Analysis of the impact of modification of cold crucible design on the efficiency of the cold crucible induction furnace

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1 IOP Confeence Seies: Mateials Science and Engineeing PPER OPEN CCESS nalysis of the impact of modification of cold cucible design on the efficiency of the cold cucible induction funace To cite this aticle: R Pzylucki et al 08 IOP Conf. Se.: Mate. Sci. Eng View the aticle online fo updates and enhancements. This content was downloaded fom IP addess on 0/0/08 at 0:6

2 nalysis of the impact of modification of cold cucible design on the efficiency of the cold cucible induction funace R Pzylucki, S Golak, P Bulinski, J Smolka, M Palacz, G Siwiec, J Lipat and L Blacha Depatment of Industial Infomatics, Silesian Univesity of Technology, Kasinskiego 8, Katowice, Poland Institute of Themal Technology Silesian, Univesity of Technology, Konaskiego, Gliwice, Poland Institute of Metals Technology, Silesian Univesity of Technology, Kasinskiego 8, Katowice, Poland oman.pzylucki@polsl.pl bstact. The aticle includes numeical simulation esults fo two induction funace with cold cucible (IFCC). Induction funaces diffe in cold cucible design, while the inducto geomety was peseved fo both vaiants. Numeical simulations wee conducted as thee dimensional one, with coupled analysis of electomagnetic, themal and fluid dynamics fields. Duing the expeiment, six calculation vaiants, diffe in amount of molten titanium (thee diffeent weights of titanium fo each type of cold cucible) wee consideed. Main paametes contolled duing the calculations wee: electical efficiency of the IFCC and the meniscus shape of liuid metal.. Intoduction Induction funaces with cold cucible ae most commonly used fo melting vey eactive metals and alloys. Such metals should be melted without contact with the cucible. Cold cucible is a compomise solution. The best, fom the point of view of lack of contact, is the levitation melting. But in levitation melting thee ae poblems with the lifting foce especially fo heavy wokpieces. In cold cucible funace, the molten metal contacts only with a bottom of the cucible. Fom the cucible walls, liuid metal is epulsed by electodynamic foces. t the bottom, the metal is in contact with the cucible not diectly, but though a solidified laye (skull). Thee ae two main poblems in cold cucible funaces design: electic (and of couse total) efficiency, and minimization of the skull []. Low electic efficiency is due to double convesion of electical enegy: fom cuent to the electomagnetic field and again to cuent. Fist convesion between inducto and cold cucible segment (finge) and the second between cold cucible segments and the molten metal. This cannot be changed but enegy losses can be educed by the appopiate cold cucible constuction []. Moeove, the skull volume depends on the cold cucible constuction. The aim of the aticle is the modification of the design of cold cucible to impove the efficiency of the melting pocess and to minimize the skull. Content fom this wok may be used unde the tems of the Ceative Commons ttibution.0 licence. ny futhe distibution of this wok must maintain attibution to the autho(s) and the title of the wok, jounal citation and DOI. Published unde licence by Ltd

3 . Models of consideed cold cucibles Two cold cucible designs ae investigated in this aticle. Simplified sketch of the fist and the second constuction is pesented in Figue and, espectively. s shown in Figue fist constuction was made fom one piece of coppe. Thee is a sepaation between segments, and the incision also includes pat of the cucible bottom (oange pat with index 6). Thee is a massive chassis below the inducto. The shuns does not have pole pieces. The cucible bottom is slightly concave. dvantage of this design is the incision of the oute pat of bottom which pevents shoting of the cuents induced in the bottom pat of the segments. Disadvantages of this constuction ae: massive chassis just below the inducto, and lack of pole pieces. Poblematic is also the ecess in the bottom. This causes a thick skull. z 4 5 h lc h cc h s h f s i h sc h bi bw i 6 s bi s f gs t s s h b Figue. Sketch of fist IFCC Model, metal melt, solid bottom, segment, 4 inducto, 5 shunt, 6 sepaated pat of the bottom. z 4 5 h lc h cc s i h sc h b 6 bw s f g i b s s h p h s h f g s Figue. Sketch of second IFCC Model, metal melt, solid bottom, segment, 4 inducto, 5 shunt, 6 ceamic element. The second constuction of the cold cucible, consideed in this aticle, consists of two main, sepaate pieces: segments and flat bottom. The shunts has pole pieces below the inducto, and thee is no conducting mateial just below inducto and segments. Such a design (moe difficult fom the constuction point of view) pevents the induction of cuents outside the cold cucible segments.

4 .. Model fo electomagnetic field analysis nalysis of electomagnetic field basis on -V fomulation euation () [] is conducted as a steady state one. Electomagnetic field analysis esults wee volumetic heat souces euation () [4] and volumetic electomagnetic foces euation (4) [4]. These values wee calculated in the melt aea only, and they ae input data fo tempeatue and fluid dynamics analysis. ot ot j gad 0 μ 0 μ σ V () whee: 0 - pemeability of vacuum; - elative pemeability; - magnetic vecto potential; - conductivity; - angula velocity; V - scala electic potential; j - unit imaginay numbe. v J () whee: v - volumetic density of active powe; J - cuent density. J σ j gadv () f m = Re (J B ) (4) B ot (5) whee: f m - time aveage fo peiod volumetic foce density; B* - conjugate value of induction. The poblem was consideed as coupled analysis of: electomagnetic, themal and fluid dynamics fields in -D domain. Electomagnetic field analysis was pefomed with use of getdp pogam [5]. Fo the tempeatue and fluid dynamics analysis, nsys-fluent pogam was used. Fo electomagnetic field calculation, only /6 of the device was modelled (Figue ). It was possible because of peiodicity of the device constuction. Figue. Calculation model fo electomagnetic field analysis of the fist IFCC. Figue 4. Calculation model fo themal and fluid dynamics field analysis of the fist IFCC.

5 On font and back model sufaces (Figue ), the peiodicity bounday condition was applied. In othe diections, the computational model is suounded by ai and on the outside ai sufaces bounday Diichlet condition setting potentials to zeo was applied. Basic dimensions of the models ae pesented in Table. Bottom and segments of cucible wee made of coppe of the conductivity of S/m, melt metal was made of titanium with the conductivity of S/m. Shunts wee made of Fluxtol 00. Table. Model paametes. Paamete (mm) Model Model bw s bi 6 s f 5 5 g s s s 0 0 s i i t 90 - h bi 4 0 h b 0 0 h s h p h f h sc h lc 5 5 h cc Model fo tempeatue field and fluid dynamics analysis nalysis of tempeatue field and fluid dynamics wee pefomed in nsys Fluent pogam. The calculation domain was limited to the melt aea and a bottom of cucible only, as pesented in Figue 4. Tempeatue calculations wee based on euation (6) [6]. ct c v gad T div k gad T v (6) t whee: - density; c - specific heat; T - tempeatue; v velocity vecto; k - themal conductivity; v - volumetic heat souce fom electomagnetic calculation; - volumetic density of adiative heat exchange deived on the basis of Gauss-Ostogadsky theoem fom suface adiative heat tansfe [7]. s in the case of electomagnetic field analysis, the calculation domain was limited to /6 of the device (Figue 4). On the font and back model sufaces adiabatic bounday condition was applied, on the outside suface in the cucible segments and below bottom (out, Figue 4.) Diichlet bounday condition setting tempeatue to 0 K was applied, on the fee molten metal suface (out ), the heat loss with convection and adiation wee taken into consideation. 4

6 The fluid dynamics calculations should detemine the shape of fee suface of molten metal in the IFCC and theefoe the flow field within cucible was teated as multiphase one. The Volume of Fluid appoach was applied in the calculation model. To obtain the flow field distibution, the continuity euation in the fom euation (7) [6] and momentum consevation euation (8) [6] should be solved. div v (7) t whee: - volume faction of the th phase; - density of the th phase. t v vv gad p gad div v ot ot v g f m f s div (8) whee: p - pessue; - dynamic viscosity; g - gavitational acceleation; f s - volume foce density calculated fom suface tension deived on the basis of Gauss-Ostogadski theoem [8]. These euations ae supplemented with bounday condition, on the font and back sufaces peiodicity bounday condition was assumed. On the top of model pessue outlet condition was adopted, fo the fee suface of molten metal shea stess eual to 0 on both sides was assumed. On the outside wall of the model (out ), no slip condition was assumed... Coupling pocedue Electomagnetic, heat tansfe and fluid flow calculation wee conducted fo two diffeent numeical submodels. Models diffes in geomety and calculation domain. Calculation model fo electomagnetic field consists of molten metal, cucible, inducto, shunt and ai. Tempeatue and fluid dynamic calculations wee conducted fo the model limited to the molten metal and ai above fee suface of metal, and bottom of the cucible. Fluid dynamics and tempeatue calculations wee pefomed in time domain, and the time step was s. Each 5 time steps the calculations of electomagnetic field wee pefomed and mean fo the peiod values of foces and powe souces wee detemined, and then tansfeed as the souce tems fo the themal submodel. Befoe the tansfe, the foces and heat souces fom electomagnetic calculation wee appoximated fo the themal - fluid dynamic calculation mesh [9].. Numeical expeiment Six simulation vaiants wee pefomed duing the expeiment. Fo each of the two IFCC models, thee calculation vaiants, diffeent in volume of the titanium, wee conducted. The vaiant designatos ae as follows: IFCC model, volume of titanium is designated as mv. Consideed uantities of titanium ae:.06 kg,.6 kg,. kg which coesponds to complete filling the cucible to the level of 0.04 m (7%), 0.06 m (4%), 0.08 m (55%). ll vaiants of calculations wee conducted fo the same inducto cuent and cuent feuency of 0 khz. The liuid metal popeties wee as follows: conductivity [0] = S/m density [] = 460 kg/m, themal conductivity [] λ= W/(m K), specific heat c = J/(kg K), dynamic viscosity [] = (Pa s). Due to the difficulty of coupling of the model to the electomagnetic field analysis with the model fo tempeatue and FD field analysis, the calculations wee made only patially. In the Figue 5, and Figue 6 calculation esults fo the mv vaiant fo two diffeent supply powes 0% of the maximum powe (40 kw) and 40% of the maximum powe (80 kw) ae shown. Figues 5 and 6 shows meniscus shape. s can be seen, fo 0% of the powe the liuid metal is not completely pushed away fom the walls of the cucible, but fo the 40% of the powe the liuid metal is completely pushed away fom the wall of the cucible pactically fom the bottom of the IFCC. But at this stage of the calculations, no metal solidification has yet be taken into account. 5

7 Figue 5. Metal meniscus shape fo 0% of the supply powe. Figue 6. Metal meniscus shape fo 40% of the supply powe. Refeences [] Spitans S, Baake E, Jakovics and Fanz H 05 Numeical simulation of electomagnetic levitation in cold cucible funace Magnetohydodynamics [] Rot D, Jiinec S, Kozeny J and Poznyak I 05 Electical efficiency of induction funace with cold cucible via diffeent segments width Electic Powe Engineeing (EPE) 6 th Intenational Confeence IEE DOI 0.09/EPE [] Fot J, Ganich M and Klymyshyn N 005 Electomagnetic and themal-flow modelling of a cold-wall cucible induction melte Metallugical and Mateials Tansaction B [4] Flux 005 D Vol5 Complement on the fomulations D Cedat 8-7. [5] Dula P, Geuzaine C GetDP efeence manual: the documentation fo GetDP, a geneal envionmental fo the teatment of discete poblems getdp.info [6] nsys 5.0 manual [7] Fluent 6. Use's Guide.. Heat tansfe theoy Fluent6/html/ug/node568.htm [8] Fluent 6. Use's Guide..8 Suface Tension and Wall dhesion Softwae/Fluent6/html/ug/node888.htm [9] Bulinski P, Smolka J, Golak S, Pzylucki R, Palacz M, Siwiec G, Lipat J, Bialecki R and Blacha L 07 Numeical and expeimental investigation of heat tansfe pocess in electomagnetically diven flow within vacuum induction funace pplied Themal Engineeing [0] Seydel U and Fucke W 980 Electical esistivity of liuid Ti, V, Mo and W Jounal of Physics F: Metal Physics 0 [] Ishikawa T 005 Themophysical popeties of molten efactoy metals measued by an elecostatic levitato Jounal of Electic Mateials [] Mills K, Monaghan B and Knee J 996 Themal conductivities of liuid metals Poceedings of the Twenty-Thid Intenational Themal Conductivity Confeence [] Padis P, Ishikawa T and Yoda S 00 Non contact measuements of suface tensions and viscosity of niobium, ziconium and titanium using and electostatic levitation funace Intenational Jounal of Themophysics cknowledgments Financial assistance was povided by gant no. 04//B/ST8/064 funded by the National Science Cente, Poland, and is hee acknowledged. 6