Brian G. Thomas

Modeling superheat removal during continuous casting of steel slabs

To investigate superheat dissipation in a continuous slab casting machine, mathematical models have been developed to compute fluid flow velocities, temperature distribution within the liquid pool, heat transfer to the inside of the solidifying shell, and its effect on growth of the shell. Three-dimensional (3-D) velocity and heat-transfer predictions compare reasonably with pre-vious experimental measurements and two-dimensional (2-D) calculations. The results indicate that the maximum heat input to the shell occurs near the impingement point on the narrow face and confirm that most of the superheat is dissipated in or just below the mold. Superheat tem-perature and casting speed have the most important and direct influence on heat flux. The effects of other variables, including mold width, nozzle jet angle, and submergence depth, are also investigated. Calculated heat flux profiles are then input to a one-dimensional (1-D) solidifi-cation model to calculate growth of the shell. Shell thickness profiles down the wide and narrow faces are compared with the predictions of conventional heat conduction models and available measurements.

Simple constitutive equations for steel at high temperature

This work develops and investigates simple unified constitutive equations to model the mechanical behavior of plain carbon steel in the austenite temperature region for use in finite element stress analysis of processes such as continuous casting. Four different forms of constitutive relations are considered: constant structure, time-hardening, strain-hardening, and simultaneous time- and strain-hardening models. Each relation is judged on its ability to reproduce experimental data from both tensile and creep tests and its ability to exhibit reasonable behavior under complex loading conditions. Three of the equations appear suitable for small strain monotonic loading conditions for a wide range of low strain rates (10−3 to 10−6 s−1), high temperatures (950 °C to 1400 °C), and varying carbon contents (0.005 to 1.54 wt pct C).

Simulation of fluid flow inside a continuous slab-casting machine

A finite element model has been developed and applied to compute the fluid flow distribution inside the shell in the mold region of a continuous, steel slab-casting machine. The model was produced with the commercial program FIDAP, which allows this nonlinear, highly turbulent problem to be simulated using the K- ε turbulence model. It consists of separate two-dimensional (2-D) models of the nozzle and a section through the mold, facing the broad face. The predicted flow patterns and velocity fields show reasonable agreement with experimental observations and measurements conducted using a transparent plastic water model. The effects of nozzle angle, casting speed, mold width, and turbulence simulation parameters on the flow pattern have been investigated. The overall flow field is relatively insensitive to process parameters.

Initial development of thermal and stress fields in continuously cast steel billets

A mathematical model has been developed to compute the thermomechanical state of the shell of continuously cast steels in a round billet casting mold. The model determines the temperature distributions, the stresses in and the gap between the casting mold and the solidifying strand. The effect of variations in steel carbon content and mold taper on the thermal, displacement, and stress fields are examined. Comparisons with available experimental observations verify the predictions of the model. The model demonstrates that the thermal shrinkage associated with the phase change from delta-ferrite to austenite in 0.1 Pct C steel accounts for the decreased heat transfer observed in that alloy, as well as its susceptibility to cracking.

Simulation of Argon Gas Flow Effects in a Continuous Slab Caster

Three-dimensional finite-volume-based numerical models of fluid, heat, and mass transport have been developed and applied to help explain the complex inter-related phenomena of multiphase fluid flow, superheat dissipation, and grade intermixing during the continuous casting of steel slabs. Gas bubbles are simulated using a continuum model, which calculates the volume fraction and velocities of the gas, and its effect on the liquid flow. Turbulence has been incorporated using the standardK-ε turbulence model. Reasonable agreement has been achieved between predicted velocities and corresponding measurements and observations in full-scale water models, both with and without gas injection. The effects of argon gas bubble injection on flow-related phenomena are investigated with simulations of a typical steel slab caster. Argon bubbles alter the flow pattern in the upper recirculation zone, shifting the impingement point and recirculation zones upward. The effect increases with increasing gas fraction and decreasing bubble size. Argon injection also causes superheat to be removed higher in the caster, moves the hot spot upward, lowers the peak heat flux, and increases heat extraction from the wide face and meniscus regions. During a steel grade transition, argon injection slightly affects slab surface composition but has no effect on intermixing in the slab interior.

Numerical study of steady turbulent flow through bifurcated nozzles in continuous casting

Bifurcated nozzles are used in continuous casting of molten steel, where they influence the quality of the cast steel slabs. The present study performs two-dimensional (2-D) and three-dimensional (3-D) simulations of steady turbulent(K- ε) flow in bifurcated nozzles, using a finite-element (FIDAP) model, which has been verified previously with water model experiments. The effects of nozzle design and casting process operating variables on the jet characteristics exiting the nozzle are investigated. The nozzle design parameters studied include the shape, angle, height, width, and thickness of the ports and the bottom geometry. The process operating practices include inlet velocity profile and angle as well as port curvature caused by erosion or inclusion buildup. Results show that the jet angle is controlled mainly by the port angle but is steeper with larger port area and thinner walls. The degree of swirl is increased by larger or rounder ports. The effective port area, where there is no recirculation, is increased by smaller or curved ports. Flow asymmetry is more severe with skewed or angled inlet conditions or unequal port sizes. Turbulence levels in the jet are higher with higher casting speed and smaller ports.

Mathematical model of the thermal processing of steel ingots: Part II. Stress model

A mathematical model has been developed to predict the internal stresses generated in a steel ingot during thermal processing. The thermal history of the ingot has been predicted by a finite-element, heat-flow model, the subject of the first part of this two-part paper, which serves as input to the stress model. The stress model has been formulated for a two-dimensional transverse plane at mid-height of the ingot and is a transient, elasto-viscoplastic, finite-element analysis of the thermal stress field. Salient features of the model include the incorporation of time-temperature and temperature-dependent mechanical properties, and volume changes associated with nonequilibrium phase transformation. Model predictions demonstrate that the development of internal stresses in the ingot during thermal processing can be directly linked to the progress of the phase transformation front. Moreover, the low strain levels calculated indicate that metallurgical embrittlement must be very important to the formation of cracks in addition to the development of high tensile stresses.

Comparison of numerical modeling techniques for complex, two-dimensional, transient heat-conduction problems

The accuracy, stability, and cost of the standard finite-element method, (Standard), Matrix method method of Ohnaka, and alternating-direction, implicit finite-difference method (ADI) have been compared using analytical solutions for two problems approximating different stages in steel ingot processing. The Standard and Matrix methods both employ triangular elements and were compared using the Dupont, Lees, and Crank-Nicolson time-stepping techniques. Other variables include mesh and time-step refinement, type of boundary condition formulation, and the technique for simulating phase change. The best overall combination of methods investigated for modeling two-dimensional, transient, heat conduction problems involving irregular geometry was the Dupont-Matrix method with a lumped boundary condition formulation and temperature dependent properties evaluated at time level two, coupled with the Lemmon latent-heat evolution technique if phase change is involved. For problems with simple geometry, the ADI method was found to be more cost effective.

FLOW AND THERMAL BEHAVIOR OF THE TOP SURFACE FLUX/POWDER LAYERS IN CONTINUOUS CASTING MOLDS

Steady-state finite-element models have been formulated to investigate the coupled fluid flow and thermal behavior of the top-surface flux layers in continuous casting of steel slabs. The three-dimensional (3-D) FIDAP model includes the shear stresses imposed on the flux/steel interface by flow velocities calculated in the molten steel pool. It also includes different temperature-dependent powder properties for solidification and melting. Good agreement between the 3-D model and experimental measurements was obtained. The shear forces, imposed by the steel surface motion toward the submerged entry nozzle (SEN), create a large recirculation zone in the liquid flux pool. Its depth increases with increasing casting speed, increasing liquid flux conductivity, and decreasing flux viscosity. For typical conditions, this zone contains almost 4 kg of flux, which contributes to an average residence time of about 2 minutes. Additionally, because the shear forces produced by the narrowface consumption and the steel flow oppose each other, the flow in the liquid flux layer separates at a location centered 200 mm from the narrowface wall. This flow separation depletes the liquid flux pool at this location and may contribute to generically poor feeding of the mold-strand gap there. As a further consequence, a relatively cold spot develops at the wideface mold wall near the separation point. This nonuniformity in the temperature distribution may result in nonuniform heat removal, and possibly nonuniform initial shell growth in the meniscus region along the wideface off-corner region. In this way, potential steel quality problems may be linked to flow in the liquid flux pool.

Mathematical model of the thermal processing of steel ingots: Part I. Heat flow model

A two-dimensional mathematical model has been developed to predict stress generation in static-cast steel ingots during thermal processing with the objective of understanding the role of stress generation in the formation of defects such as panel cracks. In the first part of a two-part paper the formulation and application of a heat-flow model, necessary for the prediction of the temperature distribution which governs thermal stress generation in the ingot, are described. A transverse plane through the ingot and mold is considered and the model incorporates geometric features such as rounded corners and mold corrugations by the use of the finite-element method. The time of air gap formation between mold and solidifying ingot skin is input, based on reported measurements, as a function of position over the ingot/mold surface. The model has been verified with analytical solutions and by comparison of predictions to industrial measurements. Finally, the model has been applied to calculate temperature contours in a 760×1520 mm, corrugated, low-carbon steel ingot under processing conditions conducive to panel crack formation. The model predictions are input to an uncoupled stress model which is described in Part II.