A Simple Model of the Mold Boundary Condition in Direct-Chill (DC) Casting of Aluminum Alloys

An accurate thermofluids model of aluminum direct-chill (DC) casting must solve the heat-transfer equations in the ingot with realistic external boundary conditions. These boundary conditions are typically separated into two zones: primary cooling, which occurs inside the water-cooled mold, and secondary cooling, where a film of water contacts the ingot surface directly. Here, a simple model for the primary cooling boundary condition of the steady-state DC casting process was developed. First, the water-cooled mold was modeled using a commercial computational fluid dynamics (CFD) package, and its effective heat-transfer coefficient was determined. To predict the air-gap formation between the ingot and mold and to predict its effect on the primary cooling, a simple density-based shrinkage model of the solidifying shell was developed and compared with a more complex three-dimensional (3-D) thermoelastic model. DC casting simulations using these two models were performed for AA3003 and AA4045 aluminum alloys at two different casting speeds. A series of experiments was also performed using a laboratory-scale rectangular DC caster to measure the thermal history and sump shape of the DC cast ingots. Comparisons between the simulations and experimental results suggested that both models provide good agreement for the liquid sump profiles and the temperature distributions within the ingot. The density-based shrinkage model, however, is significantly easier to implement in a CFD code and is more computationally efficient.     

On the development of a three-dimensional transient thermal model to predict ingot cooling behavior during the start-up phase of the direct chill-casting process for an AA5182 aluminum alloy ingot

The control of the heat transfer during the start-up phase of the direct-chill (DC) casting process for aluminum sheet ingots is critical from the standpoint of defect formation. Process control is difficult because of the various inter-related phenomena occurring during the cast start-up. First, the transport of heat to the mold is altered as the ingot base deforms and the sides are pulled inward during the start-up phase. Second, the range of temperatures and water flow conditions occurring on the ingot surface as it emerges from the mold results in the full range of boiling-water heat-transfer conditions—e.g., film boiling, transition boiling, nucleate boiling, and convection—making the rate of transport highly variable. For example, points on the ingot surface below the point of water impingement can experience film boiling, resulting in the water being ejected from the surface, causing a dramatic decrease in heat transfer below the point of ejection. Finally, the water flowing down the ingot sides may enter the gap formed between the ingot base and the bottom block due to butt curl. This process alters the heat transfer from the base of the ingot and, in turn, affects the surface temperature on the ingot faces, due to the transport of heat within the ingot in the vertical direction. A comprehensive mathematical model has been developed to describe heat transfer during the start-up phase of the DC casting process. The model, based on the commercial finite-element package ABAQUS, includes primary cooling via the mold, secondary cooling via the chill water, and ingot-base cooling. The algorithm used to account for secondary cooling to the water includes boiling curves that are a function of ingot-surface temperature, water flow rate, impingement-point temperature, and position relative to the point of water impingement. In addition, a secondary cooling algorithm accounts for water ejection, which can occur at low water flow rates (low heat-extraction rates). The algorithm used to describe ingot-base cooling includes both the drop in contact heat transfer due to gap formation between the ingot base and bottom block (arising from butt curl) as well as the increase in heat transfer due to water incursion within the gap. The model has been validated against temperature measurements obtained from two 711×1680 mm AA5182 ingots, cast under different start-up conditions (nontypical “cold” practice and nontypical “hot” practice). Temperature measurements were taken at various locations on the ingot rolling and narrow faces, ingot base, and top surface of the bottom block. Ingot-based deflection data were also obtained for the two test conditions. Comparison of the model predictions with the data collected from the cast/embedded thermocouples indicates that the model accounts for the processes of water ejection and water incursion and is capable of describing the flow of heat in the early stages of the casting process satisfactorily.     

A mathematical model of the heat and fluid flows in direct-chill casting of aluminum sheet ingots and billets

A finite-element method model for the time-dependent heat and fluid flows that develop during direct-chill (DC) semicontinuous casting of aluminium ingots is presented. Thermal convection and turbulence are included in the model formulation and, in the mushy zone, the momentum equations are modified with a Darcy-type source term dependent on the liquid fraction. The boundary conditions involve calculations of the air gap along the mold wall as well as the heat transfer to the falling water film with forced convection, nucleate boiling, and film boiling. The mold wall and the starting block are included in the computational domain. In the start-up period of the casting, the ingot domain expands over the starting-block level. The numerical method applies a fractional-step method for the dynamic Navier-Stokes equations and the “streamline upwind Petrov-Galerkin” (SUPG) method for mixed diffusion and convection in the momentum and energy equations. The modeling of the start-up period of the casting is demonstrated and compared to temperature measurements in an AA1050 200×600 mm sheet ingot.     

Determination of interface heat transfer coefficient between aluminum casting and graphite mold

To produce castings of titanium, nickel, copper, aluminum, and zinc alloys, graphite molds can be used, which makes it possible to provide a high cooling rate. No die coating and lubricant are required in this case. Computer simulation of casting into graphite molds requires knowledge of the thermal properties of the poured alloy and graphite. In addition, in order to attain adequate simulation results, a series of boundary conditions such as heat transfer coefficients should be determined. The most important ones are the interface heat transfer coefficient between the casting and the mold, the heat transfer coefficient between the mold parts, and the interface heat transfer coefficient into the environment. In this study, the interface heat transfer coefficient h between the cylindrical aluminum (99.99%) casting and the mold made of block graphite of the GMZ (low ash graphite) grade was determined. The mold was produced by milling using a CNC milling machine. The interface heat transfer coefficient was found by minimizing the error function reflecting the difference between the experimental and simulated temperatures in a mold and in a casting during pouring, solidification, and cooling of the casting. The dependences of the interface heat transfer coefficient between aluminum and graphite on the casting surface temperature and time passed from the beginning of pouring are obtained. It is established that, at temperatures of the metal surface contacting with a mold of 1000, 660, 619, and 190°C, the h is 1100, 4700, 700, and 100 W/(m² K), respectively; i.e., when cooling the melt from 1000°C (pouring temperature) to 660°C (aluminum melting point), the h rises from 1100 to 4700 W/(m² K), and after forming the metal solid skin on the mold surface and decreasing its temperature, the h decreases. In our opinion, a decrease in the interface heat transfer coefficient at casting surface temperatures lower than 660°C is associated with the air gap formation between the surfaces of the mold and the casting because of the linear shrinkage of the latter. The heat transfer coefficient between mold parts (graphite–graphite) is constant, being 1000 W/(m² K). The heat transfer coefficient of graphite into air is 12 W/(m² K) at a mold surface temperature up to 600°C.     

Heat transport and solidification in the electromagnetic casting of aluminum alloys: Part II. Development of a mathematical model and comparison with experimental results

In this second article of a two-part series, a mathematical model for heat transport and solidification of aluminum in electromagnetic casting is developed. The model is a three-dimensional one but involves a simplified treatment of convective heat transport in the liquid metal pool. Heat conduction in the solid was thought to play a dominant role in heat transport, and the thermal properties of the two alloys used in measurements reported in Part I (AA 5182 and 3104) were measured independently for input to the model. Heat transfer into the water sprays impacting the sides of the ingot was approximated using a heat-transfer coefficient from direct chill casting; because this heat-transfer step appears not to be rate determining for solidification and cooling of most of the ingot, there is little inaccuracy involved in this approximation. Joule heating was incorporated into some of the computations, which were carried out using the finite element software FIDAP. There was good agreement between the computed results and extensive thermocouple measurements (reported in Part I) made on a pilot-scale caster at Reynolds Metals Company (Richmond, VA).     

The air-gap formation process at the casting-mold interface and the heat transfer mechanism through the gap

The formation process of the air gap at the casting-mold interface and the heat transfer mechanism through the gap were investigated by measuring the displacement of, and the temperature in casting and mold for cylindrical and flat castings of aluminum alloys. The thickness of the air gap was measured as the difference between the location of the casting surface and that of the mold inner surface. For cylindrical castings, the mold began to move outward immediately after pouring, while the casting stayed until solidification progressed to a great extent. For flat castings, the mold began to move greatly toward the casting pushing the casting immediately after pouring and moved reversely after a maximum appeared. It was possible to calculate the displacement of the mold by thermal expansion. It was found that when the thickness of the air gap was not large, the heat through the gap was transferred mainly by heat conduction.     

Heat transfer and microstructure during the early stages of metal solidification

Transient heat transfer in the early stages of solidification of an alloy on a water-cooled chill and the consequent evolution of microstructure, quantified in terms of secondary dendrite arm spacing (SDAS), have been studied. Based on dip tests of the chill, instrumented with thermocouples, into Al-Si alloys, the influence of process variables such as mold surface roughness, mold material, metal superheat, alloy composition, and lubricant on heat transfer and cast structure has been determined. The heat flux between the solidifying metal and substrate, computed from measurements of transient temperature in the chill by the inverse heat-transfer technique, ranged from low values of 0.3 to 0.4 MW/m² to peak values of 0.95 to 2.0 MW/m². A onedimensional, implicit, finite-difference model was applied to compute heat-transfer coefficients, which ranged from 0.45 to 4.0 kW/m² °C, and local cooling rates of 10 °C/s to 100 °C/s near the chill surface, as well as growth of the solidifying shell. Near the chill surface, the SDAS varied from 12 to 22 (μm while at 20 mm from the chill, values of up to 80/smm were measured. Although the SDAS depended on the cooling rate and local solidification time, it was also found to be a direct function of the heat-transfer coefficient at distances very near to the casting/chill interface. A three-stage empirical heat-flux model based on the thermophysical properties of the mold and casting has been proposed for the simulation of the mold/casting boundary condition during solidification. The applicability of the various models proposed in the literature relating the SDAS to heat-transfer parameters has been evaluated and the extension of these models to continuous casting processes pursued.     

A Numerical Study of the Direct-Chill Co-Casting of Aluminum Ingots via Fusion™ Technology

For the last 70 years, direct-chill (DC) casting has been the mainstay of the aluminum industry for the production of monolithic sheet and extruded products. Traditionally, clad aluminum sheet products have been made from separate core and clad DC cast ingots by an expensive roll-bonding process; however, in 2005, Novelis unveiled an innovative variant of the DC casting process called the Fusion? Technology process that allows the production of multialloy ingots that can be rolled directly into laminated or clad sheet products. Of paramount importance for the successful commercialization of this new technology is a scientific and quantitative understanding of the Fusion? casting process that will facilitate process optimization and aid in the future development of casting methodology for different alloy combinations and ingot and clad dimensions. In the current study, a numerical steady-state thermofluids model of the Fusion? Technology casting process was developed and used to simulate the casting of rectangular bimetallic ingots made from the typical brazing sheet combination of AA3003 core clad with an AA4045 aluminum alloy. The analysis is followed by a parametric study of the process. The influence of casting speed and chill-bar height on the steady-state thermal field within the ingot is investigated. According to the criteria developed with the thermofluids model, the AA3003/AA4045 combination of aluminum alloys can be cast successfully with casting speeds up to 2.4 mm s^?1. The quality of the metallurgical bond between the core and the clad is decreased for low casting speeds and chill-bar heights >35 mm. These results can be used as a guideline for improving the productivity of the Fusion? Technology process.     

Experimental Study and Numerical Verification of Heat Transfer in Squeeze Casting of Aluminum Alloy A443

As an effective tool, simulation helps do the analysis and optimization in advance and undertake preventive action. A critical portion of casting simulation is the heat transfer at the metal/mold interface. However, it is difficult to determine the values of interfacial heat-transfer coefficients (IHTCs) in squeeze casting of aluminum alloys due to many influence factors. In this work, IHTCs were determined by using the inverse algorithm based on measured temperature histories and finite-difference analysis in a five-step squeeze casting of aluminum alloy A443. The results showed the IHTCs initially reached a maximum peak value followed by a gradually decline to a lower level. Similar characteristics of IHTC peak values were also observed at 30, 60, and 90?MPa applied pressures. With the applied pressure of 60?MPa, the peak IHTC values of aluminum alloy A443 from steps 1 to 5 varied from 5629?W/m²K to 9419?W/m²K. The comparison of the predicted cooling curves with the experimental measurement manifested the cooling temperatures calculated by the IHTC values determined in the current study were in the best agreement with experimental ones. The verification of the determined IHTC values demonstrates that the inverse algorithm is an effective tool for determination of the IHTC at the squeeze casting?Cdie interface.     

The movement of the concave casting surface during mushy-type solidification and its effect on the heat-transfer coefficient

The air gap formation process at the casting/mold interface of a hollow cylinder casting was investigated for alloys solidifying in a mushy type by measuring the displacements of the casting and the mold surfaces during solidification. The formation process of the air gap between the convex casting surface and the outer mold and the heat-transfer coefficient through the gap have been well documented by previous publications. However, the air gap between the concave casting surface and the inner mold, or the core, was found to form differently during mushy solidification, in which the air gap formed during solidification, reached a maximum gap distance, and then decreased due to the contraction of the solidified casting on the expanding inner mold. The gap formation was caused by an inward collapse of the coherent dendrite networks at the concave interface because of low pressure inside of the casting due to solidification shrinkage. The coherent dendrite networks at the convex interface did not collapse inward. The heat-transfer coefficients estimated by measuring the air gap thickness showed a similar tendency to the calculated values obtained by the inverse heat-conduction analysis.     

Film Boiling and Water Film Ejection in the Secondary Cooling Zone of the Direct-Chill Casting Process

Accurate thermal modeling of the direct-chill casting process relies nowadays on increasingly complex boundary conditions for the secondary cooling zone. A two-dimensional axisymmetric finite-element model of the direct-chill casting process was developed to quantify the importance of secondary cooling at the surface compared with internal heat conduction within the billet. Boiling water heat transfer at the surface was found to dominate and be the governing factor only when stable film boiling or water film ejection take place; all other cases were dominated by internal heat conduction. The influence of various parameters (casting speed, cooling water flow rate, and thermophysical properties of the cast material) on the occurrence of water film ejection was analyzed. An exponential relationship was found between the cooling water flow rate and the minimum casting speed at which water film ejection takes place.     

Determination of thermophysical properties and boundary conditions of direct chill-cast aluminum alloys using inverse methods

In order to quantify the cooling conditions undergone by an ingot during direct-chill (DC) casting, thermocouples were immersed in the liquid pool and consequently entrapped in the solid, thus monitoring the temperature of the metal during its descent. Assuming steady-state thermal conditions, the time-dependent temperatures measured by these thermocouples were then converted into spacedependent temperature profiles. These values were the input of a Maximum A Posteriori (MAP) inverse method described by Rappaz et al.,^[1] which has been adapted in this case to steady-state thermal conditions. This MAP method permits the deduction of the temperature-dependent thermal conductivity of the alloy, initially, and then of the highly nonuniform heat-flux distribution along the ingot rolling faces, in a second step. The obtained values are in good agreement with literature and clearly reflect the widely different boundary conditions associated with primary cooling (contact with the mold) and secondary cooling (water jet).     

7050铝合金半连铸过程应力场及开裂倾向

7050铝合金在半连铸生产过程中发生热裂和冷裂的倾向很高,不但影响了产品的质量和生产效率,还可能导致生产事故.工厂常采用试错法以找到最优的工艺参数,但这种方法成本高且效率低.运用数值模拟的方法再现铸造过程中各物理场的变化情况,已成为优化铝合金熔铸工艺非常重要的研究手段.本文通过将温度场、流场和应力场进行直接耦合,对7050铝合金的半连铸过程进行了数值模拟研究.结果显示,在糊状区沿铸锭宽度方向的应力和应变分量最大,特别是在起始铸造阶段,因而最容易在起始阶段产生垂直于宽度方向的热裂纹.冷裂与铸锭内应力集中有关,根据计算可知铸锭在冷却至200℃时冷裂倾向最大.由实际裂纹所处的部位及所需的临界尺寸可以推测,该冷裂纹极有可能是糊状区产生的热裂纹在低温时失稳扩展而形成的.      

Experimental Determination of Heat Transfer Across the Metal/Mold Gap in a Direct Chill (DC) Casting Mold��Part I: Effect of Gap Size and Mold Gas Type

An experimental apparatus to determine the heat-transfer coefficient in the gap formed between the cast metal and the mold wall of a vertical direct chill (DC) casting mold is described. The apparatus simulates the conditions existing within the confines of the DC casting mold and measures the heat flux within the gap. Measurements were made under steady-state conditions, simulating the steady-state regime of the DC casting process. A range of casting parameters that may affect the heat transfer was tested using this apparatus. In the current article, the operation of the apparatus is described along with the results for the effect of gas type within the mold, and the size of the metal-mold gap formed during casting. The results show that the gas type and the gap size significantly affect the heat transfer within a DC casting mold. The measured heat fluxes for all the conditions tested were expressed as a linear correlation between the heat-transfer coefficient and the metal-mold gap size, and the fluxes can be used to estimate the heat transfer between the metal and the mold at any gap size. These results are compared to values reported in the literature and recommendations are made for the future reporting of the metal/mold heat-transfer coefficient for DC casting. The results for the effect of the other parameters tested are described in Part II of the article.     

A correlation to describe interfacial heat transfer during solidification simulation and its use in the optimal feeding design of castings

It is known from experimental data that for pure aluminum castings manufactured via the gravity die casting process, the interfacial heat-transfer coefficient can vary in the range 500 to 16,000 W/m² K. These coefficients are of significant importance for the numerical simulation of the solidification process. The experimentally determined variation of interfacial heat-transfer coefficients with respect to time has been recalculated to highlight the variation with respect to casting temperature at the interface. This variation was observed to be of an exponential nature. Also, the pattern of variation was found to be similar in all the experimental results. It has been found that all these patterns of interfacial heat-transfer coefficient variation can be matched by a unique equation that has been proposed as a correlation to model the metal-mold interfacial heat transfer. The benefit of this correlation is in its ability to approximate the combined effects of geometry variation, insulation, chills, die coatings, air gap formation, etc. during the numerical simulation and its use in the optimal design of heat transfer at the metal-mold interface.     

A numerical simulation of the D.C. continuous casting process including nucleate boiling heat transfer

The steady-state thermal problem associated with the direct-chill continuous casting of A6063 aluminum cylindrical ingots is solved using the numerical finite element technique. Excellent correlation is demonstrated between the numerical model and experimental data from ingots cast at two different speeds. By application of the model, effective heat transfer coefficients are calculated as a function of vertical position on the outside surface of the ingot. It is shown that direct application of these coefficients to the modeling of different casting situations will produce substantial errors in the region in which heat transfer is by nucleate boiling. Using theories of nucleate boiling with forced convection and film cooling, a method is developed to calculate the external boundary conditions in the submold region of the ingot, thus making it possible for the first time to define explicitly all of the thermal boundary conditions associated with this casting configuration. These theories are incorporated into the numerical model, and a subsequent simulation shows excellent agreement with experimental data from a third ingot.     

Determination of the heat-transfer coefficient between the AK7ch (A356) alloy casting and no-bake mold

The heat-transfer coefficient h between a cylindrical cast made of AK7ch (A356) aluminum alloy and a no-bake mold based on a furan binder is determined via minimizing the error function, which reflects the difference between the experimental and calculated temperatures in the mold during pouring, solidification, and cooling. The heat-transfer coefficient is h _L = 900 W/(m² K) above the liquidus temperature (617°C) and h _S = 600 W/(m² K) below the alloy solidus temperature (556°C). The variation in the heat-transfer coefficient in ranges h _L = 900–1200 W/(m² K) (above the alloy liquidus temperature) and h _S = 500–900 W/(m² K) (below the solidus temperature) barely affects the error function, which remains at ~22°C. It is shown that it is admissible to use a simplified approach when constant h = 500 W/(m² K) is specified, which leads to an error of 23.8°C. By the example of cylindrical casting, it is experimentally confirmed that the heat-transfer coefficient varies over the casting height according to the difference in the metallostatic pressure, which affects the casting solid skin during its solidification; this leads to a closer contact of metal and mold at the casting bottom.     

Reanalysis of solidification behaviour from the microstructure in near-net-shape casting of steels

Numerical calculations revealing the relationship between the as-cast structure and cooling conditions in near-net-shape casting of steels are presented. The solidification behaviour of steels of different composition was investigated for different process conditions with a one-dimensional heat-flow model. The dependence of the secondary dendrite arm spacing (SDAS) on the distance from the chill surface was determined on the basis of the empirical relationship between local solidification time and SDAS. The numerical results were compared with experimental values of SDAS for a stainless steel, a carbon tool steel and a high-speed steel, resp. Reasonable agreement of model calculations with the experimentally determined SDAS was obtained utilizing time-dependent effective heat-transfer coefficients of the order of 2.5 to 4.5 · 10³ W/m²K for typical thin-slab dimensions and 6.0 · 10³ W/m²K for thin-strip casting.