Klaus Schwerdtfeger

Dendrite morphology of steady state unidirectionally solidified steel

Steady state directional freezing experiments have been performed with two steels containing 0.59 and 1.48 pct carbon. Primary and secondary arm spacings were directly measured. In addition, average primary arm spacings were computed from the number of arms present on the observed area using the model of a hexagonal arrangement. The latter method seems to be more objective and reproducible than the line counting method. Arm spacings λ were related by the empirical equation λ =c RmGn to growth rateR and temperature gradientG. For primary arms, the exponentsm andn were different, whereas for secondary arms they were almost identical. Some consideration is given to dendrite spacings in ingot solidified steel, where under parabolic growth conditions thermal gradients and growth velocity are coupled by heat flow. Hence, a single variable may be used if the boundary condition for heat flow remains the same. Using the present results the laws describing dendrite spacings as a function of local solidification time are derived and compared with previous data available in the literature.

Rotational electromagnetic stirring in continuous casting of round strands

A model is presented to compute the three-dimensional flow field in rotational electromagnetic stirring of round strands. The model involves the solution of the Maxwell equations, the Navier-Stokes equations, and the transport equations for the turbulence characteristicsk andε. For the limiting case of one-dimensional stirring, the computations were checked with experiments using mercury as the fluid. Several sets of computations were carried out to determine the influence of stirrer position, stirrer length, and electromagnetic parameters on the flow field in continuous casting of steel strands.

Characteristics of round vertical gas bubble jets

Radial and axial profiles of gas concentration and bubble frequency have been measured for vertical gas bubble jets in the systems air/water, helium/water, and nitrogen/mercury using an electroresistivity probe. Gas velocities have been determined in the air/water system. All radial profiles were close to Gaussian. An integral model was applied to calculate axial distributions theoretically. Entrainment coefficients were determined for the experimental conditions. Axial profiles were correlated also in nondimensional representations. The bubble frequencies were used to compute local and average values of bubble size. Jet expansion and bubble size were found to depend considerably on the physical properties of the system.

Large-scale measurements of the physical characteristics of round vertical bubble plumes in liquids

The hydrodynamics of air/water plumes in a large-scale model of a metallurgical ladle were investigated. The dimensions of the cylindrical vessel were 1600-mm ID and 2250-mm total height. The air was injected through a centered nozzle. Axial and radial profiles of gas concentration, bubble frequency, and liquid and gas velocities were measured using electrical resistivity probes and a propeller flowmeter. It was found that the bubble plume is not at a fixed position but wanders away from the vertical vessel axis. This causes difficulties in the measurements, and special methods have to be designed to define and deduce reproducible values for the characteristic plume quantities. In the analysis of the data, the various physical characteristics were related toz0, the distance from the nozzle where the axial gas concentration is 50 Pct. The maximum values of the radial profiles are presented in nondimensional correlations.

Chemical equilibria between silicon and slag melts

The equilibria between silicon and slags of the systems CaO-SiO2, Na2O-SiO2, and CaO-SiO2-Y with Y being A12O3, MgO, TiOx, B2O3, and Na2O have been investigated in silica crucibles. The calcium content under silica-saturated CaO-SiO2 slag is 262 parts per million (ppm) at 1500 °C. The aluminum and magnesium contents increase with increasing alumina or magnesium oxide contents, respectively, reaching about 1800 ppm Al at silica/mullite or about 390 ppm Mg at silica/protoenstatite saturation. Boron has a distribution ratio [B]/(B2O3) of 0.18. The sodium content under silica-saturated Na2O-SiO2 slag is 25 ppm at 1500 °C. In contrast, the titanium content of the silicon, if Y is TiOx, and (Ti) is in the percent range, is highand varies with the titanium content of the slag according to [wt Pct Ti] = 2.7 √(wt pctTi). In other experiments, it is shown that metallurgical grade (MG) silicon can be purified from aluminum, magnesium, and calcium by treatment with suitable silicate slags.

Tracer diffusivity of Si31 in CaO-SiO2 melts at 1600°C

In the present paper, the tracer diffusivity of Si31 was measured in CaO-SiO2 melts at 1600°C. The Si31 isotope was produced by neutron bombardment in a nuclear reactor, and the capillary technique was used in the diffusion experiments. The diffusivities obtained, decrease with increasing silica content, and are lower by approximately one order of magnitude than the diffusivity of Ca45 determined previously.

Flow fields in electromagnetic stirring of rectangular strands with linear inductors: Part I. theory and experiments with cold models

A model is presented to compute the electromagnetic force fields and fluid flow fields in electromagnetic stirring of continuously cast strands with rectangular cross-section. The model involves the solution of the Maxwell equations, the Navier-Stokes equations, and the transport equations for the turbulence characteristicsk and e. The procedure of depth-averaging is applied in the treatment of several three-dimensional flows. Experiments were performed to check the computations using mercury as fluid. The spatial distribution of the magnetic induction and of the force density was determined for the laboratory inductor used in the stirring experiments. The flow velocity was measured photographically or with a drag probe, respectively. The agreement between experimental and theoretical data was found to be within 25 pct. It is concluded that the theory is sufficiently reliable to predict the flow fields in electromagnetic stirring of steel strands. In Part II of this paper the model is applied to analyze stirring situations in continuous casting of steel.

Tracer diffusivity of Ca45and electrical conductivity in CaO-SiO2 melts

The tracer diffusivity of Ca45 has been measured in CaO-SiO2 melts in the temperature range 1500 to 1700°C. In addition the electrical conductivity has been determined. Both properties decrease with increasing silica content. The activation energies (~30 kcal g-atom−1) are of the same order of magnitude. The electrical conductivity as computed from the diffusivity on the assumption that the total current is transported exclusively by divalent calcium ions and that the usual Nernst-Einstein relationship is valid, is somewhat lower than the measured electrical conductivity with the difference increasing with increasing silica content.

The dependence of the oxidation state of vanadium on the oxygen pressure in melts of VOx, Na2O-VOx, and CaO-SiO2-VOx

The oxidation state of vanadium has been determined as a function of oxygen pressure in pure VOx melts at 808 °C to 1000 °C, in Na2O-VOx melts with the initial molar ratios Na2O/V2O5 = 0.2, 0.5, and 1.0 at 1000 °C, and in CaO-SiO2-VOx melts with the molar ratios CaO/SiO2 = 0.71, 1.00, and 1.36 at 1600 °C. In the VOx melts,x is close to 2.5 in the range of oxygen pressure fromPO2 to 0.94 atm. The deviation, δ, from stoichiometric V2O5(δ = 2.5-x) varies approximately proportionally toPO2-1/4, indicating an equilibrium between V4+ and V5+ ions. In the Na2O-VOx melts, and in the CaO-SiO2-VOx melts,x varies with logPO2 according to an S-shaped function, withx approaching 1.5 at low and 2.5 at high oxygen pressures. At given oxygen pressures,x increases with Na2O or CaO content, respectively. Hence, these oxides stabilize the higher valent vanadium ions. For the CaO-SiO2-VOx system, the determinedx-PO2 dependence can be interpreted quantitatively in terms of V4+/V5+ and V3+/V4+ equilibria.

Flow fields in electromagnetic stirring of rectangular strands with linear inductors: Part II. computation of flow fields in billets, blooms, and slabs of steel

The model presented in Part I of this series of papers is used to compute flow velocities in the longitudinal stirring of steel blooms and billets, and in the horizontal stirring of steel slabs. In longitudinal stirring of blooms and billets the reverse flow is on the side of the strand opposite to the inductor. The effects of penetration depth of the electromagnetic force, of the force itself, of the length of the stirrer, and of the width of the liquid core were determined. In horizontal stirring of slabs the reverse flow takes place outside of the stirrer region, forming the so-called butterfly stirring pattern. The characteristics of this flow field depend to a considerable extent on the width of the stirrer. The effects of stirrer width, of thickness of the liquid core, of force and of width of the slab were elucidated. The maximum velocities in both types of stirring are represented as simple formulae.