Numerical simulation on electromagnetic field, flow field and temperature field in semisolid slurry

RARE METALSVol. 29, No.6, Dec 2010, p.635DOI: 10.1007/s 12598-010-0184-2Numerical simulation on electromagnetic field, flow field and temperaturefield in semisolid slurry preparation by A-EMSZHANG Zhifeng, CHEN Xingrun, XU Jun, and SHI LikaiNational Engineering & Technology Research Center for Nonferrous Metal Matrix Composites, General Research Instiute for Nonferrous Metals, Beijing 100088,ChinaReceived 2 November 2009; received in revised form 14 January 2010; accepted 28 January 2010◎The Nonferous Metals Society of China and Springer-Verlag Berlin Heidelberg 2010AbstractA two-dimensional computational model coupling an annular electromagnetic stiring (A-EMS) with a macroscopic heat and fluid flowanalysis in Al-alloys semisolid slurry preparation was developed. The dynamic evolutions of the electromagnetic field, flow field, and tem-perature field were presented sccesfully by commercial software ANSYS 10.0 with corresponding experimental verification. A horizon-tally rotational electromagnetic field and, thereby, a more intensive velocity field were uniformly distributed in the stired melt even at com-mercial frequency, and thus, a lower temperature difference in the strred melt and subsequent uniformly fine microstructures were obtainedcompared with the normal electromagnetic strring. The simulation resuts were in good agreement with experimental ones.Keywords: metal forming; electromagnetic stiring; numerical analysis; semisolid slury1. Introductionimportant to precisely control the solidification process.The purpose of the present study is to develop a compu-Electromagnetic stiring characterized by nonpollution,tational model coupling electromagnetic stiring with alow cost, and easy process control has been a main method macroscopic heat and fluid flow in semisolid slurry prepara-for producing Al-alloys semisolid slurry or billets [1-5]. tion by A-EMS. The effects of electromagnetic stiring onHowever, there still exist inhomogeneous microstructures inthe flow field and temperature field dstribution were inves-the semisolid billets especially large-sized ones due to thetigated with corresponding experimental verification.skin effect resulting from electromagnetic induction [6-7].Although a low strring frequency can be chosen to enhance2. Description of physical processesthe penetration depth of the alternating electromagnetic field,an additional conversion equipment leads to a lower shear-A schematic diagram of a typical semisolid slurry prepa-ing rate and an increase of slurry preparation cost. To solveprocess with A-EMS is ilustrated in Fig. 1. The su-the problem, an advanced semisolid metal slurry preparation perheat melt was poured in a crucible around which aprocess, namely， the annular electromagneticstiringhome-made electromagnetic stirrer consisting of yokes,(A-EMS) was developed, and an intensively forced shearingcores, and coils was set up. The yoke and core of the elec-could be achieved at a higher shear rate inside the annular tromagnetic system were made of silicon steel with highchamber at the commercial frequency by means of innova-permeability, and coils made of copper wire were installedtively combining noncontact electromagnetic stirring and anon the core, forming a pair of poles. The stirrer design en-annular chamber with specially designed profiles, and thus,tails the placement of the coils around the crucible to gener-more uniformly fine microstructures of Al-alloys slurryate a rotational motion along the horizontal direction. Thewere produced in comparison with normal EMS. Neverthe-crucible with an external radius of 90 mm, an internal radiusless, few quantitative studies have been carried out to pre-of 80 mm, and a height of 300 mm was made of austeniticsent the interactive effects of electromagnetic field, flowstainless steel. The coil size was 0.02 mx 0.14 m, the ex-field, and temperature field in the A-EMS process in spite of ternal size of the stirrer yoke was 0.32 m x 0.32 m, and thethe indisputable experimental results [8], which is virtuallyintermal size was 0.24 m X 024 m. The current intensity was中国煤化工Corresponding author: ZHANG ZhifengE-mail: zhangzf@grinm.comMHCNMH G.636R4RE METALS, Vol. 29, No.6, Dec 2010changed by the adjustment of AC voltage input employed inTable 1. Physical properties of materials used in the calcula-a range of 0-200 V and frequency input employed in a rangetionof 0-50 Hz. A graphite cooler was set in the center of thePhysical propertiescrucible, and thus, an annular chamber was designed inno-Liquidus temperature, TL/K 888vatively by adjusting the gap distance between the crucibleSolidus temperature, Ts/K 830wall and the cooler wall. Therefore, an intensively forcedDensity, ρ/ (g.cm 3)2680 (A357 alloy melt)shearing could be achieved at a higher shear rate by fullyThermal conductivity,taking advantage of the intensive magnetic field distribution522/(Wm-'.K)in the penetration depth.Specife heat, C/(J.kg-"K) 973φ90 mmViscosity cofficient, pμo/3.0x 10-3φ80mm(kg:ml:s)1 (copper coil)φ40 mm2000 (ilicon steel)Relative permeabilty, φ8 (A357 aloy melt)1 (cooling graphite cooler)1 (austenitic stainless steel)1.5 x 10-7 (copper coi),0 (silicon steel)Elctrical rsistivity，,2.1 x 10-7 (A357 alloy melt)(Q:m)8.0x 10(cooling graphite cooler)1.45 x 10%(austenitic stainless ste)500 (melt/crucible)Interfacial heat transfer50 (crucible/air)十5coefficient, h/ (W.m-2.K- ')1000 (melt/cooler)our electromagnetic system and heat flow in the radial direc-Fig. 1. Schematic view of semisolid metal slurry preparationtion [9] The laminar model is adopted in the present studyapparatus by A-EMS. 1: crucible; 2: electromagnetic strrer; 3:because of the small Reynold's number of fluid flow in themelt; 4: graphite cooler; 5: insulation kaowool.slurry preparation system. The effects of thermal or solutalThe commercial A357 aluminum alloy was used in thisbuoyancy forces are relatively small and can be neglected.study. The melt with a temperature of 923 K was pouredIn an addition, this paper is concerned primarily with bulkflow in the liquid. Except for the viscosity of the fluid, theinto the austenitic stainless steel crucible preheated to agiven temperature. After pouring, a graphite cooler with another properties of the fluid are held constant, which is takento be temperature dependent. The time-changed electro-upper lid was inserted in the center of the crucible, and then,EMS would be started. The upper and lower lids were mademagnetic force is replaced by time-averaged electromag-of insulation kaowool, ensuring that thermal exchange dur-netic force. In terms of the above assumptions, the goverm-ing equations of electromagnetic stirring involve the Max-ing solidification mainly occurs in the radial direction. Thcrucible containing the semisolid slurry was quenched intowell equations for electromagnetic field as follows [10-11]:room-termperature water immediately when the slurry tem-VxH=j(1)perature was cooled to 600°C. The specimens were ob-VxE=-aB/at(2)served with a Zeiss-type optical microscope after grinding,VxB=0(3)polishing, and etching by 0.5% HF acid. The relevant dataabout the alloy are summarized in Table 1.f =;Re(JxB")(4)where H is the magnetic intensity, A/m; E is the electric3. Mathematical formulationintensity, V/m; B is the magnetic flux density, T; J is theFor the sake of simplicit, we consider a two-dimensional induction curent density, A/m; t is the time, s; f is thetransient fully developed laminar flow of viscous incom-time-changed electromagnetic force, N/m'; Re is a real partpressible electrically conducting fluid driven only by anof complex number; B is the conjugated complex of Belectromagnetic stirring force. This simplification of a two-andVistheH中国煤化工dimensional problem is valid due to the large aspect ratio ofThe goverminHC N M H Gansport cnsist.Zhang Z.E et al, Numerical simulation on elctromagnetic field, flow field and temperature field in semisolid slurry... .637of the Navier Stokes equations for fluid flow and the ther-the fraction of solid.mal balance equation for heat transfer as follows.The equation of continuity is given as4. Simulation procedureV.1=0(5)The Navier Stokes equation is given asThe commercial sofware ANSYS 10.0 was used for thenumerical simulation. This code allows solving the transientρ+ piu.Vi=V.(uVi)+f -Vp(6three-dimensional electromagnetic field, flow field, andtemperature field by a sequence couple. Therefore, the geo-where u is a velocity vector, p is the hydrostatic pressure,metric model for calculation from the cross section in Fig. 1andfL is the Lorentz force. μ is the dynamic viscosity, whichis given in Fig. 2(a), and its geometric parameters are pro-is chosen to vary exponentially with temperature in the formvided entirely on-site. In order to save computing time andμ=μoe-4(T-5)(7)capacity, coarse mesh is used for the electromagnetic system,where To is the mean nucleation temperature, and A, whichfine mesh for the slurry system, and its mesh partitioning isis an empirical constant determined numerically, is chosenshown as in Fig. 2(b). In this study, the coil is simplified to acurrent-carrying conductor with the same conductive areas,to be 0.5 in the present study. The viscosity of liquid is con-sidered to be Lo when its temperature is higher than To. Thisso the current imposed on the coil is denoted by current den-method can help stabilize the numerical calculation to dealsity. The magnetic flux leakage of the electromagnetic stir-rer is small, and the magnetic boundary condition on thewith the phase interaction effects on fluid flow.outer nodes is assumed to be“flux parallel!" [12]. No-slipEnergy balance in the system is governed byboundary condition is exerted along the solid and liquid in-，d7(8terface for the fluid flow calculation. The Newton's law ofρC,+pC,u.VT =V.(VT)+pLcooling is used at the melt/crucible interface, the melt/coolerwhere T is the temperature, Cp is the specific heat, h is the interface, and the crucible/air interface. The heat radiation isthermal conductivity, L is the latent heat of fusion, andfs isignored during the calculation.(a)' CoolerCrucibleMeltA一CoilYokeFig. 2. Geomtric model of A-EMS (a) and mesh partitioning (b).The electromagnetic problem can be treated separately the present calculation is shown in Fig. 3. In addition, thefrom the fluid flow in the low magnetic Reynolds numberspecific solution information has been provided elsewhereapproximation. Hence, our numerical simulations consist oftwo steps. First, we calculate the magnetic field by solvingthe Maxwell equations in harmonic state based on the mag-5. Results and discussionnetic-nodal to obtain the distribution of elemental Lorentzforces acting on the liquid metal. Second, the flow field and5.1. Magnetic fieldtemperature field are calculated by loading the electromag-Fig. 4 shows the comparison of the predicted and meas-netic force into the flow and temperature model to obtain theured magnetic 1中国煤化工- drction of thedistributions of velocity and temperature. The flowchart of austenitic stainlearge, e.g., thereTYHCNMHG.638RARE METALS, Vol. 29, No. 6, Dec 2010Model flow field andModel electromagnetictemperature fieldforce fieldDivide grid and incoporateDivide grid and incorporateboundary conditions| Select solution parameters andsolvePrepare solutionLoad electromagneticorce。 NoparametersTest results↓SolveNoSteady stat?YesStopFig. 3. Flowchart of the calculation procedure..0.-Measuredfrequency imposed on the electromagnetic stirrer are 10 Aand 10 Hz, respectively. Clearly, the magnetic flux density.9-increases from the center to the edge of the crucible, and the= 0.calculated results are in reasonably good agreement with the的0.7measured results.Fig. 5 ilustrates the Lorentz force distributions in the.6-melt as the frequency holding at 50 Hz and current at 10 A.5-by normal EMS and A-EMS. In the case of normal EMS,the“skin effect" is very obvious at the commercial fre-0.0.01 0.020.030.04quency, the electromagnetic force mainly ditributes at outerDistance from melt centre to edge /mFig.4. Comparison of the predicted and measured magneticpart of melt, and the strring force becomes very weak at thenner part of melt, as shown in Fig. 5(a). However, byflux density along the radial direction of the crucible withoutcharge.A- EMS, the cooler changes the mass of the stirred melt and(a)b)乙X.z _XFig. 5. Distributions of electromagnetic force field by normal EMS (a) and A-EMS中国煤化工t 50 Hz and thecurrent at 10 A.YHCNMHG.Zhang Z.E et al, Numerical simulation on elctromagnetic field, flow field and temperature field in semisolid slurry... .639the electromagnetic force distribution; a horizontally rota- pies the center of the crucible, the melt in the annular cham-tional electromagnetic force field is obtained by the adjust-ber is subject to a uniformly intensive electromagnetic field,ment of cooler size even at a frequency of 50 Hz, as shownand the fluid flow pattern changes largely, owing to thein Fig. 5(b).forced convection produced by electromagnetic field.Fig. 6 shows the comparison of radial magnetic flux den-Therefore, the velocity field distribution becomes uniformlyity from the crucible center to edge in semisolid sluryintensive in this narrow gap, as shown in Fig. 7(b).preparation by both normal EMS and A-EMS. It is noted3.that the magnetic flux density sharply decreases from the，★- Normal EMSouter part to inner part of melt in the two cases due to the3.(●A-EMS“skin effect", but a greater magnetic flux density in the radial2.direction can be obtained by A-EMS than by normal EMS.旨2.05.2. Flow field∞1.5Typical velocity vector distributions by normal EMS and1.A-EMS are depicted in Fig. 7. Melt can be rotated at the0.horizontal direction. With normal EMS, the flow field dis-tribution is similar to the electromagnetic field. The velocityin the outer part of melt is large, but small in the center of0.020.030.04Distance from crucible centre to edge /mmelt, as shown in Fig. 7(a). Its main reason is that for the“skin effect", alternating magnetic field cannot penetrateig. 6. Distribution of magnetic fux density in the radial di-into the center of melt, and thus central melt cannot be ef-rection of melt by normal EMS and A-EMS as the frequencyfectively strred. With A-EMS, as the graphite cooler occu-holding at 50 Hz and the current at 10 A.(a(bYzxFig. 7. Flow field distributions of melt by normal EMS (a) and A-EMS (b) as the frequency holding at 50 Hz and the current at 10 A. .Fig. 8 shows the calculated velocity (absolute value) inabout 30°C occurs although the forced convection changesthe stirred melt along the radial direction by normal EMSthe temperature distribution of melt, as shown in Fig. 9(a).and A-EMS. It is noted that, in the presence of the graphiteIn case of A-EMS, as noted above, the sirred melt is subjectcooler, not only the flow pattern becomes uniform, but alsoto uniformly intensive stirring force, and also, heat exchangea greater velocity can be obtained by A-EMS than normal is promoted largely as cooling takes place at both theEMS, implying that optimal design of the annular chambermelt/crucible interface and meltcooler interfere. Therefore,will have an important effect on fluid flow evolution.a lower temperature difference less than 5°C can beachieved. It is known that short stirring time benefits for5.3. Temperature fieldhigh efficiency of slurry preparation, which needs largeig. 9 shows a comparison of temperature fields in thecooling rate and high shearing rate. However, an increase ofstirred melt by normal EMS and A-EMS. It is noted that, incooling rate le;中国煤化工ar the cruciblethe case of normal EMS, a large temperature differencewall no matter v心Fing is imposed.YHCNM HG.640R4RE METALS, Vol. 29, No.6, Dec 2010neous soldification of bulk melt.0.45t - Normal EMSFig. 10 shows the distributions of temperature field in the0.40苏AEMS。000radial direction of melt by normal EMS and A-EMS as the。frequency holding at 50 Hz and the current at 10 A. It is ob-云0.30vious that the temperature difference of melt by A-EMS is自0.25smaller than that by normal EMS.三0.200.155.4. Experimental verification0.10Fig.11 shows a comparison of the microstructures of0.05A357 alloy prepared by normal EMS and A-EMS, and the0.000.010.020.030.04same experimental conditions are as follows: pouring tem-Ditance from crucible centre to edge /mperature 650°C, crucible temperature 300°C, stirring currentFig. 8. Distributions of velocity field in the radial direction of10 A, and frequency 50 Hz. It can be seen in Fig. 1 l(a) that,melt by normal EMS and A-EMS as the frequency holding atin the case of normal EMS, the microstructure morphology50 Hz and the current at 10 A.is rosette-like, and the primary a(AI) is coarse. However, themicrostructures by A-EMS become fine, and the primaryAs a result, an optimal match of shearing intensity anda(AI) particles are globular, as shown in Fig. 11(b). The re-cooling rate is of key importance for realizing the simulta-sults are identical with other experiments [8].一600614(a(b)一61460711.613 .621613//610.62628/ 6111014、613一600.Fig. 9. Temperature field distributions of melt by normal EMS (a) and A-EMS (b) as the frequency holding at 50 Hz and the cur-rent at 10 A.635Although several mechanisms have been proposed to ex-630F ★★r Normal EMSplain the microstructure evolution in the semisolid metal- 。A-EMS625slurry preparation, it seems that the increase in nucleationdensity is considered to be important [13]. In order to620achieve this purpose, copious heterogeneous nucleation, nu-° 61clei survival throughout the bulk liquid, uniform temperature610 tand composition fields inside the liquid alloy are needed. In605the present slury preparation process, heterogeneous nu-600★cleation takes place in the undercooled liquid near the mouldwall. In the case of normal EMS, the electromagnetic force59mainly distributes at the outer part of melt at the commercial0.02 0.030.0frequency, and the stirring force is weak at the inner part ofDistance from crucible centre to edge / mmelt. A large temperature difference in the liquid leads toFig. 10. Distributions of temperature field in the radial direc-the formation of coarse solidification grain structures.tion of melt by normal EMS and A-EMS as the frequencyHowever, in the中国煤化工ing flow in theholding at 50 Hz and the current at 10 A.annular chamberYHcNMHGtheatreleased.Zhang Z.E et al, Numerical simulation on electromagnetic field, flow field and temperature field in semisolid slurry...641200 μumFig. 11. Comparison of the microstructures of A357 alloy prepared by normal EMS (a) and A-EMS ().from the solidification front to the bulk liquid, and thus, a [2] Zoqui E.J，Paes M., and Es-Sadiqi E, Macro-and micro-relatively uniform temperature distribution in the liquid willstructure analysis of SSM A356 produced by electromagneticbe formed instantaneously, which is considered to be neces-strring, J. Mater: Process. 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