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Numerical modelling of macrosegregation in three-dimensional continuous casting of steel billets
Katarina Mramor, Robert Vertnik, Božidar Šarler, 2023, published scientific conference contribution

Abstract: Macrosegregation presents a considerable defect in the continuous casting of billets and can critically affect the final properties of the product. The numerical modelling can help to predict and better understand the segregation and flow patterns inside the mould. The process is modelled with a physical model described by a set of conservation equations describing the t heat transfer, turbulence, fluid flow, solidification and segregation. A two-equation low-Re k-epsilon model and Abe-Kondoh-Nagano closures are used to close governing equations in this incompressible fluid flow example. The Boussinesq approximation is applied to account for the thermo-solutal buoyancy effects, and the Darcy approximation is applied for the description of the flow through the porous mushy zone. On a microscale, a lever rule solidification model is used to couple liquid fraction, temperature and concentration. The three-dimensional model is solved with the method based on local collocation with multiquadric radial basis functions on seven-nodded subdomains. The aim of this contribution is to explore the three-dimensional macrosegregation patterns of 0.51 wt% carbon steel in the solidified shell of the steel in the mould.
Keywords: modeling, continuous casting of steel, CFD, turbulence modeling, LES, meshless methods, RANS
Published in DiRROS: 21.03.2024; Views: 57; Downloads: 41
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8.
Meshless simulation of a macrosegregation benchmark considering the solid motion
Viktor Govže, Igor Vušanović, Božidar Šarler, 2023, published scientific conference contribution

Abstract: We have extended the existing two-dimensional rigid solid phase benchmark for binary substance with the solid phase motion in the present paper. Incompressible laminar Newtonian flow is assumed, and a standard mixture formulation is used for the mass, momentum, energy, and solute transport. A coherency solid motion model accounts for the free-floating grains, assuming that the solid velocity is proportional to the mixture velocity and the liquid fraction. The lever rule is used to describe the mass fractions of the phases. A two-dimensional benchmark is solved using the semi-implicit meshless diffuse approximate method with an adaptive subdomain upwinding strategy. The results of the meshless method are compared to the finite volume method results with a reasonable agreement. The new benchmark results show that the solid motion has an essential effect on the macrosegregation pattern.
Keywords: solidification, meshless methods, grain motion, benchmarks
Published in DiRROS: 21.03.2024; Views: 65; Downloads: 37
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9.
Application of a meshless space-time adaptive approach to phase-field modelling of polycrystalline solidification
Tadej Dobravec, Boštjan Mavrič, Božidar Šarler, 2023, published scientific conference contribution

Abstract: We have developed a 2-D numerical meshless adaptive approach for phase-field modelling of dendritic solidification. The quadtree-based approach decomposes the computational domain into quadtree sub-domains of different sizes. The algorithm generates uniformly-distributed computational nodes in each quadtree sub-domain. We apply the meshless radial basis function generated finite difference method and the forward Euler scheme to discretise governing equations in each computational node. The fixed ratio between the characteristic size and the node spacing of a quadtree sub-domain ensures space adaptivity. The adaptive time-stepping accelerates the calculations further. In the framework of previous research studies, we used the approach to solve quantitative phase-field models for single dendrite growth in pure melts and dilute binary alloys. In the present study, we upgrade the solution procedure for the modelling growth of multiple differently oriented dendrites. Along with the space-time adaptive approach, we apply non-linear preconditioning of the phase-field equation to increase computational efficiency. We investigate a novel numerical approach's accuracy and computational efficiency by simulating the equiaxed dendrite growth from a dilute binary alloy.
Keywords: dendritic growth, phase-field method, meshless methods, polycrystalline solidification
Published in DiRROS: 21.03.2024; Views: 59; Downloads: 40
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10.
A meshless numerical solution of thermo-mechanics of hot-rolled steel bars on a cooling bed
Gašper Vuga, Boštjan Mavrič, Umut Hanoglu, Božidar Šarler, 2023, published scientific conference contribution

Abstract: After the continuous hot-rolling process, steel bars are immediately placed on the cooling bed. At the beginning of the cooling, the material is at high temperatures, and the yield strength is low. Due to thermal load, yield strength can be exceeded, and permanent plastic strains start accumulating, resulting in possible unwanted shape changes and residual stresses. The present paper aims to develop a thermo-mechanical model for studying and eliminating undesirable phenomena before the products leave the cooling bed. The governing equations are solved for the two-dimensional slice in a strong form, and a modified version of the radial basis function generated finite difference (RBF-FD) method [1]. The initial bar geometry is obtained from the existing meshless hot-rolling simulation system [2]. The thermal and mechanical models are one-way coupled, i.e. the temperature solution represents a driving force for the stress and strain solution. The temperature field is obtained with explicit propagation in time. The convective and radiative heat fluxes on the boundary are updated at each time step using the ray tracing procedure to determine the radiative heat flux. The mechanical part is solved by considering the small strain elasto-plasticity, where the isotropic von Mises temperature-dependent hardening is employed. The global system of nonlinear equations of the mechanical part is solved by the Newton-Raphson method. The closest point projection method is used to solve the constitutive relations. A sensitivity study is performed on the influence of cooling intensity on a rectangular steel bar’s temperature, stress and strain field. We defined the most influential factors for defect formation. For the first time, a novel meshless RBF-FD method is successfully used for solving such a complex industrial problem. The model will be perspectively upgraded from the slice to the three-dimensional model to enable also bending.
Keywords: cooling bed, steel bars, thermo-mechanics, strong form, meshless method
Published in DiRROS: 21.03.2024; Views: 46; Downloads: 28
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