Studies on Transport Phenomena during Continuous Casting of an Al

Trans Indian Inst Met (April 2013) 66(2):141–146 DOI 10.1007/s12666-012-0205-y

TECHNICAL PAPER

TP 2656

Studies on Transport Phenomena during Continuous Casting of an Al-Alloy in Presence of Electromagnetic Stirring S. Simlandi • N. Barman • H. Chattopadhyay

Received: 29 June 2012 / Accepted: 13 September 2012 / Published online: 13 December 2012 Ó Indian Institute of Metals 2012

Abstract In the present work, a numerical study is performed to predict the transport phenomena during continuous casting of an aluminum alloy (A356) in presence of weak stirring. A set of volume averaged single phase conservation equations (mass, momentum, energy and species) is used to represent the casting process. The electromagnetic forces are incorporated in the momentum equations. The governing equations are solved based on the pressure-based finite volume method according to the SIMPLER algorithm using TDMA solver along with an enthalpy update scheme. The simulation predicts the temperature, solid fraction and species in the computational domain. A parametric study is also performed. Keywords Continuous casting Weak stirring Transport phenomena Macrosegregation

1 Introduction It is observed that most alloy elements have a lower solubility in solid than in liquid phase as found in a binary phase diagram. During solidification, therefore, the solute is rejected into the liquid, which mixes with the bulk liquid by diffusion on a local scale (known as micro-segregation) and by convection on a larger scale (known as macro-segregation). In conventional castings, both the segregations result non-uniform distribution of solute in the cast alloy. The solute-rich region is called positive segregation whereas solute-lean region is termed as negative segregation [1]. The positive segregation is generally

observed in the solid that forms at the later stages of the solidification. The non-uniform distribution of the solute in the cast results in non-uniform mechanical properties [2]. An effort to prevent the non-uniformity in solute distribution will mainly involve controlling of fluid flow during casting. In this context, Barman and Dutta [3] presented a study on the solute concentration fields during solidification in presence of double diffusive convection. It is found that the double diffusive convection reduces in-homogeneity in solute concentration in the liquid phase as well as in the cast. Fluid flow may also be enhanced further by introducing the electromagnetic forces. Zhang et al. [4] studied the influence of electromagnetic forces on the macrosegregation in continuous casting of aluminum alloy. They found that the electromagnetic stirring reduces non-uniformity in the solute distribution. Dong et al. [5] produced a fine and uniform ingot at low-frequency electromagnetic stirring and found that the macrosegregation is greatly reduced. Hence, in application of electromagnetic stirring during casting, the non-uniformity in solute concentration may be minimized. Casting in presence of electromagnetic stirring has attracted a great deal of attention in the recent years, especially in the production of non-dendritic billets [6]. Such applications require vigorous stirring to facilitate fragmentation of dendrites. However, in the present work, only a weak electromagnetic stirring is considered which would influence macrosegregation. Al-7.32 % Si alloy is considered here for its high fluidity, low shrinkage and light weight properties, and also widely used in industrial applications.

2 Description of Physical Problem S. Simlandi N. Barman (&) H. Chattopadhyay Department of Mechanical Engineering, Jadavpur University, Kolkata 700032, India e-mail: [email protected]

Figure 1a shows a schematic diagram of a continuous casting system which comprises of a mold of diameter 53.34 cm. An electromagnetic stirrer of 10 cm height is

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considered at the top and outer side of the mold. The stirrer having a stack of coils around the mold generates a force field along the longitudinal direction (a linear stirrer). In the present case, a weak electromagnetic stirring is considered and hence, the dendritic fragmentation is ignored. A cooling arrangement is considered similar to a conventional continuous casting process below the stirrer. A primary cooling water jacket is considered to cool the melt first. The primary cooling water is also jetted out and impinged directly on the emerging surface of the billet. The molten metal is poured continuously into the mold through an opening of 12.70 cm at the top with a constant velocity. During cooling, the molten metal is solidified in presence of weak stirring resulting in redistribution of solute. The solid billet is drawn at a constant casting speed. In this study, Al-7.32 % Si alloy is considered. The thermophysical properties of the alloy are given in Table 1. Based on the system geometry, an axi-symmetric computational domain is considered here as shown in Fig. 1b. The height of the domain is 70 cm.

3 Mathematical Modelling The solidification process is represented by a set of volume averaged single phase mass, momentum, energy and species conservation equations. The stirring effect is incorporated considering body force terms in the momentum equations. In the present work, the flow is considered incompressible and laminar. Solidification shrinkage is also Fig. 1 a A schematic of the physical problem and b an axi-symmetric computational domain

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neglected. The governing equations for the macroscopic transport in the cylindrical coordinate are as follows: 3.1 Conservation of Mass oq þ r:ðqUÞ ¼ 0 ot

ð1Þ

3.2 Conservation of Momentums [2] 2 oðquÞ Þ ¼ r:ðlruÞ oP Að1 fl Þ u þ Fr þ r:ðqUu ot or ðfl þ bÞ ð2Þ 2 oðqvÞ Þ ¼ r:ðlrvÞ oP Að1 fl Þ v þ r:ðqUv ot oz ð f l þ bÞ þ qo g½bT ðT To Þ þ bs ðC Co Þ þ Fz

ð3Þ where u = flul ? fsus and v = flvl ? fsvs are the superficial velocity components. In Eqs. (2–3), A is a constant (1.6 9 106) and b is a computational constant (1 9 103) introduced to avoid division by zero. Fr and Fz are the Lorentz force components representing the electromagnetic stirring during solidification. The applied electromagnetic force field (Fr and Fz) is introduced in the simulation considering an analytical solution given by Milind and Ramanarayanan [8], which is also used by Barman et al. [7] successfully. The present work considers the same analytical solution.


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3.5.1 Top Surface

Table 1 The thermo physical properties of A356 [7] Properties

Values

Density of liq. phase (qs)

2,685 kg/m3

Density of sol. phase (ql)

2,685 kg/m3

Liq. thermal conductivity (kl)

60 W/mK

Sol. thermal conductivity (ks)

160 W/mK

Sp. heat of the liquid (cpl)

963 J/kg K-1

Sp. heat of the solid (cps)

963 J/kg K-1

Latent heat of fusionc (La)

3.97 9 105 J/kg

T = Ti, Cl = Ci and fs = 0. u = 0, v = -vin for inlet opening. u = 0, v = 0 for other locations on the top surface. 3.5.2 Bottom Surface u = 0, v = -vcast, qT/qz = 0, qCl/qz = 0 and fs = 1. 3.5.3 Right Wall

Partition coefficient (kp)

0.13

Eutectic temp. (Te)

568 °C

Eutectic conc (Ce)(% Si)

12.6

Solvent melting temp. (Tm) Th. exp. coeff. (bT)

660 °C 2.10 9 10-5 K-1

Solutal exp. coeff. (bs)

0.025

u = v = 0, -kqT/qr = h(Tw - Tcw), qCl/qr = 0. The heat transfer coefficient for cooling of the billet is considered as given in Vreeman et al. [2]. 3.5.4 At Axis

r sin 2½xt ð2pLs =tÞ Rb 2

ð3aÞ

r 2 1 cos 2½xt ð2pLs =tÞ 2 R2b

ð3bÞ

Fr ðz; r; tÞ ¼ l0 J0 H0 Cr2 Fz ðz; r; tÞ ¼ l0 J0 H0 Cr

where l0 is the magnetic permeability of the working medium, H0 is magnetic intensity of excitation field, J0 current density, LS stirrer length, Rb billet radius, r radius and Cr corresponds to end effects (*0.42). 3.3 Conservation of Energy [2] oðqT Þ Þ ¼ r:ðkrT Þ þ r:ðqUT ot oðqfl DH Þ þ r:ðqUDH Þ ot

ð4Þ

where the latent heat content (DH) is updated considering the enthalpy updates scheme. 3.4 Conservation of Species In the present work, the diffusion of solute in solid and liquid is neglected [9]. Hence, the species conservation equation is considered as oðqCl Þ l Þ ¼ o ð qs f s C s Þ þ r:ðqUC ot ot

ð5Þ

where the Scheil equation is used to calculate Cs. 3.5 Initial and Boundary Conditions The boundary conditions consistent with the above set of differential equations used in the context of the geometry as shown in Fig. 1b are as follows:

u = 0, qv/qr = 0, qT/qr = 0, qCl/qr = 0. The initial conditions chosen for the physical problem are T = Ti, Cl = Ci and fs = 0 at t = 0. The above governing equations along with the initial and boundary conditions are solved with a pressure-based finite volume method according to the SIMPLER algorithm using TDMA solver. The enthalpy update scheme is used to calculate the latent heat content (DH) in each control volume [10]. The liquid and solid fractions in the domain are calculated as fl = DH/La and fs = 1 - fl. ap ð6Þ DHp nþ1 ¼ DHp n þ 0 k hp n cp f 1 DHp n ap where ap, a0p are coefficients of the discretized energy equation, k is a relaxation factor and f-1 is the inverse of the latent heat function. For binary system f-1 is given [11] as ðkp 1Þ DH f 1 ðDH Þ ¼ Tm ðTm TL Þ ð7Þ La 4 Results and Discussion The present work predicts the transport phenomena in continuous casting of an A356 alloy in presence of weak electromagnetic stirring numerically. The present numerical work is validated with the experiment conducted by Vreeman et al. [2] where a case of conventional continuous casting of Al- 4.5 wt %Cu alloy is considered. Figure 2 compares the present prediction (without EM stirring) with the optical micrograph obtained in the experiment by Vreeman et al. [2]. It is found that the numerical prediction shows a good agreement with the experiment. Then, the

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validated code is extended to predict the transport phenomena during continuos casting of Al-7.32 % Si alloy in presence of weak electromagnetic stirring. 4.1 Continuous Casting of A356 Alloy Without Stirring Figure 3a shows the temperature distribution in the domain at steady state condition. The pouring temperature of the melt is considered as 707 °C. The temperature of the melt decreases due to cooling. The solidification begins as the melt temperature reaches below the liquidus and a mushy zone is formed. The mushy zone in which solid fraction varies from 0 to 1.0 is also shown in Fig. 3a. It is found that the sump depth, calculated from the top of the mould is 0.3186 m. In Fig. 3 (b), the distribution of solute (Si) in the liquid region at steady state condition is shown. The solute concentration is higher towards the axis of the billet and lower towards the billet surface. This occurs due to the thermo-solutal convection which transports the solute-rich liquid toward the axis of the billet. It is found that the average solute (Si) concentration in the melt is about 7.8 %. 4.2 Continuous Casting of A356 Alloy with Weak Stirring It is mentioned here that the problem of macrosegregation can be minimized by applying electromagnetic force field during casting. Therefore, the effect of stirring on the transport phenomena is studied here. In Fig. 4a, the pattern of the force field in the mold during casting is depicted. Figure 4b shows the corresponding stream function

Fig. 3 a Temperature distribution with solid fraction, b Species distribution (Si) in liquid region

distribution. It is observed that a circulation in the melt is developed in presence of stirring. The developed circulation lifts up the melt near the mold wall. The melt comes down along the axis due to continuity. The top loop is formed mainly due to the induced forces whereas the lower loop is formed due to the thermo-solutal convection. In this case, it is found that the maximum velocity in the liquid is 0.2 m/s and the maximum force is 4.55 kN/m3. The corresponding temperature distribution at steady state is shown in the Fig. 5a where the pouring temperature is 707 °C. It is observed that the temperature in the liquid region is almost uniform due to the stirring action and the sump depth is 0.3485 m. In Fig. 5b, the distribution of Si in the liquid region is presented. When stirring is applied, the

Fig. 2 Comparison of present prediction with experiment: a the distribution of solid fraction from the present model and b the micrograph of the grain refined billet [2]

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(a)

7.9

7.8 0.3 7.7 0.2

Sump Depth Max. Velocity Average conc.

7.6

0.1 7.5

0

7.4 0

2

4

6

8

Average Concentration (% of Si)

Sump Depth (m) / Max. Velocity (m/s)

0.4

3 Stirring Intensity (kN/m )

(b)

7.57

0.3


7.56

0.2

7.55

0.1

7.54

0 650

660

670

680

690

700

7.53 710


Fig. 4 a Distribution of forces (a zoomed view) and b the pattern of the stream lines


0.4

o

Pouring Temperature ( C)

(c) 7.56

0.3


0.2 7.54 0.1

0

7.53 0

Fig. 5 a Temperature distribution with mush and b distribution of solute (Si) in liquid region

rejected solute mixes well. Because of this, the average concentration of Si is less (7.54 %) compared to the case without stirring. 4.3 Parametric Study In the present work, the effect of process parameters on the transport phenomena is predicted. In the Fig. 6a, the effect of stirring intensity on the sump depth, average concentration and maximum velocity in the melt is plotted at a constant water flow rate (0.116 m2/h) and casting speed (5.33 9 10-4m/s). In the continuous casting in presence of

7.55



0.4

0.2

0.4

0.6

0.8

1

1.2

2

Water Flow Rate (m / hr)

Fig. 6 a Effect of stirring intensity on the average concentration (% Si), the sump depth and maximum velocity, b effect of pouring temperature on the sump depth, average concentration (% Si), and maximum velocity and (c) effect of water flow rate on the sump depth, average concentration (% Si), and maximum velocity

weak stirring, the stirring effect is confined mainly at the top of the mould and the thermo-solutal convection is predominant at the solid–liquid interface (see Fig. 4b). Under such condition, the remelting of the mush may be higher than the increase in the heat transfer. Hence, it is seen that the sump depth slightly increases with increasing stirring intensity. The average concentration of Si decreases with increasing stirring intensity as the stirring causes

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good mixing of the rejected solute. With increase in stirring intensity, the maximum velocity in the melt increases accordingly. To study the effect of pouring temperature on the sump depth and average concentration, simulations are carried out by varying the pouring temperature of the melt keeping stirring intensity (4.55 kN/m3) and water flow rate (0.116 m2/h) constant. From Fig. 6b, it is observed that the increase in pouring temperature affects the sump depth and liquid velocity slightly. It is also found that the average concentration of Si in the liquid decreases with increasing pouring temperature. To study the effect of water flow rate on the sump depth and average concentration, simulation is also performed keeping the stirring force (4.55 kN/m3) and pouring temperature (707 °C) constant. Figure 6c shows the corresponding effect. It is found that the effect of water flow rate on the transport phenomena is negligible in case of weak stirring.

5 Conclusions A numerical study has been performed to predict the transport phenomena during continuous casting of an aluminium alloy (A356) in presence of mild electromagnetic stirring. The volume averaged single phase conservation equations are used to represent the casting process. The electromagnetic forces are incorporated in the momentum equations. The governing equations are solved based on the pressurebased finite volume method according to the SIMPLER algorithm using TDMA solver along with the enthalpy

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update scheme. The simulation predicts the temperature, solid fraction and species in the computational domain in presence of weak stirring and without stirring. It is found that the rejected solute mixes well when stirring is applied. Because of this, the average concentration of Si is less (7.54 %) compared to the case without stirring. It is also noted from the parametric study that with increase in stirring intensity and pouring temperature, the sump depth increases and the solute concentration in the liquid decreases. It is also found that the effect of water flow rate on the transport phenomena is negligible.

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