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Simulation on solidification of an Al-Ni alloy under electromagnetic stirring

Female, born in 1976, Master, Associate Professor. Her research interests mainly focus on metal solidification process and numerical simulation.E-mail: hongsmh_116@163.comReceived: 2011-08-25; Accepted: 2012-04-27

*Sha Minghong

*Sha Minghong 1, 2, Wang Tongmin 2, Bai Fudong 3, Li Jun 4 and Li Tingju 2

(1. School of Materials and Metallurgy, University of Science and Technology Liaoning, Anshan 114051, China; 2. School of Materials

Science and Engineering, Dalian University of Technology, Dalian 116085, China; 3. Sinopec Fushun Research Institute of Petroleum

and Petrochemicals, Fushun 113001, China; 4. Simulation and Modeling of Metallurgical Processes, Department of Metallurgy,

University of Leoben, A-8700 Leoben, Austria)

Nickel-a luminum intermetal l ic compounds have attracted much attention in the area of materials.

NiAl and Ni3Al are considered candidate materials for high temperature applications [1-2]. Al3Ni and Al3Ni2 have been used as precursor alloys of skeletal catalyst for decades in the chemical industry [3-4]. As is well known, the microstructure of Al-Ni alloy has a significant influence on its performance. Electromagnetic field (EMF), as a new tool for material structure and function control, has been widely used in the field of material research [5-8]. Electromagnetic stirring (EMS) is one of the most suitable forms of EMF in material process because of its advantages of high energy density, non-contact and easy control. Li Tingju et al. [9-11] has successfully applied EMS to horizontal continuous casting of hollow copper billets. Numerical simulation has been widely proven to be a highly efficient and environmentally friendly method in processing optimization, performance prediction, etc. Bennon W. D. et al. [12] built a continuum model for momentum, heat, and species transport in a binary solid-liquid phase change system. Lalpoor M. et al. [13] built a model by thermo-mechanical simulation of residual thermal stresses and application of fracture mechanics to investigate the cold cracking of aluminum 7050 billets during DC casting.

Abstract: The microstructure of Al-Ni alloy has a significant influence on its performance, while electromagnetic stirring is one of the most effective methods for control of solidification structure of Al alloy. To investigate the effect of electromagnetic stirring on the solidification of the ingot, the solidification of the Al-50Ni alloy in vacuum with electromagnetic stirring was described by numerical simulation in this paper; and a three dimensional mathematical model was established. The electromagnetic field was simulated by ANSYS software and the thermal-flow field was simulated by FLUENT software. The coupling between the electromagnetic field and the thermal-flow field was implemented by user-defined subroutines. It is found that the current intensity has significant influences on the fluid flow and the microstructure of the alloy. The simulation results agree well with the experimental results, and the optimum current intensity under the exprimental conditions is 80 A, while the frequency is 50 Hz.

Key words: electromagnetic stirring; numerical simulation; Al-Ni alloy; solidificationCLC numbers: TG146.2+1/TP391 Document code: A Article ID: 1672-6421(2012)03-258-05

In this study, a three dimensional mathematical model was established to investigate the effect of EMS on the solidification of the Al-50Ni alloy ingot. The electromagnetic field was simulated by ANSYS software and the thermal-flow field was simulated by FLUENT software. The coupling between the electromagnetic field and the thermal-flow field was implemented by a user-defined subroutine. The influences of current intensity on the temperature field, flow field and microstructure of the Al-50Ni ingot were discussed.

1 Mathematical modelContinuity equation:

(1)

Momentum equation:

(2)

where ρ is density of liquid melt; ui, uj are time average velocities; μ eff is effective viscosity coefficient; gi is gravitational acceleration; and Fi is momentum source.

Energy equation:

(3)

where T is temperature; cp is specific heat at 1 bar atmospheric pressure; cl is liquid specific heat; fl is liquid rate; u→ is fluid velocity; keff is effective thermal conductivity; and q

3

is thermal source.

k-ε equation:

tk

eff

efflfl

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(5)

where k is turbulent energy; ε is dissipation rate; Gk is turbulent energy induced by average velocity gradient; Gb is turbulent energy induced by buoyancy; m is dynamic liquid viscosity; s k, sε are respectively the turbulent Prandtl number of k and ε . Cm,

C1ε, C2ε and C3ε are all constants. ; Cμ = 0.09; C1ε =

1.44; C2ε = 1.92; C3ε = 0.09; s k = 1.0; and Cε = 1.3. The effect of pulse expansion of compressible flow on dissipation rate is neglected.

Electromagnetic force equation:

(6)where B

→ is the magnetic flux density and is the current

density.

2 Experimental procedureThe metal for experiment is Al-50Ni (wt.%) alloy. The experimental apparatus consists of stainless steel mold, electromagnetic stirrer and stainless steel sleeve. The finite element model based on the experimental apparatus is shown in Fig. 1 and the origin of coodinates is the center of the electromagnetic stirrer. A round ingot was employed and its dimensions were Φ 78 mm and height 150 mm. The experimental conditions were that the ingot solidified in vacuum and the pouring temperature was 1,740 K. The current intensities employed for electromagnetic stirring are 40 A, 80 A and 140 A, and the frequency is 50 Hz. The thermo-physical properties and thermodynamic parameters of the experimental Al-50Ni alloy are listed in Table 1.

Fig. 1: Finite element model

Fig. 2: Comparison of calculated and measured magnetic flux density (B) without load

Table 1: Thermophysical properties and thermodynamic parameters of the Al-50Ni alloy

Parameters Value

Density, ρ (Kg·m-3) 4,750

Specific heat, cp (J·Kg-1·K-1) 105.4 – 154.3

Thermal conductivity, l (W·m-1·K-1) 64.1 – 88.9 Liquidus temperature, TL (K) 1,613 Solidus temperature, TS (K) 1,406

Latent heat of fusion, L (J·Kg-1) 220,000

Dynamic viscosity, m (Kg·m-1·s-1) 1.13×10-3 – 0.05 Coil turns 36

1 - Ingot, 2 - Stainless steel mold, 3 - Electromagnetic stirrer, 4 - Stainless steel sleeve

pole of the stirrer. The BRx, BRy and BR values are the calculated results of magnetic flux density for x-component, y-component, and resultant, respectively, along the radial direction. The BRx-M, BRy-M and BR-M values are the corresponding measured results. It shows that the simulated results are in agreement with the measured ones.

Figure 3 shows the temperature profiles of the ingot in the y-z plane (x=0) without or with EMS when the freezing time is 86 s. The digital in the temperature profiles of Fig. 3 and Fig. 4 represents the liquid fraction. As seen in Fig. 3(a), the thermal center in the y-z plane is about 40 to 50 mm under the liquid level without EMS. It indicates that the ingot can have shrinkage cavities. Comparison of the temperature profiles in Fig. 3(a) and Figs. 3(b), (c), (d) indicates that the freezing rate increases when the current is 40 and 80 A, while it decreases a little when the current is 140 A. The former is because the EMS increases the fluid flow and makes the temperature field uniform, which enhances the heat transfer of the fluid. The latter is because the strong turbulence [14] and joule heat decrease the freezing rate. The thermal center is near the liquid level (10 to 15 mm) from the contours in Figs. 3(c) and (d), which indicates there will be no shrinkage cavities in the ingots. While, the thermal center is about 20 to 30 mm under the liquid level in Fig. 3(b); it means that the current intensity is not large enough and the ingot may have shrinkage cavities.

Figure 4 shows the temperature profiles and velocity vectors in the x-y plane (z=0) when the freezing time is 12 s. The fluid flow without EMS is negligible, since it mainly depends on natural convection. It is observed that the flow velocity is increased with the increase of the current intensity. The maximum stirring velocities are 1.0 m·s-1, 2.2 m·s-1, 4.0 m·s-1

(4)

3 Results and analysisThe comparison of magnetic flux density (I = 80 A, f = 50 Hz) between the calculated results and the measured ones are shown in Fig. 2. The numbers 1, 2, 3 and 4 represent the measurement points between the center and the magnetic

b

b

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Fig. 3: Temperature profile and liquid fraction of the ingot in the y-z plane (x=0, freezing time = 86 s, f = 50 Hz): (a) No EMS; (b) I = 40 A; (c) I = 80 A; (d) I = 140 A

(a) (b)

(c) (d)

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Fig. 4: Temperature profile and velocity vectors of the ingot in the x-y plane (z=0) (Time = 12 s, f = 50 Hz): (a) and (b) I = 40 A; (c) and (d) I = 80 A; (e) and (f) I = 140 A

Fig. 5: Temperature (a) and velocity distribution (b) along the radial direction (z=0, x=0) of the ingot (time = 12 s, f = 50 Hz)

on the billet surface and 0.2 m·s-1 in the billet center (x=0, z=0) in Figs. 4 (b), (d), and (f), respectively. The temperature profiles in Figs. 4(a), (c), and (e) indicate that the temperature distribution is uniform from the surface to center of the billet with EMS; and that the metal in the freezing range is markedly stirred in Figs. 4 (c) and (e). Vogel et. al. [15] proposed that low temperature gradient can increase nucleation rate and refine primary phase. It means that the uniform temperature field caused by EMS can refine the grains of the ingot.

The temperature and velocity distribution along radial (y) direction (x=0, z=0) of the ingot in the early solidification are shown in Fig. 5. As seen in Fig. 5(a), the temperature gradient between the center and edge of the ingot is large without EMS. Under EMS, the temperature curves become more even with a current intensity from 40 A to 140 A due to the larger flow circulation caused by the electromagnetic force. The cooling speed is the fastest when the current intensity is 80 A and is the slowest when the current intensity is 40 A, which matches

with the result mentioned in relation to Fig. 3. It is observed in Fig. 5(b) that the maximum fluid flow velocity which appears near to the ingot surface increases with increasing the current intensity. Bai Fudong et al.[16] have verified that there is no obvious shrinkage cavity in the ingot when the current intensity is 80 A, while there are cavities in the ingot without EMS and the ingot with a current intensity of 140 A. It is concluded that EMS can enhance the heat transfer of the fluid and have a great influence on the formation of cavities. Appropriate EMS can eliminate cavities effectively; however, cavities can reappear when the electromagnetic force is too big to allow the melt to feed. Under the present experimental condition, the optimum current density is 80 A when the frequency is 50 Hz. Besides, the fluid flow caused by EMS can increase the shear rate of the fluid. Flemings et al. [17] pointed out that high shear rate caused by stirring can promote the dissolution and breaking of the dendrite. So that EMS can also refine the grain.

(a) (b)

To validate the simulation results, the microstructures of the Al-50Ni alloy ingot have been observed and are shown in Fig. 6. It can be seen that the microstructure is dendrites with shrinkage porosities without EMS in Fig. 6(a) and fine equiaxed grains with EMS (I = 80 A, f = 50 Hz) in Fig. 6(b). It is shown that with EMS, the microstructure is obviously refined and more compact, which agrees well with the numerical simulation results.

4 ConclusionA three dimensional mathematical model has been established to investigate the effects of EMS on the solidification process of Al-Ni alloy round ingot. The simulation results agree well with the experimental results. EMS homogenizes the temperature field, alters the flow field and refines grain size. The optimum

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current intensity is 80 A while the frequency is 50 Hz. In this case, the maximum stirring velocity is 2.2 m·s-1 on the billet surface and 0.2 m·s-1 in the billet center (x=0, z=0), and the microstructure is compact and fine equiaxed grains.

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[10] Li Xintao, Guo Zhaoxiang, Zhao Xiangwei et al. Continuous casting of copper tube billets under rotating electromagnetic field. Materials Science and Engineering A, 2007, 460-461(15): 648-651.

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[14] Wu Menghuai, Vakhrushev A, Nummer G, et al. Importance of melt flow in solidifying mushy zone. The Open Transport Phenomena Journal, 2010, 2: 16-23.

[15] Vogel A, Doherty R D, Cantor B. Stir-cast microstruture and slow crack growth. In: Proceedings of International Conference on Solidification. The Metals Society, London, 1979, 518-525.

[16] Bai Fudong, Sha Minghong, Li Tingju, et al. Influence of rotating magnetic field on the microstructure and phase content of Ni-Al alloy. Journal of Alloys and Compounds, 2011, 509 (14): 4835–4838.

[17] Flemings M C. Behaviour of metal alloys in the semi-solid state. Metallurgical Transactions A, 1991, 22(5): 957-981.

This study was financially supported by the National Natural Science Foundation of China (No.50971032, No.50874022 and No.50601003), the New Century Excellent Talents in University (NCET-07-0137), the Scientific Research Fund of Liaoning Provincial Education Department, and the Specialized Research Fund for the Doctoral Program of Higher Education (No.20112120120003).

Fig. 6: Microstructures of Al-50Ni ingot (a) without and (b) with EMS (I = 80 A, f = 50 Hz)

(a) (b)

Shrinkage porosities