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Materials Science and Engineering A 448 (2007) 189–203
Coupled modeling of electromagnetic field, fluid flow,heat transfer and solidification during low frequencyelectromagnetic casting of 7XXX aluminum alloysPart 1: Development of a mathematical model and
comparison with experimental results
Haitao Zhang a,∗, Hiromi Nagaumi b, Yubo Zuo a, Jianzhong Cui a
a Key Lab of Electromagnetic Processing of Materials, Ministry of Education,Northeastern University, Shenyang, Liaoning 110004, China
b Nippon Light Metal Company Ltd., Nikkei Research and Development Center, 1-34-1 Kambara Kambara-cho,Ihara-gun, Shizuoka-ken 421-3291, Japan
Received 2 April 2006; received in revised form 8 October 2006; accepted 16 October 2006
bstract
A comprehensive mathematical model has been developed to describe the interaction of the multiple physics fields during the conventionalC casting and low frequency electromagnetic casting (LFEC) process. The model is based on a combination of the commercial finite elementackage ANSYS and the commercial finite volume package FLUENT, with the former for calculation of the electromagnetic field and the latteror calculation of the magnetic driven fluid flow, heat transfer and solidification. Moreover, the model has been verified against the temperatureeasurements obtained from two 7XXX aluminum alloy billets of 200 mm in diameter, during the conventional DC casting and the LFEC casting
rocesses, respectively. There was a good agreement between the calculated results and the measured results. Further, comparison of the calculatedesults of the LFEC process with that of the conventional DC casting process indicated that velocity patterns, temperature profiles and the sumpepth are modified remarkably by the application of a low frequency electromagnetic field during the DC casting. 2006 Elsevier B.V. All rights reserved.
ling;
st
daft(s
eywords: Low frequency electromagnetic casting; DC casting; Coupled mode
. Introduction
The aluminum industry produces extrusion billets andolling-sheet ingots mainly by the direct-chill (DC) casting pro-ess. A sketch of the DC casting process is shown in Fig. 1(a).nitially, the starting block is positioned inside the mold and theiquid metal is pouring into the open mold from the top. A solid-fied shell is formed over the starting block and along the moldall. As soon as the solidified shell is strong enough to embay
he molten metal inside, the starting block is lowered. As thengot emerges from the mold, the water impinges directly on theast surface. After some distance, e.g., 1 m for a commercial-
∗ Corresponding author. Tel.: +86 24 83687734; fax: +86 24 83681758.E-mail address: haitao [email protected] (H. Zhang).
fpitsom
921-5093/$ – see front matter © 2006 Elsevier B.V. All rights reserved.oi:10.1016/j.msea.2006.10.062
Temperature field; Fluid flow; Solidification
ize sheet ingot, a nearly steady-state regime is established forhe thermal field.
In the past five decades, some new techniques have beeneveloped to apply to the semi-continuous casting of aluminumlloys by some researchers [2–7]. In particular, the techniquesor using electromagnetic field were given the researchers’ atten-ion. Firstly, a new technique named electromagnetic castingEMC) was developed by Russian, Getselev [1]. Fig. 1(b) is aketch of electromagnetic casting (Russian type [2]). A highrequency electromagnetic field is supplied during the EMCrocess in order to produce an electromagnetic pressure thats used to balance the static pressure. Therefore, there is no con-
act between the melt and the mold, which results in a superurface quality that can be obtained by using this technique, butther aspects, such as the microstructure of the billets cannot beodified.
190 H. Zhang et al. / Materials Science and Engineering A 448 (2007) 189–203
F loys:p
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ig. 1. Schematic of some semi-continuous casting processes of aluminum alrocess.
Moreover, another new casting technique called casting,efining, electromagnetic (CREM) process was developed byrenchman, Vives [3,4] by the end of the 1980s of 20th century.sketch of CREM process was shown in Fig. 1(c). This tech-
ology is characterized by the fact that the presence of a strongorced convection of electromagnetic origin lead to a significanteduction of the gain size. Based on the CREM process, anotherew casting technique, low frequency electromagnetic castingLFEC) process was developed by Cui [5,6]. Fig. 1(d) showssketch of LFEC process. Not only was the gain size reduced
ut also the distribution of the gain is uniform in the transverseross-sections of the billets by using this technique. In addition,his technique can reduce the production of the casting crackemarkably [7].
With the development of powerful numerical methods andomputers, numerical modeling is used increasingly in ordero understand the semi-continuous casting process. In one ofhe earlier studies, Peel and Pengelly [8] solved the steady-statenergy conservation equation to solve for the temperature in aylindrical billet, utilizing an equivalent specific heat method to
ccount for latent heat release. Weckman and Niessen [9] alsotudied the steady-state thermal field associated with the DCasting of AA 6063 billets, using a finite element method. Subse-uently the transport phenomena in the semi-continuous castingL
o(
(a) DC casting process, (b) EMC process, (c) CREM process and (d) LFEC
ere studied by most researchers [10–12]. In some studies, floweld and temperature field were solved coupledly to model theuid flow and the distribution of temperature in the sump [10]nd to study the evolution of the fluid flow and the tempera-ure field in the billet with the time during the semi-continuousasting process [11,12]. In recent years, predictions of macroseg-egation [13,14] and thermal stress [15,16] have drawn morettention for their industrial importance.
Some mathematic models for the semi-continuous casting inhe presence of electromagnetic field were developed to describehe effect of electromagnetic field on other fields. Lavers andhmed [17,18] were the first to calculate electromagnetic field
n EMC process. Evans and his co-workers [19,20] describedwo-dimensional and three-dimensional mathematic models foralculating electromagnetic field, melt surface shape and meltow in EMC. In addition, Prasso and Evans [21,22] developed
he mathematic model for calculating temperature field duringMC process and the Joule heat was included in this model.owever, all reports cited above were based on EMC process
nd the literatures about the numerical modeling of CREM and
FEC process were reported rarely.In this paper, a comprehensive mathematic model was devel-ped to describe the interaction of the multiple physics fieldselectromagnetic field, fluid flow, heat transfer and solidifica-
e and
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Itμ
imos
eew
μ
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wd−ρu uj(∂uj/∂xi). C1 and C2 are constants. σk and σε are theturbulent Prandtl numbers for k and ε, respectively. Sk and Sε
are source terms for k and ε, respectively. All constant, whichare used in the model, are listed in Table 1.
Table 1
H. Zhang et al. / Materials Scienc
ion) during the conventional DC casting and LEFC processes.he calculated results were compared with the measured resultsnd the effects of electromagnetic field on melt flow, temperatureeld and solidification in LFEC were analyzed.
. The mathematical model
.1. Governing equation for electromagnetic field
In order to gain the distribution of the electromagnetic field inhe billets during LFEC process, the magnetic flux density B andhe electric strength E must be obtained by solving Maxwell’squations, which can be written as:
mpere’s law : ∇ × E = −∂B
∂t(1)
araday’s law : ∇ × B = ε
μ
∂E
∂t+ J (2)
auss’s law of electric field : ∇ · E = ρe
ε(3)
auss’s law of magnetic field : ∇ · B = 0 (4)
To solve the above equations, the conduction current J shoulde solved with Ohm’s law which can be expressed as:
= σ(E + U × B) (5)
The interaction between the electromagnetic field and thether physics fields can be carried out by the electromagneticolume density fem, which can be given as:
em = J × B (6)
When the harmonic electromagnetic field is considered, thisolume force is decomposed into a time-dependent componentnd a time-independent component. Because the electromag-etic field period is far shorter than the momentum responseime of the melt, the time average value of this volume forcehould be used to couple with other physics fields. Therefore, atny point within a metallic conductor where the time harmonicurrent density is J and the magnetic flux density is B, the timeverage electromagnetic volume force density is:
= 12 Re(J × B∗) (7)
here, Re is the real part of a complex quantity.
.2. Governing equations for flow field and temperatureeld
In this research, a single domain volume-average model issed. Single domain models are based on governing equationshat apply to all regions of a solidification system. The model
quations can be integrated across the entire domain withouthe need to explicitly subdivide the domain into solid, liquidnd mushy regions. Instead, these regions are implicitly definedithin the system by the distributions of energy determined fromT
C
1
Engineering A 448 (2007) 189–203 191
he solutions of the model equations. Therefore, the conversationquations are written as:
onservation equation of mass :∂ρ
∂t+ ∇ · (ρU) = 0 (8)
Conservation equation of momentum :
∂(ρU)
∂t+ ∇ · (ρUU) = ∇ · (μeff∇U) − ∇P + Sm (9)
Conservation equation of energy :
∂(ρT )
∂t+ ∇ · (ρUT ) = ∇ ·
(k
cp∇T
)+ Sth (10)
n the Eq. (9), μeff and Sm are effective viscosity and momen-um source, respectively. The effective viscosity μeff is given by
eff = μl + μt, where μl is laminar viscosity in the liquid and μts turbulent viscosity. The momentum source Sm includes ther-
al buoyancy, Darcy source term and the time averaged valuef electromagnetic volume force. In the Eq. (10), Sth is thermalource and includes Joule heat and latent heat of solidification.
In this model, the standard k–ε model, which is a semi-mpirical model, is used to model transport of turbulence kineticnergy (k) and its dissipation rate (ε). The first form of this modelas proposed by Harlow and Nagayama and they suggested that:
t = ρCμ
k2
ε(11)
here Cμ is a function of the turbulent Reynolds number whichs a constant value; k and ε are the turbulence kinetic energynd its rate of dissipation, respectively, and obtained from theollowing transport equations:
∂(ρk)
∂t+ ∇ · (ρUk) = ∇ ·
[(μl + μt
σk
)∇k
]+ Gk − ρε + Sk
(12)
∂(ρε)
∂t+ ∇ · (ρUε)
= ∇ ·[(
μl + μt
σε
)∇ε
]+ C1
ε
kGk − C2ρ
ε2
k+ Sε (13)
here Gk represents the generation of turbulence kinetic energyue to the mean velocity gradients, calculated as follows: Gk =
′ ′
he constant used in k–ε model
1 C2 σk σε Cμ
.44 1.92 1.0 1.3 0.09
1 and E
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92 H. Zhang et al. / Materials Science
.3. Governing equations for solidification
The solidification of any alloy occurs over a temperatureange. Therefore, for the solidification process of a multi-omponent alloy the whole region is divided into three regions:amely, liquid, solid and mushy region. Moreover, the latent heats released in the mushy region during the solidification process.t present, there are two methods used frequently to model the
olidification process of the alloys. They are single and multipleomain methods. In this paper, a single domain volume-averageodel is used. Single domain models are based on governing
quations that apply in all regions of a solidification system.he model equations can be integrated across the entire domainithout the need to explicitly subdivide the domain into solid,
iquid and mushy regions. Instead, these regions are implicitlyefined within the system by the distributions of energy deter-ined from the solutions of the model equations. However, theodel includes two main problems, that is, the treatment of the
atent heat and modeling of fluid flow in the mushy region.In terms of the treatment of the latent heat, there are two
ain methods at the present, namely, the equivalent specific heatnd enthalpy methods. In this model, the first method was usedo model accurately energy transport during the solidificationrocess of the new type of 7XXX aluminum alloys. Since thenergy equation is valid for the solid, liquid and mushy region,he equivalent specific heat C* is written as:
∗(T ) = Cs(T ) × fs + Cl(T ) × fl − ΔHf × ∂fs
∂T(14)
here Cs is the specific heat of the solid, Cl the specific heat ofhe liquid and �Hf is the latent heat of fusion; fs and fl are theolid and liquid volume fraction, respectively. In this model, theevel rule is used to calculate the solid fraction fs and the liquidraction fl that are function of temperature and are formulateds follows:
l =
⎧⎪⎪⎪⎨⎪⎪⎪⎩
1 when T ≥ Tl
1 − 1
1 − kp
Tl − T
Tf − Twhen Tl > T > Ts
0 when T ≤ Ts
(15)
nd
s = 1 − fl (16)
here kp is solute partition coefficient, Tf the fusion temperaturef the pure base metal; Tl and Ts are the liquidus temperaturend solidus temperature, respectively.
t
(
able 2he viscosity and permeability in the different stages
tage Solid fraction fs
iquid 0
efore dendrite coherence in mushy region 0 < fs ≤ f ∗s
fter dendrite coherence in mushy region f ∗s ≤ fs < 1
olid 1
ngineering A 448 (2007) 189–203
Moreover, modeling of fluid flow in the mushy region andreatment of the conservation equations in the solid regionre carried out by using different viscosity and permeabilityn different regions. In the most models, the Darcy model issually used. However, when equiaxed solidification is consid-red, particularly, in the early stage of solidification when theolid fraction is small and the equiaxed grains will move freelyith the liquid, so the Darcy flow is not important. Darcy flowecomes significant when dendrite coherency is occurred, thats, when a rigid dendrite skeleton is established. Moreover, lit-ratures [5,6] have shown that the microstructure of the billetsast by the LFEC process is made up entirely of equiaxed grains.herefore, the computation region is divided into four stages and
he viscosity and the permeability of each stage must satisfy theonditions summarize in Table 2.
In Table 2, f ∗s is the solid fraction that the dendrite coher-
nce is occurred. In this study, the permeability K is given as aunction of solid fraction fs as lists in Table 2. As K decreasesith the solidification (fs → 1), the magnitude of the Darcy term
ncreases and the term becomes dominant in the conservationquations. For the limit case of fs = 1, the very small positiveumber χ is used to avoid diverging the conservation equationsue to the Darcy term. In addition, K0 is named the initial per-eability and may be related to a structural parameter like the
econdary dendrite arm spacing (DAS) [23],
0 = (DAS)2
180(17)
in Table 2 denotes a variable which will be solved, such aselocity (U), turbulence kinetic energy (k) and its dissipationate (ε). Moreover, Xs denotes velocity vector (U), turbulenceinetic energy (k) and its dissipation rate (ε) in the solid region,nd their values are Vcast, 0 and 0, respectively. Moreover, Vcasts the casting speed vector.
.4. Assumptions and simplified mathematic model
In this research, the low frequency electromagnetic field isupplied during DC casting process, so electromagnetic field,uid flow, heat transfer and solidification must be coupledlyodeled in order to describe accurately the interaction of theulti-physics fields during this process. But in order to simplify
he question, some assumptions are given as follows:
1) The displacement current ∂D/∂t is neglected, because themolten metal is sufficiently conducting body in which the
Viscosity μl Permeability K Darcy term
0.001 ∞ 0
0.001 × 1010fs ∞ 0
0.001 K0(1 − fs)3
f 2s
− μl
K + χ(X − Xs)
0.001 K0(1 − fs)3
f 2s
− μl
K + χ(X − Xs)
H. Zhang et al. / Materials Science and Engineering A 448 (2007) 189–203 193
Table 3Governing equations used in the model
Governing equations’ name Modified governing equations
Ampere’s law ∇ × E = − ∂B∂t
Faraday’s law ∇ × B = σE
Gauss’s law of electric field ∇ · E = 0Gauss’s law of magnetic field ∇ · B = 0Conservation equation of mass ∇ · U = 0
Conservation equation of momentum∂(ρU)
∂t+ ∇ · (ρUU) = ∇ · (μeff ∇U) − ∇P − μl
K + χ(U − Us) + ρgβ(T − T0) + 1
2Re(J × B∗)
Conservation equation of energy∂(ρT )
∂t+ ∇ · (ρUT ) = ∇ ·
(kth
C∗p∇T
)
Transport equation of turbulence kinetic energy∂(ρk)
∂t+ ∇ · (ρUk) = ∇ ·
[(μl + μt
σk
)∇k
]+ Gk − ρε − μl
K + χk
T (ρUε)
(
(
(
(
uTm
3
3
ct
mcietfiavoiaaT
odecs
TC
DL
ransport equation of dissipation rate ofturbulence kinetic energy
∂(ρε)
∂t+ ∇ ·
charge relaxation time is shorter than the transit time ofelectromagnetic waves.
2) The variety of the fluid field has little effect on the distribu-tion of the magnetic field, because the magnetic Reynoldsnumber Rm 1 (for the case of LFEC process of aluminumalloys, Rm = μσU0L0 = 0.048, where μ is permeability, σ
the electric conductivity, U0 the characteristic velocity andL0 is characteristic length). As a result, for Ohm’s Law(J = σ(E + U × B)), the second term of right hand side ofthis equation (U × B) is ignored.
3) Joule heat is not considered in this model, because Joule heatproduced during LFEC process was estimated to be 8 kWcompared to the entropy inflow with the liquid aluminumof 623 kW with respect of room temperature.
4) The meniscus shape and the calculation of the solute fieldare not included in this model.
5) The molten aluminum alloys behave as an incompressiblefluid, so the density of the melt is the constant. But the ther-mal buoyancy must be included in this model, therefore theBoussinesq approximation is used to calculate the thermalbuoyancy and is expressed as:
Fthermal = ρgβ(T − T0) (18)
where ρl and β are the density and the volume expansioncoefficient of the molten aluminum, respectively, T0 is thereference temperature and is frequently given as the tem-perature when the solid fraction reaches f ∗
s .
According to above assumptions, the governing equationssed in the mathematic model are modified and are listed inable 3 and the right last term of the conservation equation ofomentum is ignored during the conventional DC casting.
3
ut
able 4asting process parameters during the conventional DC casting and the LFEC proces
Casting temperature Casting speed Water flow
C casting 1003 K 85 mm/min 70 l/minFEC 1003 K 85 mm/min 70 l/min
= ∇ ·[(
μl + μt
σε
)∇ε
]+ C1
ε
kGk − C2ρ
ε2
k− μl
K + χε
. Numerical procedures and experiments
.1. Numerical procedures
In the paper, the conventional DC casting and the LFEC pro-esses of the billets of 200 mm in diameter have be modeled andhe casting process parameters are listed in Table 4.
However, in order to model the LFEC process, coupledodeling of electromagnetic field and others fields must be
arried out. Moreover, this interaction is single direction, thats, electromagnetic field has effect on others fields but noffect by contraries, according to the second assumption. Sohe governing equations of electromagnetic field and otherselds were solved by using the commercial software ANSYSnd FLUENT, respectively. The time average electromagneticolume force density is added to the conservation equationf momentum as the momentum source term during solv-ng flow field. The geometry models and the regions whichre used in ANSYS and FLUENT are shown in Fig. 2(and b), respectively. Moreover, their dimensions are given inable 5.
During calculation procedure of electromagnetic field basen ANSYS, a magnetic vector potential method is used andescribed in the document [24] in detail. Furthermore, when oth-rs fields are calculated based on FLUENT, pressure–velocityoupling algorithm is SIMPLE algorithm and the differencechemes are the first order upwind scheme in FLUENT.
.1.1. Physical propertiesIn this research, a new type of 7XXX aluminum alloy was
sed as the experimental material. The nominal composition ofhe alloy is given in Table 6.
ses
rate Electromagnetic frequency Electromagnetic intensity
None None25 Hz 9600 At
194 H. Zhang et al. / Materials Science and Engineering A 448 (2007) 189–203
Table 5The dimensions of geometry model used based o ANSYS and FLUENT
Geometry model used base on ANSYS
Aluminum alloy Mold Coil Air Infinite field
0.1 m × 0.3 m 0.1 m × 0.05 m 0.06 m × 0.07 m Radius = 0.5 m Radius = 0.55 m
Geometry model used base on FLUENT
Inlet Hot top Mold cooling
0.015 m 0.05 m 0.03 m
op
atmsatesf
(co
TN
E
W
3
btbnch9
sa
Fig. 2. Geometry model in ANSYS (a) and FLUENT (b).
The magnetic properties, the thermophysical properties andther material properties of the alloy used during the calculationrocedure, are listed in Table 7.
In Table 7, the magnetic properties of the superhigh strengthluminum alloy are obtained from literature [19]. Nevertheless,he thermal properties of the alloy were gained by the measure-
ent except density and viscosity, and the measured results ofpecific heat and thermal conductivity were shown in Fig. 3(and b). In terms of the solute partition coefficient, because theype of aluminum alloy is multiple component alloy and theutectic evolvement is not included in this model, a effectiveolute partition coefficient kp is used and obtained from theollowing equation: fs(Ts) = 1.
In addition, the initial permeability K is obtained from Eq.
017) and the different value is used during the LEFC and DCasting processes, because the secondary dendrite arm spacingf the billet is different during the two processes [5,6].able 6ominal composition of the superhigh strength Al alloys
lements Zn Mg Cu Zr Fe Si Al
t% 9.82 2.35 2.29 0.142 0.12 0.08 Balanced
Second cooling Others
0.9 m Shown as in Fig. 2
.1.2. Boundary conditionWhen electromagnetic field is solved base on ANSYS, the
oundary condition is simple because the interface betweenwo regions is automatically satisfied in ANSYS. Therefore, theoundary condition in the symmetry axis region and the infi-ite field region need only be set with the magnetic flux parallelondition and the infinite field flag, respectively. In addition, thearmonic source current with 25 Hz, whose current intensity is600 At, has been applied in the model.
When flow field, temperature field and solidification areolved base on FLUENT, the boundary condition is describeds follows:
Inlet and outlet boundary: All boundary conditions in theregion are constant value and listed in Table 8 and Rnoz ishydraulic radius of inlet.Free surface and hot top boundary: All boundary conditionsare treated as the static adiabatic wall.Symmetry axis boundary: This boundary is set to axisymmetricboundary condition.Mold cooling boundary: The velocity and turbulence bound-ary conditions are set to the static wall; the thermal boundarycondition is treated as Cauchy-type boundary condition, whichis formulated according to Eq. (19), and the heat transfer coef-ficient between the mold and the melt is assumed to vary withthe solid fraction and is written according to Eq. (20).
kthermal∂T
∂n= h(T − Ten) (19)
h = hcontact(1 − fs) + hair × fs (20)
where Ten is environment temperature and its value is 323 K;hcontact the intended to reflect good thermal contact between themold and the melt and is given as 3000 Wm−2 K−1; hair is equalto 100 Wm−2 K−1 to reflect poor thermal contact associatedwith the gap formed when the melt is solidified.Secondary cooling boundary: The velocity and turbulenceboundary conditions are treated as the moving wall andits moving velocity is 0.00144 m/s; in terms of the ther-mal boundary condition, the secondary cooling boundary is
divided into two zones, that is, the impingement zone andthe streaming zone. They are also Cauchy-type boundarycondition and their heat transfer coefficients are shown inFig. 4. In addition, the environment temperature is given as293 K.
H. Zhang et al. / Materials Science and Engineering A 448 (2007) 189–203 195
Table 7Physical properties of the superhigh strength aluminum alloy
Region Aluminum alloy Mold Air Coil
Magnetic propertiesRelative permeability, μ 1 1 1 1Electric conductivity, σ (−1 m−1) 3.85 × 106 1 × 106 0 0
Thermophysical propertiesDensity, ρ 2450 Kg/m3
Viscosity, μl As listed in TableLiquidus temperature, Tl 903 KSolidus temperature, Ts 743 KLatent heat of fusion, L 3.52 × 105 J/KgThermal conductivity, kth As shown in Fig. 3(a)Specific heat, Cp As shown in Fig. 3(b)Volume expansion coefficient, β 8 × 10−5 1/K
Other material propertiesFusion temperature of the pure aluminum, Tf 933 KSolute partition coefficient, kp 0.16
Initial permeability, K0 1 × 10−11 m2 during LFEC process2 × 10−11 m2 during DC casting process
Reference temperature, T0 887 K
ific he
3
auti
F
wft
miafo
3
TB
B
IO
Fig. 3. The measured values of spec
.1.3. InterpolationBecause the mesh used in ANSYS and FLUENT is different,
s shown in Fig. 5(a and b), the time average electromagnetic vol-me force density must be interpolated accurately between thewo different mesh. In this study, a linear interpolation methods used and expressed as following equation:
FLUENT =∑n
i=1(d−1i F i
ANSYS)∑n −1 (21)
i=1dihere FFLUENT is the time average electromagnetic volumeorce density at the interpolated point which is the centroid ofhe certain cell in FLUENT, Fi
ANSYS the time average electro-
2c8
able 8oundary conditions in inlet and outlet regions
oundary Axial velocity Radial velocity Temperature
nlet 0.064 m/s 0 1003 Kutlet 0.00144 m/s 0 293 K
at (a) and thermal conductivity (b).
agnetic volume force density at the ith node in ANSYS and di
s the distance between the interpolated point and the ith node;ll node used during the interpolation procedure must satisfy theollowing in equation: di < R, namely, all node within a radiusf R of the interpolated point, which is shown in Fig. 5(c).
.2. Experiments
Two new 7XXX aluminum alloy billets with diameter of00 mm were cast by LFEC process and conventional DCasting process at melt temperature 730 ◦C, and casting speed5 mm/min, respectively. The electromagnetic field was applied
Turbulence kinetic energy Dissipation rate of turbulence kinetic energy
k = 0.01 × u2inlet ε = k1.5/Rnoz
0 0
196 H. Zhang et al. / Materials Science and Engineering A 448 (2007) 189–203
bmap
fimcrstmts
4
c
maFeoomfciaT
Fig. 4. Heat transfer coefficient in the second cooling region.
y an 80 turns water-cooling copper coil surrounding the moldade of stainless steel. The current frequency in the coil is fixed
t 25 Hz and the current intensity is 120 A during the LFECrocess.
In order to study the effects of low frequency electromagneticeld on the sump and temperature field, temperature measure-ent were performed in various location of the billet during
asting. Seven K-thermocouples were fixed on the stainless steelods, which were jointed to the starter block along diameter. Thechematic diagram of temperature measurement and the loca-ion of thermocouples are shown in Fig. 6. These thermocouples
oved with the billet (starting in the liquid part) and were even-ually frozen into solid metal. Then the cooling curves fromurface to center of the billet can be obtained.
. Results and discussion
Predictions of the steady-state transport phenomena in theonventional DC casting and the LFEC processes have been
ttvm
Fig. 5. Mesh in ANSYS (a) and FLUENT (b) and schematic of interpolation pro
Fig. 6. Schematic diagram of the temperature measurement.
ade. The numerical results for magnetic flux density and timeverage electromagnetic volume force density are shown inig. 7(a and b). The magnetic flux density and the time averagelectromagnetic volume force density decrease with the decreasef distance from the centerline of billet because of the skin effectf the alternative electromagnetic field. The maximum values ofagnetic flux density and time average electromagnetic volume
orce density emerge at the nether zone of the graphite, that is,losed to the centerline of the coil. Moreover, the right hand partsn Fig. 7(a and b) are magnetic flux density vector and time aver-ge electromagnetic volume force density vector, respectively.he direction of magnetic flux density is approximately parallel
o the centerline of the billet within the electromagnetic pene-ration depth and the direction of time average electromagneticolume force density is always perpendicular to the direction ofagnetic flux density.
cedure (c) ( , mesh used in ANSYS; , mesh used in FLUENT).
H. Zhang et al. / Materials Science and Engineering A 448 (2007) 189–203 197
F ensityc
vitciitaacTtaafittiiros
lvvidarttaftdi
t0rbast8ttif
4e
aomtta
sfctmtctat
ig. 7. The calculated results of the electromagnetic field. (a) Magnetic flux dontours and vectors.
Fig. 8(a–h) shows temperature profiles, velocity vectors,elocity profiles, streamline patterns and solid fraction profilesn five separate plots during the conventional DC casting andhe LFEC processes, respectively. During the conventional DCasting, as seen from velocity vectors and streamlines patternsn Fig. 8(c and g), the melt is poured into the liquid pool from thenlet and then flows downwards along the symmetry axis to reachhe solidification front. In addition, due to the thermal buoyancyction, the melt ascends upwards along the solidification frontnd the mold surface, which results in a large anti-clock cir-ulation being produced in the melt pool, as seen in Fig. 8(g).he maximum velocity is found to equal to the pouring speed at
he inlet region in Fig. 8(e) and the flow velocity of the melt isll less than 0.01 m/s except near the centerline region. Fig. 8(and i) show the temperature profiles and the solid fraction pro-les during the conventional DC casting. It is observed that the
emperature in the melt pool is between 943 K and the liquidusemperature to equal to 903 K except the centerline region. Theres a very wide mushy region, as seen from the solid fractionn Fig. 8(i), because the alloy possesses the wide solidificationange. In the solid region, the temperature gradient in the surfacef the billet is more than that in the center of the billet due to theecond cooling action.
During the LFEC process, as a result of the stirring action ofow frequency electromagnetic field, the vigorous forced con-ection is produced in the metal melt pool as seen from theelocity vectors and the streamline profiles in Fig. 8(d and h). Its found that a large circulation and a small circulation are pro-uced in the melt pool because of the electromagnetic stirringction and their directions are clockwise and anti-clockwise,espectively, as Fig. 8(d and h). In details, the flow direction ofhe melt is modified as soon as it is poured into the melt pool,hat is, the melt flows along the free surface from the inlet regionnd then descends along the mold surface and the solidification
ront. When the melt reaches at the distance of a half radius fromhe centerline of the billet, it is divided into two circulations asescribed above. One returns the inlet region along the centerlinen the end; however, the other forms a closed circulation nearmptt
contours and vectors; (b) time average electromagnetic volume force density
he solidification front. The maximum velocity is observed to be.3 m/s at the contact region between the melt and the mold cor-esponding to the maximum electromagnetic force 14030 N/m3
ecause of the skin effect of the alternating electromagnetic field,s plotted the velocity profiles in Fig. 8(f). The temperature andolid fraction contours are plotted in Fig. 8(b and j). It is foundhat the temperature in the melt pool is very uniform and about90 K, which is lower than the liquidus temperature as a result ofhe vigorous forced convection of the melt induced by the elec-romagnetic force. In addition, the solid fraction in the melt pools between 0.3 and 0.27; therefore, there are a large numbers ofreely moving grains that flow with the liquid metal.
.1. Comparison between calculated results andxperimental results
Fig. 9(a) shows a comparison between the calculated resultsnd the measured results for magnetic flux density at distancef 0, 25, 50 and 100 mm from centerline of billet. Both theeasured results and the calculated results are obtained when
here is not the aluminum melt but the air in the mold. It is foundhat there is a good agreement between the calculated resultsnd the measured results.
Fig. 9(b and c) shows comparison of cooling curves for mea-urements and calculations at distance of 0, 25, 50 and 95 mmrom the center of the billets cast during the conventional DCasting and the LFEC process, respectively. It is indicated thathere is a good agreement between the calculated results and theeasured results regardless of the conventional DC casting and
he LFEC processes. In Fig. 9(b), during the conventional DCasting, the temperature of the melt decreases due to conduc-ion towards the chill until the liquidus temperature is reachedt all measured positions, and then the temperature continueso decrease but the temperature gradient in the melt become
arkedly steeper at all measured positions. Moreover, the tem-erature decreases faster at the region closed to the surface ofhe billet than other positions because of the larger heat extrac-ion rate near the surface. During the LFEC process, the change
198 H. Zhang et al. / Materials Science and Engineering A 448 (2007) 189–203
Fig. 8. calculated results during the two different processes: (a) temperature profiles, (c) velocity vectors with temperature profiles, (e) velocity profiles, (g) streamlinepatterns and (i) solid fraction profiles during the conventional DC casting process; (b) temperature profiles, (d) velocity vectors with temperature profiles, (f) velocityprofiles, (h) streamline patterns and (j) solid fraction profiles during the LFEC process.
H. Zhang et al. / Materials Science and Engineering A 448 (2007) 189–203 199
Conti
ovtetudtIt
aatItt
Fig. 8. (
f the cooling curves in the melt is the same as during the con-entional DC casting process. However, the distribution of theemperature within the sump during the LFEC process is differ-nt from that during the conventional DC casting process and theemperature within the sump is very uniform and under the liq-idus temperature. In addition, the temperature in the inlet region
ecreases highly faster to the liquidus temperature, whereas theemperature at other regions is under the liquidus temperature.t is found that the temperature gradient at all measured posi-ions except near the surface region during the LFEC processrimt
nued ).
re gentler than that during the conventional DC casting processnd the temperature gradient near the surface are same duringwo processes from the comparison between Fig. 9(b and c).n order to compare the distribution of the measured tempera-ure with the distribution of the calculated temperature withinhe whole billet, the measured data is interpolated to obtain the
ight parts in Fig. 10(a and b) during the conventional DC cast-ng and the LFEC processes, respectively. It is indicated that theeasured temperature field is the very same with the calculatedemperature field during two processes.
200 H. Zhang et al. / Materials Science and Engineering A 448 (2007) 189–203
F gnetic(
4p
ettio
iei
b
ig. 9. comparison between the calculated and the measured results: (a) the mac) the cooling curves in the presence of electromagnetic field.
.2. The effect of electromagnetic field on the castingrocess
In order to investigate and illuminate clearly the effect oflectromagnetic field on fluid flow and temperature field during
he semi-continuous casting process, the Fig. 11(a–c) shows theemperature profiles and velocity vectors and velocity contoursn the presence of the electromagnetic field and in the absencef electromagnetic field in three separate plots. The left partftca
Fig. 10. comparison of temperature field for the measurement and calculatio
flux density, (b) the cooling curves in the absence of electromagnetic field and
n the three plots is the predicted results in the absence of thelectromagnetic field and the right part is the predicted resultsn the presence of the electromagnetic field.
Both the velocity vectors and profiles are entirely modifiedecause of the presence of the electromagnetic field, as observed
rom the velocity vectors and patterns in Fig. 11(b and c). Whenhe electromagnetic field is applied during the semi-continuousasting process, the flow direction in the melt pool is reversednd a small circulation is produced near the solidification frontn during the conventional DC casting (a) and the LFEC (b) processes.
H. Zhang et al. / Materials Science and Engineering A 448 (2007) 189–203 201
F andp
acficefflsoissrtfift
ftdAcitttiwfp
ig. 11. comparison of the calculated results during the conventional DC castingrofiles and (c) velocity patterns.
t the center of the billet. In addition, compared to during theonvection DC casting, the maximum velocity is increased aboutve times and its location is moved from the inlet region to theontact position between the melt and the mold. The phenom-na are commonly explained by the forced convection resultedrom the rotational component of the electromagnetic force. Thisuid flow must result in the temperature profiles in Fig. 11(a). Aseen from the temperature profiles in Fig. 11(a), the distributionf the temperature field has been markedly modified. Firstly, its observed that the temperature contours in the right part arehifted upwards relative to the left part, which must result in theump shape being entirely modified and the sump depth beingemarkably reduced as given in the preceding chapter. In addi-
ion, compared to that in the absence of the electromagneticeld, the temperature in the bulk liquid is lower and more uni-orm in the presence of the electromagnetic field. The reason forhe great modification of the temperature field is the vigorousmfiti
LFEC processes: (a) temperature profiles, (b) velocity vectors with temperature
orced convection induced by the electromagnetic stirring andhat the heat flux along the longitudinal direction is increasedue to the vigorous forced convection in the solidification front.s explained the reason in detail, during the conventional DC
asting, the melt with high temperature reaches firstly the solid-fication front after the melt is poured into the melt pool fromhe inlet region, and then it is led to the contact region betweenhe melt and the mold due to the thermal buoyancy, therefore,he sump depth is increased. In addition, because the flow veloc-ty in the sump pool is very small, the heat transfer of the meltithin the sump depend mainly on the conductive heat trans-
er, which results in uneven temperature distribution in the meltool. However, during the LFEC process, due to the electro-
agnetic field action, the melt with high temperature reachesrstly the contact region between the melt and the mold alonghe free surface and its temperature is decreased as soon ast is poured into the melt pool, and then the melt cooled by
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02 H. Zhang et al. / Materials Science
he mold reaches the solidification front, which must resultsn the temperature at the solidification front being decreasednd the sump depth becoming very shallower. In addition, theeat transfer manner in the melt pool is mainly the conduc-ive and convective heat transfer due to the vigorous forcedonvection induced by the electromagnetic stirring, therefore,he uniform temperature distribution within the sump is seen inig. 11(a).
The microstructure of the billets cast during the conventionalC casting process is usually coarse dendritic structure in the
bsence of the master alloy, but that during the LFEC processs very fine equiaxed grain structure, as reported in literatures5,6]. From the present investigation, the reasons of generatinghe fine equiaxed grain structure are as follows:
(a) As shown in Fig. 11(a), the temperature in the sump pool isvery uniform and is lower than the liquidus temperature inthe presence of electromagnetic field, which must result inthe high undercooling and low temperature gradient. As seenfrom the temperature profile in Fig. 11(a), the whole meltwithin the sump keeps the large undercooling state, whichmust increase the nucleation rate and number. Therefore,such uniform temperature field generated by the electro-magnetic stirring is one of the main reasons for obtainingthe fine equiaxed structure of the billet cast during the LFECprocess.
b) As given in Fig. 11(b), due to the vigorous forced convec-tion caused by the electromagnetic stirring, the dendritefragments are detached from the solidification front, themold and the free surface of the melt. The causes of thedendrite detachment include as [25,26]: dendrite arm frac-ture due to shearing action, dissolution of dendrite armsand the separated grain from the mold and the free surfaceof the melt. When these fragments are detached into thesump and move within the sump with the melt flow, eachof them will all become a crystal nucleus. It is reason forsuch phenomenon that these fragments will survive and notbe remelt due to the melt as the large undercooling stateand the low thermal gradient when they move freely in themelt pool, and then they are captured by the high viscousmelt or the dendritic net at the solidification front and forma new nuclei when they sedimentate at the solidificationfront, which can not be observed during the conventionalDC casing process. Therefore, the vigorous forced con-vection induced by the electromagnetic field can promotethe formation of the fine equiaxed grain structure of thebillet.
In summary, because of the uniform temperature field andhe vigorous forced convection induced by the electromagnetictirring, the large number of the moving freely crystal nucleus areontained in the whole melt pool. Therefore, the solid fractionith the whole melt pool is uniform and high, as seen in Fig. 8(j).
n addition, the low temperature gradient mentioned above mustesult in reducing remarkably the casting stress in the billets casturing the LFEC process, further, it can retrain the productionf the crack during the casting process.
[
[
ngineering A 448 (2007) 189–203
. Conclusions
A mathematic model for the coupled calculation of electro-agnetic field, fluid flow, heat transfer and solidification during
he conventional DC casting and the LFEC processes is pre-ented. The model has been verified against the temperatureeasurements obtained from two 7XXX aluminum alloy billets
f 200 mm in diameter cast during the conventional DC castingnd the LFEC process. It was found that there was a good agree-ent between the calculated results and the measured results. In
ddition, comparison of the calculated results during the LFECrocess with that during the conventional DC casting processndicated as follows:
(a) Compared with in the absence of electromagnetic field, theflow patterns in the sump pool were remarkably modifiedand the vigorous forced convection was produced in thepresence of electromagnetic field. That is, the inverse flowdirection and the higher flow velocity were found during theLFEC process.
b) The uniform temperature field and the low temperature gra-dient in the sump pool were observed during the LFECprocess, which can not be difficultly seen during the con-ventional DC casting; in addition, it was found that theisothermal lines were shifted upward and the sump depthwas remarkably reduced. Such modifications in the tem-perature field resulted mainly from the vigorous forcedconvection induced by electromagnetic stirring.
(c) The uniform temperature field, the low temperature gradientand the vigorous forced convection produced by electro-magnetic stirring are the main causes for the formation ofthe equiaxed grain in the billet cast during the LFEC process.
d) Due to the low temperature gradient produced during theLFEC process, the casting stress in the billets was remark-ably reduced and the crack was effectively retrained.
cknowledgements
This study was supported by the national “863” foundation ofhina (grant number: 2001AA332030). The authors are gratefulo Dr. Ke, Qin and Zhihao, Zhao for their help in the experiment.
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