Macrosegregation in continuously cast steel slabs: preliminary theoretical investigation on the effect of steady state bulging

Miyazawa, Ken-ichi; Schwerdtfeger, Klaus

doi:10.1002/srin.198104599

Cited by 65 publications

(79 citation statements)

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“…close to the solidus isotherm), we can see that there is also an alternation, but opposite: the steel is in a tensile state (negative pressure of about Ϫ2 MPa) when passing in front of rolls, while it is in a compressive state in between, the value of pressure being around 2 to 3 MPa. These results are in agreement with previous structural analyses of the deformation of the solidified shell between rolls, such as those carried out in static conditions by Wünnenberg,20) Dalin and Chenot (in three dimensions), 8) Miyazawa and Schwerdtfeger, 1) or by Kajitani et al 21) on limited slab sections moving downstream between rolls and submitted to the metallurgical pressure onto the solidification front.…”

Section: Figsupporting

confidence: 92%

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A Two-dimensional Finite Element Thermomechanical Approach to a Global Stress-Strain Analysis of Steel Continuous Casting

Bellet

Heinrich

2004

ISIJ International

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This paper addresses the two-dimensional finite element simulation of steel continuous casting using a global non steady-state approach. The method aims at the calculation of the thermomechanical state (temperature, deformation, stresses) of steel all along the continuous casting machine. Both plane deformation and axisymmetric versions have been developed. The first one addresses the simulation of continuous casting of slabs, taking into account the possible curvature of the machine, whereas the second one applies to cylindrical billets. The implementation of the method is validated by comparison with results from the literature. It is applied to the study of a slab continuous caster for which successive depressive and compressive stress states are revealed in the secondary cooling region.KEY WORDS: continuous casting; finite elements; thermomechanics; stress-strain calculation.which Grill et al., 2) Kristiansson, 3) Thomas et al.,4) Boehmer et al.5) It consists in conveying throughout the machine a transverse section of the product: either a plane section or a volumic domain having a small thickness in the casting direction. Regarding heat transfer, top and bottom surfaces are adiabatic, the heat being extracted through the lateral boundary. As thermal gradients are very low along the casting direction in steel CC, this method yields good thermal results. However, it has major drawbacks regarding the mechanical analysis. Generally, a plane strain deformation state is assumed in the slice. Some authors, like Pascon 6) have extended this concept by assuming a state of generalized plane strain in order to cope with the bending and unbending. In spite of this, the slice approach does not take into account any shear effect and then cannot be representative of complex deformation states such as those associated with bulging. Global Steady-state MethodAn alternative consists of a Eulerian steady-state formulation, which operates on a quasi static computational domain covering the whole machine. This requires the integration of highly non linear constitutive equations (elasticviscoplasticity) along streamlines, which needs specific advection methods, such as those proposed by Huespe et al. 7)In addition, such a problem is a free surface problem, since the location of the mesh boundary is unknown, because of bulging. Therefore specific algorithms must be used in order to move boundary nodes so that the velocity field be tangent to the surface. This has been done by Dalin and Chenot 8) but only on short isolated sections of the secondary cooling. In order to overcome this difficulty, Fachinotti and Huespe have proposed to keep the mesh identical in the analysis and to deduce the bulging a posteriori, 7,9) which makes yet the steady-state formulation not fully consistent. In the authors' opinion, it would be extremely challenging to develop a fully consistent free surface steady-state model, especially because of the contact conditions to be satisfied with a great number of rolls (typically more than 100). The converge...

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Section: Figsupporting

confidence: 92%

“…However, the averaged profile, as drawn on the figure, is shifted in the downstream direction, which is in agreement with the literature. 1,8,20,21) • Final Discussion and Conclusion…”

Section: Figmentioning

confidence: 92%

A Two-dimensional Finite Element Thermomechanical Approach to a Global Stress-Strain Analysis of Steel Continuous Casting

Bellet

Heinrich

2004

ISIJ International

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“…Some estimated bulging with analytical solutions from beam bending [42][43][44][45] . Early finite-element models were developed by Schwerdtfeger [46,47] , by Rammerstorfer [48] , and later by several others [49][50][51][52][53] .…”

Section: Modeling Bulging and Internal Cracksmentioning

confidence: 99%

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

Thomas¹

2002

Metall Mater Trans B

134

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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 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. FORWARDIt is a great privilege to present the second ever J. Keith Brimacombe lecture at this first Electric Furnace Conference of the Third Millennium, (at least according to the Gregorian calendar). Professor Brimacombe was a giant in many fields. He also inspired many people, especially his students, including me. At the first Brimacombe lecture, last year, Indira Samarasekera [1] , gave an inspirational talk, that touched on many different facets of the research excellence that was the hallmark of this remarkable man's career. Dr. Brimacombe left a legacy of leadership, knowledge and genuine care for the people, which benefited the steel industry, the Iron and Steel Society, and many individuals here today. His technical contributions spanned a B.G. Thomas, Brimacombe Lecture,59 th Electric Furnace Conf., Pheonix, AZ, 2001, Iron & Steel Soc., pp. 3-30 4 wide range of materials engineering processes, including rotary kilns, injection, bath smelting, flash smelting, static and continuous casting, rolling, and microstructural engineering.This year's lecture will look at the history, current state, and future prospects of the mathematical modeling of the continuous casting of steel. Of the many contributions that Dr. Brimacombe gave to process metallurgy, some of his best pioneering work was done to help create this field. He was a champion of modeling and he did much to improve its credibility and usefulness, through his example. This subject is also fitting because his impact on the steel industry through short courses and publications on continuous casting made extensive use of the landmark results of his models. Indeed, he would have been the best choice to lecture on this topic, had he not suddenly left us in 1997. I am grateful to the organizers for asking me to give this lecture in an effort to continue his spirit.

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“…138) Recent models have taken additional steps to model this daunting problem. 99,[139][140][141] Further explanation can be found in recent reviews of macrosegregation, by Flemings,142) and its modeling, by Beckermann.…”

Section: Solute Transport Phenomenamentioning

confidence: 99%

Mathematical Modeling of Iron and Steel Making Processes. Mathematical Modeling of Fluid Flow in Continuous Casting.

2001

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Fluid flow is very important to quality in the continuous casting of steel. With the high cost of empirical investigation and the increasing power of computer hardware and software, mathematical modeling is becoming an important tool to understand fluid flow phenomena. This paper reviews recent developments in modeling phenomena related to fluid flow in the continuous casting mold region, and the resulting implications for improving the process. These phenomena include turbulent flow in the nozzle and mold, the transport of bubbles and inclusion particles, multi-phase flow phenomena, the effect of electromagnetic forces, heat transfer, interfacial phenomena and interactions between the steel surface and the slag layers, the transport of solute elements and segregation. The work summarized in this paper can help to provide direction for further modeling investigation of the continuous casting mold, and to improve understanding of this important process.KEY WORDS: mathematical modeling; computational simulation; review; continuous casting; nozzles; molds; multiphase; turbulent; fluid flow; electromagnetic; coupled solidification; inclusion entrapment; segregation.steel. This paper will review recent developments in modeling each of the phenomena above, which are related to fluid flow in the continuous casting mold, and the resulting implications for improving the continuous casting process. Fluid Flow ModelingA typical three dimensional fluid flow model solves the continuity equation and Navier Stokes equations for incompressible Newtonian fluids, which are based on conserving mass (one equation) and momentum (three equations) at every point in a computational domain. 17,18) The solution of these equations, given elsewhere in this issue, 19) yields the pressure and velocity components at every point in the domain. At the high flow rates involved in this process, these models must incorporate turbulent fluid flow. Many different turbulence models have been employed by different researchers for fluid flow in continuous casting, such as effective viscosity models 20,21) (for the cylindrical mold and straight nozzle), one equation turbulence models (turbulent energy plus a given length-scale), 22) two-equation turbulence models such as the K-e Model, 19,23) LES (Large Eddy Simulation), [24][25][26][27][28] possibly with a SGS (sub-grid scale) model, 29,30) and DNS (Direction Numerical Simulation). 19)Among these models, direct numerical simulation is the simplest yet most computationally-demanding method. DNS uses a fine enough grid (mesh), to capture all of the turbulent eddies and their motion with time. To achieve more computationally-efficient results, turbulence is usually modeled on a courser grid using a time-averaged approximation, such as the popular K-e model, 23) which averages out the effect of turbulence using an increased effective viscosity field, m eff . This approach requires solving two additional partial differential equations for the transport of turbulent kinetic energy and its dissipation rate.19...

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Macrosegregation in continuously cast steel slabs: preliminary theoretical investigation on the effect of steady state bulging

Abstract: Model for computation of macrosegregation in slabs due to bulging. Assumptions involved. Simplification for the case of no bulging. Introduction of a modified stream function for the mushy zone. Computation of macrosegregation profiles for various conditions.

Cited by 65 publications

References 12 publications

A Two-dimensional Finite Element Thermomechanical Approach to a Global Stress-Strain Analysis of Steel Continuous Casting

A Two-dimensional Finite Element Thermomechanical Approach to a Global Stress-Strain Analysis of Steel Continuous Casting

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

Mathematical Modeling of Iron and Steel Making Processes. Mathematical Modeling of Fluid Flow in Continuous Casting.

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