Bernard Dussoubs

Effect of discretization of permeability term and mesh size on macro- and meso-segregation predictions

The effect of interpolation schemes used for discretization of permeability in numerical simulations on macrosegregation and channel segregation (mesosegregation) during solidification has been studied. The different ways to discretize the permeability term and its effect on the interdendritic velocity are illustrated by a simplified 1D model which solves the Darcy equation for a porous medium. The Darcy equation is solved numerically using the SIMPLE algorithm for the coupled velocity–pressure fields. For this simplified case, an analytical reference solution can also be obtained. In the numerical solution four different interpolation schemes for permeability discretization have been employed, and the results obtained are compared. For coarse mesh, different interpolation schemes produce large differences from the analytical reference solution. We thereafter, present simulation results for solidification of Sn–Pb alloy in a two-dimensional rectangular cavity using different discretization schemes. It is observed that solute-rich liquid flowing towards the bottom of the rectangular cavity in the mushy zone due to thermosolutal convection results in patches of thin structure known as channels. These channels are formed by perturbation by the interdendritic fluid flow in the mushy zone and in some cases by the localized remelting in some portions of the solid/mush interface. The role of discretization schemes and mesh size on the formation of channel segregates and macrosegregation is discussed.

Influence of Discretization of Permeability Term and Mesh Size on the Prediction of Channel Segregations

Macro- and meso-segregations correspond to compositional heterogeneities at the scale of a casting. They develop during the solidification process. One of the parameters that have an essential effect on these segregations is the mush permeability, which is highly nonlinear, and varies over a wide range of magnitudes. We present simulation results for solidification of a Sn-Pb alloy in a two-dimensional cavity, highlighting the role of (i) the numerical interpolation schemes used for the finite-volume discretization of the highly-nonlinear permeability term and (ii) of the mesh size on the prediction of mesosegregations and macrosegregation. We observe that solute-rich liquid flowing through the mushy zone due to thermo-solutal convection results in patches of thin channel structures, which develop into mesosegregations. We notice little sensitivity of the predicted macrosegregation to different discretization schemes for the permeability term. However, we found their influence on the prediction of channel segregates to be significant when using coarse computational grids, customary in the simulation of industrial castings. Mesh refinement is crucial for capturing the complex phenomena in the formation of channel segregates. With a very fine mesh channels have been captured with more than one grid point along their width, allowing the determination of their width.

Coupling of CFD and PBE Calculations to Simulate the Behavior of an Inclusion Population in a Gas-Stirring Ladle

Gas-stirring ladle treatment of liquid metal has been pointed out for a long time as the processing stage is mainly responsible for the inclusion population of specialty steels. A steel ladle is a complex three-phase reactor, where strongly dispersed inclusions are transported by the turbulent liquid metal/bubbles flow. We have coupled a population balance model with CFD in order to simulate the mechanisms of transport, aggregation, flotation, and surface entrapment of inclusions. The simulation results, when applied to an industrial gas-stirring ladle operation, show the efficiency of this modeling approach and allow us to compare the respective roles of these mechanisms on the inclusion removal rate. The comparison with literature reporting data emphasizes the good prediction of deoxidating rate of the ladle. On parallel, a simplified zero-dimensional model has been set-up incorporating the same kinetics law for the aggregation rate and all the removal mechanisms. A particular attention has been paid on the averaging method of the hydrodynamics parameters introduced in the flotation and kinetics kernels.

Study and modelling of microstructural evolutions and thermomechanical behaviour during the tempering of steel

A model for the evolution of microstructures and flow stress during the tempering of low alloyed steels has been developed. The competitive precipitations of e carbide and cementite are simulated. The results are used to calculate the flow stress of the tempered martensite by a thermo-elasto-viscoplastic law that takes into account solid solution, dislocation and precipitation hardenings. The model is applied to a 80MnCr5 steel and the calculated results are compared with the experimental ones.

Influence of the Mold Current on the Electroslag Remelting Process

The electroslag remelting process is widely used to produce high value-added alloys. The use of numerical simulation has proven to be a valuable way to improve its understanding. In collaboration with Aubert & Duval, the Institute Jean Lamour has developed a numerical transient model of the process. The consumable electrode is remelted within a mold assumed to be electrically insulated by the solidified slag skin. However, this assumption has been challenged by some recent studies: the solidified slag skin may actually allow a part of the melting current to reach the mold. In this paper, the evolution of our model, in order to take into account this possibility, is presented and discussed. Numerical results are compared with experimental data, while several sensitivity studies show the influence of some slag properties and operating parameters on the quality of the ingot. Even, a weakly conductive solidified slag skin at the inner surface of the mold may be responsible for a non-negligible amount of current circulating between the slag and crucible, which in turn modifies the fluid flow and heat transfer in the slag and ingot liquid pool. The fraction of current concerned depends mainly on the electrical conductivities of both the liquid and solidified slag.

Impact of the Solidified Slag Skin on the Current Distribution During Electroslag Remelting

The ESR process is commonly used to produce defect-free ingots of high added value alloys such as special steels or Ni-based superalloys. Numerous simulation tools have been developed for the last 30 years to get better insight into the process and help its optimization. Most assume that no electrical current is able to cross the solidified slag skin and flow in the water-cooled mold. However, it has recently been claimed that the slag skin does not ensure perfect insulation, which is prone to modify the current distribution, hence some of the results previously assessed. This paper presents the assumptions made to simulate that phenomenon and some results in terms of current flow into the mold, depending on the thickness and electrical conductivity of the solidified slag skin. Results show that both parameters can have a great influence on the current distribution, hence the slag behaviour and final ingot quality.

Mathematical Modeling of the Mold Current and Its Influence on Slag and Ingot Behavior during ESR

Abstract ElectroSlag Remelting (ESR) is widely used to produce high added value alloys for critical applications (aerospace industry, nuclear plants, etc.). In collaboration with Aubert & Duval, Institut Jean Lamour has been developing for several years a numerical transient model of an ESR heat. In the previous version of the model, the crucible was assumed to be perfectly electrically insulated from the electrode-slag-ingot system. However, this assumption must be challenged: the solidified slag skin at the slag/mold and ingot/mold interfaces may actually allow a fraction of the melting current to reach the crucible. In this paper, an evolution of the model is presented that enabled us to take into account the possibility of mold current. The simulation results were compared with actual experimental data. Sensitivity studies showed the influence of slag properties and operating parameters on the final quality of the ingot. Results highlighted that even a weakly conductive solidified slag skin at the inner surface of the model can be responsible for a non-negligible amount of current circulating between the slag and crucible, which modifies the fluid flow, heat transfer and solidification of both the slag phase and the metallic ingot.