Roderick I. L. Guthrie

Coupled turbulent flow, heat, and solute transport in continuous casting processes

A fully coupled fluid flow, heat, and solute transport model was developed to analyze turbulent flow, solidification, and evolution of macrosegregation in a continuous billet caster. Transport equations of total mass, momentum, energy, and species for a binary iron-carbon alloy system were solved using a continuum model, wherein the equations are valid for the solid, liquid, and mushy zones in the casting. A modified version of the low-Reynolds numberk-ε model was adopted to incorporate turbulence effects on transport processes in the system. A control-volume-based finite-difference procedure was employed to solve the conservation equations associated with appropriate boundary conditions. Because of high nonlinearity in the system of equations, a number of techniques were used to accelerate the convergence process. The effects of the parameters such as casting speed, steel grade, nozzle configuration on flow pattern, solidification profile, and carbon segregation were investigated. From the computed flow pattern, the trajectory of inclusion particles, as well as the density distribution of the particles, was calculated. Some of the computed results were compared with available experimental measurements, and reasonable agreements were obtained.

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,Up α (Q1/3L1/3)/R1/3 whereUp 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.

Bubble formation at nozzles in pig iron

An experimental study was undertaken to determine how several variables affect the size of gas bubbles formed at nozzles in liquid pig iron. The frequency of bubble formation was measured by an acoustic device, which could detect the vibrations produced by the bubble release. Accurate knowledge of the gas flow rate then enabled the calculation of bubble volumes. The use of large baths (60 Kg), melted by induction heating, permitted a wide range of experimental parameters: gas flow rate (0.5 to 1000 cc/s), outside nozzle diameter (0.64 to 5.1 cm), inside diameter (0.16 to 0.64 cm), chamber volume (23 to 2200 cc), nozzle depth (7.6 to 20 cm), surface tension (700 to 1500 dynes/cm) and nozzle orientation (up, down and sideways). The resulting bubble volumes were between 0.5 and 100 cc. The bubbles were found to form at the outer diameter of the nozzles due to the nonwettability of the nozzles. Furthermore, the bubbles were of a uniform size at low flow rates, but increased in volume with the flow rate, so that a constant frequency was established. In addition, the bubble volume was strongly dependent on the chamber volume upstream from the nozzle. This is known as a “capacitance” effect and is due to compressibility of the gas. “Doublets” or “double bubbles” at small chamber volumes and bubble “pairs” at large chamber volumes were also observed. These phenomena result in smaller bubbles, which make precise predictions of bubble size difficult. The results are compared with those obtained by other investigators in aqueous and metallic systems.

Hydrodynamic Modeling of Some Gas Injection Procedures in Ladle Metallurgy Operations

Experimental studies of flows generated in a 0.30 scale water model of a 150 ton steelmaking ladle are reported. These were used to test the adequacy of a generalized two-dimensional computational scheme for predicting flows generated by fully submerged and partially submerged gas injection lances. The roles of turbulence models and grid configuration were assessed. Predictions for flow fields generated in a 150 ton steelworks ladle with and without tapered side walls, and with and without surface baffles around the rising plume were considered.

Hydrodynamics of gas stirred melts: Part II. Axisymmetric flows

A predictive model of gas stirred melt is presented. Based on the differential approach and following a review of previous models, the importance of natural convection or buoyancy driven phenomena is underscored. Predicted flow patterns are shown to be consistent with laboratory and pilot scale experiments, and with the macroscopic plume model in Part I of this paper.

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:τmαεm−1/3L−1R5/3. Hereτm is the 95 pct mixing time,εm 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).

Modeling flows and mixing in steelmaking ladles designed for single- and dual-plug bubbling operations

Through solutions of appropriate forms of the Navier-Stokes equation, the intermixing of fluid within gas-stirred ladles, with asymmetric single and multiporous plugs, can be modeled quite satisfactorily. In this study, mixing behavior and mixing mechanisms are analyzed as a function of porous plug location, tracer injection point, and ladle monitoring point. It is shown that off-centered bubbling gives the most consistent results in terms of minimizing mixing times, since angular momentum intermixes fluid across the width of a ladle. Comparisons between mathematical and experimental data are presented.

Mathematical modeling of flows in large tundish systems in steelmaking

Numerical solutions of the three-dimensional turbulent Navier-Stokes equations, incorporating thek-ε turbulence model, are presented for the turbulent flow of liquid within a tundish of high aspect ratio. Experimental results, obtainedvia Laser-Doppler anemometry and flow visualization techniques, are also reported. Calculated flow fields were shown to be similar to corresponding experimental flow fields. Such results can provide useful technological information regarding the design of tundishes in the steel industry for optimization of steel cleanliness.

The effect of oxygen concentration on the oxidation of low-carbon steel in the temperature range 1000 to 1250°C

This paper describes the oxidation behavior of low-carbon steel samples in binary gas mixtures of oxygen and nitrogen, at oxygen concentrations ranging between 1% and 15% and temperatures ranging between 1000 and 1250°C. Sample weight gains versus time were analyzed, along with measurements and calculations of sample heating rates due to exothermic heat of reaction at the sample surface. It was found that initial rates of oxidation depended on oxygen content in the gasmixture and that these reaction rates were linear up to oxide thicknesses of 0.4 to 0.5 mm. Calculations of linear oxidation rate constants based on equations for mass transport of oxygen in the gas mixture to the sample surface showed good agreement with those measured experimentally, indicating that the initial period of oxidation is controlled by the mass transport of oxygen to the reaction interface. The linear rate constants showed little dependency on temperature, an activation energy of approximately 17kJ/mole being obtained. Measurements of sample surface temperatures have shown that within this linear-oxidation regime, interfacial temperatures of the samples increase with increasing oxygen contents in the gas mixture, owing to exothermic heats of oxidation. Subsequent oxidation kinetics were found to be parabolic. Measured parabolic rates constants were in good agreement with previous investigations, with activation energy values of approximately 127kJ/mole.

Inclusion behavior and heat-transfer phenomena in steelmaking tundish operations: Part II. Mathematical model for liquid steel in tundishes

Fluid flow, heat transfer, and inclusion flotation have been modeled mathematically for several types of industrial tundish designs. Computations are presented to illustrate the importance of thermal natural convection currents in mixing the upper and lower layers of steel. The use of flow modification devices was shown to be reasonably effective in further reducing inclusion density levels at the intermediate to larger size ranges. Small inclusions (≦40 μm) were not readily removed with or without flow controls because of their low Stokes rising velocities.