[0001] The present application claims the benefit of U.S. Provisional Patent Application No. 62/313,493 filed on March 25, 2016 and entitled“LIQUID METAL JET OPTIMIZATION IN DIRECT CHILL CASTING,” which is hereby incorporated by reference in its entirety. Technical Field

[0002] The present disclosure relates to metal casting generally and more specifically to controlling the introduction of liquid metal in a molten metal sump during direct chill casting. Background

[0003] In the metal casting process, molten metal is passed into a mold cavity. For some types of casting, mold cavities with false, or moving, bottoms are used. As the molten metal enters the mold cavity, generally from the top, the false bottom lowers at a rate related to the rate of flow of the molten metal. The molten metal that has solidified near the sides can be used to retain the liquid and partially liquid metal in the molten sump. Metal can be 99.9% solid (e.g., fully solid), 100% liquid, and anywhere in-between. The molten sump can take on a V-shape or a U-shape, due to the increasing thickness of the solid regions as the molten metal cools. The interface between the solid and liquid metal can be known as the solidifying interface.

[0004] As the molten metal in the molten sump becomes between approximately 0% solid to approximately 5% solid, nucleation can occur and small crystals of the metal can form (e.g., endogenously, such as from homogenous nucleation or formation from dendrite fragmentation, or exogenously, such as through added grain refiner). These small (e.g., nanometer to micron size) crystals begin to nucleate and form dendrites as the molten metal cools. As the molten metal cools to the dendrite coherency point (e.g., 632 °C in 5182 aluminum used for beverage can ends), the dendrites begin to stick together to form an interconnected network. Between the melting temperature and the coherency temperature, these crystals may be mobile and may be susceptible to fluid dynamic drag and gravitational forces, which can lead to accumulation of these crystals in the bottom of the sump. Due to the constraints of commercial solidification processes complete diffusion does not occur, resulting in individual grains being depleted in solute. When these individual grains accumulate, the bulk effect can drastically change local compositions within the cast product, which can lead to changes in properties of the cast product. Also, depending on the temperature and percent solid of the molten metal, crystals can include or trap different particles, such as particles of FeAl ₆ , Mg ₂ Si, FeAl ₃ and Al ₈ Mg ₅ in certain stocks of aluminum, or impurities, such as bubbles of H ₂ .

[0005] Additionally, when crystals during solidification and subsequent cooling, extra solute materials (e.g., alloying elements) can be drawn between the crystals (e.g., between the dendrites of the crystals) and can accumulate in the molten sump, typically at the mid- thickness, resulting in an uneven balance of alloying elements within the ingot. The separation of alloying elements on a macro scale can be known as macrosegregation. When an ingot or semi-finished product is analyzed, macrosegregation can be seen as variations in the composition of the cast ingot across a dimension (e.g., width, length, height, or diameter) of the cast product. Macrosegregation in a cast ingot can result in waste and increased cost. Macrosegregation can further result in weakened ingots or semi-finished products, which may be particularly undesirable for certain uses, such as aerospace frames.

[0006] An ingot may be required to fall within certain desired specifications for various measurable quantities, such as composition. These quantities may be negatively affected by undesirable macrosegregation. While an ingot with undesirable macrosegregation may, as a whole, have measurable quantities that fall within desired specifications, individual regions of the ingot, especially those with higher levels of macrosegregation, may have measurable quantities that fall outside of the desired specifications. For example, an ingot may have composition that varies by approximately 25% or more across a dimension of the ingot. In such an example, the ingot, as a whole, may result in measurable quantities that fall within desired specifications for the ingot, but the amount of macrosegregation near the center of the ingot may be substantially more intense, such that the center region of the ingot has measurable quantities that fall well outside of desired specifications. Therefore, due at least in part to undesirable macrosegregation, various specifications for products made using such standard ingots may require large safety factors (e.g., where the average material strength far exceeds the expected load on the material at any given point), as the performance of any given portion of the ingot may be less than expected.

[0007] Attempts to reduce unwanted macrosegregation in cast products have relied on the use of excessive grain refiner, which may be undesirable for various reasons, including cost and risk of ingot contamination. In some cases, attempts to reduce unwanted macrosegregation in cast products have relied on the use of physical dams to slow down or reduce the amount of fluid flow within the liquid sump. Brief Description of the Drawings

[0008] The specification makes reference to the following appended figures, in which use of like reference numerals in different figures is intended to illustrate like or analogous components.

[0009] FIG. 1 is a partial cut-away view of an example metal casting system for supplying a liquid metal jet. [0010] FIG. 2 is a schematic representation of a liquid metal jet impinging a slurry region of a molten metal sump.

[0011] FIG.3 is a plot depicting predicted, non-dimensional jet processing parameters for various example aluminum alloys, the parameters designed to provide an optimal liquid metal jet for re-suspending grains in the slurry region of a metal sump according to certain aspects of the present disclosure.

[0012] FIG. 4 is a contour plot depicting intensity of macrosegregation according to vertical and horizontal position in an aluminum alloy Al4.5Cu ingot cast using existing techniques, without the liquid metal jet optimization techniques disclosed herein.

[0013] FIG. 5 is a contour plot depicting intensity of macrosegregation according to vertical and horizontal position in an aluminum alloy Al4.5Cu ingot cast using parameters set to achieve a mold Reynolds number of approximately 1600 and a nozzle opening selected to achieve a jet Reynolds number of approximately 64000.

[0014] FIG. 6 is a contour plot depicting intensity of macrosegregation according to vertical and horizontal position in an aluminum alloy Al4.5Cu ingot cast using parameters set to achieve a mold Reynolds number of approximately 1600 and a nozzle opening selected to achieve a jet Reynolds number of approximately 69000.

[0015] FIG. 7 is a contour plot depicting intensity of macrosegregation according to vertical and horizontal position in an aluminum alloy Al4.5Cu ingot cast using parameters set to achieve a mold Reynolds number of approximately 1600 and a nozzle opening selected to achieve a jet Reynolds number of approximately 81000.

[0016] FIG. 8 is a contour plot depicting intensity of macrosegregation according to vertical and horizontal position in an aluminum alloy Al4.5Cu ingot cast using parameters set to achieve a mold Reynolds number of approximately 1600 and a nozzle opening selected to achieve a jet Reynolds number of approximately 97000. [0017] FIG. 9 is a contour plot depicting intensity of macrosegregation according to vertical and horizontal position in an aluminum alloy Al4.5Cu ingot cast using parameters set to achieve a mold Reynolds number of approximately 1600 and a nozzle opening selected to achieve a jet Reynolds number of approximately 121000.

[0018] FIG. 10 is a plot depicting the Macrosegregation Index (MI) as a function of jet Reynolds number for each of the ingots of FIGs.5-9.

[0019] FIG. 11 is a flowchart depicting a process for determining optimized casting parameters based on a known mold according to certain aspects of the present disclosure. Detailed Description

[0020] Certain aspects and features of the present disclosure relate to optimization of a liquid metal jet used to supply molten metal during a direct chill (DC) casting operation. The erosion of solidifying grains in the slurry region of the molten sump can be modeled to determine an optimized liquid metal jet that can be used to erode the slurry region of the molten sump, but not the solidified metal, at a rate equal to the casting speed. A non- dimensional version of the model can be used to generate casting parameters (e.g., optimally sized nozzle openings and optimal molten metal flow rates) that would provide the optimized liquid metal jet during the casting process, resulting in a metal ingot having improved macrosegregation properties (e.g., reduced or nearly eliminated macrosegregation, more evenly distributed solute, or more uniform macrosegregation profiles). An ingot cast using the optimized liquid metal jet described herein can have low macrosegregation, with solute concentrations varying from the molten metal supply concentration approximately 10% or less or 5% or less across the width, length, or height of the ingot.

[0021] Macrosegregation can occur due to the relative movement of liquid and solid phases during solidification. The micro-scale partitioning of solute between liquid and solid phases (e.g., microsegregation) can be translated to larger scale differences in chemical composition (e.g., macrosegregation). This relative movement may be driven by various factors, whose magnitude may depend not only on casting practice, but also on alloy composition and shape of the transition region. Various factors, such as temperature convection and shrinkage flow in the molten sump, may be difficult to control. In some cases, macrosegregation can occur due to one or more of a combination of shrinkage flow as grains form and sedimentation of grains at the bottom of the liquid sump. In relatively large ingots and billets (e.g., having diameters or thicknesses at or above approximately 300 mm), the sedimentation of grains becomes a dominant factor in macrosegregation, whereas in relatively small ingots and billets (e.g., having diameters or thicknesses at or below approximately 300 mm), shrinkage flow becomes a dominant factor in macrosegregation. Shrinkage flow can cause inhomogeneity of solute distribution in the liquid sump. Certain aspects and features of the present disclosure relate to techniques for improving macrosegregation by counteracting certain macrosegregation-inducing effects of shrinkage flow and/or grain sedimentation.

[0022] Commercially cast aluminum alloys may tend to solidify as equiaxed grains, often due to the addition of exogenous nucleation sites (e.g., grain refiners). In the slurry region between the liquidus and coherency isotherms, solidified grains can be mobile and can travel short or long distances depending on the conditions of the molten sump (e.g., temperature convection, shrinkage flow, and volume change with contacting aluminum). When free moving grains are transported and settle at the bottom of the sump, a fraction of solid phase larger than at the targeted equilibrium condition may be obtained. These grains settling at the bottom of the sump can be known as grain sedimentation. In hypoeutectic aluminum alloys, which include many, if not most, DC cast products, the solid phase can be less rich in solute than the liquid, resulting in more of the solid phase having negative segregation (e.g., a solute concentration that is lower than the average solute concentration of the molten metal supply). In an example, the concentration in solute at the centerline of a DC cast ingot may be approximately 15% to 20% lower than that of the furnace composition of the molten metal used to cast the ingot.

[0023] Negative segregation can dramatically alter the ultimate mechanical properties of cast ingots or semi-finished products (e.g., ingots or semi-finished products cast of 1xxx, 2xxx, 3xxx, 4xxx, 5xxx, 6xxx, 7xxx, and 8xxx series aluminum alloys). Preventing the preferential sedimentation of free-moving grains can alter macrosegregation, ultimately reducing variations in the composition of DC cast ingots across dimensions of the ingots. A molten metal jet can be introduced directly into the base of the sump to prevent the sedimentation of grains. In some cases, such as billet (e.g., round extrusion or forging ingot) castings, introducing certain jets to the base of the sump can cause erosion of the sump itself (e.g., erosion of the fully solidified metal), which can cause problems and negatively affect the solidification of the ingot. For example, in billet casting, an ideal diameter jet can have a very narrow range, with too-small diameter jets creating an undesirably deep hole in the sump with an undesirably steep sump profile, and a too-large diameter jet creating an undesirably wide hole in the sump with an undesirably wide sump profile. Certain aspects of the present disclosure relate to optimizing a molten metal jet of sufficient power to suspend sedimentation of grains without causing sump erosion. In some cases, aspects of the present disclosure are used with DC casts of rectangular ingots. In some cases, aspects of the present disclosure are used with vertical casting. In some cases, aspects of the present disclosure are used with casting occurring at or within 30°, 25°, 20°, 15°, or 10° from vertical. In some cases, aspects of the present may be used with horizontal casting.

[0024] Optimized casting parameters (e.g., metal flow rate and/or nozzle opening diameter) can produce a liquid metal jet sufficient to remove extra grains from the slurry region of the sump while allowing some grains to settle and fully solidify. Such a jet can counteract the effects of grain sedimentation, as well as potentially counteracting some effects of shrinkage flow. The optimal energy of the liquid metal jet may fall within a narrow range defined by the dimensionless Reynolds number of the jet. The optimized casting parameters can be determined such that the dimensionless Reynolds number of the resultant jet and the dimensionless Reynolds number of the resultant mold fall within a predicted range of values based on the techniques disclosed herein.

[0025] In addition to or alternatively to grain sedimentation, shrinkage flow can induce macrosegregation problems. For example, solidifying grains can cause localized increases in solute concentration in the liquid metal directly adjacent the solidifying grains, while portions of the liquid sump distant from the solidifying grains remain relatively lower in solute concentration. As grains solidify, solute can become entrapped within or between grains. Because the liquid adjacent solidifying grains tends to be relatively high in solute concentration, this solute entrapment can result in undesirable intermetallics. These entrapped regions of high solute concentration can be a result of shrinkage flow.

[0026] In some cases, optimizing casting parameters can produce a liquid metal jet sufficient to optimize or increase the homogeneity of solute distribution within the liquid metal sump. Such a jet can counteract the effects of shrinkage flow, as well as potentially counteracting some effects of grain sedimentation. A sufficient liquid metal jet can be directed into the liquid sump and can induce sufficient liquid movement within the sump to mix the localized regions of relatively high solute concentration with the localized regions of relatively low solute concentration to result in an overall more homogenized liquid metal sump. Therefore, when a sufficient liquid metal jet is used, any entrapped solute may be at relatively lower concentrations than when no liquid metal jet is used (e.g., when a combo bag or filter bag is used). [0027] Additionally, a sufficient liquid metal jet can reduce porosity due to the presence of hydrogen gas in the liquid metal. Hydrogen gas can become entrapped between dendrite arms under standard casting conditions. However, when a sufficient liquid metal jet is provided, the resultant liquid movement within the liquid metal sump can facilitate coalescing of hydrogen bubbles, allowing the hydrogen bubbles to more easily float to the top of the sump and be released from the liquid metal. In some cases, at least some of the hydrogen gas being rejected adjacent solidifying grains can be mixed within the liquid metal instead of being entrapped between dendrite arms.

[0028] Thus, certain aspects and features of the present disclosure can improve macrosegregation by counteracting certain macrosegregation-inducing effects of shrinkage flow and/or grain sedimentation. The resultant metal ingot or billet can have improved macrosegregation properties over a metal ingot or billet formed without using certain aspects and features of the present disclosure. The improved macrosegregation properties can be expressed by a macrosegregation index, as described herein, wherein higher numbers represent increased, undesirable macrosegregation within an ingot or billet. The improved macrosegregation properties can have a macrosegregation index that is smaller than an ingot cast without using certain aspects and features of the present disclosure.

[0029] For purposes of modeling the DC casting process, an assumption can be made that heterogeneous nucleation acts as the sole source of grains at the solidifying interface. Thus, the conservation of mass can provide the governing transport equation in the slurry region as demonstrated in Equation 1. Equation 1 can be based on a simplified version of the Eulerian transport equation, where N is a source term for nucleation (e.g., in m ^-3 s ^-1 ), n is the number density of the grains (e.g., in m ^-3 ), and u _t is the velocity of the moving liquid metal (e.g., in meters per second).

[0030] A statistical model for the grain density as a function of the mean undercooling and the maximum grain density can be determined, using a

Gaussian distribution, as demonstrated in Equation 2, where is the mean undercooling,

ο _ఙ^ is the standard deviation of the undercooling, and is an amount of undercooling.

[0031] The specific parameters of Equation 2 (e.g., undercooling terms) can be determined experimentally for a given alloy composition, the type of grain refiner used, and the duration of the grain refiner’s addition. Each unique undercooling can correspond to a certain nucleation radius given, for example by the Gibbs-Thomson relation.

[0032] The nuclei formation and melting in Equation 1 can be included in a single source term, N, related to the total grain density at a particular given undercooling ο^

via integration of Equation 2, as demonstrated in Equation 3:

[0033] An additional condition exists in a steady state grain density (e.g., where in Equation 1). Therefore, the overarching transport equation to solve can be defined

by equating the advective contribution with the nucleation at the interface, taking into account the local undercooling. The application of this form of the equation as a boundary condition at the solidifying interface can be implemented into a finite-element code to determine the appropriate jet parameters. Such approach may provide an accurate solution, but may be computationally expensive (e.g., in computing time, energy costs, and monetary costs). It can be desirable, therefore, to present the problem in a non-dimensional version, which can be used rapidly by practitioners, without substantial computational expense. [0034] Modeling grain flow, and in particular grain erosion, on granular surfaces can begin by characterizing the suspension and transport of particles in statistically steady turbulent flow over a granular bed by the Shields parameter, Sh. The Shields parameter can represent the ratio of shear stress due to fluid flow relative to the weight per area of individual grains inside the bed, as demonstrated in Equation 4, where U is the characteristic flow velocity, d _g , grain diameter, g, is the acceleration due to gravity (e.g., in a vertical DC casting process), and and are the fluid and grain densities respectively.

[0035] Transport of grains occurs if the Shields parameter exceeds a critical value, which may depend on grain size, shape, cohesion and buoyancy. This critical Shields parameter can be difficult to determine experimentally, partially because the physical mechanism for resuspension occurs transiently due to turbulent fluctuations.

[0036] An alternative classification of granular resuspension and sedimentation can be expressed by the Rouse number, Rs, which is proportional to the ratio of the settling speed of the grains and the turbulent shear velocity of the bed. This relation is expressed below in Equation 5 where is the shear velocity, k is the von Kármán constant (e.g., approximately

0.40 or 0.41), and is the terminal settling velocity of the grains.

[0037] Below a critical value of Rs, the flow may be capable of maintaining grains in suspension because turbulent velocity fluctuations are larger than the terminal velocity of each grain. In unidirectional, steady flow, full bed transport is anticipated for and

significant resuspension occurs if Unlike the Shields number, the Rouse number may

account for the influence of viscosity upon each particle through the value of its respective settling speed, For very small grains (e.g., a diameter of approximately 70 ^m or less in the aluminum system), can be given by the Stokes settling velocity, as demonstrated in

Equation 6, where is the kinematic viscosity (e.g., approximately 5.5 x 10 ^-7 m ² /s for molten aluminum).

[0038] The granular Reynolds number can then be most usefully defined using

^ _^ as the characteristic velocity, as demonstrated in Equation 7, where is the grain

diameter.

[0039] As described herein, the aforementioned parameters have been experimentally determined for horizontal flow over a horizontal granular bed. However, the counterparts of the defining parameters can be redefined for a jet impinging perpendicularly onto a granular bed, as described in further detail below with reference to FIG. 2. As a result, a non- dimensionalized model can be generated, which can be used to optimize casting parameters to ensure an optimized liquid metal jet is present that can minimize the intensity of macrosegregation in the cast ingot.

[0040] Minimizing the intensity of macrosegregation in the cast ingot can have direct benefits (e.g., a more commercially desirable ingot or more consistent ingot formation), as well as additional benefits, such as reduced grain sizes, improved dendrite formation, and reduced need for grain refiners. In some cases, a desirable cast ingot can be produced with little or no added grain refiner. Additionally, the optimized liquid metal jet can fragment grains, which can promote the proliferation of smaller-sized grains throughout the cast product, which can be desirable. For example, an optimized liquid metal jet can produce globular grains using otherwise standard DC casting. [0041] In some cases, an optimized liquid metal jet can assist in degassing the molten metal. For example, hydrogen that is dissolved in the liquid aluminum can be washed out through the agitation provided by the optimized liquid metal jet at the slurry region of the molten sump. Since hydrogen has limited solubility in solid aluminum, small amounts of hydrogen, including amounts insufficient to nucleate a bubble, can be agitated and washed towards the surface by the liquid metal jet. Hydrogen that has been washed to the surface may be able to be removed as an impurity. Additionally, in some cases, tailoring nozzle size or flow rate as disclosed herein can be used to alter the morphology or distribution of secondary phase particles. Additionally, in some cases, tailoring nozzle size or flow rate as disclosed herein can be used to provide improved mixing, such as by providing additional molten metal into regions enriched in solute (e.g., adjacent the solidification front) to dilute those regions.

[0042] These illustrative examples are given to introduce the reader to the general subject matter discussed here and are not intended to limit the scope of the disclosed concepts. The following sections describe various additional features and examples with reference to the drawings in which like numerals indicate like elements, and directional descriptions are used to describe the illustrative embodiments but, like the illustrative embodiments, should not be used to limit the present disclosure. The elements included in the illustrations herein may not be drawn to scale.

[0043] FIG.1 is a partial cut-away view of a metal casting system 100 for supplying a liquid metal jet 134. A metal source 102, such as a tundish, can supply molten metal down a feed tube 136 and out a nozzle 110. A bottom block 122 may be lifted by a hydraulic cylinder 124 to meet the walls of the mold cavity 116. As molten metal begins to solidify within the mold, the bottom block 122 can be steadily lowered. The cast metal 106 can include sides 120 that have solidified, while molten metal added to the cast can be used to continuously lengthen the cast metal 106. In some cases, the walls of the mold cavity 116 define a hollow space and may contain a coolant 118, such as water. The coolant 118 can exit as jets from the hollow space and flow down the sides 120 of the cast metal 106 to help solidify the cast metal 106. The ingot being cast can include a solidified metal region 130, a transitional metal region 128, and a molten metal region 126.

[0044] The nozzle 110 through which molten metal is supplied to the molten sump 112 can be positioned under the surface 114 of the molten sump 112, at least during steady state operation (e.g., after starting the casting process, but before finishing the casting process). The nozzle 110 can be shaped to have an opening 108 (e.g., outlet) sized to produce an optimized liquid metal jet 134 into the molten sump 112. In some cases, a nozzle 110 can include multiple openings designed to produce one or more liquid metal jets. The liquid metal jet 134 exiting the nozzle 110 can be turbulent or laminar. The optimized liquid metal jet 134 can be optimized to impinge into the slurry region of the metal sump 112, such as the portion of the transitional region 128 near the center of the ingot being cast, with enough force sufficient to re-suspend any sedimented grains therein, but without the amount of force that would erode the bottom of the molten sump 112 (e.g., the solidified region 130).

[0045] In some cases, an optional flow control device 104 can be operatively coupled to the nozzle 110 to provide control of the flow of molten metal exiting the nozzle 110. In some cases, the flow control device 104 is a flow reducing device, capable of reducing the flow of molten metal from the feed tube 136. An example of a suitable flow reducing device is a control pin located within the feed tube 136. In some cases, the flow control device 104 can be a flow increasing device, capable of increasing the flow of molten metal from the feed tube 136. Examples of a suitable flow increasing device can be metal pumps, such as a non- contacting molten metal pump as described in U.S. Application No. 14/719,050, filed May 21, 2015, which is incorporated by reference in its entirety. In some cases, a flow increasing device can also act as a flow reducing device.

[0046] A flow control device 104 can be controlled by a controller 132 to adjust the flow rate of molten metal exiting the nozzle 110. In some cases, the controller 132 can be coupled to one or more sensors for sensing parameters of the metal casting system 100, which can be used by the controller 132 to estimate or calculate the depth of the metal sump 112. Examples of suitable sensors include distance sensors (e.g., laser, ultrasonic, or other), temperature sensors, or others.

[0047] When a flow control device 104 is used, control of the molten metal flow through the nozzle 110 by the flow control device 104 can be used, along with knowledge of the size of the nozzle 110 and/or characteristics of the mold cavity 116, to provide an optimized liquid metal jet 134 to the molten sump 112. The controller 132 can adjust one or more flow control devices 104, such as pumps and/or control pins, to adjust metal flow through the nozzle 110. In some cases, the controller 132 can monitor the casting process to determine a casting speed or estimated depth of the metal sump 112 to make adjustments to the flow of molten metal through the nozzle 110 via the flow control device 104 to optimize the liquid metal jet 134 exiting the nozzle 110.

[0048] In some cases, a flow control device 104 is used to slow the flow rate of molten metal through the nozzle 110 at least during the initial phases of casting, such as the first 100-300 mm of casting, so that the flow rate of molten metal can ramp up slowly along with the casting speed from zero to full speed.

[0049] In some cases, controller 132 can control one or more flow control devices 104 to adjust metal flow through the nozzle 110 in an oscillating pattern. The oscillating pattern can include increasing and decreasing metal flow through the nozzle 110 over time, which can further facilitate counteracting factors that cause macrosegregation, such as grain sedimentation and/or solute inhomogeneity.

[0050] FIG. 2 is a schematic representation 200 of a liquid metal jet 234 impinging a slurry region 228 of a molten metal sump 212. For example, the liquid metal jet 234 can be the liquid metal jet 134 impinging the transitional region 128 of the metal sump 112 of FIG. 1. The liquid metal jet 234 can have a volume flux Q ₀ of molten metal injected onto a granular bed 236 through a nozzle 210 having an opening 208 of diameter Ø , where Ø =2b _o . The velocity of the jet 234 exiting the nozzle 210 can be represented by U ₀ . The jet 234 can be situated a height, H ₀ , above the coherency isotherm 238. In the case of DC casting, H ₀ can be approximated based on the sump depth 244, because the slurry zone may be difficult to probe. Various relationships can be used to estimate the depth of the sump as a function of casting parameters. A granular bed 236 of material forming the slurry region 228 of the molten metal sump 212 can be positioned above the coherency isotherm 238. The slurry region 228 can have a height h ₀ above the coherency isotherm 238. Individual grains 242 in the slurry region 228 can be defined has having a diameter

[0051] As described above, Equation 5 representing the Rouse number for a turbulent jet impacting a bed of particles in a horizontal domain can be redefined for a jet 234 impinging perpendicularly onto a granular bed 236, as seen in FIG. 2. The redefined equation for this perpendicular domain can be represented by Equation 8, where is the velocity of the jet 234 at the surface of the granular bed 236 (e.g., at a distance H ₀ - h ₀ from the nozzle opening 208), ^ is the von Kármán constant (e.g., approximately 0.40 or 0.41), and is the terminal settling velocity of the grains 242.

[0052] The velocity of the jet 234 at the surface of the granular bed 236 can be determined by applying the theory of turbulent jets as demonstrated in Equation 9, where is the nozzle opening 208 radius, and represent the approximate overall height of the

fluid (e.g., molten metal) and the granular bed 236 respectively, and is the mean velocity

of the fluid at the nozzle opening 208 into the molten sump as determined by Equation 10 (e.g., expressed as a function of the volumetric flow rate

[0053] For a turbulent jet, the entrainment constant can be taken to be

approximately 0.08.

[0054] For spherical particles obeying stokes law Sh, Rs, and can thus be related by Equation 11.

[0055] The critical Shields number, can be seen to relate to the granular Reynolds

number according to Therefore, the critical Rouse number can be determined

to scale with the granular Reynolds number according to Equation 12.

[0056] The presence of several grains falling together falling in a swarm velocity, s provided by Equation 13, where is the volume fraction of solid particles and m is a

constant derived for the granular Reynolds numbers by Equation 14.

[0057] Using equation 5 from M.G. Chu, J.E. Jacoby. “Macrosegregation characteristics of commercial size aluminum alloy ingot cast by the direct chill method”. In: C.M. Bickert (Ed.), Light Metals, TMS, PA, (1990) for the volume fraction of sedimented grains in conjunction with the observed degree of centerline solute depletion in Wagstaff, S.R., Allanore, A.“Experimental Observations and Analysis of Macrosegregation in Rolling Slab Ingots”, In: M. Hyland (Ed.), Light Metals, TMS, PA,2015, which references are incorporated herein, the volume fraction of solid particles can be determined to be on the

order of 0.2. Applying this effect to Equation 11 leads to Equation 15.

[0058] As described above, the liquid metal jet 234 is capable of suspending grains 242 from the granular bed 236 if the critical Shields parameter Sh _c is exceeded or if the Rouse number is below (e.g., a critical Rouse number). For horizontal channel flow, bedload

transport may be defined by the volume flux of grains per unit width of flow A non- dimensional flux per unit width can then be obtained by normalizing the bedload transport by the grain size and settling speed.

[0059] For bedload transport of uniform horizontal flow over granular beds, empirical relationships have been determined to relate to the difference, following

equation 16, where the values of are constants dependent upon grain size, density,

and the stress imposed by the flow over the bed. The constant ^ and ^ _^ can be experimentally determined.

[0060] The radius of a crater 240 generated by an impinging jet 234 may not vary significantly with increasing jet power. Therefore, the crater 240 may deepen with increasing jet velocity at the base of the crater 240, while maintaining an almost constant radius (^ _^ ). This assumption and extrapolation may be valid at least for cohesionless grains forming a permeable bed. Cohesive granular beds (e.g., welded grains), however, may rely on high- temperature creep effects for re-suspension in addition to the applied shear stress. Therefore, cohesive granular beds may“reflect” at least a portion of the impinging jet and thus cause the jet’s effects to be less uniform and predictable. Additionally, the act of impingement may lead to a surface pressure distribution and a seepage flow within the bed. This seepage flow may allow shear stresses to act deep within the bed instead of dissipating rapidly, as is the case for non-permeable beds.

[0061] Therefore, the volume flux of grains suspended from the crater 240 due to the liquid metal jet 234 can be represented according to Equation 17, where the crater descent velocity (e.g., the speed at which the crater 240 deepens) is assumed to be constant (e.g., the volume flux is also assumed to be constant). In other words, Equation 17 can represent the volume flux of grains being displaced from the slurry region 228 due to impingement of the liquid metal jet 234. The term ^ _^ ^can represent the radius of the crater.

[0062] The granular flux per area density of grains can be represented by

which uses the hindered settling velocity to account for inter-granular interactions

within the crater.

[0063] The granular flux per area density of grains can be used to non-dimensionalize Equation 17, as demonstrated in Equation 18, where is the non-dimensional volume flux.

[0064] The relationship shown in Equation 18 defines a relative crater descent velocity, suggesting that the crater 240 descends independently of the properties of the grains themselves.

[0065] Because the definition of in Equation 8 explicitly invokes the settling

velocity of the grains 242, and thus can account for the influence of turbulent fluctuations, Equation 16 can be replaced with a non-dimensional flux of grains as demonstrated in Equation 19, where is a proportionality constant dependent upon grain size, density, and the stress imposed by the flow over the bed. The constant can be experimentally

determined.

[0066] Therefore, using Equations 8 and 18 and the relationship for the critical Rouse number from Equation 15, Equation 19 provides an explicit expression for the crater descent speed as a function of the velocity of the jet 234 on the bed 326, as demonstrated in Equation 20, where are proportionality constants dependent upon grain size,

density, and the stress imposed by the flow over the bed. The constant can be

experimentally determined.

[0067]

[0068] To provide an optimal solidifying environment, at least for the purposes of improving macrosegregation, it can be desirable to design a liquid metal jet 234 having power in a precise range that is sufficient to re-suspend the sedimented grains 242, but insufficient to erode the bottom of the sump 212. Therefore, the liquid metal jet 234 should be designed to evoke a crater descent velocity that is approximately equal to the casting

velocity (e.g., the vertical speed of displacement of the solid ingot). This criteria can ensure there is no or little accumulation of grains 242 in the center of the ingot, and that the power of the jet is dissipated in granular resuspension (e.g., rather than erosion of the fully solidified metal). In some cases, a desirable ingot can be cast using a nozzle that provides a liquid metal jet sufficient to maintain crater descent velocity at approximately equal to or not more than 1%, 2%, 3%, 4%, or 5% slower than the casting velocity, at least during steady casting. In some cases, a desirable ingot can be cast using a nozzle that provides a liquid metal jet sufficient to maintain crater descent velocity within approximately 1%, 2%, 3%, 4%, 5%, 6%, 7%, 8%, 9%, 10%, 11%, 12%, 13%, 14%, 15% or less variation from the casting velocity, at least during steady state casting.

[0069] Since the jet velocity at the surface of the granular bed ( _^^ ^ can be defined as a function of the volumetric flow rate, and thus also the casting velocity, an iterative computational solver can be implemented until convergence. The equations described above can be applied to determine optimal casting parameters, including nozzle openings and flow rates, as described herein.

[0070] FIG. 3 is a plot 300 depicting predicted, non-dimensional jet processing parameters for various example aluminum alloys that are designed to provide an optimal liquid metal jet for re-suspending grains in the slurry region of a metal sump according to certain aspects of the present disclosure. The mold Reynolds number (Re _m ) 304 can be based on an equivalent hydraulic radius and casting speed. The jet Reynolds number (Re _j ) 302 can be based on the jet velocity and diameter. The shaded region 312 can represent a range of values dependent on alloy properties that are suitable for providing an optimal liquid metal jet for re-suspending grains in the slurry region of a metal sump. For example, line 306 can represent the predicted non-dimensional jet processing parameters for aluminum alloy 5182, line 308 can represent the predicted non-dimensional jet processing parameters for aluminum alloy Al4.5Cu, and line 310 can represent the predicted non-dimensional jet processing parameters for aluminum alloy 1050.

[0071] The data of plot 300 can be considered optimization correlation data, which acts to correlate a known mold Reynolds number to a jet Reynolds number which can be used to determine optimal casting parameters, as disclosed in further detail herein. The data of plot 300 can be determined through experimentation, through modeling, or through application of existing data. [0072] By manipulating casting parameters (e.g., diameter of the nozzle opening and flow rate of the molten metal exiting the nozzle) such that the resultant non-dimensional jet processing parameters (e.g., jet Reynolds number and mold Reynolds number) fall on the appropriate prediction line of plot 300, an optimal liquid metal jet can be obtained. For example, for aluminum alloy Al4.5Cu, an optimal set of casting parameters (e.g., nozzle size and metal flow rate) can be selected such that the resultant jet Reynolds number is approximately 88000 and the resultant mold Reynolds number is approximately 1600, which meets line 308 at point 318. Other optimal casting parameters for aluminum alloy Al4.5Cu or for other aluminum alloys can be obtained similarly.

[0073] Alloy composition can be an important parameter of the model, as it influences both the relative density of the solid phase and the steady-state depth of the sump. Indeed, for DC casting where the majority of the heat is removed through the bottom solid block, certain elements such as magnesium or zinc may significantly influence the sump depth due to their lower thermal conductivity with respect to pure aluminum. Such sump depth differences can affect the extent of the jet expansion. As the centerline velocity of a jet will decrease with increasing depth, different jet diameters may be desirable for different alloy compositions. Experimental or modeled data can be used to generate boundary curves representing the effective processing parameters for minimum centerline segregation for the range of aluminum alloys typically used in DC casting, as depicted in the plot 300. The plot 300 represents the range of predicted jet Reynolds numbers as a function of mold Reynolds number where jet and mold Reynolds numbers (i.e., respectively) are

respectively defined according to Equations 21 and 22, where represent the mold

length and width respectively.

[0074] The boundary lines 306 and 310 of the shaded region 312 are created for two alloys identified as limiting cases (e.g., aluminum alloys 5182 and 1050). Most aluminum alloys used in DC casting will fall between these boundaries.

[0075] In some cases, the plot 300 can be approximated using linear approximations, for computationally fast or computationally easy determination of optimized Reynolds numbers. The relationship to mold parameters is present as a relationship of Reynolds numbers for the purpose of providing non-dimensionalized numbers for ease of use with various shapes of molds, however other relationships to mold parameters (e.g., dimensionalized relationships) can be used.

[0076] Sample points 314, 316, 318, 320, 322 represent the actual casting parameters used in the examples of FIGs.5-9, as described below.

[0077] FIGs. 4-9 are contour plots depicting intensity of macrosegregation according to vertical and horizontal position in various ingots of aluminum alloy Al4.5Cu cast using different techniques. The horizontal axis of each of these plots represents horizontal distance from the center of the ingot in mm, with the exterior of the ingot at the left end of the plot and the center of the ingot at the right end of the plot. The vertical axis of each of these plots represents vertical distance from the center of the ingot in mm, with the exterior of the ingot at the top end of the plot and the center of the ingot at the bottom end of the plot. The contour plots are based on lateral cross sections of the ingot taken along a plane perpendicular to a length of the ingot. The intensity of macrosegregation in these plots is given in the percentage differentiation of solute concentration from the molten metal supply. For example, an intensity of macrosegregation of -15 can represent a solute concentration that is 15% lower than the expected solute concentration (e.g., the concentration in the molten metal supplied form the furnace), whereas an intensity of macrosegregation of 10 can represent a solute concentration that is 10% higher than the expected solute concentration. Therefore, highly positive and highly negative numbers represent intense, and often undesirable, macrosegregation, whereas substantially low numbers (e.g., near zero) represent low, and often desirable, macrosegregation.

[0078] FIG. 4 is a contour plot 400 depicting intensity of macrosegregation according to vertical and horizontal position in an aluminum alloy Al4.5Cu ingot cast using existing techniques, without the liquid metal jet optimization techniques disclosed herein. As seen in plot 400, significant negative macrosegregation (e.g., at or worse than approximately -10% or -15%) is seen within 0 to 600 mm of the center of the ingot along the horizontal axis and within 0 to 50 mm of the center of the ingot along the vertical axis. Additionally, significant positive macrosegregation is seen in certain regions between the ingot center and the exterior of the ingot (e.g., at or around 100mm from the center along the vertical axis and between 200 and 500 mm from the center along the horizontal axis). The regions of intense macrosegregation seen in an ingot cast without using the liquid metal jet optimization techniques disclosed herein are relatively large and continuous.

[0079] FIGs. 5-9 are contour plots of an aluminum alloy Al4.5Cu ingot cast using various degrees of liquid metal jet optimization techniques disclosed herein across varying jet Reynolds numbers, yet maintaining a constant mold Reynolds number of approximately 1600. The jet Reynolds number was varied for the ingots cast through modification of the nozzle opening used during casting while all other casting parameters remained constant. The jet Reynolds numbers depicted in FIGs.5-9 correspond to points 314, 316, 318, 320, 322 of FIG.3.

[0080] FIG. 5 is a contour plot 500 depicting intensity of macrosegregation according to vertical and horizontal position in an aluminum alloy Al4.5Cu ingot cast using parameters set to achieve a mold Reynolds number of approximately 1600 and a nozzle opening selected to achieve a jet Reynolds number of approximately 64000. As seen in plot 500, no or very little negative segregation exists near the center of the ingot, however some positive segregation exists near center of the ingot and the short edges of the ingot.

[0081] FIG. 6 is a contour plot 600 depicting intensity of macrosegregation according to vertical and horizontal position in an aluminum alloy Al4.5Cu ingot cast using parameters set to achieve a mold Reynolds number of approximately 1600 and a nozzle opening selected to achieve a jet Reynolds number of approximately 69000. As seen in plot 600, no or very little negative segregation exists near the center of the ingot, however some positive segregation exists near center of the ingot and the edges of the ingot.

[0082] FIG. 7 is a contour plot 700 depicting intensity of macrosegregation according to vertical and horizontal position in an aluminum alloy Al4.5Cu ingot cast using parameters set to achieve a mold Reynolds number of approximately 1600 and a nozzle opening selected to achieve a jet Reynolds number of approximately 81000. As seen in plot 700, no or very little negative segregation exists near the center of the ingot, however some positive segregation exists near center of the ingot and the long edges of the ingot. Overall, however, the intensity of macrosegregation across the entire cross section depicted in plot 700 is mostly near zero (e.g., within a ±5% or ±10% variation of solute concentration from the molten metal supply).

[0083] FIG. 8 is a contour plot 800 depicting intensity of macrosegregation according to vertical and horizontal position in an aluminum alloy Al4.5Cu ingot cast using parameters set to achieve a mold Reynolds number of approximately 1600 and a nozzle opening selected to achieve a jet Reynolds number of approximately 97000. As seen in plot 800, very little segregation exists throughout most of the cross section, except for some positive segregation along the edges of the ingot. [0084] FIG. 9 is a contour plot 900 depicting intensity of macrosegregation according to vertical and horizontal position in an aluminum alloy Al4.5Cu ingot cast using parameters set to achieve a mold Reynolds number of approximately 1600 and a nozzle opening selected to achieve a jet Reynolds number of approximately 121000. As seen in plot 900, very little segregation exists throughout most of the cross section, except for some positive segregation along the edges of the ingot.

[0085] As seen in FIGs. 5-9, ingots cast with a jet Reynolds number below approximately 97000 exhibit positive (e.g., enriched) centerline segregation (e.g., as opposed to the negative segregation observed in FIG. 4). Additionally, ingots cast with a jet Reynolds number of 97000 or above exhibit very low centerline segregation and, if any, a negative (e.g., depleted) segregation. In addition, the extent of the centerline region is significantly narrower (e.g., an order of magnitude smaller) with respect to the short axis when using some degree of an optimized liquid metal jet (e.g., as seen in FIGs. 5-9) as opposed to no such jet (e.g., as seen in FIG.4).

[0086] FIGs. 4-9 illustrate the potential for optimized liquid metal jets to modify centerline segregation in DC cast products, such as rolling slab ingots. The fact that the centerline segregation zone itself is reduced can be desirable, since thermo-mechanical processing of the ingot may reduce the remaining segregation. A more quantitative analysis of the process performance can be made using a Macrosegregation Index (MI) metric, which quantifies the degree of centerline segregation. Equation 23 is a modified second-area moment equation that assigns quantitative values to the concentration measured at each position, based on its deviation from the target alloy composition and its distance from the center, where ^ is the half thickness of the ingot, ^ _ௗ^^ is the area of the measured slab cross section, ^ is the distance from the mid thickness of the measured point, A is the delimiter indicating the boundaries of integration over the ingot cross section, ^ _^ is the solute concentration of the target alloy composition, and is the solute concentration at a position as measured (e.g., distance through the ingot thickness).

[0087] Billet (along a radius or diameter). Ingot (through thickness)

[0088] Incorporating distance in the metric can be important, as enriched chill zone, which can be handled by physical means post casting, could skew the analysis of the whole section of the ingot. Since the index includes a squared term, it counts positive or negative segregation as equally unfavorable. The MI is minimal for the cross section with the less macrosegregation (e.g., where solute concentration variation from the molten metal supply is closest to zero).

[0089] FIG. 10 is a plot 1000 depicting the Macrosegregation Index (MI) as a function of jet Reynolds number for each of the ingots of FIGs. 5-9. Dashed line 1002 represents the MI from the standard ingot of FIG. 4, depicting a MI of approximately 0.104. In some cases, a suitable metal jet according to certain aspects of the present disclosure can result in an ingot or billet having a MI that is at or below approximately 0.115, 0.110, 0.105, 0.104, 0.100, 0.095, 0.090, 0.085, 0.080, 0.075, 0.070, 0.065, 0.060, 0.055, 0.050, 0.045, or 0.040.

[0090] Point 1022 depicts a MI of approximately 0.06 for the ingot of FIG.5 having a jet Reynolds number of 64000, associated with point 322 of FIG. 3. Point 1020 depicts a MI of approximately 0.07 for the ingot of FIG. 6 having a jet Reynolds number of 69000, associated with point 320 of FIG. 3. Point 1018 depicts a MI of approximately 0.06 for the ingot of FIG. 7 having a jet Reynolds number of 81000, associated with point 318 of FIG. 3. Point 1016 depicts a MI of approximately 0.04 for the ingot of FIG. 8 having a jet Reynolds number of 97000, associated with point 316 of FIG. 3. Point 1014 depicts a MI of approximately 0.07 for the ingot of FIG. 9 having a jet Reynolds number of 121000, associated with point 314 of FIG.3.

[0091] For the ranges of jet Reynolds numbers depicted in FIGs. 5-9, the macrosegregation index shows at least approximately a 30% reduction from the standard casting method. The best performing jet with a jet Reynolds number of 97000 shows approximately a 60% reduction in centerline segregation. In some cases, a suitable metal jet according to certain aspects of the present disclosure can provide a reduction in centerline segregation from the standard casting method of at or more than approximately 5%, 10%, 15%, 20%, 25%, 30%, 35%, 40%, 45%, 50%, 55%, 60%, or 65%.

[0092] The non-dimensional models, as described herein, can be used to determine casting parameters for various aluminum alloys and various mold dimensions.

[0093] FIG. 11 is a flowchart depicting a process 1100 for determining optimized casting parameters based on a known mold according to certain aspects of the present disclosure. At block 1102, the mold dimensions can be determined. The mold dimensions can include any suitable dimensions for determining the Reynolds number, as described herein. For example, dimensions of length and width can be determined for a rectangular mold, however, other dimensions can be determined for differently shaped molds. The mold dimensions can be predetermined based on other criteria, such as the desired ingot size or preexistence of a suitable mold. Examples of ways to determine mold dimensions can be measuring an existing mold, determining measurements from a plot or plan (e.g., through computer aided design), or presetting measurements for a to-be-produced mold. At block 1104, the casting speed can be determined. The casting speed can be predetermined based on other casting considerations. In some cases, determining a casting speed at block 1104 can include determining multiple potential desired casting speeds, which can further be used to determine multiple potential mold Reynolds numbers at block 1106 below, which can be used to calculate multiple optimized casting parameters, which in turn can be used to select one of the multiple casting speeds to be used.

[0094] At block 1106, a mold Reynolds number is determined. The mold Reynolds number can be determined using Equation 22 and the mold dimensions determined at block 1102 and the casting speed determined at block 1104. For example, a mold having dimensions of 1.5 m by 0.7 m, where the casting speed and crater descent rate are held equal at approximately 0.001 m/s, can provide a mold Reynolds number of

[0095] At optional block 1110, a metal composition can be determined. For example, the desired metal composition (e.g., type of aluminum alloy) can be determined by testing a sample, checking a database, or manual entry. In some cases, a generic metal composition can be assumed when the actual metal composition is not determined.

[0096] At block 1108, a jet Reynolds number is determined. The jet Reynolds number can be determined by matching the mold Reynolds number determined at block 1106 with optimization correlation data defining optimized relationships between mold Reynolds numbers and jet Reynolds numbers. The optimization correlation data can be in the form of a plot, such as plot 300 from FIG. 3, or in the form of an equation, such as an equation defining a line or an approximate from the plot 300 of FIG. 3 (e.g., a linear approximate following or in the form of individual data points. Optimization

correlation data can take other forms as well. In some cases, the metal composition determined at block 1110 can be used with the optimization correlation data to determine the jet Reynolds number. In the example above of a mold having a mold Reynolds number of approximately 1735, the corresponding jet Reynolds number for an aluminum alloy Al4.5Cu can be approximately 78000, as depicted in FIG.3. [0097] In some cases, optimization correlation data can be obtained through experimentation. In some cases, optimization correlation data can be obtained as described above with reference to FIG.3.

[0098] At block 1112, the desired casting parameters can be determined based on the determined jet Reynolds number from block 1108 and the determined mold Reynolds number from block 1106. In some cases, determining the desired casting parameter can include determining desired metal flow rate at block 1114. In some cases, determining the desired casting parameter can include determining the size of the nozzle opening at block 1116. In some cases, the radius of the nozzle opening (b ₀ ) can be determined by applying the mold Reynolds number from block 1106 and the jet Reynolds number from block 1108 to Equations 21 and 22, such that In the example above where the jet Reynolds

number is determined to be approximately 78000, the radius of the nozzle opening can be calculated to be

[0099] At optional block 1118, the casting environment can be prepared using the optimized casting parameter(s) determined at block 1112. The casting environment can be prepared by fabricating or selecting a nozzle having a suitable nozzle opening size as determined at block 1116. In the example above where the jet Reynolds number is determined to be approximately 78000, the suitable nozzle can be selected as one having an opening that is approximately 15.6 mm in radius, or 31.2 mm in diameter. In some cases, preparing the casting environment can include attaching a suitable nozzle to casting equipment associated with the particular mold used to determine the mold Reynolds number at block 1106. In some cases, the casting environment can be prepared by controlling a molten metal flow control device based on the metal flow rate determined at block 1114.

[0100] The foregoing description of the embodiments, including illustrated embodiments, has been presented only for the purpose of illustration and description and is not intended to be exhaustive or limiting to the precise forms disclosed. Numerous modifications, adaptations, and uses thereof will be apparent to those skilled in the art.

[0101] As used below, any reference to a series of examples is to be understood as a reference to each of those examples disjunctively (e.g.,“Examples 1-4” is to be understood as “Examples 1, 2, 3, or 4”).

[0102] Example 1 is a direct chill casting system, comprising: a mold cavity; a supply of molten metal for providing the molten metal to the mold cavity; and a nozzle coupled to the supply of molten metal and having an opening sized to produce a flow rate inducing a liquid metal jet having sufficient force to induce re-suspension of grains in a slurry region of a molten sump without altering a shape of the slurry region during steady state operation.

[0103] Example 2 is the system of example 1, wherein the opening of the nozzle is sized such that the liquid metal jet has sufficient force to induce a crater in the molten sump of a metal product being cast at a casting speed, wherein the opening of the nozzle is sized such that the liquid metal jet produced induces a crater descent velocity of the crater having a variation of 10% or less from the casting speed during steady state operation.

[0104] Example 3 is the system of examples 1 or 2, further comprising a bottom block for extending away from the nozzle at a casting speed during steady state operation.

[0105] Example 4 is the system of examples 1-3, further comprising a flow control device coupled between the supply of molten metal and the nozzle for controlling a flow rate of the molten metal into the mold cavity.

[0106] Example 5 is the system of example 4, further comprising a controller coupled to a sensor to estimate a depth of the molten sump and coupled to the flow control device to adjust the flow rate of the molten metal based on the estimated depth of the molten sump.

[0107] Example 6 is a method for optimizing metal casting during a casting operation, comprising: determining mold dimensions for a mold cavity suitable for receiving liquid metal from a nozzle coupled to a liquid metal source; determining a casting speed; and determining an optimized casting parameter using the mold dimensions and the casting speed, wherein determining the optimized casting parameter includes determining at least one of a metal flow rate and an opening size of the nozzle such that a liquid metal jet produced by liquid metal exiting the opening of the nozzle at the metal flow rate is suitable for inducing re-suspension of grains in a slurry region of a molten sump without altering a shape of the slurry region during steady state operation.

[0108] Example 7 is the method of example 6, wherein determining the optimized casting parameter comprises ensuring at least one of the metal flow rate and the opening size of the nozzle is calculated so that the liquid metal jet has sufficient force to induce a crater in the molten sump, wherein the opening of the nozzle is sized such that the liquid metal jet produced induces a crater descent velocity of the crater having a variation of 10% or less from the casting speed during steady state operation.

[0109] Example 8 is the method of examples 6 or 7, wherein determining an optimized casting parameter comprises: determining a mold Reynolds number using the mold dimensions and the casting speed; determining a jet Reynolds number using the mold Reynolds number; and calculating the optimized casting parameter using the mold Reynolds number and the jet Reynolds number.

[0110] Example 9 is the method of example 8, wherein determining the jet Reynolds number comprises determining a metal composition of the product being cast and determining the jet Reynolds number using the metal composition and the mold Reynolds number.

[0111] Example 10 is the method of examples 6-9, wherein the optimized casting parameter is the opening size of the nozzle. [0112] Example 11 is the method of examples 6-10, further comprising selecting or fabricating the nozzle based on the opening size of the nozzle.

[0113] Example 12 is the method of examples 6-11, further comprising controlling a flow control device using the metal flow rate.

[0114] Example 13 is a process of casting a metal product comprising: providing molten metal from a molten metal supply to a mold cavity through an opening of a nozzle at a flow rate during steady state operation, wherein providing molten metal through the opening of the nozzle at the flow rate includes producing a liquid metal jet in a molten sump; and re- suspending grains in a slurry region of a molten sump, using the liquid metal jet, without altering a shape of the slurry region during steady state operation.

[0115] Example 14 is the process of example 13, wherein the opening is sized such that the liquid metal jet has sufficient force to produce a crater in the slurry region and maintain a crater descent velocity within a 10% variation from a casting speed during steady state operation.

[0116] Example 15 is the process of example 14, further comprising: fabricating or selecting the nozzle to have an opening size suitable for producing the liquid metal jet having sufficient force to maintain the crater descent velocity within the 10% variation from the casting speed during the steady state operation; and coupling the nozzle to the molten metal supply.

[0117] Example 16 is the process of examples 13-15, further comprising retracting a bottom block away from the nozzle during steady state operation.

[0118] Example 17 is the process of examples 13-16, wherein providing the molten metal through the nozzle at the flow rate further comprises controlling the flow rate using a flow control device coupled between the molten metal supply and the nozzle. [0119] Example 18 is the process of example 17, wherein re-suspending the grains using the liquid metal jet comprises controlling the flow rate through the opening to ensure the liquid metal jet has sufficient force to maintain the crater descent velocity within a 5% variation from a casting speed during steady state operation.

[0120] Example 19 is the process of examples 13-18, wherein re-suspending the grains using the liquid metal jet comprises orienting the liquid metal jet in a direction at or within 30° from vertical.

[0121] Example 20 is a cast metal product producing using the process of examples 13-19, wherein the cast metal product has a macrosegregation index below 0.104.

[0122] Example 21 is a metal product having a macrosegregation index at or below 0.10, wherein the metal product is cast in a mold cavity using a nozzle coupled to a supply of molten metal to direct the molten metal into the mold cavity through an opening sized to produce a flow rate inducing a liquid metal jet into a molten sump.

[0123] Example 22 is the metal product of example 21, wherein the macrosegregation index is calculated according to:

wherein is a half thickness or a half diameter of the metal product, is an area of a

measured cross section of a measured point, ^ is a distance from a mid-thickness of the measured point, A is a delimiter indicating boundaries of integration over a cross section of the metal product, is a solute concentration of a target alloy composition, and ^ is a solute

concentration at the measured point.

[0124] Example 23 is the metal product of examples 21 or 22, wherein the liquid metal jet has sufficient force to induce re-suspension of grains in a slurry region of the molten sump without altering a shape of the slurry region during steady state operation. [0125] Example 24 is the metal product of examples 21-23, wherein the opening of the nozzle is sized such that the liquid metal jet has sufficient force to induce a crater in the molten sump, wherein the opening of the nozzle is sized such that the liquid metal jet produced induces a crater descent velocity of the crater having a variation of 10% or less from a casting speed during steady state operation.

[0126] Example 25 is the metal product of examples 21-24, wherein the liquid metal jet has sufficient force to induce fluid flow within the molten sump sufficient to homogenize solute concentrations throughout the molten sump.

[0127] Example 26 is the metal product of examples 21-25, wherein the macrosegregation index is at or below 0.090.

[0128] Example 27 is the metal product of examples 21-26, wherein the macrosegregation index is at or below 0.070.

[0129] Example 28 is the metal product of examples 21-27, wherein a flow control device is coupled between the supply of molten metal and the nozzle for controlling a flow rate of the molten metal into the mold cavity.

[0130] Example 29 is the metal product of example 28, wherein a controller is coupled to a sensor to estimate a depth of the molten sump and coupled to the flow control device to adjust the flow rate of the molten metal based on the estimated depth of the molten sump.

[0131] Example 30 is a method for optimizing metal casting during a casting operation, comprising: determining mold dimensions for a mold cavity suitable for receiving liquid metal from a nozzle coupled to a liquid metal source; determining a casting speed; and determining an optimized casting parameter using the mold dimensions and the casting speed, wherein determining the optimized casting parameter includes determining at least one of a metal flow rate and an opening size of the nozzle such that a liquid metal jet produced by liquid metal exiting the opening of the nozzle at the metal flow rate is suitable for reducing macrosegregation in a cast metal product such that a metal product cast using the optimized casting parameter has a macrosegregation index at or below 0.100.

[0132] Example 31 is the method of example 30, wherein the macrosegregation index is calculated according to:

wherein is a half thickness or a half diameter of the metal product, is an area of a

measured cross section of a measured point, is a distance from a mid-thickness of the

measured point, A is a delimiter indicating boundaries of integration over a cross section of the metal product, is a solute concentration of a target alloy composition, and ^ is a solute

concentration at the measured point.

[0133] Example 32 is the method of examples 30 or 31, wherein determining the optimized casting parameter comprises ensuring at least one of the metal flow rate and the opening size of the nozzle is calculated so that the liquid metal jet is suitable for inducing re- suspension of grains in a slurry region of a molten sump without altering a shape of the slurry region during steady state operation.

[0134] Example 33 is the method of examples 30-32, wherein determining the optimized casting parameter comprises ensuring at least one of the metal flow rate and the opening size of the nozzle is calculated so that the liquid metal jet has sufficient force to induce a crater in the molten sump, wherein the opening of the nozzle is sized such that the liquid metal jet produced induces a crater descent velocity of the crater having a variation of 10% or less from the casting speed during steady state operation.

[0135] Example 34 is the method of examples 30-33, wherein determining an optimized casting parameter comprises: determining a mold Reynolds number using the mold dimensions and the casting speed; determining a jet Reynolds number using the mold Reynolds number; and calculating the optimized casting parameter using the mold Reynolds number and the jet Reynolds number.

[0136] Example 35 is the method of example 34, wherein determining the jet Reynolds number comprises determining a metal composition of the product being cast and determining the jet Reynolds number using the metal composition and the mold Reynolds number.

[0137] Example 36 is the method of examples 30-35, wherein the optimized casting parameter is the opening size of the nozzle.

[0138] Example 37 is the method of examples 30-36, further comprising selecting or fabricating the nozzle based on the opening size of the nozzle.

[0139] Example 38 is the method of examples 30-37, further comprising controlling a flow control device using the metal flow rate.

[0140] Example 39 is the method of examples 30-38, wherein determining the optimized casting parameter comprises ensuring at least one of the metal flow rate and the opening size of the nozzle is calculated so that the liquid metal jet has sufficient force to induce fluid flow within a molten sump sufficient to homogenize solute concentrations throughout the molten sump.

[0141] Example 40 is the method of examples 30-39, wherein the macrosegregation index is at or below 0.090.

[0142] Example 41 is the method of examples 30-40, wherein the macrosegregation index is at or below 0.070.

[0143] Example 42 is a process of casting a metal product comprising: providing molten metal from a molten metal supply to a mold cavity through an opening of a nozzle at a flow rate during steady state operation, wherein providing molten metal through the opening of the nozzle at the flow rate includes producing a liquid metal jet in a molten sump sufficient to reduce macrosegregation in the metal product such that the metal product has a macrosegregation index at or below 0.100.

[0144] Example 43 is the process of example 42, wherein the macrosegregation index is calculated according to:

wherein is a half thickness or a half diameter of the metal product, is an area of a

measured cross section of a measured point, is a distance from a mid-thickness of the

measured point, A is a delimiter indicating boundaries of integration over a cross section of the metal product, ^ _^ is a solute concentration of a target alloy composition, and ^ is a solute concentration at the measured point.

[0145] Example 44 is the process of examples 42 or 43, further comprising re- suspending grains in a slurry region of a molten sump, using the liquid metal jet, without altering a shape of the slurry region during steady state operation.

[0146] Example 45 is the process of example 44, wherein the opening is sized such that the liquid metal jet has sufficient force to produce a crater in the slurry region and maintain a crater descent velocity within a 10% variation from a casting speed during steady state operation.

[0147] Example 46 is the process of examples 42-45, further comprising inducing fluid flow within a molten sump sufficient to homogenize solute concentrations throughout the molten sump.

[0148] Example 47 is the process of examples 42-46, wherein providing the molten metal through the nozzle at the flow rate further comprises controlling the flow rate using a flow control device coupled between the molten metal supply and the nozzle. [0149] Example 48 is the process of examples 42-47, wherein the macrosegregation index is at or below 0.090.

[0150] Example 49 is the process of examples 42-48, wherein the macrosegregation index is at or below 0.070.