2D/3D Simulation of macrosegregation: a comparison between codes on a small cavity and on a large ingot

International audienceThis paper presents the coupled resolution of momentum, energy and solute conservation equations, for binary alloys by three different codes. The microsegregation is governed by the lever rule and the liquid flow in the mushy zone is modeled by a Darcy law. A 2D FV code, SOLID, a 2D FE code, R2SOL and a 3D FE code, THERCAST, are compared on an academic case on which experimental measurements have been done by Hebditch and Hunt, and on a benchmark steel ingot for industrial application. An adaptive anisotropic remeshing technique is used in each FE codes. For both codes, this technique is shortly described

Effect of Discretization of Permeability Term and Mesh Size on Macro- and Meso-segregation Predictions

Macro- and meso-segregations correspond to heterogeneities of composition at the scale of a casting. They develop during the solidification. One of the parameters that has an essential effect on these segregations is the mush permeability which varies over a wide range of magnitude. We present simulation results for solidification of Sn-Pb alloy in a two-dimensional cavity. The role of discretization schemes and mesh size on the formation of channel segregates and macrosegregation is discussed

Modelling of Columnar-to-Equiaxed and Equiaxed-to- Columnar Transitions in Ingots Using a Multiphase Model

International audienceWe present a new method to handle a representative elementary volume (REV) with a mixture of columnar and equiaxed grains in ingot castings in the framework of an Eulerian volume averaged model. The multiscale model is based on a previously established fully equiaxed model. It consists of a three-phase (extra-granular liquid, intra-granular liquid and solid) grain-growth stage coupled with a two-phase (solid and liquid) macroscopic transport stage accounting for grain and nuclei movement. In this context, we take into account the formation of a columnar structure and its development using a simplified front-tracking method. Columnar solidification is coupled with the growth of equiaxed grains ahead of the columnar front. The particularity of the model is the treatment of concurrent growth of mixed columnar and equiaxed structures only in the volumes that contain the columnar front. Everywhere else, the structure is considered either fully columnar or fully equiaxed. This feature allows for reasonable computational times even in industrial size castings, while describing the solutal and mechanical blocking phenomena responsible for the Columnar-to-Equiaxed Transition. After a validation of the model, we discuss the numerical results for a 6.2-ton industrial steel ingot by comparison with experimental measurements. Final maps for macrosegregation and grain structures size and morphology are analysed. Furthermore, we quantify the impact of nuclei formation through fragmentation along the columnar front on the result. An attempt at predicting the occurrence of the Equiaxed-to-Columnar Transition in the later phases of the process is also made

A 3D-fem model solving thermomechanics and macrosegregation in binary alloys solidification

International audienceThis paper introduces a three-dimensional numerical model for the coupled solution of momentum, energy and solute conservation equations, for binary alloys solidification. The spatial discretisation is carried out using linear tetrahedral finite elements, particularly those of P1+/P1 type for the velocity-pressure resolution of momentum equation. The liquid flow in the mushy zone is assumed to be governed by the Darcy's law. Thermal and buoyancy forces are taken into account by means of the Boussinesq's model. Microsegregation obeys the lever rule. The resulting solute transport equation is solved by the SUPG method. Coupling strategy between momentum, energy and solute equations is discussed and two applications are studied

Multi-scale finite element modelling of solidification structures by a splitting method taking into account the transport of equiaxed grains

International audienceIn solidification processes of large industrial castings and ingots, the transport of solid in the liquid has an important effect on the final grain structure and macrosegregation. Modeling is still challenging as complex interactions between heat and mass transfers at microscopic and macroscopic scales are highly coupled. This paper first presents a multi-scale numerical solidification model coupling nucleation, grain growth and solute diffusion at microscopic scales with heat and mass transfer, including transport of liquid and solid phases at macroscopic scales. The resolution consists of a splitting method, which considers the evolution and interaction of quantities during the process with a transport stage and a growth stage. This splitting reduces the nonlinear complexity of the set of considered equations and provides an efficient numerical implementation. It is inspired by the work of Založnik et al. [1,2], which used a finite volume method (FVM). The present work develops the solution based on the finite element method (FEM). Numerical results obtained with this model are presented and simulations without and with grain transport are compared to study the impact of solid-phase transport on the solidification process and on the formation of macrosegregation

Transferts de chaleur et de masse dans un bain liquide avec fusion de la paroi et effets de composition

Ce travail traite de la thermohydraulique d un bain de melt couplée à la physicochimie pour ladescription du comportement de mélanges de matériaux (non-eutectiques).On décrit le transitoire d établissement de température dans un liquide avec dégagement de puissancevolumique en présence de solidification sur une paroi refroidie. Le modèle développé à cet effet estvalidé par rapport aux résultats des essais LIVE réalisés à KIT. Dans les conditions de ces essais onmontre que la température d interface suit la température liquidus (correspondant à la composition dubain liquide) pendant le transitoire d établissement de la température dans le bain et des croûtessolides.Par ailleurs, on propose un modèle d interaction entre un liquide non-eutectique (soumis à dissipationvolumique de puissance) et une paroi fusible dont la température de fusion est inférieure à latempérature liquidus du bain. Les prédictions du modèle sont comparées aux résultats des essaisARTEMIS 2D. On en déduit une nouvelle formulation de la température d interface (inférieure àliquidus température) entre le liquide et la couche pâteuse en paroi.This work deals with the thermal-hydraulics of a melt pool coupled with the physical chemistry for thepurpose of describing the behaviour of mixtures of materials (non-eutectic).Evolution of transient temperature in a liquid melt pool heated by volumetric power dissipation hasbeen described with solidification on the cooled wall. The model has been developed and is validatedfor the experimental results given by LIVE experiment, performed at Karlsruhe Institute ofTechnology (KIT) in Germany. Under the conditions of these tests, it is shown that the interfacetemperature follows the liquidus temperature (corresponding to the composition of the liquid bath)during the whole transient. Assumption of interface temperature as liquidus temperature allowsrecalculating the evolution of the maximum melt temperature as well as the local crust thickness.Furthermore, we propose a model for describing the interaction between a non-eutectic liquid meltpool (subjected to volumetric power dissipation) and an ablated wall whose melting point is below theliquidus temperature of the melt. The model predictions are compared with results of ARTEMIS 2Dtests. A new formulation of the interface temperature between the liquid melt and the solid wall(below liquidus temperature) has been proposed.SAVOIE-SCD - Bib.électronique (730659901) / SudocGRENOBLE1/INP-Bib.électronique (384210012) / SudocGRENOBLE2/3-Bib.électronique (384219901) / SudocSudocFranceF

Mesoscopic modeling of spacing and grain selection in columnar dendritic solidification: Envelope versus phase-field model

We investigate and assess the capability of the mesoscopic envelope model of dendritic solidification to represent the growth of columnar dendritic structures. This is done by quantitative comparisons to phase-field simulations in two dimensions. While the phase-field model resolves the detailed growth morphology at the microscale, the mesoscopic envelope model describes a dendritic grain by its envelope. The envelope growth velocities are calculated by an analytical dendrite-tip model and matched to the numerical solution of the solute concentration field in the vicinity of the envelope. The simplified representation of the dendrites drastically reduces the calculation time compared to phase field. Larger ensembles of grains can therefore be simulated. We show that the mesoscopic envelope model accurately reproduces the evolution of the primary branch structure, the undercooling of the dendrite tips, and the solidification path in the columnar mushy zone. We further show that it can also correctly describe the transient adjustments of primary spacing, both by spacing increase due to elimination of primary branches and by spacing reduction due to tertiary rebranching. Elimination and tertiary rebranching are also critical phenomena for the evolution of grain boundaries between columnar grains that have a different crystallographic orientation with respect to the temperature gradient. We show that the mesoscopic model can reproduce the macroscopic evolution of such grain boundaries for small and moderate misorientation angles, i.e., up to 30°. It is therefore suitable for predicting the texture of polycrystalline columnar structures. We also provide guidelines for the calibration of the main parameters of the mesoscopic model, required to obtain reliable predictions.ANR-11-LABX-0008/11-LABX-0008 - DAMAS - Design des Alliages Métalliques pour Allègement des Structures (2011) - German Space Agency DLR under Contract FKZ 50WM144

Solidification path and phase transformation in super-austenitic stainless steel UNS S31254

The solidification path and the σ-phase precipitation mechanism of UNS S31254 alloy were studied on the basis of directional solidified experiments accompanied by scanning electron microscopy observations and energy dispersive X-ray a nalysis. The resulting temperatures of solidification paths and phase transformation were compared with Gulliver-Scheil and equilibrium calculations predicted using ThermoCalc© software. It was confirmed that the experimental solidification path was in agreement with the thermodynamic calculations. The complementarity of the results have made it possible to propose a solidification path and a σ-phase precipitation mechanism for the UNS31254 steel