momentum transfer widens the separation of both jets, enhancing the fluid velocities of the upper rolls, which promotes a high-amplitude standing wave. It is inferred, based on the experimental results, that this flow distortion originated from an instantaneous unbalance of the turbulent kinetic energy in the discharging jets. The negative production of kinetic energy is ascribed as the source of this unbalance, which is compensated by a higher contribution of the turbulent kinetic energy through mean convection and turbulent transport mechanisms manifested through higher velocities. After the restoration of the energy balance, the system yields a stable meniscus to repeat the low-frequency cycle.     

Interface morphology development during stress corrosion cracking: Part I. Via surface diffusion

The initiation of a crack in a specimen under tensile or compressive stresses is treated from the point of view of perturbation analysis. A surface distortion is Fourier analyzed into a series of waves and the amplitude response of a single component of varying frequency is theoretically investigated. The response of the individual components yields a Griffith-type criterion for wave amplitude growth. The model is applied to alloy systems undergoing stress corrosion cracking via surface diffusion.     

Human C-peptide. Part I: Radioimmunoassay

Synthetic human C-peptide bearing a Tyrosine group at its amino end is labelled with 125iodine using chloramin T or hydrogen peroxide and lactoperoxidase. The results are compared applying both methods. Antiserum to synthetic human C-peptide (without Tyrosine) which was partially compared to rabbit albumin, is raised in guinea pigs and goats. Goats show to be superior to guinea pigs concerning antibody production. The so-called "hook effect" phenomenon is observed in setting up the standard curves for the radioimmunoassay. Monotonically decreasing standard curves are obtained on dilution of antiserum with a high antibody titer which was produced by repeated immunization in goats. Free C-peptide and C-peptide bound to antiserum are separated with the anxion exchange resin Amberlite. Using this separation technique we excluded unspecific binding of labelled C-peptide to protein fractions in serum of diabetics. The sensitivity of our radioimmunoassay is approx. 0.3 ng C-peptide/ml serum. Intra- and interassay variability are below 10%. Human proinsulin is the only substance found to crossreact with the antiserum.