Application of particle method to the casting process simulation

Transcription

1 IOP Conference Seres: Materals Scence an Engneerng Applcaton of partcle metho to the castng process smulaton To cte ths artcle: N Hrata et al 1 IOP Conf. Ser.: Mater. Sc. Eng Vew the artcle onlne for upates an enhancements. Relate content - Smulatng non-newtonan flows wth the movng partcle sem-mplct metho wth an SPH ernel Hao Xang an Bn Chen - Smulaton stuy on contnuous castng process of Al/Al bmetal roun bllet uner mult-electromagnetc L Wu, Tongmn Wang, Yng Fu et al. - A parttone resoluton for concurrent flu flow an stress analyss urng solfcaton: applcaton to ngot castng Mchel Bellet, Oba Boughanm an Grégory Fel Ths content was ownloae from IP aress on 13/11/18 at 3:5

2 IOP Conf. Seres: Materals Scence an Engneerng 33 (1) 1114 IOP Publshng o:1.188/ x/33/1/1114 Applcaton of partcle metho to the castng process smulaton N Hrata 1, Y M Zulaa 1 an K Anza 1 1 Department of Metallurgy, Grauate School of Engneerng, Tohou Unversty , AobaAramaaza, Aoba-u, Sena-sh, Myga-en, , JAPAN Abstract. Castng processes nvolve many sgnfcant phenomena such as flu flow, solfcaton, an eformaton, an t s nown that castng efects are strongly nfluence by the phenomena. However the phenomena complexly nteracts each other an t s ffcult to observe them rectly because the temperature of the melt an other apparatus components are qute hgh, an they are generally opaque; therefore, a computer smulaton s expecte to serve a lot of benefts to conser what happens n the processes. Recently, a partcle metho, whch s one of fully Lagrangan methos, has attracte conserable attenton. The partcle methos base on Lagrangan methos nvolvng no calculaton lattce have been evelope raply because of ther applcablty to mult-physcs problems. In ths stuy, we combne the flu flow, heat transfer an solfcaton smulaton programs, an tre to smulate varous castng processes such as contnuous castng, centrfugal castng an ngot mang. As a result of contnuous castng smulaton, the power flow coul be calculate as well as the melt flow, an the subsequent shape of nterface between the melt an the power was calculate. In the centrfugal castng smulaton, the mol was smoothly moele along the shape of the real mol, an the flu flow an the rotatng mol are smulate rectly. As a result, the flow of the melt ragge by the rotatng mol was calculate well. The eccentrc rotaton an the nfluence of Corols force were also reprouce rectly an naturally. For ngot mang smulaton, a shrnage formaton behavor was calculate an the shape of the shrnage agree well wth the expermental result. 1. Introucton Nowaays, computer smulaton has acqure an mportant role n prectng castng efects. However, the castng process nvolves varous complcate phenomena whch nteracts each other. Therefore t s qute ffcult to prect the castng efects. Recently, partcle methos base on Lagrangan methos nvolvng no calculaton lattce have been evelope raply because of ther applcablty to mult-physcs problems[1]. Ths characterstcs of the fully Lagrangan metho has attracte conserable attenton as a powerful tool to smulate complcate phenomena occurrng n the castng processes. The SPH (smoothe partcle hyroynamcs) metho an the MPS (movng partcle sem-mplct) metho are the most commonly use partcle methos[]. Dscrete obects (partcles) are use as the calculaton elements n these methos. Because partcles can be place an move freely n space, partcle methos are funamentally free from spatal constrant. Ths feature allows the partcle methos to smulate the heat an mass transfer phenomena that are observe urng the solfcaton process more easly an rectly than other methos that use the calculaton lattce. In aton, an algorthm usng the MPS metho s smple an smlar to the conventonal FDM (fnte fference Publshe uner lcence by IOP Publshng Lt 1

3 IOP Conf. Seres: Materals Scence an Engneerng 33 (1) 1114 IOP Publshng o:1.188/ x/33/1/1114 metho); therefore, mult-physcal smulatons base on the MPS metho have been evelope raply n varous fels[3 8]. However, few stues have been conucte n the fel of castng. Cleary et al. reporte on the applcaton of the SPH metho to the mol fllng problem. In ther stuy, SPH smulatons that combne the effects of flow, heat transfer an solfcaton were use an showe goo agreement wth the expermental results[9]. Recently, a heat transfer an solfcaton smulaton program that was base on the MPS metho an ncorporate nterfacal heat resstance was reporte by Hrata et al. They emonstrate that the accuracy of ther program was as hgh as a commercal solfcaton smulaton software base on FVM (fnte volume metho)[1]. Hrata et al. also reporte a flow smulaton program base on the MPS metho[11], an the couplng smulaton of flow an solfcaton smulaton programs[1]. In ths stuy, the flu flow an solfcaton smulaton programs base on the MPS metho were apple to varous castng processes. Power entrapment problem, flu flow n centrfugal castng an solfcaton shrnage formaton behavor n the ngot mang were emonstrate to show the applcablty of partcle metho on the castng smulaton.. Numercal metho.1. The MPS metho.1.1. Weght Functon In the MPS metho, governng equatons consst of partcle nteracton equatons. All nteractons between partcles are lmte to a fnte stance. The strength of nteracton can be escrbe usng a weght functon of stance between two partcles. The graent or other operators can be escrbe usng the weght functon. Whereas numerous types of weght functon have been propose, equaton (1) was use n ths stuy. Equaton (1) s base on the ernel functon of SPH metho, an Atae-Ashtan reporte that equaton (1) gves better stablty for flu flow analyss[13]. w r, c r 4 7c r r cr cr 3 1 r 7c cr 3 r.5c r.5c r r c r c r r (1) Here, r s the stance between the neghborng partcles. r, whch enotes the specfc sze of the partcle, has the same sgnfcance as the lattce sze n FDM. c s the ernel sze coeffcent an usually vares between an 4. Partcle number ensty n of the partcle s use n the MPS metho to calculate the nteracton between partcle an the surrounng partcles. n s the sum of the weght functon of the partcles surrounng the partcle, an s expresse as follows. n w r, cr r () Here, r an r are the poston vectors of partcles an, respectvely. n s equal to n n the case that a partcle has no surface partcle aroun t. Assumng that the flu s ncompressble an

4 IOP Conf. Seres: Materals Scence an Engneerng 33 (1) 1114 IOP Publshng o:1.188/ x/33/1/1114 conserng that the partcle number ensty n s rectly relate to the flu ensty, we can use n for the mass conservaton conton n the ncompressble flow analyss usng the MPS metho[1]..1.. Partcle nteracton moels Partcle nteracton moels are use to escrbe fferental operator n the partcle metho [3]. If an are arbtrary scalars at postons r an r, then the partcle nteracton moels for the fferental operators can be expresse as follows. r r w r r, c r (3) n r r r r w r r, cr (4) n r r Equaton (3) s a graent moel an equaton (4) s a Laplacan moel. the assgne numbers of partcles. s the number of space mensons. Suffxes an represent.. Flu flow Analyss The governng equatons for ncompressble flow consst of the contnuty equaton an Naver-Stoes equaton as follows. D Dt (5) Du 1 p u f Dt (6) Here, ncates ensty (g/m 3 ); u, velocty vector (m/s); p, pressure (Pa);, nematc vscosty (m /s); an f, the boy force vector nclung gravty. Flow calculaton by the MPS metho s base on the prector-corrector metho smlar to that n the case of the FDM or other conventonal methos. The maor fferences between the MPS metho an the FDM are the formulaton of the Posson equaton of pressure an the calculaton of partcle poston. In the MPS metho, the tentatve partcle poston s calculate usng tentatve velocty n the precton phase; therefore, the correcton n poston s calculate along wth the correcton n velocty n the correcton phase. The Posson equaton for pressure n the MPS metho s escrbe usng the tentatve partcle number ensty n * an n as follows[1]. n * s the partcle number ensty calculate usng the tentatve partcle postons. 1 p t n * n n (7).3. Heat Transfer Analyss Heat transfer equatons are escrbe as follows. DH T Dt (8) t Q T 1 T R (9) 3

5 IOP Conf. Seres: Materals Scence an Engneerng 33 (1) 1114 IOP Publshng o:1.188/ x/33/1/1114 Here, H represents the enthalpy per unt volume (J/m 3 ); t, tme (s);, thermal conuctvty (W/m K); an T, temperature (K). Q (J/m ) s the thermal flux per unt area n tme t (s), R s heat resstance (m K/W), an T 1 (K) an T (K) are the surface temperatures of materals 1 an at the nterface between the materals. Heat transfer equatons (equaton (8) an (9)) were transforme usng the Laplacan moel (equaton (4)), an the enthalpy at the next tme step +1 was obtane from the temperature strbuton at the tme step as follows. Superscrpts an +1 sgnfy tme steps n the followng equaton. 1 1 T T H H t wr r, c r n 1 1 R r r r r (1) The enthalpy metho was use to calculate the effect of solfcaton..4. Temperature epenence of ensty Temperature-epenent r varaton was ntrouce to escrbe shrnage usng the followng equaton. 1 M, r (11) Here, r,, M an sgnfy specfc sze (m), mass (g) an ensty (g/m 3 ) of the partcle, respectvely. Assumng that the masses of each partcle are constant, we can calculate the solfcaton shrnage usng the temperature-epenent ensty as escrbe n equaton (11). Partcles havng varous values of r can be hanle smultaneously n the MPS metho usng the mofe weght functon. The mofe weght functon w at partcle s escrbe as follows. w r r, c r r wr r, c r r, w,,, (1) r, 3. Applcaton 3.1. Power entrapment n contnuous castng Calculaton Moel Frstly, mol power entrapment problem was smulate. Mol power entrapment s one of the fatal efects n contnuous castng, whch occurs by the vortex or complex flow at the melt-power nterface. In partcle metho, plural ns of flu partcles are easly hanle only by efnng the propertes for each partcle. In ths case, two ns of flu were efne; A, heavy flu (representng the melt); an B, lght flu (representng the power). The values of ensty were lower than the actual values of melt an power for the calculaton stablty. The calculaton was performe usng half moel of the mol n the contnuous castng as shown n the fgure 1. A force convecton regon was efne to represent the melt nflow from the nozzle, an a baffle representng the nozzle was set above the convecton regon. If a partcle comes nto the convecton regon, the velocty of the partcle was fxe at 1.5 m/s to a 3 egree ownwar recton. 4

6 .5 MCWASP XIII IOP Conf. Seres: Materals Scence an Engneerng 33 (1) 1114 IOP Publshng o:1.188/ x/33/1/ Results Fgure shows the example of the result of the mol power entrapment calculaton. The result was vsualze usng ray-tracng software POV-Ray 3.6. In the vsualzaton, the melt was set to be transparent an only the power was vsble. As a result of -phase flow calculaton, the menscus curve of melt-power nterface coul be observe (fgure (a)). In fgure (b), complex behavor of the power was calculate well; the flow was sturbe by the baffle, the power was entrappe by the vortex, an the surfacng of the power by the buoyancy force was taen nto account. Because the behavor of the power was escrbe by the movement of partcles (.e. calculaton elements themselves), the entrappe power partcles never sappear by numercal ffuson (fgure (c)) an coul be trace well. The smulaton program coul also reprouce the nfluence of flow conton on the entrapment qualtatvely. The amount of entrappe power vare epenng on the vscosty of flu or ensty fference between melt an power; hgher vscosty of flus an the larger fference of ensty reuce the amount of entrapment. Baffle Flu B (5g/m 3 ) Force convecton 1.5(m/s) (m).1. Flu A (1,g/m 3 ).5 Fgure 1. Calculaton moel : half moel of the contnuous castng mol wth a baffle. (a) (c) (b) Melt flow Fgure. Calculate result of mol power entrapment problem. Only power partcles are ncate usng ray-tracng software POV-Ray 3.6. (a) -phase flow reproucng the shape of the power-melt nterface. (b) Influence of the vortex an the buoyancy on the entrapment of the power. (c) Tracng the entrappe power. 5

7 IOP Conf. Seres: Materals Scence an Engneerng 33 (1) 1114 IOP Publshng o:1.188/ x/33/1/ Centrfugal castng Calculaton Moel Centrfugal castng s the process usng a mol wth hgh rotatonal spee. The melt flow s nuce by the rotatng mol, therefore the process s generally calculate usng the specal bounary conton at the mol surface. However, n the conventonal metho usng calculaton lattce, t s ffcult to ntrouce the eccentrc rotaton or other complex movements of components. In ths secton, the mol was smoothly moele along the shape of the real mol, an the flu flow an the rotatng mol are smulate rectly. Velocty (m/s) (a).1 s (b).3 s (c).5 s (). s Fgure 3. Flu flow of centrfugal castng : 5rpm. (a).1 s (b).3 s (c).5 s (). s Fgure 4. Flu flow of centrfugal castng : 5rpm, wth eccentrc rotaton Results Fgure 3 an 4 show the results of the -mensonal calculaton. Inner ameter of the mol was 1 mm, rotaton spee was 5 rpm. Vscous flu (the nematc vscosty was 1. x 1-5 m /s) flowe nto the cavty by 1. m/s, an nflow uraton was.3 s. The centrfugal force s wea uner ths conton, therefore an abrason of the melt occurre. The abrason coul be observe even after s (fgure 3 ()) uner the normal conton. In contrast, no abrason coul be observe after s n the fgure 4 (), n whch eccentrc rotaton s consere; rotaton was ecentere by mm. In ths case, raus of rotaton was partally longer, therefore centrfugal force an subsequent rotaton spee ncrease. As shown n the results, Corols force was mplemente naturally, an the nfluence of movements of obects was easly mplemente usng the partcle metho Shrnage formaton Calculaton Moel Fnally, a shrnage formaton behavor was smulate. Inner an outer shrnage are sometmes separate at the upper part of the castng, an the bounary s calle brgng. The solfcaton behavor of the upper part of castng s complcate; at whch heat transfer, solfcaton an shrnage flow occur smultaneously. In ths secton, the smulaton programs for 6

8 IOP Conf. Seres: Materals Scence an Engneerng 33 (1) 1114 IOP Publshng o:1.188/ x/33/1/1114 solfcaton an flow were combne conserng temperature epenency of ensty. The combne program was apple to cylnrcal shape castng, an the calculate result was compare wth the expermental result. Pure Sn was use for melt, san for a mol. Ar partcles were use to conser the nfluence of ar-coolng. (a) s (b) s (c) 5 s External shrnage lne Internal shrnage () 85 s (e) Expermental result. Fgure Fg.5 5. Calculate shrnage formaton behavor an the expermental result Results Fgure 5 (a) to () shows the brgng formaton behavor that separate nner an outer shrnage of the castng. The results were vsualze usng ray-tracng software POV-Ray 3.6. Fgure 5(e) s the expermental result. The fgures show the cross secton of the castng. In fgure 5 (a) to (), the shrnage formaton behavor was escrbe realstcally, an the brgng at upper part of the castng was observe; the nfluence of ar-coolng was necessary to reprouce the brgng formaton. The partcle metho coul tae nto account the surface rop by the solfcaton shrnage, an the nfluence of subsequent shape varaton on the heat transfer pathway between the castng an the ar, easly an rectly. 4. Concluson The flow an solfcaton smulaton program base on the MPS metho was apple to the castng processes, an the applcablty of the partcle metho on the castng smulaton were scusse. Frstly, the mol power entrapment problem n contnuous castng was calculate. As a result, complex behavor of the melt an the power aroun the menscus was calculate an the tracng ablty of trappe power was emonstrate. The results show the mass conservaton ablty of the partcle metho an the ease of the hanlng the mult-phase flow. Next, the flow n the centrfugal castng was smulate. The melt flow ragge by the rotatng mol was escrbe rectly, an nfluence of eccentrc rotaton was emonstrate. The partcle metho coul calculate the movement 7

9 IOP Conf. Seres: Materals Scence an Engneerng 33 (1) 1114 IOP Publshng o:1.188/ x/33/1/1114 of the mol rectly an Corols force was mplemente naturally. Fnally, the shrnage formaton was calculate usng the combne smulaton program for solfcaton an flow. As a result, the shrnage formaton behavor n the pure Sn castng was smulate realstcally, an the nfluence of ar-coolng on the brgng formaton was reprouce well. In concluson, the partcle metho has hgh capablty to smulate complex phenomena nvolvng mult-phase an mult-physcs wth the large movement of the obects, an s expecte to smulate complcate castng processes. 5. References [1] Koshzua S 5 Ryushhou (Toyo: Maruzen) [] Koshzua S 8 Ryushhou Smulaton (Toyo: Bafuan) [3] Koshzua S, Tamao H an Oa Y 1995 Computatonal Flu Dynamcs J [4] Koshzua S an Oa Y 1996 Nucl. Sc. Eng [5] Koshzua S, Nobe A an Oa Y 1998 Int. J. Numer. Methos Flus [6] Koshzua S an Oa Y 1996 Nucl. Sc. Eng [7] Belytcho T, Krongauz Y, Organ D, Flemng M an Krysl P 1996 Comput. Methos appl.mech. Eng [8] Shao S an Lo E Y M 3 Av. Water Resour [9] Cleary P W an Ha J 6 Apple Mathematcal Moellng [1] Hrata N an Anza K 8 Journal of Japan Founry Socety [11] Hrata N an Anza K 11 Journal of Japan Founry Socety [1] Hrata N an Anza K 11 Materals Transactons [13] Atae-Ashtan B an Farha L 6 Flu Dynamcs Research