Accretion growth on single-pipe tuyeres: Part I. Model development and preliminary analysis

A mathematical model of the growth of accretions on submerged single pipes has been developed based on the heat transfer in the vicinity of the injection point. The model is able to predict the formation of either pipe or hemispherical accretions based only on the input con-ditions. It is assumed that a hemispherical accretion is formed only when a porous plug is formed within the tuyere tip by the freezing of bath material during regular penetration episodes. Gas flow within the bath is calculated from physical modeling results, and allowances are made for the possibility of a gas/bath reaction. A preliminary analysis of the model predictions for copper converter and steel ladle stirring applications has been carried out. The model predicts that, under normal operating conditions, the accretions formed in copper converters are very small but can become appreciable under low superheat conditions. The time required to reach steady state depends upon the final accretion length but can be as much as 5 minutes. In ladle stirring applications, the model predicts that the accretion formed will be approximately 4.5-cm high with a slightly larger basal radius. This accretion requires approximately 10 minutes to reach steady state. The final shape and size of an accretion are dependent upon the balance of heat flows around it, with steady state occurring when heat inputs to the accretion exactly equal heat outputs. Formerly Associate Professor, University of British Columbia, Vancouver.     

A kinetic model of the Peirce-Smith converter: Part II. Model application and discussion

A sensitivity analysis of a kinetics-based model of the Peirce-Smith converter has been carried out, and the model has then been applied to an analysis of copper converter operation. The results of the sensitivity analysis indicate that only factors relating to the mass-transfer rates have a significant effect on the model predictions. However, even with large changes in diffusivities, the model predictions remain within the error of the plant measurements. The converter analysis indicates that considerable improvements to converter productivity can be made, particularly through changes to gas injection practices.     

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 II. Theory

A theoretical model is developed to predict the characteristics of cellular or dendritic interface during the controlled solidification of binary alloys. Both heat and mass transport fields near a growing cellular and dendritic front have been considered. A perturbative stability criterion has been developed to determine the dimension and the solute concentration of a tip. It is shown that the fields are composed of two contributions; one characterizes the average field and the other characterizes the cellular and dendritic fields ahead of the growing front. The perturbation in the shape is classified into two categories; one is responsible to the cellular growth and the other to the dendritic growth. Good correlations are obtained between theory and experiments.     

Fundamental Mathematical Model for AOD Process. Part II: Model validation

A fundamental mathematical model for AOD process has been developed and proposed in “Fundamental Mathematical Model for AOD Process. Part I: Derivation of the Model” 1 . Validation of the model with process data, measured from full scale AOD process, is presented in this paper. A broad selection of input data for the model was exported from various types of full scale industrial AOD heats. In this study 6 different types of heats were studied and simulated. Process data was measured from two AOD converters (95 t, 150 t). Validation of the model was then done by comparing simulated and measured values for carbon and chromium content, carbon release rate, melt composition, slag composition and bath temperature during final stages of carbon removal. The validation results showed that the model was in good agreement with the measured process data, and same model parameters were valid in all of the simulated heats.     

Vacuum evaporation of KCl-NaCl salts: Part II. vaporization-rate model and experimental results

A model based on the Hertz-Langmuir relation is used to describe how evaporation rates of the binary KCl-NaCl system change with time. The effective evaporation coefficient (α), which is a ratio of the actual evaporation rate to the theoretical maximum, was obtained for the KCl-NaCl system using this model. In the temperature range of 640 °C to 760 °C, the effective evaporation coefficient ranges from ～0.4 to 0.1 for evaporation experiments conducted at 0.13 Pa. At temperatures below the melting point, the lower evaporation coefficients are suggested to result from the more complex path that a molecule needs to follow before escaping to the gas phase. At the higher liquid temperatures, the decreasing evaporation coefficients result from a combination of the increasing vaporflow resistances and the heat-transfer effects at the evaporation surface and the condensate layer. The microanalysis of the condensate verified that composition of the condensate changes with time, consistent with the model calculation. The microstructural examination revealed that the vaporate may have condensed as a single solution phase, which upon cooling forms fine lamellar structures of the equilibrium KCl and NaCl phases. In conclusion, the optimum design of the evaporation process and equipment must take the mass and heat transfer factors and equipment materials issues into consideration.     

Dendritic growth of undercooled nickel-tin: Part II

High-speed optical temperature measurements were made of the solidification behavior of levitated metal samples within a transparent glass medium. Two undercooled Ni-Sn alloys were examined, one a hypoeutectic alloy and the other of eutectic composition. Recalescence times for the 9 mm diameter samples studied decreased with increasing undercooling from the order of 1.0 second at 50 K under-cooling to less than 10⁻³ second for undercoolings greater than 200 K. Both alloys recalesced smoothly to a maximum recalescence temperature at which the solid was at or near its equilibrium composition and equilibrium weight fraction. For the samples of hypoeutectic alloy that recalesced above the eutectic temperature, a second nucleation event occurred on cooling to the eutectic temperature. For samples which recalesced only to the eutectic temperature, no subsequent nucleation event was observed on cooling. It is inferred in this latter case that both the α and β phases were present at the end of recalescence. The thermal data obtained suggest a solidification model involving (1) dendrites of very fine structure growing into the melt at temperatures near the bulk undercooling temperature, (2) thickening of dendrite arms with rapid recalescence, and (3) continued, much slower recalescence accompanying dendrite ripening.     

Test burning: Part II.

A research program, sponsored by the Rip Van Winkle Foundation, concerned with mental health in rural areas was started in 1955. A few members of the Hudson Post of the American Legion opposed the organized "mental health movement." Local newspaper articles linked "mental health with 'world citizenship, one worldism, internationalism, communism, and socialism.'… Actually, the ruckus did not blow up until the period of data collection from the children was in its last week. Data from only three children were destroyed in compliance with the wishes of their parents." Details of the background and the problem are presented. From Psyc Abstracts 36:02:2AA37E. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Competitive growth of stable and metastable Fe- C- X eutectics: Part II. mechanisms

The competition between stable and metastable solidification in Fe-C-X alloys has been studied theo-retically, with particular regard to phase stability, nucleation, and growth processes. The effects of small additions of Si, P, Cr, Mn, Ti, Al, and S upon the transition velocities from grey to white and from white to grey in directional solidification are related to their influence on the eutectic tempera-tures, and nucleation and growth undercoolings. It is shown that the consequences of simultaneously adding Si and Cr upon the transition velocities can be deduced from the results of adding of Si and Cr separately only when the detailed effects of these elements upon phase stability, nucleation, and growth are known. The well-known carburizing effect of a high thermal gradient (superheat) has been shown to influence only the nucleation process. A three-phase austenite-graphite-cementite mi-crostructure resulting from the cooperative growth of a double stable/metastable eutectic has been observed for the first time.     

Cyclic Turbulent Instabilities in a Thin Slab Mold. Part II: Mathematical Model

Mathematical simulations are employed to describe short- and large-scale flow distortions observed in a water model of a thin slab mold using a submerged entry nozzle (SEN) located at deep and shallow positions, operating at two casting speeds of 5 and 7 m/min. Two types of meniscus oscillations are identified; the first (high frequencies) has a relatively long life and short length scales, whereas the second (low frequencies) has a short life and its length scales are similar to those length scales in the mold. It was found, by turbulent flow principles, that the high-oscillation frequencies of the discharging jets are the same as those of the oscillating meniscus. Therefore, the discharging jets transfer vibrating momentum, with frequencies of 1.1 to 5 Hz, to the two upper roll flows during long periods of time, inducing those meniscus oscillations. The large-scale and short-life oscillations originate a dynamic distortion of the flow, forming deep meniscus depressions, especially for a casting speed of 7 m/min with the SEN in a shallow position. These dynamic distortions give origin to rotational flows in the lower boundaries of both jets, below the SEN tip, and even in the recirculatory eyes of the upper roll flows. The time scale of low-frequency oscillations agrees with the time scale of the production rate of kinetic energy along the jet’s length. Their origin is linked to a kinetic energy unbalance by the generation of a negative production rate. Because the flow must keep its energy budget, the fluid will transport, through mean convection and pressure–viscous mechanisms, further increases of momentum transfer during a short time, giving place to those dynamic distortions. Because of their large length scale, these dynamic and energetic distortions are the most dangerous to slab quality.     

Simulation of Slag Freeze Layer Formation: Part II: Numerical Model

The experiments from Part I with CaCl₂-H₂O solidification in a differentially heated, square cavity were simulated in two dimensions using a control volume technique in a fixed grid. The test conditions and physical properties of the fluid resulted in Prandtl and Rayleigh numbers in the range of 50 and 2.1 × 10⁸, respectively, and the solidification was observed to be planar with dispersed solid particles. In the mathematical model, temperature-dependent viscosity and density functions were employed. To suppress velocities in the solid phase, various models were tested, and a high effective viscosity was found most appropriate. The results compare well with the experiments in terms of solid layer growth, horizontal and vertical velocities, heat transfer coefficients, and temperature distributions. Hydrodynamic boundary layers on the solidified front and on the hot vertical wall tend to be nonsymmetric, as well on the top and bottom adiabatic walls. The high viscosity value imposed on the two-phase zone affects the velocity profile close to the solid front and modifies the heat transfer rate.     

Dendritic solidification of Cu-Ni alloys: Part II. The influence of initial dendrite growth temperature on microsegregation

Microsegregation measurements and calculations were carried out for solidification of small melts of Cu-40 wt pct Ni under conditions in which both the cooling rate and the local rate of heat extraction during dendrite growth were varied. These demonstrated that the supercooling required to support dendrite growth significantly reduces the microsegregation in the completely frozen ingot. The importance of this for the different microsegregation in columnar and equiaxed regions of large ingots is briefly discussed. E. A. FEEST, formerly Graduate Student, University of Sussex, Brighton, Sussex, England     

Multiphase precipitation of carbides in Fe-C system: Part II. Model based on kinetics of complex reactions

The precipitation of carbides in the Fe-C system aged at constant temperature is simulated considering two transformation kernels of complex reactions, involving different impingement and rate-time factors. The metastable and stable phase are identified by deconvolution of the experimental kinetics. The activation energy of carbides is found to depend, slightly, on the transformation kernel in which it is used.     

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.     

Macrotransport-solidification kinetics modeling of equiaxed dendritic growth: Part II. Computation problems and validation on INCONEL 718 superalloy castings

In Part I of the article, a new analytical model that describes solidification of equiaxed dendrites was presented. In this part of the article, the model is used to simulate the solidification of INCONEL 718 superalloy castings. The model was incorporated into a commercial finite-element code, PROCAST. A special procedure called microlatent heat method (MLHM) was used for coupling between macroscopic heat flow and microscopic growth kinetics. A criterion for time-stepping selection in microscopic modeling has been derived in conjunction with MLHM. Reductions in computational (CPU) time up to 90 pct over the classic latent heat method were found by adopting this coupling. Validation of the model was performed against experimental data for an INCONEL 718 superalloy casting. In the present calculations, the model for globulitic dendrite was used. The evolution of fraction of solid calculated with the present model was compared with Scheil’s model and experiments. An important feature in solidification of INCONEL 718 is the detrimental Laves phase. Laves phase content is directly related to the intensity of microsegregation of niobium, which is very sensitive to the evolution of the fraction of solid. It was found that there is a critical cooling rate at which the amount of Laves phase is maximum. The critical cooling rate is not a function of material parameters (diffusivity, partition coefficient,etc.). It depends only on the grain size and solidification time. The predictions generated with the present model are shown to agree very well with experiments.     

Kinetics of environmental fatigue crack growth in a nickel-copper alloy: Part II. In hydrogen

A systematic matrix of fatigue crack growth rate data in a hydrogen environment has been generated in a nickel-copper alloy and compared with the base line data in the milder oxygen and vacuum environments described in the preceding paper. It is found that crack growth in the hydrogen environment is characterized by high values of the Paris equation exponent and faster crack propagation rates as compared to those in the milder environments. Fractographic examination shows that brittle inter granular separation occurs superimposed on an otherwise ductile crack mode in the hydrogen tests. Quantitative fractographic analysis of the hydrogen affected fracture surfaces indicates that the percentage of intergranular failure (area fraction) is a uniquely related function of the mean stress intensity rather than the maximum stress intensity level of fatigue loading. This dependence is discussed in terms of dislocation sweep-in transport of hydrogen deep into the plastic zone during fatigue cycling. Formerly a Graduate Student at Columbia University Formerly Senior Staff Associate, Science Center, Rockwell International     

Oxidation of cobaltite: Part II. kinetics

A kinetics study has been performed on cobaltite to understand the oxidation processes over a temperature range of 573 to 1173 K using a thermogravimetric method. The results show that oxidation of cobaltite occurs in two stages. In the first stage, which occurs between 823 and 913 K, the majority of the sulfur is removed. However, the arsenic remains in the lattice of the reacted region. A pore-blocking kinetic model yields a satisfactory fit to these experimental data. At higher temperatures, there is a concurrent release of As and S from the crystal lattice of CoAsS. The shrinking-core kinetic model is applicable. Complementary X-ray diffraction and scanning electron microscopic analyses on these partially oxidized samples support the kinetic models. The effects of partial pressure of oxygen and particle size on roasting have been evaluated.