2017 Volume 58 Issue 12 Pages 1721-1728
A mathematical model based on commercial finite volume package FLUENT has been developed to describe the melt flow and heat transfer during planar solidification casting process of 7050 alloy ingot with cross-section size of 600 × 600 mm. The effects of two fixed sprues and two movable sprues served as the feeding system on the temperature field and velocity field of planar solidification were investigated. Moreover, the model has been verified by the temperature measurements obtained from experiments. The numerical results reveal that the effect of feeding system on melt temperature field is dominating during planar solidification casting process and the movable sprues are significantly superior to the fixed sprues. The characteristics of planar solidification front and uniform temperature field are achieved by movable dense sprues. According to the numerical results, an ingot without V- shaped shrinkage and crack on the surface, and with uniform microstructure and small difference in composition was casted successfully.
Direct Chill Casting (DC Casting) is the main method of producing aluminum alloy ingots for the subsequent manufacture1,2). Although this technology has been developed for 80 years, some deficiencies have not been solved till now. The schematic diagram of DC casting was shown in Fig. 1(a). During the solidification of DC casting, the melt shell is directly chilled by cooling medium, while the internal melt is indirectly chilled by transferring heat to solidified shell in multiple directions. There is a noticeable temperature difference between the central part and the periphery of the ingot and the cooling rate at the center of the ingot is significantly smaller than the periphery. Thus, the grain size changes distinctly along the cooling direction in the cross-section of ingots3). Besides, high internal stresses and even cracks caused by shrinkage will generate in some aluminum alloys since the solidification is not synchronized4,5). In addition, the macrosegregation of the ingot due to thermal convection in the liquid sump is really a serious problem as it cannot be eliminated during downstream processing6,7). These problems are exacerbated when casting aluminum alloy ingots with high alloying elements. In order to solve these problems, some methods have been developed in recent decades, including hot top casting8), ultrasonic casting9) and electromagnetic casting10). Although these technologies have improved the quality of ingots, but the severe macrosegregation of alloying elements is still a key issue deteriorating ingot metallurgical quality.
Schematic diagram of DC casting (a) and planar solidification casting (b).
Recently, planar solidification technology, a new aluminum alloy casting method, has been proposed for the preparation of high-strength aluminum alloy to reduce macrosegregation and other DC casting defects11). The method depends on the principle of unidirectional solidification. As shown in Fig. 1(b), the melt is cooled on the sole direction from the bottom of the mold to the top surface during casting. Two essential factors, the uniformity of the chilling and the uniformity of the sprue distributions, are ensured to make the interface of solid and liquid remains flat and rises horizontally. The speed of molten metal flow into the mold and the coolant spray on the bottom of mold are both controlled to provide a relatively constant rate of solidification. At the beginning of the casting, the melt is chilled by the cooling plate at the bottom of the mold. When the melt at the bottom of the mold solidify, the underneath of the solidified shell is exposed by removing the cooling plate so that it can be directly contacted with the coolant. The coolants such as air, water mist or water column are evenly arranged in a flat under the mold to provide uniform cooling. Men G. Chu12) demonstrated different ways of cooling (fixed perforated plate and movable wire netting) and different types of feed chamber fixed on side of the mold (the melt into mold in a horizontal or vertical direction) during the planar solidification. However, the ways of cooling and the feed chamber are not suitable for large-sized ingots. Because the liquid sump at the feed chamber is significantly deepened in large mold, resulting in the inability to achieve planar solidification.
In this paper, a new feeding system with movable sprues was proposed for all-size planar solidification casting. The sprues moved horizontally within the mold rely on the guide rails outside the mold. The influences of movable sprues and fixed sprues on the temperature field and flow fields in the mold were compared. A transient mathematical model was established to describe the planar solidification casting process. Computer simulation performed with FLUENT software was used to optimize the feeding system. Based on the optimal feeding system, the planar solidification casting of high strength aluminum alloy AA7050 was realized.
AA7050(Al-6.2Zn-2.1Cu-2.2Mg, mass%) alloy ingots with a cross section of 600 mm × 600 mm were fabricated by planar solidification process. The schematic diagram of planar solidification experiment apparatus with movable sprues is shown in Fig. 2. The apparatus is mainly composed by feeding system, insulation boards and cooling system. The insulation boards are mounted on the cooling system and combine with cooling system to form a mold. In the initial stage of casting, the insulation board was connected with the water-cooled steel plate to form the mold. The melt was poured into mold through feeding system steadily and cooled by the steel plate. The steel plate was withdrew rapidly when solid shell had sufficient strength to support itself. Then the water mist from densely arranged water mist nozzles was sprayed on the bottom of the solidified shell to cool the melt uniformly. The pressure of the mist can be controlled to get uniform solidification velocity during casting. Temperature measurement was employed to verify the reliability of the mathematical model for planar solidification process. Three K-type thermocouples were placed at height of 40 mm, 80 mm and 120 mm from the bottom of the ingot to measure the temperature during casting. These thermocouples were vertically fixed on a stainless steel bar with the diameter of 1.5 mm which was placed at the corner of mold. The horizontal cross-section and vertical cross-section samples were cut at the bottom, middle and top of the ingot, respectively. The samples were polished and then observed with optical microscope. The elements distribution along the thickness direction of the ingot is analyzed by chemical composition analysis.
Schematic diagram of plane solidification casting with movable sprues: (a) The initial stage of casting; (b) stable stage of casting. 1, melt; 2, insulation board; 3, water-cooled steel plate; 4, liquid layer; 5, semi-solid layer; 6, solid layer; 7, water mist; 8, movement direction of movable sprues; 9, movement direction of mold.
In order to make the melt flow into the mold evenly, two types of fixed and two types of movable sprues were designed to optimize the feeding system, as can be seen in Fig. 3. For the fixed sprues, melt is poured onto shunt plate and dispersed into the mold. As shown in Fig. 3(a), the shunt plate is fixed in the center of the mold; as shown in Fig. 3(b), the shunt plate is divided into two halves and fixed on both side of the mold. For the movable sprues, melt is divided into several pieces in chutes and poured into mold directly through sprues. These sprues are limited to reciprocating in horizontal direction. The movable sparse feeding system with four big sprues are shown in Fig. 3(c), and for the movable dense feeding system, as shown in Fig. 3(d), the four sprues are changed to twelve small sprues so the melt is more dispersed when entering the mold. As shown in the coordinate system in Fig. 3, the xy plane is a cross section and the Z axis is the height direction.
Feeding system models used in numerical simulation: (a) fixed middle splitter; (b) fixed side splitter; (c) movable sparse sprues; (d) movable dense sprues.
Based on Fig. 2, a three-dimensional transient state model was established to describe the effect of sprue distributions on the melt flow and temperature field during the casting. In order to reduce the amount of calculation, the computational domain could be reduced according to the symmetry of the 3D model. A quarter of the mold is used as computational domain for the fixed sprues, and to ensure entirely display the sprues movement, half of the mold was used for the movable sprues.
2.2.1 Governing equationsBased on the continuum mixture model of melt and heat flow for the solid–liquid material proposed by Bennon and Incropera13,14), computational domain is not directly divided into solid region, semisolid region and liquid region. Instead, a single-domain was used to define all regions implicitly. The control equations are applied to computational domain, and the temperature distribution and flow velocity were obtained by solving the model equations. An equivalent specific heat method was used to treat the latent heat of crystallization, and the Darcy model was used to treat fluid flow in the semi-solid region. The conversation equations are expressed as follows.
Conservation equation of mass:
| \[\frac{\partial \rho}{\partial t} + \nabla \cdot(\rho U) = 0\] | (1) |
Conservation equation of momentum:
| \[\frac{\partial(\rho U)}{\partial t} + \nabla \cdot(\rho UU) = \nabla \cdot(\mu_{\rm eff} \nabla U) - \nabla P + S_m\] | (2) |
| \[(\rho - \rho_0)g \approx - \rho_0 \beta(T - T_0)g\] | (3) |
Where $\rho _0$ (constant) is the density of the flow, $T_0$ is the operating temperature, and $\beta$ is the thermal expansion coefficient.
Conservation equation of energy:
| \[\frac{\partial(\rho T)}{\partial t} + \nabla \cdot (\rho UT) = \nabla \cdot \left(\frac{k}{c_{\rm p}} \nabla T \right) + S_{\rm th}\] | (4) |
In this equation, $S_{\rm th}$ is thermal source which includes Joule heat and latent heat of solidification, $c_p$ is equivalent specific heat.
Low-Reynolds number k–ε model was applied in the whole domain to account for the solidification phase change15). The damping of turbulence in the mushy region is achieved using a Darcian term in this model. The transport equations for k and ε was written as follows:
| \[\frac{\partial(\rho k)}{\partial t} + \nabla \cdot(\rho Uk) = \nabla \cdot \left[ \left( \mu_{\rm l} + \frac{\mu_{\rm l}}{\sigma_{\rm k}} \right) \nabla k \right] + G_{\rm k} - \rho \varepsilon - S_k\] | (5) |
| \[ \begin{split} & \frac{\partial (\rho \varepsilon )}{\partial t} \nabla \cdot (\rho U \varepsilon) \\ & \quad = \nabla \cdot \left[ \left(\mu_{\rm l} + \frac{\mu_{\rm l}}{\sigma_{\rm \varepsilon}} \right) \nabla \varepsilon \right] + 1.44 \cdot \frac{\varepsilon}{k} G_{\rm k} - 1.92 \cdot \rho \frac{\varepsilon^2}{k} - S_{\rm \varepsilon } \end{split} \] | (6) |
Where $G_{\rm k}$ represents the generation of turbulence kinetic energy due to the mean velocity gradients, $\sigma _{\rm k}$ and $\sigma_{\rm \varepsilon }$ are the turbulent Prandtl numbers for k and ε. In this equation, the values are constants 1.0 and 1.3, respectively. $S_{\rm k}$ and $S_{\rm \varepsilon}$ are source terms for k and ε, respectively.
2.2.2 Material propertiesIn this paper, materials properties of 7050 alloy for mathematical model were calculate by materials properties simulation software JMatPro. The calculate result of specific heat, thermal conductivity and fraction solid were shown in Fig. 4. Other constant properties were shown in Table 1.
materials properties of 7050 alloy for mathematical model: (a) specific heat; (b) thermal conductivity; (c) fraction solid.
| Density, ρ | 2453 Kg/m3 |
| Liquidus temperature, Tl | 907 K |
| Solidus temperature, Ts | 735 K |
| Volume expansion coefficient, β | 6 × 10–51/K |
| Initial permeability, K0 | 2 × 10–11 m2 |
| Solid fraction of dendrite contact, f * | 0.3 |
| Reference temperature, T0 | 887 K |
Figure 3 shows all boundaries setting on the computational domain. The boundary conditions are described as follows.
Inlet boundary. The inlet velocity is calculated from the casting velocity according to the principle of equal mass flow. When the casting velocity is 0.0003333 m/s (20 mm/min), the details of inlet boundary conditions for four feeding system are listed in Table 2.
| style | Velocity (m/s) |
Temperature | Turbulent kinetic energy |
Turbulent dissipation rate |
|---|---|---|---|---|
| fixed middle splitter | 0.06667 | 973 K | 4.44E-5 | 9.88E-5 |
| fixed side splitter | 0.06667 | 973 K | 4.44E-5 | 5.93E-5 |
| movable sparse sprue | 0.09554 | 973 K | 9.13E-5 | 8.72E-5 |
| movable dense sprue | 0.08493 | 973 K | 7.21E-5 | 8.17E-5 |
Cooling boundary. Cooling boundary is treated as Cauchy-type boundary condition, which is formulated according to eq. (7). The heat exchange on the boundary is determined by the heat transfer coefficient (HTC) and free stream temperature.
| \[k_{\rm thermal} \frac{\partial T}{\partial n} = h(T - T_{\rm st})\] | (7) |
Where $T_{st}$ is free stream temperature and its value is 320 K. During the planar solidification, the heat transfer distance increases as the casting height increases. Steel plate cooling, water mist cooling and water column cooling were used for cooling boundary to maintain the solidification rate of the melt. In the initial stage of casting, steel plate cooling was used, then the water mist cooling was applied instead of steel plate cooling after the formation of solid shell. At the final stage, water column cooling mode was used to increase the cooling intensity. The heat transfer coefficients (HTCs) were obtained by inverse algorithm16) and then corrected by the MAP algorithm17). An aluminum alloy ingot was heated to a certain temperature and then cooled to ambient temperature with different cooling modes respectively, the HTCs according to the temperature measurements for all cooling modes are shown in Fig. 5.
Heat transfer coefficient in the cooling region.
Moving boundary. The dynamic mesh technique was used to simulate the growth of ingot. The cooling boundary is also set as a moving rigid body, and the movement of the boundary simulated the elongation of the ingot. The speed of moving boundary is equal to the casting speed.
Interface boundary. In order to achieve the movement of the sprue, the computational domain is divided into the sprue zones and mold zone in which the sprue zones can reciprocate relative to the mold zone. The contact surface between sprue zones and mold zone is set as Interface to make the temperature field and the flow field continuous. The movement of the sprue zones is equivalent to the movement of the sprues, and the speed is set to 0.08 m/s.
The simulation parameters set in the casting process are demonstrated as follows. The casting speed is controlled to 0.0003333 m/s (20 mm/min) throughout the process, and the final casting height is 150 mm. The casting process is divided into three stages. In the initial casting stage with the height of ingot 10 to 50 mm, the cooling boundary is set as steel plate cooling. In the second stage of casting with the height 50 to 100 mm, the cooling boundary is set as water mist cooling. In the final stage of the casting, water column cooling is used to provide larger cooling intensity to ensure a uniform solidification rate as the heat transfer distance increases.
The temperature fields of ingots with at the end of initial casting stage is shown in Fig. 6, where (a), (b), (c) and (d) are fixed middle splitter, fixed side splitter, movable sparse sprues and movable dense sprues, respectively. In the legend, the scale 899 K, 890 K, 846 K and 735 K are the temperature corresponding to the solid fraction of 0.3, 0.5, 0.8 and 1, respectively. For the fixed sprues, as shown in Fig. 6(a)–(b), the support layer under the sprues is eroded by melt. In areas around the sprue, liquid cave is formed because of long period of eroding. The presence of liquid sump on the support layer tends to cause leakage of the melt after removing the steel plate at the end of initial stage. And this leakage is difficult to remove by changing the position of fixed sprues. In areas away from the sprues, the temperature and flow capacity of melt decrease as the distance of melt flow increases, making it difficult to evenly fill the mold. The temperature field of movable sprues were shown in Fig. 6(c)–(d). It can be seen that movable sprues are significantly superior to fixed sprues. The isotherms of the melt in the mold at different temperatures become planar. The eroding of fresh melt is dispersed throughout the mold with the moving of sprues, making it difficult to form a liquid sump. For movable dense sprues, as the sprues are more dispersed, the melt can be directly poured into each position of the mold, which significantly reduce the requirements of melt flow. The shape of the underside of the liquid layer is slightly undulating, and the solidification front is relatively flat, which allow the casting to proceed smoothly to the next stage.
Temperature fields of simulated results at height of 50 mm: (a) fixed middle splitter, (b) fixed side splitter, (c) movable sparse sprues, (d) movable dense sprues.
The temperature fields and flow velocity fields of ingot at the end of second stage are shown in Fig. 7 and Fig. 8 respectively. As shown in Fig. 7 (a)–(b), the thickness of the support layer increases along with the casting progress, while the shape of liquid sump of fixed sprues change little. In the areas away from sprues, the temperature is low due to the long period insufficient feeding. Different colors are used to mark the melt flow rate in Fig. 8. The green or even yellow vector arrows near the sprues indicate that greatest melt flow rate is obtained at the sprues and melt flow rate decreases rapidly with increasing in distance to sprues. For fixed sprues, as shown in Fig. 8(a)–(b), the fresh hot melt directly flow into the liquid sump and is blocked by semi-solid layer to form an eddy, and then the melt will upward reflow to the top of ingot to fill the mold. The melt flow rate is significantly reduced after the reflux, which resulting in insufficient mold filling capacity. For movable sparse sprues as shown in Fig. 7(c) and Fig. 8(c), with the increase of the height the isotherm surface become flat. The fresh melt can directly flow into the mold by the moving sprues, which significantly reduces the size of the eddy. With the increasing in number of sprues, the interval between the sprues decreases. For movable dense sprues as shown in Fig. 7(d) and Fig. 8(d), the results show that the fresh flows mainly horizontally after pouring into the mold, resulting in a to reduction in the impact on the semi-solid layer. Thus, the horizontal temperature isotherms of the melt is obtained.
Temperature fields of simulated results at height of 100 mm: (a) fixed middle splitter, (b) fixed side splitter, (c) movable sparse sprues, (d) movable dense sprues.
Flow velocity fields of simulated results at height of 100 mm: (a) fixed middle splitter, (b) fixed side splitter, (c) movable sparse sprues, (d) movable dense sprues.
Figure 9 shows the temperature fields under different feeding system at the end of final stage. The 735 K (solid fraction is 1.0) isothermal surface are relatively flat under four kinds of sprues, but there are still significant differences in liquid layer and semi-solid layer. An isothermal surface with a solid fraction of 0.3(i.e. the solid fraction of dendrite coherency point) is used as the solidification front. In order to quantitatively compare the effects of each feeding system on the melt temperature field, the profiles of the solidification front are extracted from the simulation results, as shown in Fig. 10. The position of the profiles is indicated in Fig. 3. For fixed sprues, the profiles of the melt solidification front fluctuate wildly in the width direction, but the fluctuation tends to become gentle as the casting progresses. Since the melt is only gently cooled in a single direction from the bottom, the cooling effect around the bottom of liquid sump cannot be ignored. As the bottom of the liquid sump is subject to a larger cooling intensity, the deepening of the liquid sump is suppressed. The results indicate that the melt feeding by different sprues has a tendency to solidify as planar solidification in the unidirectional cooling. For movable dense sprues shown in Fig. 10, the height of the solidification front stably maintain at 30 mm, and the height difference of solidification front is less than 2 mm. The solidification front can be obtained by movable dense sprues.
Temperature fields of simulated results at height of 150 mm: (a) fixed middle splitter, (b) fixed side splitter, (c) movable sparse sprues, (d) movable dense sprues.
The profiles of solidification front under ecah feeding systems: (a)initial stage, (b) second stage, (c) final stage.
Base on simulation results, the feeding system with movable dense sprues is superior to other feeding systems and reduces the possibility of leakage during the casting.
3.2 Verification of the mathematic modelAccording to the simulation results, movable dense sprues was used for planar solidification and the temperature of the ingot was recorded. Figure 11 shows the calculated and the measured results at the height of 40 mm, 80 mm, and 120 mm. The temperature measuring point is shown by the arrow 1 in Fig. 12(a). In order to reduce the internal stress, cooling was terminated after the melt completely solidified instead of cooling to ambient temperature. The results show that the simulation results are basically accurate compared with the experimental results. The cooling rates of the melt at the height of 40 mm, 80 mm and 120 mm from the initial temperature to the solidification temperature were calculated to quantify the difference, and the results were 0.42 K/s, 0.41 K/s and 0.37 K/s, respectively. Cooling rate of melt at height of 120 mm position is smaller because the curve ended at 777 K and the cooling rate gradually increases with the decrease of temperature. This indicates that the ingot has similar cooling intensity at different locations. Compared with semi-continuous casting, the cooling rate of the planar solidified ingot is more uniform.
Comparison between the measured and calculated temperature results.
The macro morphology of the top and bottom surfaces of the ingot: (a) top surface; (b) bottom surface.
Figure 12 shows the macro morphology of the top and bottom surfaces of the planar solidified ingot. As shown in Fig. 12 (a), despite the large ingot size, there is no significant V-shaped shrinkage on the top of the ingot, indicating that there is no liquid cave occurred during the casting process. As shown in Fig. 12 (b), at the bottom of the ingot, the cooling surface is flat without collapse, revealing that the semi-solid layer has sufficient support strength when the cooling steel plate was withdrew. The area indicated by arrow 2 is the support surface which support the ingot after the withdrawal of the cooling steel.
The microstructure of horizontal cross-section and vertical cross-section specimens is shown in Fig. 13. The samples are cut vertically from the ingot at the position indicated by arrow 3 shown in Fig. 12. The microstructure consists of coarse dendritic primary α(Al) surrounded by interdendritic secondary phases and some equiaxed grains. No obvious variation and columnar crystal is observed both at the horizontal cross-section and vertical cross-section of ingot. In addition, defects such as oxide inclusions are not found, due to the smooth flow of the melt during the casting process.
Microstructure of ingot in cross section (a), (b), (c) and longitudinal section (d), (e), (f) : (a) (d) 40 mm, (b) (e) 80 mm, (d) (f) 120 mm.
The grain size was measured using the mean linear intercept method and the results are given in Fig. 14. The results reveal that the grain size in different regions are nearly uniform, and the average grain size of different regions of the ingot is 312.3 μm. The grain size of the horizontal cross-section is slightly smaller than the vertical cross-section, which indicates that the longitudinal heat transfer during the solidification makes the grain grow more favorable in the longitudinal direction. For DC casting ingots, the grain size varies greatly from the edge to the center of the ingot, for example, from 100 μm to 300 μm as pointed by Haghayeghi3), while the grain size of planar solidification ingot fluctuates by 30 μm.
Grain size on different section of planar solidification ingot.
The chemical compositions distribution along the thickness direction of the ingot at intervals of 10 mm are shown in Fig. 15. The results show that all major alloying elements of the ingot are very uniform. This is a very significant improvement over conventional DC casted ingot in which about 8% of the negative macrosegregation is generally present at T/2 location. This advantage is attributed to the planar solidification front without thermal convection and floating crystals which are usually presented in the DC casting. Therefore, the macroscopic segregation of the alloying elements is reduced.
Composition profile of planar solidification ingot through thickness.
A three-dimensional mathematic model for planar solidification casting is presented and was used to simulate casting process with different sprue distributions. The simulation results show that the feeding system is an important factor to realize the planar solidification casting. For the fixed sprues, the melt is difficult to uniformly fill the mold whether the gate is placed in the middle or both sides when the ingot cross-sectional size is large. Movable sprues greatly reduced the requirement of melt flowability during casting and distribute the scour of the fresh melt evenly throughout the mold. With movable dense sprue, the uniform temperature field and flat solidification front are observed during planar solidification process.
The ingot in size of 600 × 600 mm is fabricated successfully using movable dense sprue. It is found that there is a good agreement between the calculated and the measured results which verify the reliability of the mathematical model. There is no V-shaped shrinkage at the top of the ingot and no collapse at the bottom. In the cooling direction, the microstructures of the cross section and the longitudinal section at different positions are significantly comparable, and the whole structure was uniform. In addition, the variability of the composition throughout thickness is also minimized.
The authors gratefully acknowledge the supports of Natural Science Foundation of Liaoning Province of China (Grant number 2014020031) and the doctoral foundation of China Ministry of Education (Grant number 20130042130001).
T Temperature, K
t Time, s
ρ Density, kg/m3
μl Laminar viscosity, Pa s
μt Turbulent viscosity, Pa s
μeff Effective viscosity, Pa s
k Turbulence kinetic energy, m2/s2
Sk Source terms for k
Gk Generation of k
T0 Operating temperature, K
β Volume expansion coefficient, 1/K
cp Equivalent specific heat, J/(kg K)
Sm Momentum source, kg/(m3 s)
Sth Thermal source, J
c Specific heat capacity, J/(kg K)
ε Dissipation rate, m2/s3
Sε Source terms for ε
h Heat transfer coefficient, W/(m2 K)
