A simple, but comprehensive model of heat transfer and solidification of the continuous casting of steel slabs is described, including phenomena in the mold and spray regions. The model includes a one-dimensional (1-D) transient finite-difference calculation of heat conduction within the solidifying steel shell coupled with two-dimensional (2-D) steady-state heat conduction within the mold wall. The model features a detailed treatment of the interfacial gap between the shell and mold, including mass and momentum balances on the solid and liquid interfacial slag layers, and the effect of oscillation marks. The model predicts the shell thickness, temperature distributions in the mold and shell, thickness of the resolidified and liquid powder layers, heat-flux profiles down the wide and narrow faces, mold water temperature rise, ideal taper of the mold walls, and other related phenomena. The important effect of the nonuniform distribution of superheat is incorporated using the results from previous three-dimensional (3-D) turbulent fluid-flow calculations within the liquid pool. The FORTRAN program CONID has a user-friendly interface and executes in less than 1 minute on a personal computer. Calibration of the model with several different experimental measurements on operating slab casters is presented along with several example applications. In particular, the model demonstrates that the increase in heat flux throughout the mold at higher casting speeds is caused by two combined effects: a thinner interfacial gap near the top of the mold and a thinner shell toward the bottom. This modeling tool can be applied to a wide range of practical problems in continuous casters.

http://ccc.illinois.edu/pdf files/publications/03_mtb_meng_con1d_reprint_post.pdf

Heat-transfer and solidification model of continuous slab casting: CON1D

Continuous casting is used to solidify most of the 750 million tons of steel produced in the world every year. Like most commercial processes, continuous casting involves many complex interacting phenomena. Most previous advances have been based on empirical knowledge gained from experimentation with the process. To further optimize the design and improve the continuous casting process, mathematical models are becoming increasingly powerful tools to gain additional quantitative insight. The best models for this purpose are mechanistic models based on the fundamental laws and phenomena which govern the process, because they are more reliably extended beyond the range of data used to calibrate them.

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Continuous Casting of Steel

Continuous casting is a mature, sophisticated technological process, used to produce most of the world’s steel, so is worthy of fundamentally-based computational modeling. It involves many interacting phenomena including heat transfer, solidification, multiphase turbulent flow, clogging, electromagnetic effects, complex interfacial behavior, particle entrapment, thermal-mechanical distortion, stress, cracks, segregation, and microstructure formation. Furthermore, these phenomena are transient, three-dimensional, and operate over wide length and time scales. This paper reviews the current state of the art in modeling these phenomena, focusing on practical applications to the formation of defects. It emphasizes model verification and validation of model predictions. The models reviewed range from fast and simple for implementation into online model-based control systems to sophisticated multiphysics simulations that incorporate many coupled phenomena. Both the accomplishments and remaining challenges are discussed.

Review on Modeling and Simulation of Continuous Casting

This lecture honoring Keith Brimacombe looks over the history, current abilities, and future potential of mathematical models to improve understanding and to help solve practical problems in the continuous casting of steel. Early finite-difference models of solidification, which were pioneered by Keith Brimacombe and his students, form the basis for the online dynamic models used to control spray water flow in a modern slab caster. Computational thermal-stress models, also pioneered by Brimacombe, have led to improved understanding of mold distortion, crack formation, and other phenomena. This has enabled process improvements, such as optimized mold geometry and spray-cooling design. Today, sophisticated models such as transient and multiphase fluid-flow simulations rival water modeling in providing insights into flow-related defects. Heat-flow and stress models have also advanced to yield new insights. As computer power increases and improvements via empirical plant trials become more costly, models will likely play an increasing role in future developments of complex mature processes, such as continuous casting.

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Modeling of the continuous casting of steel - past, present and future

In both continuous casting of steel slabs and direct chill (DC) casting of aluminum alloy ingots, water is used to cool the mold in the initial stages of solidification, and then below the mold, where it is in direct contact with the newly solidified surface of the metal. Water cooling affects the product quality by (1) controlling the heat removal rate that creates and cools the solid shell and (2) generating thermal stresses and strains inside the solidified metal. This work reviews the current state-of-the-art in water cooling for both processes, and draws insights by comparing and contrasting the different practices used in each process. The heat extraction coefficient during secondary cooling depends greatly on the surface temperature of the ingot, as represented by boiling water-cooling curves. Thus, the heat extraction rate varies dramatically with time, as the slab/ingot surface temperature changes. Sudden fluctuations in the temperature gradients within the solidifying metal cause thermal stresses, which often lead to cracks, especially near the solidification front, where even small tensile stresses can form hot tears. Hence, a tight control of spray cooling for steel, and practices such as CO2 injection/pulse water cooling for aluminum, are now used to avoid sudden changes in the strand surface temperature. The goal in each process is to match the rate of heat removal at the surface with the internal supply of latent and sensible heat, in order to lower the metal surface temperature monotonically, until cooling is complete.

/pdf/the-use-of-water-cooling-during-the-continuous-casting-of-frke0qxlrd.pdf

The use of water cooling during the continuous casting of steel and aluminum alloys

Axial heat-flux profiles have been determined quantitatively from temperature measurements conducted on a slab mold under routine operating conditions. As in earlier studies, the heat flux was observed to have a maximum value at the meniscus and to decline with increasing distance down the mold. The mold heat flux increased with increasing casting speed and was greater with a mold powder having lower viscosity and melting point being applied as lubricant. The heat extraction was largest while casting 0.29 pet carbon steel and least for a 0.09 pet carbon grade; reducing the depth of the submerged entry nozzle increased the heat flux slightly in the upper region of the mold. Most significant was the higher heat flux observed at the meniscus of the outside-radius face, attributable to the locally greater copper plate thickness compared to that of the opposite broad face. All of the measurements can be explained straightforwardly by heat flow in the vicinity of the meniscus and the resulting behavior of the so-called slag rim adjacent to the mold wall. It is postulated that the difference in copper plate thickness between the two broad faces at the meniscus causes the slag rim to be smaller on the outside-radius face which gives rise to shallower oscillation marks, as observed, higher heat transfer, and a slightly thicker solid shell. The dissimilar behavior has implications for quality because the inside-radius shell, experiencing reduced heat extraction, cools and shrinks less than the outside-radius shell. Thus, for a given end-plate taper, the narrow face of the slab adjacent to the inside radius can push against the end plate, accelerating copper wear, and, owing to squeezing of the broad face, cause an off-corner depression and subsurface crack toward the mold exit. If this is correct, maintenance of the same copper plate thickness at the meniscus is fundamental to preventing such an occurrence. Moreover, adjustment of the heat extraction at the meniscus should be achievable by changing copper plate thickness, mold coating thickness/conductivity, cooling water velocity, cooling channel configuration, and mold flux composition for a given steel grade.

Mold behavior and its influence on quality in the continuous casting of steel slabs: Part II. Mold heat transfer, mold flux behavior, formation of oscillation marks, longitudinal off-corner depressions, and subsurface cracks

An extensive study has been conducted to elucidate mold behavior and its influence on quality during the continuous casting of slabs. The study combined industrial measurements, mathe matical modeling, and metallographic examination of cast slab samples. The industrial mea surements involved instrumenting an operating slab mold with 114 thermocouples in order to determine the axial mold wall temperature profiles for a wide range of casting conditions. A three-dimensional (3-D) heat-flow model of the mold wall was developed to characterize the heat fluxes in the mold quantitatively from the measured mold temperature data. Furthermore, heat-flow models were developed to examine steel solidification phenomena and mold flux behavior at the meniscus. Slab samples collected during the industrial trials were examined metallographically to evaluate the cast structure and defects. Owing to the length of the study, it is presented in two parts, the first of which describes the experimental techniques employed in the instrumentation of the mold together with the details of the industrial trials and mold temperature measurements. Also, the mathematical modeling technique applied to determine the axial heat-flux profiles from the measured mold temperature data is presented. It is shown that a fully 3-D model of the mold wall is needed to convert the measured temperatures to heat-flux profiles properly.

Mold behavior and its influence on quality in the continuous casting of steel slabs: Part i. Industrial trials, mold temperature measurements, and mathematical modeling

R. B. Mahapatra

Papers

Mold behavior and its influence on quality in the continuous casting of steel slabs: Part II. Mold heat transfer, mold flux behavior, formation of oscillation marks, longitudinal off-corner depressions, and subsurface cracks

Mold behavior and its influence on quality in the continuous casting of steel slabs: Part i. Industrial trials, mold temperature measurements, and mathematical modeling