NOTE: End date changed to 07/31/2023 per NSSC information (Ed., 12/6/22)

NOTE: End date changed to 07/31/2022 per NSSC information (Ed., 12/28/21)

NOTE: End date changed to 9/30/2021 with new grant number awarded (80NSSC20K0828) (Ed., 9/9/20)

NOTE: End date changed to 2/29/2020 per NSSC information (Ed., 2/12/19)

NOTE: End date is now 2/28/2019 per NSSC information (Ed., 12/1/15)

The project examines the mechanisms giving rise to the columnar-to-equiaxed grain structure transition (CET) during alloy solidification. On Earth, experimental investigations of the CET are affected by thermosolutal buoyant convection and grain sedimentation/flotation, making it impossible to separate these effects from the effects of solidification shrinkage and diffusive processes in determining mechanisms for the CET. Long duration microgravity experiments suppress the convective effects and grain movement, thus isolating the shrinkage and diffusive phenomena. The project increases the base of knowledge relevant to the development of solidification microstructure/grain structure of metals and alloys. Therefore, this topic is of high interest from a fundamental science point of view and it is important to those engineers practicing casting and other solidification processes. Open scientific questions include the role played by melt convection, fragmentation of dendrite arms, and the transport of fragments and equiaxed crystals in the melt. The research utilizes computational models at three different length scales: phase-field, mesoscopic, and volume-averaged models. The phase-field model is needed to resolve the growth and transport processes at the scale of the microstructure, the mesoscopic model allows for simulations at the scale of individual grains, while the volume-averaged model is used to perform simulations of entire experiments. The models help to define and interpret previous and future microgravity and ground-based experiments.

All samples exhibit inverse segregation due to shrinkage driven flow, as demonstrated by the eutectic fraction and macrosegregation measurements. Shrinkage effects are therefore important to include in any future modeling efforts related to these samples. Samples solidified on Earth show pockets of high solute concentration and eutectic percentage that are evidence of melt convection. The terrestrially solidified Al-18 wt pct Cu sample exhibits negative solute segregation and low eutectic percentage at the top, which is attributed to solute-poor primary solid grains floating to and accumulating there. Eutectic and macrosegregation measurements show excellent agreement with each other except for the Al-4 wt pct Cu alloy. The high level of agreement in general indicates that the macrosegregation and eutectic fraction data can be confidently used as benchmarks, except in the case of the Al-4 wt pct Cu samples, where only the macrosegregation measurements should be used.

Temperatures on the exterior surface of the ampoule are successfully predicted by a thermal model of the entire furnace. Heat flux boundary conditions on the sample surface are determined from the furnace model and validated using a second sample-only heat diffusion model. The boundary conditions are necessary for future modeling efforts. Selected predicted temperatures along the sample axis are presented as benchmark temperature data for the sample interior. In all samples, the liquidus isotherm passes through the full sample length before the eutectic isotherm begins to traverse the samples. Thermal process parameters calculated at the liquidus isotherm along the sample axis, including the isotherm velocity, axial temperature gradient, and cooling rate, are similar in all samples.

The benchmark solidification data reported in this work is valuable for future modeling efforts. The data gives the ability to validate combined models for grain structure and macrosegregation development in the presence of melt convection and transport of unattached solid. Models considering only diffusive processes and shrinkage can be validated using results from the microgravity experiments. The inclusion of the neutrally buoyant Al-10 wt pct Cu experiment allows for modeling solidification in the presence of gravity with minimal concern for buoyancy of the solid. The Al-4 and 18 wt pct Cu cases can then be used to validate models that account for transport of unattached grains.

NOTE: End date changed to 07/31/2023 per NSSC information (Ed., 12/6/22)

NOTE: End date changed to 07/31/2022 per NSSC information (Ed., 12/28/21)

NOTE: End date changed to 9/30/2021 with new grant number awarded (80NSSC20K0828) (Ed., 9/9/20)

NOTE: End date changed to 2/29/2020 per NSSC information (Ed., 2/12/19)

NOTE: End date is now 2/28/2019 per NSSC information (Ed., 12/1/15)

The project examines the mechanisms giving rise to the columnar-to-equiaxed grain structure transition (CET) during alloy solidification. On Earth, experimental investigations of the CET are affected by thermosolutal buoyant convection and grain sedimentation/flotation, making it impossible to separate these effects from the effects of solidification shrinkage and diffusive processes in determining mechanisms for the CET. Long duration microgravity experiments suppress the convective effects and grain movement, thus isolating the shrinkage and diffusive phenomena. The project increases the base of knowledge relevant to the development of solidification microstructure/grain structure of metals and alloys. Therefore, this topic is of high interest from a fundamental science point of view and it is important to those engineers practicing casting and other solidification processes. Open scientific questions include the role played by melt convection, fragmentation of dendrite arms, and the transport of fragments and equiaxed crystals in the melt. The research utilizes computational models at three different length scales: phase-field, mesoscopic, and volume-averaged models. The phase-field model is needed to resolve the growth and transport processes at the scale of the microstructure, the mesoscopic model allows for simulations at the scale of individual grains, while the volume-averaged model is used to perform simulations of entire experiments. The models help to define and interpret previous and future microgravity and ground-based experiments.

The benchmark solidification data obtained in this work are valuable for future modeling efforts. The data give the ability to validate combined models for grain structure and macrosegregation development in the presence of melt convection and transport of unattached solid. Models considering only diffusive processes and shrinkage can be validated using results from the microgravity experiments. The inclusion of the neutrally buoyant Al-10 wt pct Cu experiment allows for modeling solidification in the presence of gravity with minimal concern for buoyancy of the solid. The Al-4 and 18 wt pct Cu cases can then be used to validate models that account for transport of unattached grains.

NOTE: End date changed to 7/31/2022 per NSSC information (Ed., 12/28/21)

NOTE: End date changed to 9/30/2021 with new grant number awarded (80NSSC20K0828) (Ed., 9/9/20)

NOTE: End date changed to 2/29/2020 per NSSC information (Ed., 2/12/19)

NOTE: End date is now 2/28/2019 per NSSC information (Ed., 12/1/15)

The project examines the mechanisms giving rise to the columnar-to-equiaxed grain structure transition (CET) during alloy solidification. On Earth, experimental investigations of the CET are affected by thermosolutal buoyant convection and grain sedimentation/flotation, making it impossible to separate these effects from the effects of solidification shrinkage and diffusive processes in determining mechanisms for the CET. Long duration microgravity experiments suppress the convective effects and grain movement, thus isolating the shrinkage and diffusive phenomena. The project increases the base of knowledge relevant to the development of solidification microstructure/grain structure of metals and alloys. Therefore, this topic is of high interest from a fundamental science point of view and it is important to those engineers practicing casting and other solidification processes. Open scientific questions include the role played by melt convection, fragmentation of dendrite arms, and the transport of fragments and equiaxed crystals in the melt. The research utilizes computational models at three different length scales: phase-field, mesoscopic, and volume-averaged models. The phase-field model is needed to resolve the growth and transport processes at the scale of the microstructure, the mesoscopic model allows for simulations at the scale of individual grains, while the volume-averaged model is used to perform simulations of entire experiments. The models help to define and interpret previous and future microgravity and ground-based experiments.

Microgravity samples were returned to the University of Iowa in July 2021. Terrestrial and microgravity samples were sectioned, mounted in epoxy, polished, and electropolished using the Struers LectroPol-5 machine at the NASA Marshall Space Flight Center in November 2021. After electropolishing, micrographs of the samples were taken using a polarized light optical microscope.

The electropolishing, combined with polarized light, allows for clear visualization of the grains due to orientation contrast. The microstructures may then be straightforwardly characterized. It is immediately apparent that all Aluminum-Copper (Al-Cu) alloys exhibit purely equiaxed microstructures in the microgravity experiments. This is contrasted with the terrestrial experiments where these alloys exhibit clearly columnar or mixed columnar-equiaxed microstructures. The 4 and 10 wt.% Cu alloys exhibit obvious columnar grains near the bottom while the 18 wt.% Cu alloy exhibits elongated but not clearly columnar grains near its bottom. Grain characteristics have not yet been quantified. Qualitatively however, Al-Cu alloys solidified in microgravity appear to have a uniformly fine grain size. Terrestrial samples show an initially fine grain size near the transition from columnar or elongated grains to equiaxed grains. The grains appear to become coarser near the top of these samples. The Aluminum-Silicon (Al-Si) alloys, on the other hand, display almost purely columnar microstructures. There appears to be some grain competition near the bottoms of these alloys, resulting in shorter grains in that region. However, grains whose growth aligns with the temperature gradient eventually win out, resulting in relatively few grains near the top.

Further analysis of the samples will include Scanning Electron Microscopy (SEM) imaging and Energy Dispersive X-Ray Spectroscopy (EDX). These analyses are currently being performed at NASA Marshall Space Flight Center as time allows. Upon completion of these analyses, the samples will be returned to the University of Iowa. Thermal simulations of the experiments were performed using the software codes MAGMA and OpenFOAM. Excellent agreement was achieved between measured and predicted temperatures. Currently the OpenFOAM code is being expanded to allow for fully temperature-dependent thermophysical properties. From these simulations, spatio-temporally varying heat flux boundary conditions describing the experiments will be calculated, validated, and published.

NOTE: End date changed to 9/30/2021 with new grant number awarded (80NSSC20K0828) (Ed., 9/9/20)

NOTE: End date changed to 2/29/2020 per NSSC information (Ed., 2/12/19)

NOTE: End date is now 2/28/2019 per NSSC information (Ed., 12/1/15)

The project examines the mechanisms giving rise to the columnar-to-equiaxed grain structure transition (CET) during alloy solidification. On Earth, experimental investigations of the CET are affected by thermosolutal buoyant convection and grain sedimentation/flotation, making it impossible to separate these effects from the effects of solidification shrinkage and diffusive processes in determining mechanisms for the CET. Long duration microgravity experiments suppress the convective effects and grain movement, thus isolating the shrinkage and diffusive phenomena. The project increases the base of knowledge relevant to the development of solidification microstructure/grain structure of metals and alloys. Therefore, this topic is of high interest from a fundamental science point of view and it is important to those engineers practicing casting and other solidification processes. Open scientific questions include the role played by melt convection, fragmentation of dendrite arms, and the transport of fragments and equiaxed crystals in the melt. The research utilizes computational models at three different length scales: phase-field, mesoscopic, and volume-averaged models. The phase-field model is needed to resolve the growth and transport processes at the scale of the microstructure, the mesoscopic model allows for simulations at the scale of individual grains, while the volume-averaged model is used to perform simulations of entire experiments. The models help to define and interpret previous and future microgravity and ground-based experiments.

After testing and approval, samples of Al-4, 10, and 18% Cu and Al-7%Si were constructed by Techshot, Inc. These samples are intended for microgravity experiments. On October 2, 2020, the samples were successfully sent to the International Space Station on board the Cygnus Northrup-Grumman 14 resupply flight. The samples are currently awaiting testing.

Numerical simulation models were again recalibrated for the new configuration. Other than the necessary geometric adjustments, only small interfacial heat transfer coefficient adjustments were necessary. Excellent agreement between measured and predicted temperature was achieved. Simulations were first performed without flow and only for columnar solidification. The effects of undercooling nucleation temperature and nucleation grain density on the location of the columnar-to-equiaxed transition (CET) within the sample was investigated. Beginning with 0 K nucleation undercooling temperature, the grain density was varied between 102 and 1010 grains/m3. A value of 60 mm, the sample length, indicates that CET did not occur. At 0 K undercooling, there is a sharp transition between no CET, CET at halfway along the sample, and at CET occurring effectively at the sample bottom. Further investigation using other nucleation undercooling values is ongoing.

NOTE: End date changed to 2/29/2020 per NSSC information (Ed., 2/12/19)

NOTE: End date is now 2/28/2019 per NSSC information (Ed., 12/1/15)

The project examines the mechanisms giving rise to the columnar-to-equiaxed grain structure transition (CET) during alloy solidification. On Earth, experimental investigations of the CET are affected by thermosolutal buoyant convection and grain sedimentation/flotation, making it impossible to separate these effects from the effects of solidification shrinkage and diffusive processes in determining mechanisms for the CET. Long duration microgravity experiments suppress the convective effects and grain movement, thus isolating the shrinkage and diffusive phenomena. The project increases the base of knowledge relevant to the development of solidification microstructure/grain structure of metals and alloys. Therefore, this topic is of high interest from a fundamental science point of view and it is important to those engineers practicing casting and other solidification processes. Open scientific questions include the role played by melt convection, fragmentation of dendrite arms, and the transport of fragments and equiaxed crystals in the melt. The research utilizes computational models at three different length scales: phase-field, mesoscopic, and volume-averaged models. The phase-field model is needed to resolve the growth and transport processes at the scale of the microstructure, the mesoscopic model allows for simulations at the scale of individual grains, while the volume-averaged model is used to perform simulations of entire experiments. The models help to define and interpret previous and future microgravity and ground-based experiments.

Narrow cylinders of aluminum copper alloys (AlCu) were entirely melted and then solidified at Techshot Inc. using the Solidification Using a Baffle in Sealed Ampoules (SUBSA) furnace. Compositions of 4, 10, and 18 wt. % Cu were tested in two ampoule configurations. One configuration uses an alumina bottom spacer while the other uses graphite. Cooling conditions necessitate that the AlCu cylinder be 1 cm shorter for the graphite configuration. Based on temperature histories, final microstructures, and leakage behavior, the graphite configuration was chosen to for future experiments. Subsequently, a second set of AlCu cylinders was melted and solidified in the SUBSA furnace at Techshot Inc. One cylinder each of 4, 10, and 18 wt. % Cu was tested. Two cylinders of aluminum with 7 wt. % silicon (Al-7%Si) were also tested. Tests confirmed the behavior of the graphite configuration for all compositions. Preparations are now being made to conduct official flight and ground based experiments using the graphite configuration.

Previous simulations of SUBSA cylinders in this project required unrealistic nucleation grain density values in order to predict any CET. Further improvements to the numerical code have produced CET predictions in line with experimental measurements without requiring the unrealistic values.

Motion of equiaxed dendrites or fragmented dendrite arms will have a significant effect on CET prediction. To this end, a mathematical model for solidification with solid motion has been derived based on the work of Wang and Beckermann. Numerical implementation of this model is ongoing.

NOTE: End date is now 2/28/2019 per NSSC information (Ed., 12/1/15)

The project examines the mechanisms giving rise to the columnar-to-equiaxed grain structure transition (CET) during alloy solidification. On Earth, experimental investigations of the CET are affected by thermosolutal buoyant convection and grain sedimentation/flotation, making it impossible to separate these effects from the effects of solidification shrinkage and diffusive processes in determining mechanisms for the CET. Long duration microgravity experiments suppress the convective effects and grain movement, thus isolating the shrinkage and diffusive phenomena. The project increases the base of knowledge relevant to the development of solidification microstructure/grain structure of metals and alloys. Therefore, this topic is of high interest from a fundamental science point of view and it is important to those engineers practicing casting and other solidification processes. Open scientific questions include the role played by melt convection, fragmentation of dendrite arms, and the transport of fragments and equiaxed crystals in the melt. The research utilizes computational models at three different length scales: phase-field, mesoscopic, and volume-averaged models. The phase-field model is needed to resolve the growth and transport processes at the scale of the microstructure, the mesoscopic model allows for simulations at the scale of individual grains, while the volume-averaged model is used to perform simulations of entire experiments. The models help to define and interpret previous and future microgravity and ground-based experiments.

Very long, narrow cylinders of aluminum copper alloys (AlCu) were melted and then solidified at NASA Marshall Space Flight Center using the Solidification Using a Baffle in Sealed Ampoules (SUBSA) furnace. Compositions of 4, 10, and 18 wt. % Cu were tested. These 3 alloys represent cases in which the solid equiaxed grains will be heavier than the liquid, neutrally buoyant, and lighter than the liquid, respectively. These varying buoyancies are crucial to the modeling of the solid motion. The solidified samples were removed from the crucible and then prepared for microstructure analysis. Although the columnar-to-equiaxed transition (CET) should have been identifiable in all three alloys, it was only visible in the Al-18%Cu sample.

The modeling of the SUBSA experiments focuses on the solidification stage. However, as the experiments go through a melting, a steady holding, and a solidification stage, there are complications for modeling. These complications are primarily the initial condition for simulation and the thermal boundary conditions for the simulation. OpenFOAM simulations, based on the code previously developed by Torabi Rad and Beckermann, will only simulate the metal cylinder itself so the question of what boundary conditions to apply are important. In order to determine the proper initial and boundary conditions, a simplified model of the SUBSA furnace was constructed and simulated using MAGMASoft. Once agreement was achieved between these simulations and the experiments, time dependent temperature gradients were extracted from the cylinder boundary and applied in OpenFOAM. By modeling the entire furnace, properties of the various materials can be approximated, and the most accurate temperature gradients can be determined. Agreement between simulated and experimental results was very good in all cases. After this agreement was achieved, simulations to predict the CET were conducted. Initially, these simulations neglected melt convection and solid movement. Only the Al-18%Cu case showed CET in the simulation results, and this was only achieved using unrealistic grain nucleation parameters. This confirms that considering the motion of equiaxed grains will be crucially important to more accurately predict the CET. Currently, simulations are also being conducted that consider the effect of thermal convection and solutal.

In the field of solidification, macroscale models are models that make predictions on the scale of the whole casting. These models need to incorporate phenomena that occur on the scales lower than the macroscale: microscale and mesoscale. Those phenomena can be incorporated in the macroscale models using volume-averaging methods. In these methods, which were first applied in the solidification field by Beckermann and coworkers in the 1980s and 1990s, the local equations (i.e., equations that are valid at the microscopic scale) for each phase are averaged over a volume that contains all the phases present in the system and is called the Representative Elementary Volume (REV). The volume-averaged equations contain source terms that depend on variables that are not predicted by the macroscopic model, because the lower scale information that these variables represent has been lost in the averaging process. Accurate calculation of these source terms, therefore, requires one to do a formal analysis on the REV scale and then pass up the information to the macroscale, through constitutive relations, in a process called upscaling. The term upscaling simply means that, in the ladder of length scales, information is passed up from a smaller scale to a larger scale by averaging. This upscaling has never been tried in the field of solidification, mainly because of the complexity that arises as the result of the large range of length scales that need to be resolved. In other words, in solidification, there is a large gap between the involved micro and macro length scales. Therefore, the currently available constitutive relations have been based on somewhat simplistic assumptions rather than a formal analysis of the REV scale. In this study, the gap between the micro and macro scales was bridged using the mesoscopic model of Delaleau and Beckermann. The model directly resolves the transport phenomena on the REV scale, and incorporates microscale phenomena, by using a local analytical solution for the microscale heat/solute transport. The model is used to perform three-dimensional simulations of equiaxed dendritic growth on a spatial scale that corresponds to a REV. The first set of mesoscopic simulations were performed for isothermal growth at a large range of initial undercoolings and grain densities (including a single grain).

The mesoscopic simulation results were upscaled by averaging them over the REV. For example, at any time during growth, the solute concentration field in the extra-dendritic liquid was averaged over the volume of the REV to give the average solute concentration in the extra-dendritic liquid at that time. The upscaled mesoscopic results were carefully examined and it was found that, based on the sign of the time derivative of the scaled primary arm length, the entire growth period can be divided into two stages: the variable-sphericity stage and constant-sphericity stage. The start of the constant-sphericity stage is denoted by the squares in the plot. During the variable-sphericity stage, the envelope growth is mainly due to the growth of the primary arms, while during the constant-sphericity stage, it is mainly due to the growth of the secondary arms. It was also found that using the average undercooling in the extra-dendritic liquid in the Ivantsov solution significantly underpredicts the tip velocities.

For the first time in the field of solidification, the upscaled mesoscopic results, rather than simplifying assumptions, were used to develop constitutive relations for macroscopic models of equiaxed solidification. This upscaling enabled us to present relations that incorporate changes in the shape of grains and solute diffusion conditions around them during growth. Relations were proposed for the envelope sphericity, average growth velocity, far-field undercooling that needs to be used in the Ivantsov solution to accurately predict the primary tip velocities, and for the average diffusion length around the envelopes. The constitutive relations were verified by comparing the predictions of the macroscopic model with the upscaled mesoscopic results for the isothermal cases and also for the new mesoscopic cases. These new cases involved external cooling and a recalescence in the cooling curves.

The project examines the mechanisms giving rise to the columnar-to-equiaxed grain structure transition (CET) during alloy solidification. On Earth, experimental investigations of the CET are affected by thermosolutal buoyant convection and grain sedimentation/flotation, making it impossible to separate these effects from the effects of solidification shrinkage and diffusive processes in determining mechanisms for the CET. Long duration microgravity experiments suppress the convective effects and grain movement, thus isolating the shrinkage and diffusive phenomena. The project increases the base of knowledge relevant to the development of solidification microstructure/grain structure of metals and alloys. Therefore, this topic is of high interest from a fundamental science point of view and it is important to those engineers practicing casting and other solidification processes. Open scientific questions include the role played by melt convection, fragmentation of dendrite arms, and the transport of fragments and equiaxed crystals in the melt. The research utilizes computational models at three different length scales: phase-field, mesoscopic, and volume-averaged models. The phase-field model is needed to resolve the growth and transport processes at the scale of the microstructure, the mesoscopic model allows for simulations at the scale of individual grains, while the volume-averaged model is used to perform simulations of entire experiments. The models help to define and interpret previous and future microgravity and ground-based experiments.

The modelling of these experiments focused on the solidification phase. However, as the experiments go through a melting, a steady holding, and a solidification stage, there are complications for modeling. These complications are primarily the initial condition for simulation and the thermal boundary conditions for the simulation. Simulations using the in-house OpenFOAM code will only simulate the metal cylinder itself so the question of what boundary conditions to apply are important. In order to do this, a simplified model of the SUBSA furnace was simulated using the commercial casting simulation software MAGMAsoft. If agreement can be achieved between these simulations and the experiments, time dependent heat fluxes can be extracted from the cylinder boundary and applied in OpenFOAM. By modeling the entire furnace, properties of the various materials can be approximated and the most accurate heat fluxes can be determined. Good agreement between simulated and experimental temperatures was obtained in all cases.

With good agreement in the MAGMAsoft simulation, heat fluxes can be extracted and applied in OpenFOAM. In OpenFOAM, the cylinder will be represented by an axisymmetric wedge. With the boundary conditions supplied by MAGMAsoft, the initial conditions for the solidification simulation must still be determined. It was determined that the code previously used for OpenFOAM solidification simulations was unable to handle melting. Starting the code at the steady holding phase is also not possible because it is impossible to guess or impose the distributions for the various solidification quantities in OpenFOAM. As such, the best way to initiate the simulation is to have the cylinder be entirely liquid and let the boundary conditions guide it to the steady holding phase. This should result in the proper distribution necessary for the beginning of solidification. Further work on this subject is ongoing.

The simultaneous prediction of macrosegregation and CET is still an important challenge in the field of solidification. One of the open questions is the role of melt convection in CET and the effect of CET on macrosegregation. We are developing a general multi-phase framework for modeling macrosegregation and CET. This modeling framework consists of conservation equations and constitutive relations for the two types of growth: columnar and equiaxed. The conservation equations of the model are obtained by volume-averaging the local transport equations for the solid, inter-dendritic liquid, and extra-dendritic liquid over a representative elementary volume (REV). The constitutive relation for columnar solidification are borrowed from the available relations in the literature. However, for the equiaxed solidification, the constitutive relation that are currently available in the literature are based on highly simplified assumptions and have not been validated. Therefore, instead of using these relations, we developed new accurate relations by using simulation results from a mesoscopic envelope model developed previously. In the mesoscopic simulations, the evolution of the dendrite envelopes and the solute diffusion field in the extra-dendritic liquid were directly resolved on a spatial scale that corresponds to a REV. The mesoscopic results were first averaged over the REV (upscaled) and the averaged data was then used to develop accurate constitutive relations for envelope sphericity, primary tip and volume-equivalent sphere velocities, and average diffusion length. These relations were verified against the mesoscopic results and can now be used, in macroscopic models of equiaxed solidification, to incorporate more realistically the average growth kinetics and solute diffusion rates.

The general multi-phase model, which accounts for undercooling both behind and in front of the columnar front, was then used to develop two different sub-models for macrosegregation during fully-columnar solidification. The first sub-model does not account for undercooling and assumes Scheil-type solidification (i.e., solidification without undercooling) behind the liquidus line. The second sub-model accounts for the primary dendrite tip undercooling and assumes Scheil-type solidification behind the primary tips. The two sub-models and the general multi-phase model were used to predict macrosegregation in a numerical solidification benchmark problem, involving columnar solidification of lead 18 wt. pct. tin alloy in a side-cooled rectangular cavity. The overall macrosegregation patterns predicted by the models were found to be similar.

The model was also validated by performing macrosegregation and CET simulations of a recent benchmark solidification experiment. The overall macrosegregation map predicted by the model is similar to the macrosegregation map observed in the experiments. It consists of a region with negative lead segregation close to the bottom-right corner of the ingot and a region with positive lead segregation at the bottom-left corner. The CET positions predicted by the general model are in reasonable agreement with the CET positions observed in the experiments. Work is continuing to improve the model. Once the model is complete, it will be applied to the Al-Cu SUBSA experiments previously described in this report.

The project examines the mechanisms giving rise to the columnar-to-equiaxed grain structure transition (CET) during alloy solidification. On Earth, experimental investigations of the CET are affected by thermosolutal buoyant convection and grain sedimentation/flotation, making it impossible to separate these effects from the effects of solidification shrinkage and diffusive processes in determining mechanisms for the CET. Long duration microgravity experiments suppress the convective effects and grain movement, thus isolating the shrinkage and diffusive phenomena. The project increases the base of knowledge relevant to the development of solidification microstructure/grain structure of metals and alloys. Therefore, this topic is of high interest from a fundamental science point of view and it is important to those engineers practicing casting and other solidification processes. Open scientific questions include the role played by melt convection, fragmentation of dendrite arms, and the transport of fragments and equiaxed crystals in the melt. The research utilizes computational models at three different length scales: phase-field, mesoscopic, and volume-averaged models. The phase-field model is needed to resolve the growth and transport processes at the scale of the microstructure, the mesoscopic model allows for simulations at the scale of individual grains, while the volume-averaged model is used to perform simulations of entire experiments. The models help to define and interpret previous and future microgravity and ground-based experiments.

Much progress has also been made during the present reporting period to develop computational models for simulating previous and future terrestrial and microgravity experiments on the CET. Models at three different length scales are investigated: phase-field, mesoscopic, and volume-averaged models. The phase-field model is needed to resolve the growth and transport processes at the scale of the microstructure, the mesoscopic model allows for simulations at the scale of individual grains, while the volume-averaged model is used to perform simulations of entire experiments. For simulating terrestrial experiments, the models include melt convection and transport of solid.

Three-dimensional phase-field simulations of alloy solidification were conducted to study the evolution of the specific interfacial area. A key aspect in predicting the microstructure in metal alloys is the detailed knowledge of how the shape of the solid-liquid interface evolves during solidification. Often, local features, such as the secondary dendrite arm spacing, are used for the geometrical characterization of the microstructure. However, they represent incomplete descriptions of the solid structure and their measurement can become difficult during the late stages of solidification, when the structure undergoes fundamental transformations. Alternatively, integral measures, such as the specific area of the solid-liquid interface (interface area per unit volume of solid), can be introduced to more generally characterize the overall morphology. By performing phase-field simulations for different cooling rates, we have been able to develop a general equation for the specific interface area that is valid for any cooling rate, including isothermal coarsening. This equation was validated by using data from four different synchroton tomography experiments, spanning a range of alloys and cooling rates.

Mesoscopic simulations of columnar and equiaxed solidification were performed in order to investigate in detail the evolution of the grain structure on an intermediate scale. In this type of simulation, the evolution of the dendrite envelopes is tracked, while the solute field is calculated only in the extra-dendritic space between the envelopes. A three-dimensional computer code was written and simulations have been performed to compare the predicted envelope shapes with available measurements. During the present reporting period, these results have been used to develop constitutive equations for volume averaged models. For example, the sphericity of an equiaxed dendrite envelope has been related to the length of its primary arm. Also, the ratio of the solute diffusion length of the envelope to that of a sphere, which is important for calculating the internal solid fraction evolution, has been related to the envelope sphericity. These and other relations are now ready to be used in volume-averaged models of equiaxed solidification.

Macroscopic simulations were conducted to study the CET on the scale of an entire casting. A volume-averaged model was used for these simulations. The governing equations were solved using the public domain OpenFoam CFD software platform. The code was tested for columnar and equiaxed solidification without melt convection and transport of solid. Gravity-driven convection is included in the model in order to simulate terrestrial experiments. During the present reporting period, much effort was devoted to validating the model against benchmark experimental data that have been obtained by other CETSOL team members in the past. The main new feature of the present model is the inclusion of dendrite tip undercooling. Accounting for dendrite tip undercooling not only changes the solid fraction evolution, but also allows for more realistic tracking of the columnar front. A comparison of the predicted CET with the grain structure observed in the experiment shows reasonably good agreement. This agreement can be expected to improve once the movement of equiaxed grains is incorporated into the model. During the next reporting period, the macroscopic model will be used to simulate the terrestrial and microgravity experiments that are being planned for the SUBSA furnace.

The project examines the mechanisms giving rise to the columnar-to-equiaxed grain structure transition (CET) during alloy solidification. On Earth, experimental investigations of the CET are affected by thermosolutal buoyant convection and grain sedimentation/flotation, making it impossible to separate these effects from the effects of solidification shrinkage and diffusive processes in determining mechanisms for the CET. Long duration microgravity experiments suppress the convective effects and grain movement, thus isolating the shrinkage and diffusive phenomena. The project increases the base of knowledge relevant to the development of solidification microstructure/grain structure of metals and alloys. Therefore, this topic is of high interest from a fundamental science point of view and it is important to those engineers practicing casting and other solidification processes. Open scientific questions include the role played by melt convection, fragmentation of dendrite arms, and the transport of fragments and equiaxed crystals in the melt. The research utilizes computational models at three different length scales: phase-field, mesoscopic, and volume-averaged models. The phase-field model is needed to resolve the growth and transport processes at the scale of the microstructure, the mesoscopic model allows for simulations at the scale of individual grains, while the volume-averaged model is used to perform simulations of entire experiments. The models help to define and interpret previous and future microgravity and ground-based experiments.

As part of the Principal Invesitgator (PI)'s collaboration with the Columnar-to-Equiaxed Transition in SOLidification Processing (CETSOL) team in Europe, experiments were performed using a ground-based version of the Transparent Alloys instrument that is being developed by ESA (European Space Agency). The experiments use various compositions of the transparent organic alloy Neopentylglycol-(D)Camphor (NPG-DC). The present PI is responsible for the CETSOL II experiments, which are intended to simulate thermal conditions that are close to those encountered in metal casting. For this purpose, the cold and hot zones are held at all times at the same temperature, such that the adiabatic zone is close to isothermal. As opposed to the directional solidification experiments planned for CETSOL I, the sample is not moved. Instead, the cold and hot zones are cooled at a certain rate to induce solidification. The central adiabatic zone is characterized by an equiaxed dendritic grain structure. These equiaxed grains are homogeneously distributed over the experimental cell of 5 mm thickness. Experiments have been conducted to investigate the effect of the cooling rate on the nucleation and growth of the equiaxed grains. In February 2016, the PI will perform additional experiments using this setup to study different alloy compositions. The results will be used to finalize the experimental plan for the CETSOL II experiments that are being planned for the International Space Station (ISS) in 2017.

Much progress has also been made during the present reporting period to develop computational models for simulating previous and future terrestrial and microgravity experiments on the CET. Models at three different length scales are investigated: phase-field, mesoscopic, and volume-averaged models. The phase-field model is needed to resolve the growth and transport processes at the scale of the microstructure, the mesoscopic model allows for simulations at the scale of individual grains, while the volume-averaged model is used to perform simulations of entire experiments. For simulating terrestrial experiments, the models include melt convection and transport of solid.

Three-dimensional phase-field simulations of alloy solidification were conducted to study the evolution of the specific interfacial area. It is found that Sv varies in accordance with a well-known empirical equation from Speich and Fisher. This equation, which was originally developed for pure growth, fits the present data for the interfacial area density, even though dendritic solidification is characterized by concurrent growth and coarsening. The calculated temporal evolution of the inverse specific interface area is fit to a standard coarsening equation in order to determine the coarsening exponent n. Good agreement with previous studies on concurrent growth and coarsening is obtained. Additional research is necessary to obtain a generally valid relation for the evolution of the specific interface area in alloy solidification. Simulations are underway that investigate the effect of different cooling rates and other alloy characteristics on the interface evolution.

Mesoscopic simulations of columnar and equiaxed solidification were performed in order to investigate in detail the evolution of the grain structure on an intermediate scale. In this type of simulation, the evolution of the dendrite envelopes is tracked, while the solute field is calculated only in the extra-dendritic space between the envelopes. A three-dimensional computer code was written and simulations have been performed to compare the predicted envelope shapes with available measurements. During the present reporting period, these results have been carefully validated against experimental measurements. In addition, they have been used to develop constitutive equations for volume averaged models. Details are provided in the publications listed in the Bibliography section.

Macroscopic simulations were conducted to study the CET on the scale of an entire casting. A volume-averaged model was used for these simulations. The governing equations were solved using the public domain OpenFoam CFD software platform. The code was tested for columnar and equiaxed solidification without melt convection and transport of solid. Gravity-driven convection is included in the model in order to simulate terrestrial experiments. During the present reporting period, much effort was devoted to validating the model against benchmark experimental data that have been obtained by other CETSOL team members in the past. The main new feature of the present model is the inclusion of dendrite tip undercooling. Accounting for dendrite tip undercooling not only changes the solid fraction evolution, but also allows for more realistic tracking of the columnar front. A comparison of the predicted CET with the grain structure observed in the experiment shows reasonably good agreement. This agreement can be expected to improve once the movement of equiaxed grains is incorporated into the model. During the next reporting period, the macroscopic model will be used to simulate the terrestrial and microgravity experiments that are being planned for the SUBSA furnace.

The project examines the mechanisms giving rise to the columnar-to-equiaxed grain structure transition (CET) during alloy solidification. On earth, experimental investigations of the CET are affected by thermosolutal buoyant convection and grain sedimentation/flotation, making it impossible to separate these effects from the effects of solidification shrinkage and diffusive processes in determining mechanisms for the CET. Long duration microgravity experiments suppress the convective effects and grain movement, thus isolating the shrinkage and diffusive phenomena. The project increases the base of knowledge relevant to the development of solidification microstructure/grain structure of metals and alloys. Therefore, this topic is of high interest from a fundamental science point of view and it is important to those engineers practicing casting and other solidification processes. Open scientific questions include the role played by melt convection, fragmentation of dendrite arms, and the transport of fragments and equiaxed crystals in the melt. The research utilizes computational models at three different length scales: phase-field, mesoscopic, and volume-averaged models. The phase-field model is needed to resolve the growth and transport processes at the scale of the microstructure, the mesoscopic model allows for simulations at the scale of individual grains, while the volume-averaged model is used to perform simulations of entire experiments. The models help to define and interpret previous and future microgravity and ground-based experiments.

Three-dimensional phase-field simulations of alloy solidification are being conducted to study the dendrite evolution and fragmentation process on a microscopic (microstructure) scale. Fragmented dendrite sidebranches are believed to be a potent source of equiaxed grains. For this purpose, simulations are being conducted for columnar dendritic growth with an imposed temperature gradient and cooling rate. After a fully dendritic structure is obtained, the cooling rate is suddenly reduced. This leads to fragmentation of the dendrites at the junction between primary and secondary sidebranches. The fragmentation dynamics and rates are being studied as a function of the growth conditions. Considerable effort was devoted to parallelizing the code in order to allow for large scale simulations to be conducted. During the next project year, these simulations will be continued. A theory of the evolution of the specific interface area and fragmentation is being developed. Mesoscopic simulations of columnar and equiaxed solidification are being performed in order to investigate in detail the evolution of the grain structure on an intermediate scale. In this type of simulation, the evolution of the dendrite envelopes is tracked, while the solute field is calculated only in the extra-dendritic space between the envelopes. A three-dimensional computer code has been written and simulations have been performed to compare the predicted envelope shapes with available measurements. The next step is to include melt convection.

Macroscopic simulations are being conducted to study the CET on the scale of an entire casting. A volume-averaged model is used for these simulations. The governing equations are solved using the public domain OpenFoam CFD software platform. The code was tested for columnar and equiaxed solidification without melt convection and transport of solid. Gravity-driven convection and grain sedimentation/floatation have been added to the model during the past project year. Macroscopic simulations have been conducted to analyze and design future microgravity experiments.

The project examines the mechanisms giving rise to the columnar-to-equiaxed grain structure transition (CET) during alloy solidification. On earth, experimental investigations of the CET are affected by thermosolutal buoyant convection and grain sedimentation/flotation, making it impossible to separate these effects from the effects of solidification shrinkage and diffusive processes in determining mechanisms for the CET. Long duration microgravity experiments suppress the convective effects and grain movement, thus isolating the shrinkage and diffusive phenomena. The project increases the base of knowledge relevant to the development of solidification microstructure/grain structure of metals and alloys. Therefore, this topic is of high interest from a fundamental science point of view and it is important to those engineers practicing casting and other solidification processes. Open scientific questions include the role played by melt convection, fragmentation of dendrite arms, and the transport of fragments and equiaxed crystals in the melt. The research utilizes computational models at three different length scales: phase-field, mesoscopic, and volume-averaged models. The phase-field model is needed to resolve the growth and transport processes at the scale of the microstructure, the mesoscopic model allows for simulations at the scale of individual grains, while the volume-averaged model is used to perform simulations of entire experiments. The models help to define and interpret previous and future microgravity and ground-based experiments.

NOTE Project continues "Effect of Convection on Columnar-to-Equiaxed Transition in Alloy Solidification," grant # NNX10AV35G with period of performance 10/1/2010-2/28/2014. See that project for previous reporting.