Dendritic Mushy Zone Research Articles

Multi-scale and multi-physics simulation of central segregation in an equiaxed dendritic mushy zone during continuous casting of steel

Centreline segregation during continuous casting of steel is highly detrimental to the end-product mechanical properties. In this study, a 3D multi-scale and multi-physics model is developed and validated that directly predicts alloy segregation occurring in peritectic steel grades having centreline equiaxed grain morphology. The model consists of four models: (1) a 1D macroscale heat transfer and solidification model, (2) a 3D mesoscale dendritic solidification model, (3) a 3D mesoscale dendritic fluid flow model, and (4) a 3D mesoscale solute transport and redistribution model. The use of a mesoscale domain where the solid and liquid phases are separately discretized allows for consideration of physical phenomena affecting segregation that are classically hidden by the averaging procedures of fully continuum approaches. Thus the new model is able to account for the multiple phenomena occurring during continuous casting while also directly considering the stochastic effects resulting from grains having randomly-placed nuclei as well as interactions between the liquid and solid phases. The results demonstrate that solute partitioning combined with intra-dendritic fluid flow leads eventually to liquid channels enriched with solute that result in centreline segregation. The predicted composition in these discrete liquid channels shows excellent agreement with a Mn centreline segregation profile experimentally-measured via microscopic X-ray fluorescence of a commercially-cast steel slab. Finally, the effects of alloy composition, and soft reduction on the degree of centreline segregation are examined.

Macrosegregation and thermosolutal convection-related freckle formation in directionally solidified Sn–Ni peritectic alloy in crucibles with different diameters

Different from other alloys, the observation in this work on the dendritic mushy zone shows that the freckles are formed in two different regions before and after peritectic reaction in directional solidification of Sn–Ni peritectic alloys. In addition, the experimental results demonstrate that the dendritic morphology is influenced by the temperature gradient zone melting and Gibbs–Thomson effects. A new Rayleigh number (RaP) is proposed in consideration of both effects and peritectic reaction. The prediction of RaP confirms the freckle formation in two regions during peritectic solidification. Besides, heavier thermosolutal convection in samples with larger diameter is also demonstrated.

Macrosegregation and channel segregation formation of faceted mushy zone in solidification of Sn–Ni hypereutectic alloy in a temperature gradient

Numerous investigations on the macrosegregation and channel segregation formation have been reported during eutectic solidification. However, the current analyses are focused on the non-faceted dendritic mushy zone while the faceted mushy zone during solidification has not been reported before. In this work, the macrosegretion and channel segregation formation are studied in directional solidification of Sn-15at.%Ni hypereutectic alloy where the solidified Ni3Sn4 phase exhibits faceted lath-type growth morphology. Similar to previous works on non-faceted mushy zone, more channels can be witnessed in the (Liquid + Ni3Sn4) mushy zone at lower growth velocities. More obvious macrosegregation can be formed in samples at lower growth velocities where the thermosolutal convection is more severe. However, distinct from previous reports, the effective solute distribution coefficient is not constant in the faceted mushy zone of this alloy. Besides, the experimental results demonstrates that the convection can reduce the interspacing of Ni3Sn4 phase during directional solidification. In addition, the thermosolutal convection has more significant influence on the interspacing of Ni3Sn4 phase than the solutal buildup at the tip of Ni3Sn4 phase.

Macrosegregation and thermosolutal convection-induced freckle formation in dendritic mushy zone of directionally solidified Sn-Ni peritectic alloy

Compared with the growing applications of peritectic alloy, none research on the freckle formation during peritectic solidification has been reported before. Observation on the dendritic mushy zone of Sn-36 at.%Ni peritectic alloy during directional solidification at different growth velocities shows that the freckles are formed in two different regions: region I before peritectic reaction and region II after peritectic reaction. In addition, more freckles can be observed at lower growth velocities. Examination on the experimental results demonstrates that both the temperature gradient zone melting (TGZM) and Gibbs-Thomson (G–T) effects have obvious influences on the morphology of dendritic network during directional solidification. The current theories onKI Rayleigh number Ra characterizing the thermosolutal convection of dendritic mushy zone to predict freckle formation through the maximum of Ra can only explain the existence of region I while the appearance of region II after peritectic reaction cannot be predicted. Thus, a new Rayleigh number RaP is proposed in consideration of evolution of dendritic mushy zone by both effects and peritectic reaction. Theoretical prediction of RaP also shows a maximum after peritectic reaction in addition to that before peritectic reaction, thus, agreeing well with the freckle formation in region II. In addition, more severe thermosolutal convection can be predicted by the new Rayleigh number RaP at lower growth velocities, which further demonstrates the reliability of RaP in describing the dependence of freckle formation on growth velocity.

Analysis on fluid permeability of dendritic mushy zone during peritectic solidification in a temperature gradient

Compared with the growing applications of peritectic alloys, none research on the fluid permeability K of dendritic network during peritectic solidification has been reported before. The fluid permeability K of dendritic network in the mushy zone during directional solidification of Sn-Ni peritectic alloy was investigated in this study. Examination on the experimental results demonstrates that both the temperature gradient zone melting (TGZM) and Gibbs-Thomson (G–T) effects have obvious influences on the morphology of dendritic network during directional solidification. This is realized through different stages of liquid diffusion within dendritic mushy zone by these effects during directional solidification. The TGZM effect is demonstrated to play a more important role as compared with the G–T effect during directional solidification. Besides, it is shown that the evolution of dendrite network is more complex during peritectic solidification due to the involvement of the peritectic phase. Through the specific surface SV, analytical expression based on the Carman–Kozeny model was proposed to analyze the fluid permeability of dendritic mushy zone in directionally solidified peritectic alloys. In addition, it is interesting to find a rise in permeability K after peritectic reaction in both theoretical predication and experimental results, which is different from that in other alloys. The theoretical predictions show that this rise in fluid permeability K after peritectic reaction is caused by the remelting/resolidification process on dendritic structure by the TGZM and G–T effects during peritectic solidification.

Mushy zone solidification in a static thermal gradient: The effect of dendrite orientation

The solidification dynamics of a mushy zone, i.e. an array of tilted dendrites, kept in a static thermal gradient has been investigated by phase-field simulations. In comparison to our previous study of a well-aligned, i.e. non-tilted dendritic mushy zone [Acta Mat. 122, 310 (2017)], we show that for the general case of dendrites with growth orientations tilted to the thermal gradient, the ”Temperature Gradient Zone Melting” phenomenon also affects the primary trunks, yielding a similar solidification kinetic but different microsegregation pattern in the solid. We briefly discuss the relevance of the presented observations for the microstructure formation in additive manufacturing processes.

Prediction of mushy zone permeability of Al-4.5wt%Cu alloy during solidification by phase field model and CFD simulation

Liquid permeability of the mushy zone is important for porosity formation during the solidification process. In order to investigate the permeability of the mushy zone, an integrated model was developed by combining the phase field model and computational fluid dynamics (CFD) model. The three-dimensional multigrain dendrite morphology was obtained by using the phase field model. Subsequently, the computer-aided design (CAD) geometry and mesh were generated based on calculated dendrite morphologies. Finally, the permeability of the dendritic mushy zone was obtained by solving the Navier-Stokes and continuity equations in ANSYS Fluent software. As an example, the dendritic mushy zone permeability of Al-4.5wt%Cu alloy and its relationship with the solid fractions were studied in detail. The predicted permeability data can be input to the solidification model on a greater length scale for macro segregation and porosity simulations.

Mushy Zone Morphology Calculation with Application of CALPHAD Technique

Mushy zone morphology in AlSiMn alloys was studied using directional solidification, and the CALPHAD (Computer Coupling of Phase Diagrams and Thermochemistry) technique was applied for thermodynamic calculations. The specimens solidified with forced convection presented segregation across the sample diameter, and the measured compositions were located on the Al-Si-Mn phase diagram. Scheil-Gulliver calculations for measured compositions were used to determine various solidification paths that may occur in specimens. Property diagrams and solidification paths presented the segregation effect on the characteristic temperatures, mushy zone length and the sequence of occurring phases whilst 2D maps enabled visualization of the mushy zone during directional solidification. Melt stirring was found to change solidification range, as well as mushy zone length and shape, and the dendrite tips formed a rough profile across the specimens. The study revealed mushy zones with dense dendritic structure and liquid channels empty of Mn phases, where intermetallics had no possibility to flow in the liquid, whilst in other samples with channels filled with Al15Si2Mn4, Mn-precipitates also flowed above the α-Al. The melt flow may lead to a mainly dendritic mushy zone or to a mushy zone with dendrites reaching only lower half of mushy length with intermetallics forming and freely flowing above dendrites in the liquid upper half.

Numerical Investigation of Shell Formation in Thin Slab Casting of Funnel-Type Mold

The key issue for modeling thin slab casting (TSC) process is to consider the evolution of the solid shell including fully solidified strand and partially solidified dendritic mushy zone, which strongly interacts with the turbulent flow and in the meantime is subject to continuous deformation due to the funnel-type mold. Here an enthalpy-based mixture solidification model that considers turbulent flow [Prescott and Incropera, ASME HTD, 1994, vol. 280, pp. 59–69] is employed and further enhanced by including the motion of the solidifying and deforming solid shell. The motion of the solid phase is calculated with an incompressible rigid viscoplastic model on the basis of an assumed moving boundary velocity condition. In the first part, a 2D benchmark is simulated to mimic the solidification and motion of the solid shell. The importance of numerical treatment of the advection of latent heat in the deforming solid shell (mushy zone) is specially addressed, and some interesting phenomena of interaction between the turbulent flow and the growing mushy zone are presented. In the second part, an example of 3D TSC is presented to demonstrate the model suitability. Finally, techniques for the improvement of calculation accuracy and computation efficiency as well as experimental evaluations are also discussed.

A numerical simulation of columnar solidification: influence of inertia on channel segregation

We investigate the role of the inertia of the flow through the dendritic mushy zone in the numerical prediction of channel segregations during columnar solidification. The contribution of inertia is included in the momentum transport equation through the quadratic Forchheimer correction term. The study reveals a significant influence of the Forchheimer term in the vicinity of the liquidus front, i.e. at high liquid fractions. The natural convective flow field in this region is modified due to the additional inertial drag. This strongly influences the convective transport of solute and thereby incurs a modification of the dynamics of the advancement of the mushy zone. The most notable consequence is a significant decrease in the predicted channel segregation.

In situ experimental observation of the time evolution of a dendritic mushy zone in a fixed temperature gradient

This paper describes a series of experiments performed on BM05 at the European Synchrotron Radiation Facility (ESRF), dedicated to the analysis of a mushy zone evolution in a fixed temperature gradient. A mushy zone is the partially solid/partially liquid zone that is formed when solidification proceeds with the development of dendrites, and it has been recently shown that synchrotron X-ray radiography is a powerful technique, perfectly adapted for such a study. In situ and real-time characterisation clearly evidences the microstructural changes of the mushy zone during the holding stage, and measurements of the mushy zone boundary positions using image processing enable us to analyse the successive regimes. Each regime is directly related to solute diffusion mechanisms, namely temperature gradient zone melting, solute diffusion in the inter-dendritic liquid channels due to the solid-fraction gradient and solute diffusion in the melt.

3D simulation of interdendritic flow through a Al-18wt.%Cu structure captured with X-ray microtomography

A central parameter to describe the formation of porosity and macrosegregation during casting processes is the permeability of the dendritic mushy zone. To determine this specific feature for a binary Al-18wt.%Cu alloy, flow simulations based on the Lattice Boltz-mann (LB) method were performed. The LB method allows an efficient solving of fluid flow problems dealing with complex shapes within an acceptable period of time. The 3D structure required as input for the simulations was captured with X-ray microtomography, which enables the generation of representative geometries for permeability investigations. Removing the eutectic phase from the measured dataset generated a remaining network of solid primary dendrites. In the simulations, a pressure gradient was applied to force the liquid through the free interdendritic channels. The permeability of the structure was then calculated from the resulting flow velocity pattern using Darcy's law. To examine the influence of different boundary conditions on the results obtained, several simulations were conducted.

Melting kinetics in microgravity

We analyzed the large data archive obtained from microgravity experiments called the Isothermal Dendritic Growth Experiment (IDGE). The final orbital mission of the IDGE allowed streaming of real-time video of crystal growth and melting in low-Earth orbit of high-purity pivalic acid anhydride (PVA). Melting kinetics was observed in detail for the first time under microgravity conditions. Normally, terrestrial gravity precludes observation and analysis of conduction-limited melting by stimulating buoyancy flows and inducing collapse of the solid-liquid structure. The initial dendritic mushy zone melts under steady heating into isolated crystallite clusters that remain stationary within the melt, and eventually shrink toward their complete extinction. Near the end of conduction-limited melting, a few needle-like crystallites remain, exhibiting various axial ratios, C/A, of their major ellipsoidal axis, C, to their minor axis, A. Analysis of their convection-free melting, based on quasi-static thermal conduction, yields rates in agreement with the microgravity video and IDGE thermal data. Theory and experiment compare well, when the melting Stefan numbers, based on thermal data telemetered from the space-borne thermostat are used. Isolated PVA fragments shrink in scale at an accelerating rate toward total extinction. The 'point effect' of thermal conduction operates during most of the melting process when C/A remains almost constant. Prior to extinction, when the radius of a typical crystallite's minor axis approaches circa 100 micrometers, capillary effects become important. Then the crystallite's C/A ratio abruptly falls toward unity, as the needle-like crystals contract into spheres by accelerated melting near their poles. These experiments, and the accompanying field-theoretic analysis, introduce some new considerations, and raise questions concerning the roles of capillarity, heat conduction, interface shape, and solid-liquid phase change kinetics.

Melting in Microgravity

The Isothermal Dendritic Growth Experiment constituted a series of three NASA-supported microgravity experiments (USMP-2, -3, and -4), which flew aboard the space shuttle Columbia. These space flight experiments grew and recorded dendrites in the absence of gravity-induced convective heat transfer. USMP-4, for the first time, allowed streaming of near-real-time video data. Using 30-fps video data, we studied both freezing and melting sequences for pivalic acid (PVA) at different supercoolings. We report on the melting process of a PVA dendritic mushy zone, observed for the first time under convection-free conditions. Conduction-limited melting processes are of importance in orbital melting of materials, meteoritic genesis, mushy-zone evolution, and in fusion weld pools where the length scales for thermal buoyancy are highly restricted. Microgravity video data show that PVA dendrites melt into fragments that shrink at accelerating rates to extinction. The melting paths of individual fragments follow a characteristic time dependence for the diminishing length scales within the mushy zone. The theoretical melting kinetics against which the experimental observations are compared is based on the conduction-limited quasi-static process of melting under shape-preserving conditions. Good agreement between theory and experiment was found for the melting of a selected needle-shaped prolate spheroidal PVA crystal fragment with an aspect ratio of C/A = 12.

Average momentum equation for interdendritic flow in a solidifying columnar mushy zone

This paper deals with the derivation of the macroscopic momentum transport equation in a non-homogeneous solidifying columnar dendritic mushy zone using the method of volume averaging. One of the originalities of this study lies in the derivation of an associated closure problem for the determination of the spatial evolution of the effective transport properties in such a complex situation. In this analysis—where the phase change has been included at the different stages of the derivation—all the terms arising from the averaging procedure (geometrical moments, phase interactions, interfacial momentum transport due to phase change, porosity gradients, etc.) are systematically estimated and compared on the basis of the characteristic length-scale constraints associated with the porous structures presenting evolving heterogeneities. For dendritic structures with “moderate” (but not small) evolving heterogeneities, we show that phase change and non local effects could hardly affect the determination of the permeability and inertia tensors. Finally, a closed form of the macroscopic momentum equation is proposed and a discussion is presented about the need to consider inertia terms and the second Brinkman correction (explicitly involving gradients of the liquid volume fraction) in such non-homogeneous systems.

An experimental study of deformation of a columnar dendritic mushy zone using a transparent succinonitrile-acetone alloy

The deformation of a directionally solidified columnar dendritic mushy zone in a transparent succinonitrile-acetone (SCN-ACE) alloy has been studied expermentally. In addition to solidifying dendritically like a metal alloy, this alloy also has mechanical properties that are similar to those of metals near the melting point. The experiments are relevant, for example, to the deformation of a partially solidified strand during continuous casting of steel slabs. A test cell was designed which allows for directional solidification of the alloy and controlled compression of the solid-liquid mush which forms. Measurements during solidification and deformation include temperatures, interface positions, local displacements of the solid skeleton in the mush, and liquid concentrations. Results are presented for a range of initial test-cell thicknesses, deformation amounts, and deformation start times. The measurements are suitable for validation of future models.

Passive dispersion in dendritic structures

In order to improve mass transport description in solidification modeling, this study deals with the determination of the solute dispersion tensor in columnar dendritic mushy zone. The closure problem associated with the derivation of the macroscopic species conservation equation, using the volume averaging method, is solved numerically. Using schematic structures and digitized images of real dendritic structures observed experimentally during solidification of succinonitrile-4 wt.% acetone, the influence of tortuosity and microscopic dispersion on the determination of the effective solute dispersion coefficients is represented in terms of the Péclet number.

3D Simulation of Surface Tension Driven Interdendritic Convection and Microsegregation during Laser Surface Alloying

The development of solute distribution at dendritic interface for one step laser surface processing is investigated by numerical simulation. The dendritic mushy zone is approximated by columnar dendritic structure whereby the geometrical dimension and orientation within the liquid domain is derived from experimental results. Results concerning penetration depth of Marangoni flow in interdendritic zone and local solute distribution at dendrites surface are presented.

Numerical calculation of the permeability in a dendritic mushy zone

An averaging procedure applied to the local Stokes equations in a columnar dendritic-like porous structure yields the heterogeneous form of Darcy’s law, with three Brinkman correction terms explicitly involving gradients of the liquid volume fraction. Because of these extra terms, the associated closure problem leading to the determination of the permeability becomes very complex, and the full solution is still out of reach. However, in some cases, a simplified closure problem can be used to physically describe the spatial evolution of the permeability components in the columnar dendritic mushy zone. From digitized images of dendritic structures observed experimentally during solidification of a 26 wt pct solution of aqueous NH4Cl and succinonitrile-4 wt pct acetone, components of the permeability tensor in a direction parallel and normal to the primary dendrite arm are numerically calculated. Comparisons to experimental correlations and physical models show that the closure problem provides a more realistic physical description of the structure, especially in the vicinity of the tip of the dendrites. Finally, numerical calculations performed on a schematic dendritic structure point out that the permeability for flow parallel to the primary dendritic arms is hardly dependent on the secondary arm spacing (d 2).

Suppression of channel convection in solidifying Pb-Sn alloys via an applied magnetic field

Channel convection through the porous, dendritic mushy zone in solidifying alloys results from a nonlinear focusing mechanism, whereby liquid enriched in the solute melts dendrites as it convects away from the solid. The local melting reduces the parameterized (Darcy) viscous force and increases the flow speed to form a convective channel. However, it has been predicted that an applied magnetic field might prevent channels from forming because, as the Lorentz force replaces the Darcy force as the primary resistance to flow, the retarding force becomes less sensitive to the lengthscale of the flow, so that the focusing mechanism no longer operates. In this study, it is found experimentally that, as predicted, an applied horizontal magnetic field can suppress channel convection when Q m , the Chandrasekhar number appropriate to a mushy zone, exceeds an order of one. The nondimensional number Q m is a measure of the strength of the Lorentz force relative to the Darcy force in the mushy zone and, for a given magnetic field, is much smaller than the analogous Chandrasekhar number (Q) for the fluid melt, since the Darcy force in the mushy zone far exceeds the viscous force in the fluid. Previous experimental work failed to find that magnetic fields could suppress channel convection because, although Q exceeded an order of one, Q m did not. For experiments with a smaller cooling rate, and, thus, a larger permeability and larger mushy zone Rayleigh number (Ra m ) a stronger magnetic field is necessary to suppress channel convection. The longitudinal macrosegregation is not affected by the absence of channel convection, suggesting that such channels are not always primarily responsible for the mass flux between the mushy zone and the melt.