M. Wu

Modelling the thermosolutal convection, shrinkage flow and grain movement of globular equiaxed solidification using a three phase model

Abstract A three phase volume averaging model has been developed to simulate globular equiaxed solidification, the three phases being liquid, solid and air. The basic conservation equations of mass, momentum and enthalpy have been solved for each phase, and the thermal and mechanical (drag force) interactions among the phases have been considered. Grain nucleation, growth rate (mass exchange), solute partitioning at the liquid/solid interface and solute transport have also been accounted for. Due to its low density, the air phase floats always at the top region, forming a definable air/liquid melt interface, i.e. free surface. By tracking this free surface, the shrinkage cavity in an open casting system can be modelled. As the temperature and concentration dependent density and solidification shrinkage are explicitly included, the thermosolutal convection, together with feeding flow and grain movement can be taken into account. This paper focuses on the model description; preliminary results on a benchmark ingot casting (Al–4Cu) are presented and discussed.

Reformulation of time averaged Joule heating in presence of temperature fluctuations

Abstract Strong temperature fluctuations might exist in non-isothermal turbulent flow. When a RANS approach is used for simulation it is necessary to time average all properties that are temperature dependant. Here we focus on the time average of the Joule heating released within the turbulent slag region of an electroslag remelting process (ESR). For that the average temperature dependant electric conductivity of the slag was expressed as a function of the time averaged temperature field and its standard deviation. The results using this new approach are compared with the results given by the classical approach using only the electric conductivity at the time averaged temperature. It will be shown that the temperature fluctuations decrease strongly the amount of electric current flowing directly to the mould, and increase the efficiency of the remelting process by 50%.

Modelling macrosegregation in a 2.45 ton steel ingot

A three phase model for the mixed columnar-equiaxed solidification was proposed by the current authors [Wu and Ludwig 2006 Metall. Mater. Trans. 37A 1613-31]. The main features of the mixed columnar-equiaxed solidification are considered: the growth of the columnar dendrite trunks from the ingot surface, the nucleation and growth of the equiaxed crystals, the sedimentation of the equiaxed crystals, the thermal and solutal buoyancy flow and its interactions with the growing crystals, the solute partitioning at the solid-liquid interface during solidification, the solute transport due to melt convection and equiaxed sedimentation, the mechanical interaction/impingement between columnar and equiaxed crystals and the columnar-to-equiaxed transition (CET). However, due to the model complexity and the limited computational capability the model has not yet applied to the large steel ingots of engineering scale. This paper is going to simulate a 2.45 ton big-end-up industry steel ingot, for which some experimental results were reported [Marburg 1926 Iron Steel Inst. 113 39-176]. Here a simplified binary phase diagram for the steel (Fe-0.45 wt. %C) is considered. Comparison of the modelling results such as as-cast columnar and equiaxed zones, macrosegregation with the experimental results is made. Details about the formation sequence of the distinguished crystal zones and segregation patterns are analyzed.

Importance of Melt Flow in Solidifying Mushy Zone

A mixture solidification model is employed to study the interaction between the melt flow and the growing mushy zone. The goal is to address the importance of considering the melt flow and flow pattern (laminar or turbulent) in the growing mushy zone. A simple 2D benchmark with parallel flow passing by/through a vertically growing mushy zone is considered. Parameter studies with different velocities and flow patterns are performed. It is found that the flow velocity and flow pattern in and near the mushy zone plays an extremely important role in the formation of the mushy zone. The mushy zone thickness is dramatically reduced with the increasing melt velocity. Simulations with/without considering turbulence show significantly different results. The turbulence in the mushy zone is currently modeled with a simple assumption that the turbulence kinetic energy is linearly reduced with the mush permeability.

Multiphase/multicomponent modeling of solidification processes: coupling solidification kinetics with thermodynamics

Abstract This paper is an extension and improvement of the previous work of the authors. It presents further development of a coupling method between a multiphase Eulerian solidification model and the thermodynamics of multicomponental alloys. The transport equations of the multiphase solidification model are closed by the interphase transfer/exchange terms. The derivation of these terms is based on the diffusion-controlled solidification kinetics and thermodynamics. Direct online coupling of a computational fluid dynamics solver with a thermodynamic software package is time-consuming, therefore a way to access thermodynamic data by means of the tabulation and interpolation technique (In-Situ Adaptive Tabulation) is suggested. The coupling procedure is described and tested with a 0-D solidification benchmark case. Additionally, the suggested coupling method is used to simulate a casting process of a CuSn6P0.5 round strand, which demonstrated the application potential of the coupling idea. The predicted macrosegregations of Sn and P for this casting process shows the same distribution pattern as observed in practice, namely positive segregation in the vicinity of the wall region and negative one in the center of the casting.

Using four-phase Eulerian volume averaging approach to model macrosegregation and shrinkage cavity

This work is to extend a previous 3-phase mixed columnar-equiaxed solidification model to treat the formation of shrinkage cavity by including an additional phase. In the previous model the mixed columnar and equiaxed solidification with consideration of multiphase transport phenomena (mass, momentum, species and enthalpy) is proposed to calculate the as- cast structure including columnar-to-equiaxed transition (CET) and formation of macrosegregation. In order to incorporate the formation of shrinkage cavity, an additional phase, i.e. gas phase or covering liquid slag phase, must be considered in addition to the previously introduced 3 phases (parent melt, solidifying columnar dendrite trunks and equiaxed grains). No mass and species transfer between the new and other 3 phases is necessary, but the treatment of the momentum and energy exchanges between them is crucially important for the formation of free surface and shrinkage cavity, which in turn influences the flow field and formation of segregation. A steel ingot is preliminarily calculated to exam the functionalities of the model.

Simulation of the as-cast structure of Al-4.0wt.%Cu ingots with a 5-phase mixed columnar-equiaxed solidification model

Empirical knowledge about the formation of the as-cast structure, mostly obtained before 1980s, has revealed two critical issues: one is the origin of the equiaxed crystals; one is the competing growth of the columnar and equiaxed structures, and the columnar-to-equiaxed transition (CET). Unfortunately, the application of empirical knowledge to predict and control the as-cast structure was very limited, as the flow and crystal transport were not considered. Therefore, a 5-phase mixed columnar-equiaxed solidification model was recently proposed by the current authors based on modeling the multiphase transport phenomena. The motivation of the recent work is to determine and evaluate the necessary modeling parameters, and to validate the mixed columnar-equiaxed solidification model by comparison with laboratory castings. In this regard an experimental method was recommended for in-situ determination of the nucleation parameters. Additionally, some classical experiments of the Al-Cu ingots were conducted and the as-cast structural information including distinct columnar and equiaxed zones, macrosegregation, and grain size distribution were analysed. The final simulation results exhibited good agreement with experiments in the case of high pouring temperature, whereas disagreement in the case of low pouring temperature. The reasons for the disagreement are discussed.

Shallow water model for horizontal centrifugal casting

A numerical model was proposed to simulate the solidification process of an outer shell of work roll made by the horizontal centrifugal casting technique. Shallow water model was adopted to solve the 2D average flow dynamics of melt spreading and the average temperature distribution inside the centrifugal casting mould by considering the centrifugal force, Coriolis force, viscous force due to zero velocity on the mould wall, gravity, and energy transport by the flow. Additionally, a 1D sub-model was implemented to consider the heat transfer in the radial direction from the solidifying shell to the mould. The solidification front was tracked by fulfilling the Stefan condition. Radiative and convective heat losses were included from both, the free liquid surface and the outer wall of the mould. Several cases were simulated with the following assumed initial conditions: constant height of the liquid metal (10, 20, and 30 mm), uniform temperature of the free liquid surface (1755 K). The simulation results have shown that while the solidification front remained rather flat, the free surface was disturbed by waves. The amplitude of waves increased with the liquid height. Free surface waves diminished as the solidification proceeded.

Modeling of the flow-solidification interaction in thin slab casting

A key issue for modelling the thin slab casting (TSC) is to consider the evolution of the solid shell, which strongly interacts with the turbulent flow and in the meantime is subject to continuous deformation due to the funnel shape (curvature) of the mould. Here an enthalpy-based mixture solidification model with consideration of turbulent flow (Prescott and Incropera, ASME HTD, vol. 280, 1994, pp. 59) is employed, and further enhanced to include the deforming solid shell. The solid velocity in the fully-solidified strand shell and partially-solidified mushy zone is estimated by solving the Laplaces equation. Primary goals of this work are to examine the sensitivity of the modelling result to different model implementation schemes, and to explore the importance of the deforming and moving solid shell in the solidification. Therefore, a 2D benchmark, to mimic the solidification and deformation behaviour of the thin slab casting, is firstly simulated and evaluated. An example of 3D TSC is also presented. Due to the limitation of the current computation resources additional numerical techniques like parallel computing and mesh adaptation are necessarily applied to ensure the calculation accuracy for the full-3D TSC.

Observation of flow regimes and transitions during a columnar solidification experiment

Experimental data for the validation of numerical models coupling solidification and hydrodynamics are very rare. Many experiments made in the field of solidifications are performed with pure metals or alloys (Al-Cu, Pb-Sn, etc) which are opaque and do not allow direct observation of the hydrodynamic. Only the results related to solidification such as grain size and orientation, or macro-segregation are usually used for the validation. The present paper is dedicated to the description of well-controlled experiments where both solidification and fluid dynamic can be simultaneously observed. The important point is the almost purely columnar nature of the solidified mushy region. To our knowledge this is the very first reported macro-scale experiment with almost purely columnar solidification where the flow was measured with a PIV technique. The experiments consist in studying the hydrodynamics during the columnar solidification of a H2O-NH4Cl hypereutectic alloy in a die cast cell. Particle image velocimetry was employed to measure the flow velocity in the liquid bulk. Different flow regimes generated by complex thermo-solutal double diffusive convection were observed. In the beginning of the solidification the solutal buoyancy generates a turbulent flow, which is progressively replaced by the development of stratification from the top of the cell. Later, the stratification leads to the development of a long lasting meandering flow, which filled almost all the liquid region. The kinetic energy of the flow was calculated and it was found out that it decreased with time. The solidification front was smooth and no freckles appeared in the mushy zone. The evolution of the thickness of the mushy zone was measured. As this experiment showed a good reproducibility it represents an excellent benchmark for validation of the numerical models that target the simultaneous prediction of flow dynamics and solidification.