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The main purpose of our investigation is to show the impact of pertinent parameters; such Lewis and porous thermal Rayleigh numbers as well as the buoyancy and the aspect ratios; on the double-diffusive convection phenomena which occur within a porous annulus; found between a cold (and less concentric) outer circular cylinder and a hot (and concentric) inner one, to come out with global correlations which predict the mean transfer rates in such annulus. To do so, the physical model for the momentum conservation equation is made using the Brinkman extension of the classical Darcy equation. The set of coupled equations is solved using the finite volume method and the SIMPLER algorithm. Summarizing the numerical predictions, global correlations of overall transfer within the porous annulus as a function of the governing studied parameters are set forth which predict within ±2% the numerical results. These correlations may count as a complement to previous researches done in the case a Newtonian-fluid annulus. It is to note that the validity of the computing code used was ascertained by comparing our results with the experimental data and numerical ones already available in the literature.

In this study, the linear stability analysis is used to determine the onset of thermosolutal convection in fluids confined in rotating annular Hele-Shaw cell. The fluid layer is submitted to radial gradients of temperature and concentration. The effects of both Coriolis force and curvature parameter on the stationary and oscillatory convection are investigated when the Prandtl number is of the order of unity or larger than unity.

The effect of an anisotropic inertia coefficient in the Darcy equations is studied. How such anisotropy affects the critical Rayleigh number for the onset of convective motion in a porous layer with thermal and solutal effects is analyzed quantitatively. The mathematical analyses employed involve both linear instability techniques and the energy method for nonlinear stability.

Experimental studies have been conducted in the two-phase region of the Pb-Bi peritectic system to investigate the effect of thermosolutal convection on the banded microstructure. A systematic study is carried out by varying convection effects through the use of thin cylindrical samples of different diameters. A strong oscillatory convection is found in a 6.0-mm-diameter sample that produces a large treelike primary phase in the center of the sample that is surrounded by the peritectic phase matrix. The length of the treelike structure is found to decrease as the diameter of a sample is reduced to 0.8 mm. When the sample diameter is further reduced to 0.4 mm, laminar flow is present that gives rise to discrete bands of the two phases. The banded microstructure, however, is found to be transient and only the peritectic phase forms after a few bands. Composition variations in the banded structure are measured to determine the nucleation undercoolings for both phases and to characterize the banding cycle. The banding cycle is determined by the nucleation undercoolings and is independent of convection in the melt, but the banding window closely depends on convection. The presence of the transient banding process is analyzed by using a boundary layer model, and the number of transient bands is found to agree with the model for samples of different compositions and lengths.

Pb-2.2 and 5.8 wt pct Sb alloys were directionally solidified with a positive thermal gradient of 140 K cm−1 at growth speeds ranging from 0.8 to 30 µm s−1, and then quenched to retain the mushyzone morphology. Chemical analysis along the length of the directionally solidified portion and in the quenched melt ahead of the dendritic array showed extensive longitudinal macrosegregation. Cellular morphologies growing at smaller growth speeds are associated with larger amounts of macrosegregation as compared with the dendrities growing at higher growth speeds. Convection is caused, mainly, by the density inversion in the overlying melt ahead of the cellular/dendritic array because of the antimony enrichment at the array tip. Mixing of the interdendritic and bulk melt during directional solidification is responsible for the observed longitudinal macrosegregation.

The essential principles of thermosolutal convection are outlined, and how convection provides a transport mechanism between the mushy region of a casting and the open bulk liquid is illustrated. The convective flow patterns which develop assist in heat exchange and macroscopic solute segregation during solidification; they also provide a mechanism for the transport of dendritic fragments from the mushy region into the bulk liquid. Surviving fragments become nuclei for equiaxed grains and so lead to blocking of the parental columnar, dendritic growth front from which they originated. The physical steps in such a sequence are considered and some experimental data are provided to support the argument.

Thermosolutal convection caused by the solute build up ahead of growing arrays of cells and dendrites results in macrosegregation along the length of Pb-Sn alloy (10 to 58 wt pct Sn) specimens when they are directionally solidified in a positive thermal gradient(melt on top, solid below, and gravity pointing down). At a constant thermal gradient, the extent of macro-segregation increases with decreasing growth speed as the microstructure changes from dendritic to cellular and to planar. An empirical parameter, effective partition coefficient (keff), obtained from the dependence of the longitudinal macrosegregation on fraction distance solidified can be used to represent the extent of macrosegregation. The extent of macrosegregation appears to be related to a parameter, [g(Ct - Co) Dl/RCo]1/2, where Co is the tin content of the alloy, Ct is the tin content of melt at the array tips, R is the growth speed, Dl is the diffusivity of tin in the melt, and g is the acceleration due to gravity.

Numerical simulations of a binary metal alloy (Pb-Sn) undergoing solidification phase change are performed using a continuum model for conservation of total mass, momentum, energy, and species. The system is contained in an axisymmetric, annular mold which is cooled along its outer vertical wall. Results show that thermosolutal convection in the melt and mushy zones is strongly coupled and that macrosegregation is reduced with increased cooling rate. For low cooling rates, solutally induced convection in the mushy zone favors the development of channels, which subsequently spawn macrosegregation in the form of A-segregates. With increasing solidification rate, however, thermosolutal interactions in the melt contribute to reducing the formation of channels and A-segregates.

During solidification of a binary alloy at constant velocity vertically upward, thermosolutal convection can occur if the solute rejected at the crystal-melt interface decreases the density of the melt. We assume that the crystal-melt interface remains planar and that the flow field is periodic in the horizontal direction. The time-dependent nonlinear differential equations for fluid flow, concentration, and temperature are solved numerically in two spatial dimensions for small Prandtl numbers and moderately large Schmidt numbers. For slow solidification velocities, the thermal field has an important stabilizing influence: near the onset of instability the flow is confined to the vicinity of the crystal-melt interface. Further, for slow velocities, as the concentration increases, the horizontal wavelength of the flow decreases rapidly — a phenomenon also indicated by linear stability analysis. The lateral in-homogeneity in solute concentration due to convection is obtained from the calculations. For a narrow range of solutal Rayleigh numbers and wavelengths, the flow is periodic in time.

A mathematical model of thermosolutal convection in directionally solidified dendritic alloys has been developed that includes a mushy zone underlying an all-liquid region. The model assumes a nonconvective initial state with planar and horizontal isotherms and isoconcentrates that move upward at a constant solidification velocity. The initial state is perturbed, nonlinear calculations are performed to model convection of the liquid when the system is unstable, and the results are compared with the predictions of a linear stability analysis. The mushy zone is modeled as a porous medium of variable porosity consistent with the volume fraction of, interdendritic liquid that satisfies the conservation equations for energy and solute concentrations. Results are presented for systems involving lead-tin alloys (Pb-10 wt pct Sn and Pb-20 wt pct Sn) and show significant differences with results of plane-front solidification. The calculations show that convection in the mushy zone is mainly driven by convection in the all-liquid region, and convection of the interdendritic liquid is only significant in the upper 20 pct of the mushy zone if it is significant at all. The calculated results also show that the systems are stable at reduced gravity levels of the order of 10−4 g 0 (g 0=980 cm·s−1) or when the lateral dimensions of the container are small enough, for stable temperature gradients between 2.5≤G l≤100 K·cm−1 at solidification velocities of 2 to 8 cm·h−1.

This paper describes the simulation of thermosolutal convection in directionally solidified (DS) alloys. A linear stability analysis is used to predict marginal stability curves for a system that comprises a mushy zone underlying an all-liquid zone. In the unperturbed and nonconvecting state .e.}, the basic state), isotherms and isoconcentrates are planar and horizontal. The mushy zone is realistically treated as a medium with a variable volume fraction of liquid that is con-sistent with the energy and solute conservation equations. The perturbed variables include tem-perature, concentration of solute, and both components of velocity in a two-dimensional system. As a model system, an alloy of Pb-20 wt pct Sn, solidifying at a velocity of 2 X 10-3 cm s-1 was selected. Dimensional numerical calculations were done to define the marginal stability curves in terms of the thermal gradient at the dendrite tips,G L ,vs the horizontal wave number of the perturbed quantities. For a gravitational constant of 1g,0.5 g, 0.1g, and 0.01g, the marginal stability curves show no minima; thus, the system is never unconditionally stable. Nevertheless, such calculations quantify the effect of reducing the gravitational constant on reducing convection and suggest lateral dimensions of the mold for the purpose of suppressing convection. Finally, for a gravitational constant of 10-4 g, calculations show that the system is stable for the thermal gradients investigated (2.5 ≤G L ≤ 100 K-cm-1).

International audience; Freckles are common defects in industrial casting. They result from thermosolutal convection due to buoyancy forces generated from density variations in the liquid. The present paper proposes a numerical analysis for the formation of channel segregation using the three-dimensional (3D) cellular automaton (CA)—finite element (FE) model. The model integrates kinetics laws for the nucleation and growth of a microstructure with the solution of the conservation equations for the casting, while introducing an intermediate modeling scale for a direct representation of the envelope of the dendritic grains. Directional solidification of a cuboid cell is studied. Its geometry, the alloy chosen as well as the process parameters are inspired from experimental observations recently reported in the literature. Snapshots of the convective pattern, the solute distribution, and the morphology of the growth front are qualitatively compared. Similitudes are found when considering the coupled 3D CAFE simulations. Limitations of the model to reach direct simulation of the experiments are discussed.

The influence of carbide precipitation on grain-defect formation during unidirectional solidification of experimental single-crystal Ni-based superalloys has been assessed over a wide range of compositions with large variations in Re, W, and Ta. In all instances, carbon additions of up to 0.15 wt pct were determined to be statistically significant with respect to stabilizing against the formation of grain defects, such as freckle chains, during solidification. Assessment of the segregation behavior of the constituent alloying additions via a Scheil-type analysis enabled estimation of critical Rayleigh numbers denoting the onset of thermosolutal convection. Precipitation of Ta-rich MC carbides near the liquidus temperature of the alloy was found to interact strongly with the mechanisms associated with freckle formation. Segregation analyses and phase-transformation temperature measurements were used to assess the corresponding Rayleigh numbers for the experimental alloys and to modify the Rayleigh criterion to account for carbide precipitation. Mechanisms pertaining to the interaction of carbides with the onset of thermosolutal convection are discussed.

Solidification in microgravity aboard the space shuttle Endeavour resulted in a dramatic change in the morphology of the primary Al2Cu phase compared to ground-based solidification in unit gravity. An Al-38 wt pct Cu ingot directionally solidified at a rate of 0.015 mm/s with a temperature gradient of 1.69 K/mm exhibited large, well-formed dendrites of primary Al2Cu phase. Ingots solidified under similar conditions in unit gravity contained primary Al2Cu phase with smooth, faceted surfaces. The primary Al2Cu phase spacing in the microgravity ingot was much greater than that in the unit gravity ingot, 670 µm compared to 171 µm. It is suggested that thermosolutal mixing in the unit gravity ingot reduces the buildup of an Al-rich layer at the solid/liquid interface, which increases the stability of the interface resulting in smooth, faceted particles of Al2Cu phase. It is also suggested that the large difference in primary phase spacings is due mostly to the difference in morphology rather than changes in parameters that might influence dendrite ripening mechanisms. The presence or absence of gravity had no effect on the interlamellar spacing of the inter-Al2Cu phase eutectic. The ingot solidified in microgravity exhibited almost no longitudinal macrosegregation, in agreement with the theory of inverse segregation in the absence of thermosolutal convection. The ingot solidified in unit gravity exhibited considerable longitudinal macrosegregation, with the chilled end having about 6 wt pct more Cu than the average composition. It is not clear whether the segregation results from thermosolutal convection during solidification or from sedimentation during melting.

A numerical model is built for the solidification of a binary alloy with thermosolutal convection under centrifugal condition. The model is based on the macroscopic transport equations derived using the volume-averaging method. New formulations are derived for a non-linear phase diagram and temperature-dependent thermophysical properties. Simulations are performed to substantiate experiments with TiAl alloys carried out on ESA’s Large Diameter Centrifuge (LDC) using different angular velocities, ω. These experiments comprise a region of transient columnar growth of β-Ti dendrites under decreasing temperature gradient and increasing growth velocity followed by the columnar-to-equiaxed transition (CET). The simulation results show that CET is triggered by a sudden drop of the temperature gradient ahead of the advancing solidification front being a consequence of a sudden change of the flow pattern. We show that the flow pattern driven by density inversion changes abruptly once the permeability of the columnar structure increases above some critical value. This promotes the Rayleigh–Benard instability and the development of local convection cells along with an extended region of very low temperature gradient. The intensity and asymmetry of the flow in the local convection cells increase with increasing ω. The results show that a mushy zone developing in transient conditions and with gradually increasing permeability can significantly alter the flow pattern even in centrifugal conditions with a dominant contribution from Coriolis forces.

The thermosolutal convection can alter segregation pattern, change dendrite morphology and even cause freckles formation in alloy solidification. In this work, the multiphase-field model was coupled with lattice Boltzmann method to simulate the dendrite growth under melt convection in superalloy solidification. In the isothermal solidification simulations, zero and normal gravitational accelerations were applied to investigate the effects of gravity on the dendrite morphology and the magnitude of melt flow. The solute distribution of each alloy component along with the dendrite tip velocity during solidification was obtained, and the natural convection has been confirmed to affect the microsegregation pattern and the dendrite growth velocity. In the directional solidification simulations, two typical temperature gradients were applied, and the dendrite morphology and fluid velocity in the mushy zone during solidification were analyzed. It is found that the freckles will form when the average fluid velocity in the mushy zone exceeds the withdraw velocity.

Abstract The influence of the melt flow on the solidification structure is bilateral. The flow plays an important role in the solidification pattern, via the heat transfer, grain distribution, and segregations. On the other hand, the crystal structure, columnar or equiaxed, impacts the flow, via the thermosolutal convection, the drag force applied by the crystals on the melt flow, etc. As the aim of this research was to further explore the solidification–flow interaction, experiments were conducted in a cast cell (95 * 95 * 30 mm3), in which an ammonium chloride–water solution (between 27 and 31 wt pct NH4Cl) was observed as it solidified. The kinetic energy (KE) of the flow and the average flow velocity were calculated throughout the process. Measurements of the volume extension of the mush in the cell and the velocity of the solid front were also taken during the solidification experiment. During the mainly columnar experiments (8 cm liquid height) the flow KE continuously decreased over time. However, during the later series of experiments at higher liquid height (9.5 cm), the flow KE evolution presented a strong peak shortly after the start of solidification. This increase in the total flow KE correlated with the presence of falling equiaxed crystals. Generally, a clear correlation between the strength of the flow and the occurrence of equiaxed crystals was evident. The analysis of the results strongly suggests a fragmentation origin of equiaxed crystals appearing in the melt. The transition from purely columnar growth to a strongly equiaxed rain (CET) was found to be triggered by (a) the magnitude of the coupling between the flow intensity driven by the equiaxed crystals, and (b) the release and transport of the fragments by the same flow recirculating within the mushy zone. Graphical Abstract Coupling mechanism at the origin of CET: 1-2 strong flow running through the mush transporting out dendrite fragments (white dots); 3-4 equiaxed growth and drag of the downward flow. If the vortex is sufficiently stable, the horizontal configuration can lead to freckle appearing; a) vertical solidification front; b) horizontal solidification front.

In the current study, the evolutions of channel segregations in several alloy systems, such as the typically used model alloys (e.g., Ga-In, Sn-Pb, Sn-Bi, Al-Cu, and Ni-based superalloy) and some special steels, are numerically simulated in a cavity solidified unidirectionally. The simulations are based on a modified continuum macrosegregation model with an extension to the multicomponent systems. The results of model alloys and steels indicate that when the thermosolutal convection is strong enough, flow instability occurs, which in turn destabilizes the mushy zone. Subsequently, the channel segregation forms with the continuous interaction between solidification and flow. The formation behavior and severity of channel segregations in various systems are different owing to their distinct melt convection strengths and solidification natures. In the current simulations, channels are apparent for model alloys with high content of solutes, whereas they are slight in some special steels, such as 27SiMn steel, and totally disappear in carbon steels. These occurrence features of channel segregation in simulations of steels are consistent with the analyses by a modified Rayleigh number associated with alloying elements, and both outcomes are well supported by the fully sectioned steel ingots in experiments.

With the aid of a coupling electromagnetic-thermal-solute transportation model validated by the industrial investigation, a three-dimensional (3-D) plus two-dimensional (2-D) hybrid modeling method has been presented for the exploration of the macrosegregation and macroscale transport phenomena in the bloom continuous casting (CC) processes of high-carbon GCr15-bearing steel. The evolution and characteristics of solute distribution and its influence on the porosity formation in the strand during CC process have been revealed. Solute segregation degree changes from a positive to a negative value with distance from strand surface in the region of initial solidification shell within thickness of 25 mm, which can be attributed to the circulation flow ahead the solidification front and the floatation of solute-rich molten steel at the upper part of the mold. The discontinuous, nonfrozen band induced by the zigzag solute distribution is proven to be the main reason that leads to the porosity formation in the final solidification stage of the CC strand. As the solidification proceeds, the segregation degree of C at the strand center is increased from 1.0 to 1.2, while the melt liquidus temperature is reduced from 1726 K (1453 °C) to 1706.91 K (1433.91 °C) during the CC process. Moreover, with the action of gravity and thermosolutal convection, a negative segregation region in the concave shape and an irregular positive segregation zone are produced in the fixed and loosened side of shell, respectively.

The directional solidification of Ga-25wt pct In alloys within a Hele-Shaw cell under the influence of thermosolutal convection was observed by means of X-ray radioscopy. The unstable density stratification at the solidification front causes the formation of rising plumes containing solute-rich liquids. The development of the chimneys and the probability of their surviving depend sensitively on the spatial and temporal properties of the flow field. Variations of the vertical temperature gradient along the solidification cell lead to the observation of different mechanisms for chimney formation. Perturbations of the dendritic structure are the origin of development of segregation freckles in case of low temperature gradients. The long-term stabilities of these segregation channels are strongly influenced by the transient nature of the melt convection. The situation at higher temperature gradients is characterized by two dominating convection rolls in the liquid phase which are driven by a lateral temperature gradient and the convex shape of the solidification front. The penetration of this flow pattern into the mushy zone results in continuous accumulation of solute in the central part of the mushy zone followed by a remelting of the solid fraction and the occurrence of a stable chimney.

Modeling the formation of macroscopic segregation channels during directional solidification processes has important applications in the casting industry. Computations that consider thermosolutal convection involve different length scales ranging from the small solute boundary layer at the dendrite tips to the characteristic size of the casting. In general, numerical models of solidification in the presence of a developing mushy zone are computationally inefficient because of nonlinear transport in an anisotropic porous medium. In the current work, mesh adaptation with triangular finite elements is used in conjunction with an efficient fractional-step solver of the momentum equations to predict the occurrence of channel-type segregation defects or freckles. The triangulations are created dynamically using an unstructured grid generator and a refinement criterion that tracks the position of the channel segregates. The efficiency of mesh adaptation is illustrated with simulations showing channel formation and macrosegregation in directional solidification of a Pb–Sn alloy.

In this article, a single-phase, one-domain macroscopic model is developed for studying binary alloy solidification with moving equiaxed solid phase, along with the associated transport phenomena. In this model, issues such as thermosolutal convection, motion of solid phase relative to liquid and viscosity variations of the solid-liquid mixture with solid fraction in the mobile zone are taken into account. Using the model, the associated transport phenomena during solidification of Al-Cu alloys in a rectangular cavity are predicted. The results for temperature variation, segregation patterns, and eutectic fraction distribution are compared with data from in-house experiments. The model predictions compare well with the experimental results. To highlight the influence of solid phase movement on convection and final macrosegregation, the results of the current model are also compared with those obtained from the conventional solidification model with stationary solid phase. By including the independent movement of the solid phase into the fluid transport model, better predictions of macrosegregation, microstructure, and even shrinkage locations were obtained. Mechanical property prediction models based on microstructure will benefit from the improved accuracy of this model.

Experimental studies were performed to investigate the role and influence of grain movement on macrosegregation and microstructure evolution during equiaxed solidification. Casting experiments were performed with a grain-refined Al-Cu alloy in a rectangular sand mold. For the aluminum alloy studied, the equiaxed grains are lighter than the bulk melt and thus float up. Experiments were designed to investigate floatation phenomena of equiaxed grains in the presence of thermosolutal convection. Cooling curves were recorded at key locations in both the casting and the chill. Quantitative image analysis and spatial chemical analysis were performed on the solidified casting to observe the chemical and microstructural inhomogeneity created by the melt convection and solid floatation. Several notable features that can be attributed to grain movement were observed in temperature histories, macrosegregation patterns, and microstructures. In our experiments, the floatation of grains influences the thermal conditions and the overall flow direction in the casting cavity. In some cases, the induced flow resulting from the grain movement caused a flow reversal. This in turn influences the solidification direction, microstructure evolution, and the overall macrosegregation behavior.

A promising approach is proposed for controlling the channel formation during solidification, which is characterized as inserting alloy inserts into the cavity before pouring the melt. A mathematical model, which couples melting with solidification, is developed for simulating the channel formation during solidification of the Sn-10 wt pct Bi alloy in the cavity with alloy inserts. The validity of the model is tested by real-time X-ray observation and experimental measurement. With different superheats, the effects of insert parameters, such as the amount (0.0 pct and 1.2 pct), shape (rod and particle), and initial position, on the melting process of the insert itself, thermosolutal convection, and channel formation are investigated numerically. Calculated results reveal that at a higher superheat, the extent of channel segregation is reduced with the addition of alloy inserts. Because inserts dissolve quickly, only a slight difference in channel formation is noted when the shape and initial position of inserts are changed. At a lower superheat, no channel is formed by adding the alloy inserts. Results are better with the addition of alloy balls. The local positive segregations around the unmelted inserts, which occur when alloy rods are added, are avoided.

An analysis of published experimental and numerical results shows that there is a scaling relationship between the magnitude and direction of centerline segregation in direct-chill (DC) cast billets from aluminum alloys and the process parameters, i.e., billet diameter and casting speed. It seems that there is always a range of these process parameters where the centerline segregation is positive, and there is a threshold when the centerline segregation vanishes. Numerical simulations of macrosegregation during DC casting of a binary Al-Cu alloy were performed at different ratios of casting speed and billet diameter. The macrosegregation model takes into account only two mechanisms of macrosegregation, i.e., thermosolutal convection and shrinkage-induced flow. The results of these computer simulations fit well to the dependence obtained using numerous reference data. The results are discussed in terms of the contribution of different mechanisms of macrosegregation and the shape of the billet sump.

In this work, a two-dimensional thermosolutal convection flow under a sinusoidal gravity modulation (g-jitter) field is studied to understand the effects of the periodic source on flow field, as well as heat and mass transfer mechanisms. A semi-implicit projection finite element method is adopted to solve the transient Navier–Stokes, energy and species concentration equations. The fingering regime and the diffusive regime are explored for a series of gravity modulation frequencies. Two types of flow evolution, synchronous and subharmonic responses, are obtained for different frequencies. Distribution of unstable responses for the singly unstable condition is in agreement with the literature predict. The results show that heat and mass transfer rates are affected by the response type. For a subharmonic variation flow field, the overall Nusellt number and Sherwood number exhibit larger values. In addition, the augmenting condition in combining thermally driving force and solutally driving force is analyzed for a practical crystal material and displays a different response distribution from those in the fingering regime and the diffusive regime.

The formation of macrosegregation defects known as “freckles” was simulated using a three-dimensional finite element model that calculates the thermosolutal convection and macrosegregation during the dendritic solidification of multicomponent alloys. A recently introduced algorithm was used to calculate the complicated solidification path of alloys of many components, which can accommodate liquidus temperatures that are general functions of liquid concentrations. The calculations are started from an all-liquid state, and the growth of the mushy zone is followed in time. Simulations of a Ni-Al-Ta-W alloy were performed on a rectangular cylinder until complete solidification. The results reveal details of the formation of freckles not previously observed in two-dimensional simulations. Liquid plumes in the form of chimney convection emanate from channels within the mushy zone, with similar qualitative features previously observed in transparent systems. Associated with the formation of channels, there is a complex three-dimensional flow produced by the interaction of the different solutal buoyancies of the alloy solutes. Regions of enhanced solid growth develop around the channel mouths, which are visualized as volcanoes on top of the mushy zone. The prediction of volcanoes differs from our previous calculations with multicomponent alloys in two dimensions, in which the volcanoes were not nearly as apparent. These and other features of freckle formation phenomena are illustrated.

Experiments were performed with a new radioscopic flow visualization technique on natural convection during melting of a binary metallic Ga-In alloy. This technique provides visualization of the density fields within opaque low Prandtl number fluids and their solids. Upon applying a horizontal temperature gradient to a gallium melt alloyed with 5 weight percent indium, the binary melt developed a vertical concentrational stratification and heat transfer was by conduction only. Convective flow developed at a higher temperature difference, which may be termed “critical”. After reducing the temperature difference the thermosolutal convection breaks down and a conductive state reappears at ΔT0 K. This threshold for onset of natural convection in binary Ga-In melts is in need of a theoretical explanation.

Thermosolutal convection in the dendritic mushy zone occurs during directional solidification of hypoeutectic lead tin alloys in a positive thermal gradient, with the melt on the top and the solid below. This results in macrosegregation along the length of the solidified samples. The extent of macrosegregation increases with increasing primary dendrite spacings for constant mushy zone length. For constant primary spacings, the macrosegregation increases with decreasing mushy zone length. Presence of convection reduces the primary dendrite spacings. However, convection in the interdendritic melt has significantly more influence on the spacings as compared with that in the overlying melt, which is caused by the solutal buildup at the dendrite tips.

The breakdown of single-crystal solidification has been studied over a wide range of solidification conditions in ten superalloys with large variations in Re, Ta, and W content. Over the range of experimental conditions investigated, grain defect formation was sensitive to local thermaland solutal conditions. For a fixed alloy composition and withdrawal rate, the transition from single-crystal to equiaxed solidification did not occur abruptly. Instead, as thermal gradients were decreased in a series of experiments, isolated, highly misoriented columnar grains with the same composition as that of the base alloy developed in the presence of positive (stabilizing) thermal gradients with increasing frequency until the advance of the single-crystal front was completely blocked. The onset of columnar grain formation occurred when the primary dendrite arm spacing exceeded a critical value, corresponding to a morphological transition in the dendritic array. The onset of “freckling” was observed at the same primary dendrite arm spacing where misoriented columnar grains began to appear. In experiments with varying levels of refractory alloy content, there was also a strong correlation between the onset of grain formation and freckle formation. These observations strongly suggest that in high refractory content superalloys, the breakdown of single-crystal solidification and the formation of misoriented grains as well as freckle-type defects are sensitively dependent on thermosolutal convection processes.

An investigation into the influence of a transverse magnetic field (0.45 T) on the mushy zone morphology and macrosegregation in directionally solidified hypoeutectic Pb-Sn alloy shows that the field has no influence on the morphology of dendritic arrays. The field does, however, cause severe distortion in the cellular array morphology. Cellular arrayed growth with the magnetic field results in an extensive channel formation in the mushy zone, as opposed to the wellaligned and uniformly distributed cells formed in the absence of the field. The channels are produced due to the anisotropy in the thermosolutal convection caused by the magnetic field. Macrosegregation, however, along the length of the directionally solidified samples is not influenced by this magnetic field for either the cellular or dendritic arrays.

A mathematical model has been established to predict the formation of macrosegregation for a unidirectional solidification of aluminum-copper alloys cooled from the bottom. The model, based on the continuum formulation, allows the calculation of transient distributions of temperature, velocity, and species in the solidifying alloy caused by thermosolutal convection and shrinkage-induced fluid flow. Positive segregation in the casting near the bottom (inverse segregation) is found, which is accompanied by a moving negative-segregated mushy zone. The effects of shrinkage-induced fluid flow and solute diffusion on the formation of macrosegregation are examined. It is found that the redistribution of solute in the solidifying alloy is caused by the flow of solute-rich liquid in the mushy zone due to solidification shrinkage. A higher heat-extraction rate at the bottom increases the solidification rate, decreasing the size of the mushy zone, reducing the flow of solute-rich liquid in the mushy zone and, as a result, lessening the severity of inverse segregation. Comparisons between the theoretical predictions from the present study and previous modeling results and available experimental data are made, and good agreements are obtained.

Macrosegregation along the length of the directionally solidified samples is produced when Pb-Sn alloys (10 to 58 wt pct Sn) are directionally solidified in a positive thermal gradient (melt on top, solid below, and gravity pointing down) with steady-state dendritic arrayed morphology (the length of the mushy zone, much smaller than the initial length of the melt column, re- maining nearly constant during growth). The extent of the macrosegregation increases with increasing tin content, becomes maximum for 33.3 wt pct Sn, and decreases with further in- crease in tin content. The intensity of the interdendritic thermosolutal convection responsible for the longitudinal macrosegregation can be represented by the effective partition coefficient (k e), anempirical parameter obtained from the dependence of the longitudinal macrosegregation on fraction distance solidified. The extent of the macrosegregation appears to be related to a parameter, {λ 1 2 ƒ E (C E -C t )}, where λ1, is the primary dendrite spacing,f E is the volume fraction of the interdendritic melt, andC E andC t , are the eutectic composition and the melt composition ahead of the dendrite tips, respectively.

The thermosolutal instability of a partially-ionized plasma in the presence of a horizontal magnetic field is considered to include the frictional effect of collisions of ionized with neutrals. The sufficient conditions for non-existence of overstability are derived. The solute gradient and magnetic field introduce oscillatory modes in thermosolutal convection which were non-existent in their absence. The magnetic field and stable solute gradient are found to have stabilizing effects whereas collisional effect of ionized with neutrals is found to have destabilizing effect on thermosolutal instability of a partially ionized plasma.