PRELIMINARY SPH MODELLING OF OXIDE FORMATION DURING THE MOULD FILLING PHASE IN DC CASTING OF EXTRUSION BILLETS

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1 Fifth Interntionl Conference on CFD in the Process Industries CSIRO, Melourne, Austrli Decemer 2006 PRELIMINARY SPH MODELLING OF OXIDE FORMATION DURING THE MOULD FILLING PHASE IN DC CASTING OF EXTRUSION BILLETS Mhesh PRAKASH #1, Joseph HA #1, Pul W. CLEARY #1 nd John GRANDFIELD #2 # CAST Coopertive Reserch Centre, 1 CSIRO Mthemticl nd Informtion Sciences, Clyton, VIC CSIRO Mnufcturing nd Mterils Technology, Preston, VIC 3072 ABSTRACT Direct chill (DC) csting is widely used to produce luminium ingots nd illets. One of the issues with such cstings is the oxide generted especilly during the filling of the csting tle in the strt-up phse. This oxide cn ffect the performnce of the product during susequent extrusion. While the very first mteril is cut off nd discrded the distriution of oxides long the cst length is not known. It is therefore highly desirle to hve n ility to predict the mount nd distriution of the oxide generted during the process strt-up. In this pper, we use the mesh-free Smoothed Prticle Hydrodynmics (SPH) method to model the mould filling phse of DC csting. The free surfce nture of the flow during this phse is especilly menle to the mesh-free SPH modelling technique. Additionlly this method is very suitle for predicting surfce driven nd history dependent properties such s oxides. The pper presents preliminry predictions of cumultive interior nd exterior oxide levels with time in typicl DC csting opertion. The mount of interior oxide will indicte the effect of oxide on the finl metl microstructure. The mount of exterior oxide determines the surfce qulity of the illet. INTRODUCTION In direct chill (DC) csting, molten luminium is poured from the furnce through troughing system into refrctory mould tle plced on wter ox contining moulds of the desired illet dimeter s shown in Figure 1.After filling the strting heds in the mould, the mould descends nd the emerging illets re cooled y the direct chill wter spry. During luminium melt trnsfer oxides cn form which re detrimentl to the product qulity nd cuse defects during extrusion. Filters re used in the trnsfer from the furnce to the DC csting process to remove oxides nd other prticles. However, filling of the mould tle tkes plce fter the filter nd during this filling stge oxides cn e generted. At present there is no esy wy of experimentlly evluting the mount of oxide produced during such opertions s function of tle design or filling prctice. Therml relted defects cn lso occur t the strt of csting due to too short or too long mould filling time. Thus, one desires mould tle design which minimizes filling time vrition from mould to mould, fills fst enough nd does not crete turulence, splshing nd oxides. The mould tle cn hve more thn 100 illets depending on the dimeter. In the pst, modelling of the flow nd tempertures during DC csting tle filling hve een crried out using mesh sed methods such s the generl purpose FEM code FIDAP (Schneider nd Grun, 1995, Grun nd Schneider, 1997 nd Grun nd Schneider, 1998). Smoothed Prticle Hydrodynmics (SPH), due to its Lgrngin nture, is well suited to simulting the complex free surfce flow, such s found in the DC csting strt-up phse. It lso hs strong dvntges in simplifying predictions of oxide genertion nd trnsport, llowing estimtes to e mde of interior nd exterior oxide content in given metl csting system. These dvntges hve led to the use of SPH in severl csting processes including prediction of oxide content nd optimiztion of wheel design in luminium re-melt ingot csting reported in Clery et l. (2004) nd Prksh et l. (2006), high pressure die-csting in Clery et l. (2000) nd Clery nd H (2003) nd grvity die csting H et l. (1999). Trough Mould tle () Figure 1: Schemtic showing () verticl nd () side view of the DC Csting configurtion with trough nd mould tle contining six moulds. () 1

2 SPH MODELLING SPH is numericl method for modelling coupled fluid flows, solid structures nd het trnsfer with some unique cpilities. SPH is prticle sed rther thn using conventionl fixed grids or meshes to trck the fluid nd clculte the fluid velocities. The fluid is represented s los tht move round in response to the fluid or solid stresses produced y the interction with other prticles. SPH is prticulrly well suited to momentum dominted flows, flows involving complex free surfce ehviour nd flows with complex physics such s solidifiction or flow through industril porous medi. It is lso useful for flows round moving ojects, since there re no mesh structures to e ffected. A rief summry of the SPH method is presented here. For more comprehensive detils one cn refer to Gingold nd Monghn (1977), Monghn (1992) nd Clery nd Monghn (1999). The interpolted vlue of function A t ny position r using SPH smoothing cn e written s: A A ( r) = m W ( r r, h) (1) ρ where m nd r re the mss nd density of prticle nd the sum is over ll prticles within rdius 2h of r. Here W(r,h) is C 2 spline sed interpoltion or smoothing kernel with rdius 2h, tht pproximtes the shpe of Gussin function ut hs compct support. The grdient of the function A is given y differentiting the interpoltion eqution (1) to give: A A ( r) = m W ( r r, h) (2) ρ Using these interpoltion formule nd suitle finite difference pproximtions for second order derivtives, one is le to convert prolic prtil differentil equtions into ordinry differentil equtions for the motion of the prticles nd the rtes of chnge of their properties. Continuity eqution: From Monghn (1992), the SPH continuity eqution is: d ρ = m ( v v ) W (3) dt where ρ is the density of prticle with velocity v nd m is the mss of prticle. We denote the position vector from prticle to prticle y r = r r nd W = W r, h e the interpoltion kernel with let ( ) smoothing length h evluted for the distnce r. This form of the continuity eqution is Glilen invrint (since the positions nd velocities pper only s differences), hs good numericl conservtion properties nd is not ffected y free surfces or density discontinuities. Momentum eqution: The SPH momentum eqution used here is: P P d v m ρ ρ (4) = g W dt ξ 4µ µ v r 2 2 ρ ρ ( µ + µ ) r + η where P nd µ re pressure nd viscosity of prticle nd v = v v. Here ξ is fctor ssocited with the viscous term (Clery, 1996), η is smll prmeter used to smooth out the singulrity t r = 0 nd g is the grvity vector. The first two terms involving the pressure correspond to the pressure grdient term of the Nvier- Stokes eqution. The next term involving viscosities is the Newtonin viscous stress term. Eqution of stte: Since the SPH method used here is qusi-compressile one needs to use n eqution of stte, giving the reltionship etween prticle density nd fluid pressure. This reltionship is given y the expression: γ ρ (5) P = P0 1 ρ0 where P 0 is the mgnitude of the pressure nd ρ 0 is the reference density. For wter nd liquid metls we use γ =7. This pressure is then used in the SPH momentum eqution (4) to give the prticle motion. The pressure scle fctor P 0 is given y: γ P 2 2 (6) 0 = 100V = cs ρ0 where V is the chrcteristic or mximum fluid velocity. This ensures tht the density vrition is less thn 1% nd the flow cn e regrded s incompressile. Oxide modelling: Aluminium oxide grows on the surfce of molten luminium due to exposure to ir. This oxide lyer cn e roken y flow of the melt creting new surfce. The surfce my e folded over on itself entrining the oxide films. Any splshing will result in droplets of melt surrounded y oxide film tht ecome dross on the surfce melt. To quntify this oxide formtion, liner oxide (O x ) growth model suggested y Bker et l. (1995) is used: do x = k dt l (7) where k l is the rte constnt nd t time. These uthors 3 2 estimted the rte constnt to e k l = kg/m s. Note tht the oxide is trnsported with the fluid nd no ccount of ny pprent density difference cusing the oxide to sink or rise is llowed for. DC CASTING MODEL SETUP A unit of 6 moulds ws modelled for simplicity. The dimension of the DC csting mould tle given in Figure 1 is 0.83 m long nd m wide with gte width of m. There re six circulr moulds in the tle ech with dimeter m. The design used is conceptul one typicl of industry prctice. A strting hed, mounted to hydrulic rm, forms flse ottom to the mould. When the mould is filled nd the metl egins to solidify, the strting hed is lowered t controlled rte. As the strting hed lowers, wter jets uilt into the mould spry wter onto the illet to cool the surfce nd further solidify the metl. Multiple moulds in the tle contriute to high production rtes in the cst house. The metl height in the lunder system is kept constnt t 70 mm with respect to the se of the mould tle. This pressure hed thus controls the flow to the mould tle. In prctice the metl hed depends on the flow rte from 2

3 the furnce. To represent this pressure hed in the SPH simultion, reservoir of fluid of fixed height is plced in the lunder in front of the gte s shown in Figure 2. A pressure inflow oundry condition of 1614 P is pplied t the inflow to the reservoir to mintin stedy hed of 70 mm while t the sme time chieving mould tle fill time of round 30 seconds. The descent of the strting hed is not simulted. The model is isotherml. Inflow Reservoir To Mould Tle ) Inflow Pressure (P) Time (s) Figure 2: Cross section of the constnt hed inflow reservoir used to control the inflow to the mould tle. A resolution of 5 mm ws used for the prticles representing the molten metl, the moulds nd mould tle. The numer of prticles used for the geometry is 123,321. The numer of fluid prticles increses with time s more nd more prticles re generted y the inflow. The finl numer of fluid prticles when the mould is full is round 120,000. Figure 3 shows the vrition of inflow pressure nd velocity s it dpts to fluid flow cusing rmp up in pressure to mintin the specified pressure hed. FLOW PATTERN IN DC CASTING TABLE Figure 4 shows the filling of the mould tle. The molten metl is coloured y speed in frmes on the left nd y oxide frction in the frmes on the right. The metl speed is coloured with red eing the mximum of 0.21 m/s nd lue eing sttionry. The oxide frction is coloured with lue representing no oxide content nd red representing mximum of 6.8 µg/kg. At 3.0 s, the metl strts jetting into the tle nd hs very frgmented structure. There is some metl flowing into the first two moulds ut most of it flows forwrd further into the tle t high speed. At 5.0 s, the molten metl is still very frgmented nd the leding mteril hs now hit the end of the DC tle. Once the metl hits the end of the tle it slows nd strts to ckfill. The two moulds t the end of the tle therefore strt filling fster thn the other four moulds. At 7.0 s, the ck filling nture of the flow is evident with the two moulds t the end now lmost 30 to 40% full. The se of these moulds is lmost fully covered y liquid metl. The four other moulds re less thn 10% full t this stge. Modest ut meningful oxide levels re now oserved close to the centre of the moulds s shown y the ple lue colour of the metl in the right frme. Inflow Velocity (m/s) ) Time (s) Figure 3: Vrition of inflow pressure (ottom) nd velocity (top) nd with time. At 9.0 s, the lst two moulds re lmost 80% full with metl now strting to ckfill the two moulds in the middle of the tle. There is strong centrl jet of clen new metl coming into the tle seen from the red coloured liquid in the centre t this stge. The liquid metl hs slowed down considerly on the sides in the moulds s well s t the end leding to the ck filling. At 11.0 s, the ckfilling of the middle two moulds is still in progress ut the lst two moulds t the end of the tle re now lmost completely full. The length of the centrl strong jet hs strted to diminish with this now occupying only one third of the tle length. By 13.0 s the entire surfce of the tle is covered with metl. By this stge the ck filling of the moulds hs lmost cesed nd the strength of the centrl jet hs lso reduced considerly. Between 13.0 nd 25.0 s there is no significnt chnge in the metl flow pttern. During this stge the entire surfce of the tle is covered with metl nd the filling consists of stedily rising depth of metl until it reches the hed level of 70 mm. The lrgest increse in metl fill level t this stge is for the two moulds t the front. The velocity nd oxide distriutions on the surfce of the metl do not vry significntly during this stge. 3

4 Figure 4: Filling ptterns of DC mould tle t different times. The fluid is coloured y speed (left column) nd y oxide mss (right column). 4

5 Figure 4: Filling ptterns of DC mould tle t different times. The fluid is coloured y speed (left column) nd y oxide mss (right column). 5

6 By 25.0 s, the entire tle is filled with the metl depth reching the required level of 70 mm thus completing the strt-up phse of the DC cst process. The centrl jet of metl hs now ecome wek s indicted y the ple lue colour on the left frmes. Higher velocity regions re ctully seen in the mould s the metl swirls round s indicted y the yellow to red colour in the six moulds. There is stedy increse of oxide level in the metl mss during this stge s seen y the chnge in colour of the metl surfce from ple lue to yellow. In generl, the mount of oxide in the metl shows grdul increse from the gte to the end of the tle nd decrese from the centrl region to the sides of the tle. Due to the constnt hed condition the metl flow rte in the centrl region grdully diminishes s the metl in the tle rises up to the requisite level of 70 mm. Due to the low metl flow rte in the centrl region the mount of oxide in this region is higher s the reltively slow moving metl is exposed to ir for longer time. Since the metl in the six moulds is moving round in swirling pttern the oxide produced on the surfce ecomes entrined into the moulds leding to lower oxide on the exterior moulds s seen from the ple lue colour of metl in the moulds in the right frme t 25.0 s. As fresh metl flows into the tle from the gte, its exposure to the ir s it flows down the tle cuses oxide to form. The metl in the region ove the mould is constntly replenished y metl flowing from the centrl region. In these regions, the flow hs circulr pttern with significnt mixing. These results suggest tht the surfce lyer of the metl in the centrl region of the tle is the primry loction for oxide formtion. OXIDE GENERATED DURING DC CAST FILLING Figure 5 shows the time vrition of the totl, interior nd exterior oxide in the metl s percentge of the metl mss in the tle. The mount of oxide formed represents only smll frction of the totl metl. However this cn e significnt solute mount when the totl luminium DC cst production is tken into ccount. The percentge of totl oxide in the metl increses lmost linerly with time. By round 20 s the totl percentge of oxide reches pek vlue of round 0.31% nd then strts to gently decline. The percentge of externl oxide increses rpidly t the strt with level only slightly lower thn for the totl oxide. This indictes tht most of the erly oxide is on the surfce where it is creted. The externl oxide percentge reches mximum of out 0.15% t round 12 s nd then slowly decreses s proportion of totl metl. This is expected since the totl surfce of the mould tle is constnt, nd thus the mximum surfce re of the metl tht cn e exposed to ir, is fixed. At the sme time the totl mount of metl in mould tle increses stedily with time. The interior oxide curve hs slow rte of increse t first ut then increses more rpidly etween 12 nd 20 s. The totl interior oxide content reches stedy percentge of round 0.25% t 25 s. The stedy level of interior oxide is mintined even with the ddition of more metl into the tle suggesting tht the ctul level of interior oxide is incresing with time. This is ecuse the strong levels of mixing in the moulds oserved towrds the end of the filling process, promotes the entrinment of oxide into the metl interior. The interior oxide cn result in possile defects in the illet. The exterior oxide on the other hnd hs significnt effect on the surfce finish of the illet. Oxide (% of totl metl mss) Internl Oxide Externl Oxide Totl Metl Oxide Time (s) Figure 5: Temporl vrition of oxide s percentge of totl metl. CONCLUSIONS SPH simultion of DC csting gives detiled prediction of the flow pttern of molten metl from the lunder to the mould tle, the rte of oxide formtion on the exposed metl surfce nd its susequent entrinment into the metl. The Lgrngin nture of SPH mkes it simple to trck the movement of oxide from its formtion on the exposed surfce of the molten metl to its mixing into the fluid s the metl flows from the refrctory to the mould tle through the lunder system. The simultion demonstrtes: The metl fill pttern in the mould tle is strongly dependent on the metl flow speed. Fster metl speeds leds to more ck filling wheres slower speeds cn led to more front filling pttern. Exterior nd interior oxide in the metl cn e predicted during the strt-up phse using SPH. Exterior oxide is responsile for the surfce finish of the illet wheres interior oxide cn ffect the metl microstructure. Both properties significntly ffect the usility of the finl product. SPH simultions cn e used to evlute oxide levels nd fill ptterns for different metl flow rtes nd mould rrngements in DC tle leding to n optimised DC csting system. In the next stge we will e compring the SPH simultion results with wter nlogue modelling results s well s ctul DC csting experimentl results using molten metl. 6

7 ACKNOWLEDGMENTS This project ws conducted y the CASTcrc. The support of Comlco nd ODT Engineering re grtefully cknowledged. CSIRO, Comlco nd ODT Engineering re core prticipnts in the CASTcrc, which ws estlished under nd is supported in prt y the Austrlin Government's Coopertive Reserch Centres scheme. REFERENCES BAKER, P.W., NGUYEN, K., KIRKALDIE, R., (1995), in Aluminium Cst House Technology 4th Austrlsin Asin Pcific Conference, TMS, p CLEARY, P., (1996), New implementtion of viscosity: tests with Couette flows. SPH Technicl Note 8, CSIRO DMS, Technicl Report DMS C 96/32. CLEARY, P.W., HA, J. nd AHUJA, V., (2000), High pressure die csting simultion using smoothed prticle hydrodynmics. Int. J. Cst Metls Res, 12, CLEARY, P.W. nd HA, J., (2003), Threedimensionl SPH simultion of light metl components. J. Light Metls, 2/3, CLEARY, P. W. & MONAGHAN, J. J., (1999), Conduction modelling using smoothed prticle hydrodynmics, J. Computt. Phys., 148, CLEARY, P., PRAKASH, M., HA, J., SINNOTT, M., NGUYEN, T. nd GRANDFIELD, J., (2004), Modelling of cst systems using smoothed prticle hydrodynmics, JOM, 3, GINGOLD, R.A. & MONAGHAN, J.J., (1977), Smoothed prticle hydrodynmics, Theory nd ppliction to non-sphericl strs, Mon. Not. Roy. Astron. Soc., 181, GRANDFIELD, J, CLEARY, P., PRAKASH, M, SINNOTT, M., OSWALD, K. & NGUYEN, V, (2004), Mthemticl Modelling of Ingot Cster Filling Systems, Light Metls 2004, Edited y A.T. Tereux TMS (The Minerls, Metls & Mterils Society), GRUN, G.U. nd SCHNEIDER, W., (1997), Influence of Fluid Flow Field nd Pouring Temperture on Therml Grdients in the Mushy Zone During Level Pour Csting of Billets., Light Metls 1997: TMS, USA. p GRUN, G.U. nd SCHNEIDER, W., (1998), Numericl Modelling of Fluid Flow Phenomen in the Lunder- Integrted Tool Within Csting Unit Development., Light Metls 1998: TMS, USA. p HA, J., CLEARY, P. W., ALGUINE, V. nd NGUYEN, T., (1999), Simultion of die filling in grvity die csting using SPH nd MAGMAsoft, Proc. 2nd Int. Conf. on CFD in Minerls & Process Industries, Melourne, Austrli, MONAGHAN, J. J., (1992), Smoothed prticle hydrodynmics. Ann. Rev. Astron. Astrophys., 30, PRAKASH, M., CLEARY, P. W., GRANDFIELD J., ROHAN, P. nd NGUYEN, V., (2006), Optimiztion of ingot csting wheel design using SPH simultions, ccepted for puliction in Progress in CFD. SCHNEIDER, W. nd GRUN, G.U., (1995), The New Airsol Veil Billet Csting System - Improvements, Mthemticl Modelling, Cst House Experiences., Fourth Austrlin Asin Pcifice Aluminium Cst House Technology Conference. 1995: TMS. p