Water Analog Experimental Method for the Diffusion and Distribution of Alloy Elements in Liquid Steel during Ingot Filling Process

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1 , pp Water Analog Experimental Method for the Diffuion and Ditribution of Alloy Element in Liquid Steel during Ingot Filling Proce Jinu KANG, Chao DONG,* Xiaokun HAO, Gang NIE, Houfa SHEN and Baicheng LIU Key Laboratory for Advanced Material Proceing Technology, Minitry of Education, School of Material cience and Engineering, Tinghua Univerity, Beijing, China. (Received on Augut 16, 2013; accepted on October 21, 2013) To phyically imulate the alloy element tranportation and diffuion in the liquid teel during the making of heavy ingot, a ater analogy experimental method i preented. In thi method, methylene blue dye i ued a olute to imulate the alloy element carbon in the melt teel. And a meaurement method i propoed to meaure the concentration of the olute, in hich the laer reflection intenity detection method i ued. The ater analogy experiment etup i contructed. The multi-concentration pouring of a 438 t ingot i invetigated by thi method. The concentration of the ladle decreae ith the pouring conequence. The concentration variation curve ith time at the tundih outlet and in the mold are acquired and analyzed. The tundih outlet concentration decreae gradually and no fluctuation occur during the change of ladle. Negative concentration gradient i achieved at the end of pouring, hich can be helpful for controlling of the macroegration uually occurring in the heavy ingot. KEY WORDS: ater analogy; methylene blue dye; concentration; diffuion; liquid teel; ingot. 1. Introduction For large ingot, macroegregation i a common defect and a bottleneck in their quality control. 1,2) Generally peaking, macroegregation i caued by the re-organization of chemical element over long ditance rather than around the dendrite arm. 3) The flo driven by temperature gradient, denity difference of alloy element and the mother alloy, and the depoition of advanced olidified grain into the bottom may lead to the macroegregation of alloy element. A it i hard to directly oberve the macroegregation occurrence during the olidification of an ingot, numerical imulation ha been a favorite reearch tool. Berkermann developed a model for multicomponent teel olidification ith the conideration of the melt convection and fully coupled the conervation equation for the tranport phenomena in the liquid, muh and olid. 4) Li et al. developed a tophae macroegregation model that incorporate heat tranfer, melt convection, olute tranport, equiaxed grain motion, and grain nucleation and groth. 5) Natec developed a generic frameork tudying macroegregation in variou cating procee uing a computational fluid dynamic (CFD) code by olving the temperature, flo and olute balance in the multi-component alloy ytem. 6) Hervé Combeau preented a multiphae and multi-cale model that decribe the evolution of the morphology of the equiaxed crytal. 7) Li et al. invetigated the formation of * Correponding author: dongchao_thu@163.com DOI: macroegregation in a 360 t multi-concentration poured teel ingot and found that the delay time for the lat ladle ha a ignificant effect on the macroegregation. 8) On the other hand, ater analogy experimental tudy i often applied in the invetigation of the filling proce of cating and the fluid flo in the tundih and mold for ingot and continuou cating. 9,10) Dye or particle are uually added a tracer to trace the fluid flo. And particle are added for the tudy of the removal of incluion. In the area of egregation tudy, Zhang et al. adopted alt olution to imulate the concentration variation during the ingot pouring, he obtained the RTD curve by meauring the alt concentration at the tundih outlet. 11) Michalek et al. adopted aqueou olution of KCl for imilar reearch. 12) Chen et al. compared the effect of KCL and NaCl olution a tracer in fluid flo in the tundih and found KCl olution i more accurate. 13) Methylene blue or platic particle are alo ued to illutrate the flo field of the tundih in ome ater analogy experiment. 14) Up to date, the ater analogy experiment i mainly applied for invetigating the fluid flo. A for the reearch of multi-concentration pouring, it i of a potential method to invetigate the concentration field in the tundih and ingot. But, there in t yet reearch relating to olute election and relative concentration meaurement method. Thi article preent a ater analogy experimental method to phyically imulate the alloy element diffuion and tranportation during filling proce of ingot. Epecially, the election of olute and it meaurement method i preented. And thi method i applied into the reearch of the multi-concentration pouring proce of a heavy ingot ISIJ

2 2. Theoretical Analyi of the Water Analogy Method 2.1. Similarity Analyi The theoretical bai for ater analogy experiment i the imilarity principle that if all of the imilarity criterion are atified, the flo field are imilar to each other. In order to imulate the diffuion proce of the alloy element in liquid teel, both the velocity and concentration field mut be imilar beteen ater analogy experiment and the reality. According to the hydraulic imilarity theory, the Froude and Reynold number of the ater analogy experiment hould accord ith thoe of the real filling proce. Moreover, hen both meet the elf-molding condition, the influence of Reynold number on the flo field can be ignored. 15) A a reult, the Froude criteria i the imilarity condition for the velocity field. 16) The Froude criteria i 2 F = U r... (1) gl Where U i the characteritic velocity, L i the characteritic length, g i gravitational acceleration. If the ize of the etup of the ater analogy experiment i one n-th of the reality, i.e, the ratio of characteritic length beteen the ater experiment and the reality i L : L =1: n... (2) Where the footnote denote ater analogy, liquid teel. Thu, according to Froude criteria, the ratio of the velocity hould atify U : U =1: n... (3) Where U i the characteritic velocity in the ater analogy experiment and the U i the characteritic velocity in the reality. The average velocity of the liquid teel at the outlet i V U =... (4) At Where V i the volume of the liquid teel, A i the ection area of the outlet, t i the pouring time. Among the imilarity criteria, the ma tranfer Peclet number (Pe D) i defined a the ratio of the convective velocity to the diffuive velocity. 17) With Peclet number and Prandtl number, the heat and ma tranfer imilarity i obtained. 18) In other ord, according to the imilarity among flo, heat and ma tranfer proce, the flo field and ma tranfer proce ill be imilar at the ame time by atifying the Peclet criteria hen the flo field i imilar. The Peclet number i calculated by the folloing equation. P = UL ed... (5) D To meet the imilarity of olute ditribution, the Peclet criteria mut be ame. Thu, the ratio of diffuion coefficient i: D D U L 15. : = =1: n... (6) UL Where D i the diffuion coefficient of the imulate medium and D i the diffuion coefficient of the alloy element in teel. If the ratio of characteritic length, velocity and diffuion atify Eq. (2), (3) and (6), repectively, the flo field and olute ditribution ill be imilarly beteen the ater analogy experiment and reality, i.e., the concentration variation ill be the ame. Δc : Δc = 1... (7) Where Δc and Δc i the relatively change of concentration, hich doen t change ith the change of actual concentration of the olute Selection of the Solute for Water Analogy Experiment According to the equation decribed above, the election of the olute depend on the alloy element in the liquid teel. Their diffuion coefficient ratio hould be in accordance ith the imilarity condition. The diffuion coefficient for carbon in liquid teel under C i 0.2~ m 2 /, 19) hile the diffuion coefficient for mot olute in ater under room temperature i about 10 9 m 2 /. Therefore, a n i in the range of 2~10, i.e., the ize of ater analogy experimental etup i reduced to 1/10~1/2 of the actual one, the diffuivity i roughly in accordance ith Eq. (6). Salt ha been ued a olute in the ater experiment. Hoever, the meaurement of alt concentration i not convenient becaue of meaurement device may interfere ith the flo for it relatively big ize. Here, methylene blue dye, a popular ued dye a tracer in ater analogy experiment, i ued a olute. It diffuivity i m 2 /. 20) 3. Meaurement of the Concentration of Methylene Blue ith Optical Fiber Senor A ne kind of concentration meaurement method baed on optical fiber enor i developed to meaure the concentration of colored olute in ater. The meaurement equipment i mall enough to make the influence on flo field negligible and the range of meaurement can be adjuted according to the experiment and the olute Meaurement Principle and Device Meaurement of the concentration of methylene blue ith optical fiber enor i baed on the principle that colored olute alter the tranmittance of the olution. A the intenity of emiion light i fixed, the intenity of light that return varie ith the concentration of the colored olute. By calibrating the concentration and the intenity of the return laer, the concentration of olute can be meaured. The optical fiber enor meaurement ytem conit of a probe, a pair of optical fiber including an emiion fiber and a reception fiber, and a fiber amplifier hich can produce monochromatic light and convert light ignal to electric ignal and record it. The probe i made of a U haped heet metal ith one ide attached to the fiber, the other ide a reflection urface. The ditance of the end of the fiber to the reflection urface i d, than the ditance that the light travel i 2d. The chematic diagram of the ytem i hon in Fig. 1. The light from the emiion fiber travel through the olution and i reflected by the metal urface to the fiber ampli ISIJ 276

3 fier through the reception fiber. The fiber amplifier convert the light ignal to an electric ignal and record it. A the reflection metal urface i about 10 mm from the emiion end, the probe i relatively mall, it influence on the flo field can be neglected. The U haped metal i made of high trength heet metal to avoid ditortion caued by pule of flo. The repone time of thi optical fiber enor meaurement ytem i le than 0.1. It meaurement error i limited to 5%. And it i table and i not influenced by the environment light Meaurement of the Concentration of Methylene Blue Solution The intenity decay of light i mainly influenced by the ditance paing through the olution and the darkne of the olution. Lambert-Beer la point out that hen a light of intenity I 0 travel through olution ith concentration c and ditance d, Auming there in t cattering, the relation beteen I 0 and the reception light intenity I i hon a belo. I0 1 lg lg 2d c... (8) I = T = ε ( ) Where T i called the tranmittance of olution and ε i a molar aborption coefficient. For a certain kind of olution, it molar aborption coefficient for a monochromatic light i a contant. The light ignal i tranferred to a digital ignal by the fiber amplifier by the folloing equation, Γ=klg I... (9) Where, Γ i the apparent light intenity hon on the creen, k i a contant. So, the concentration of olute can be expreed a the function of the fiber amplifier output Γ a the equation belo. c = B AΓ... (10) Where A and B are contant determined by the ytem and Γ i the amplifier output. The contant A i determined by ε and d. So, the range of meaurement can be atified by adjuting the reflection ditance. For a given fiber meaurement ytem, the avelength of the laer i 640 nm, and the concentration range of methylene blue varie from 0.001% 0.041%. The reflection ditance d i 10 mm and reflection urface i 4 mm 2 mm large. The diameter of the optical fiber cable i 2 mm. The methylene blue olution i obtained by diolving eighted pure methylene blue poder into ditilled ater. The relation beteen the concentration c and the amplifier output Γ for the given meaurement ytem i hon a Fig. 2. From Fig. 2 the linear fitting equation beteen c and Γ for thi meaurement enor i obtained c = Γ...(11) By thi equation, everal methylene blue olution are teted and their reult are hon in Fig. 3. The error i ithin ±5%. The parameter of the ytem are lited in Table 1. The probe i o mall compared to the analogy model that it influence on the flo field can be neglected. The meaurement ytem hould be calibrated at the firt time and regularly after a period of time becaue of haking of fiber, bubble attaching on the reflection metal urface and the contaminated fiber connector may lead to error. To better Fig. 2. The relationhip beteen the output Γ and the concentration c of methylene blue olution a re-flection ditance i 10 mm. Fig. 1. Optical fiber enor meaurement ytem for colored olution. Fig. 3. Error of the meaurement of fiber enor ytem ISIJ

4 meaure the concentration of methylene blue, the range of 0.012% 0.045% i uggeted. 4. Filling Proce Experiment of a 438 t Ingot The ater analogy experiment of the multi-concentration pouring proce of a 438 t ingot i carried out. The material of the ingot i 30Cr 2Ni 4MoV, and it carbon content i 0.26%. Table 1. Condition of the enor and feature of the meaurement ytem. Condition of the enor Meaurement feature Reflection ditance (mm) 10 Error (%) <5 Probe ize (mm) Repone time () <0.1 Fiber cable diameter (mm) 2 Meaurement range (10 1 %) Wave length of light (nm) 640 Meaurement enitivity (10 1 %) Experiment Proce and Parameter The multi-concentration pouring proce in tundih i divided into three tage. Stage I i called tundih filling tage during hich the outlet of tundih i clogged by a topper rod and the liquid teel i poured into tundih from the firt ladle till the liquid level in the tundih rie to 2/3 height. Stage II i called the table tage, the tundih outlet i releaed for pouring, and keep the liquid level unchanged by adjuting the flo rate. When the reidual liquid teel in ladle 1 i all poured into the tundih, the liquid teel in ladle 2 tart to fill the tundih. And then pour all the other ladle by equence. Stage III i called tundih empty tage. In thi tage, there i no more filling of the tundih, the liquid level in the tundih begin to decend till the pouring proce end. The carbon concentration may be different for all the ladle to form nonuniform ditribution of carbon, uually from high concentration to lo concentration and finally negative egregation in the mold o a to reduce the macroegregation formed during the olidification proce. Thi multi-concentration pouring proce i hon in Fig. 4. To atify the Eq. (6), the imilarity ratio beteen ater analogy model and the real ituation i 8. All the production and experiment parameter are lited in Table 2. For the ingot, four ladle ith different concentration are determined, hich are 90 t ith 0.33%C, 90 t ith 0.30%C, 105 t ith 0.26%C and 155 t ith 0.33%C in pouring equence, o the ladle in the ater analogy experiment are 22.5 kg ith 0.04%, 22.5 kg ith 0.036%, 26 kg ith 0.032% and 40 kg ith 0.24% methylene blue, repectively. The ize of tundih model i Φ400 mm 400 mm, one eighth of Φ3200 mm mm of the real tundih. While the flo rate in experiment and production are 3.2 L/min and 573 L/min (characteritic velocity 0.47 mm/ and 1.22 mm/), repectively. The tundih outlet ize i alo reduced to one eight. During the experiment, the flo rate i controlled, o the pouring time i alo fitful for the imilarity ratio. An experiment model of thi proce i et up. One probe i et at the tundih outlet to meaure the outlet concentration of the tundih and three probe are placed in the center of the mold along a fixed bracket to meaure the center concentration variation at different height, 150 mm, 300 mm, and 450 mm. The fixed bracket i a thin a 5 mm in diameter. The experiment ytem i hon in Fig Reult and Analyi Becaue of the imilarity beteen the ater analogy experiment and the real teel liquid, the relative olute concentration i the ame, and then the concentration variation of the methylene blue ith time can be converted to the variation of carbon concentration in liquid teel ith time. Figure 6 ho experimental concentration variation at the tundih outlet and the converted carbon concentration during the pouring proce of the 438 t ingot and the change of the liquid level in the tundih. The reult of ater analogy Table 2. real ituation and experiment parameter. Real ituation Water analogy Ratio Tundih ize Φ (mm) Φ (mm) 8 Outlet ize Φ100 (mm) Φ12 (mm) 8 Ingot ize Ladle concentration 4140 mm mm 7931 mm (0.33, 0.30, 0.26, 0.20) (%) 500 mm 500 mm mm (0.40, 0.36, 0.32, 0.24) (10 1 %) Ladle pouring quantity (90, 90, 105, 155) (t) (22.5, 22.5, 26, 40) (Kg) Ladle pouring time (20, 20, 24, 34) (min) (7, 7, 8.5, 12) (min) Ladle pouring flo 573 (L/min) 3.2 (L/min) Fig. 4. Multi-concentration pouring proce of large ingot ISIJ 278

5 experiment i hon on the top and right axe, hile the carbon concentration i hon on the bottom and left axe. It can be een from Fig. 6 that the concentration at the tundih outlet doen t change until the liquid of ladle 2 get into the tundih. During the pouring of ladle 2 to the final one, the concentration decend continuouly. And almot no fluctuation occur during the change of ladle. The outlet concentration of tundih i alay higher than that of the ladle being poured. At the beginning of the empty proce of the tundih, the outlet concentration i till higher than that of the lat ladle. The final concentration i cloe to that of the lat ladle. Form the reult it can be deduced that there i a mixing proce of the current flo and the exited liquid in the tundih during pouring. So, the concentration at the tundih outlet change gradually. Becaue the concentration of the former ladle i higher than that of the current ladle, the tundih outlet concentration i alay higher than that of the current ladle, epecially for ladle 2. On the other hand, it i alo affected by the volume of each ladle. The bigger a Fig. 5. Water analogy experiment apparatu of multi-concentration pouring proce of a 438 t ingot. ladle i, the maller concentration difference at the end of thi ladle pouring. For example, at the end of ladle 3, the concentration difference beteen the tundih outlet and that of ladle 3 i 0.17%, hile the difference at the end of ladle 4 i 0.01%. Becaue ladle 4 i far bigger than ladle 3. If the lat ladle i of mall volume, the final tundih outlet concentration hould be far higher than that of the lat ladle. The meaurement reult of three point ith height of 150 mm, 300 mm, 450 mm in the ingot are hon in Fig. 7. The probe at 150 mm i ubmerged at 17.5 min during the experiment, hile the probe at 300 mm and 450 mm are ubmerged at 29 min and 39 min repectively. Only after the probe i ubmerged, it concentration detection reult i recorded and plotted in Fig. 7. From Fig. 7 it can be een that, like the outlet concentration of the tundih, the concentration of the meaurement point alo decreae gradually during the pouring proce. When the probe i ubmerged, it concentration i above the tundih outlet concentration at ame time. That mean mixing occur in the mold, hich ill decreae the concentration gradient. Therefore, the bottom concentration hould be higher than that of the firt ladle, and the top concentration higher than the lat ladle. The effective concentration difference beteen the firt and lat ladle ill be narroed. And for point at different height, there ho a concentration gradient ith concentration decreae ith height. At the end of the pouring proce, the concentration in the height of 150 mm, 300 mm, and 450 mm i 0.26%, 0.21%, 0.20%, repectively. Baed on the reult and analyi, it can be found that the multi-concentration-pouring proce lead to a certain kind of concentration ditribution in the ingot from bottom to up, the bottom concentration i cloe to the firt ladle, the top i cloe to the lat ladle. If the concentration of ladle decreae ith the pouring equence, a negative concentration gradient appear in the ingot after pouring, hich can be helpful for controlling the macroegregation in ingot that uually feature a a poitive concentration gradient. Hoever, after the convection and diffuion in the mold, the concentration gradient i reduced than that of the ladle. Fig. 6. Concentration at the tundih outlet of the 438 t ingot in four-ladle pouring. We enlarged Fig. 6 and ISIJ

6 Fig. 7. Concentration in the ingot during pouring proce. 5. Concluion (1) A ater analogy experimental method i propoed to tudy the ma tranfer in tundih and ingot. According to the imilarity analyi, Methylene blue dye can be ued to imulate the alloy element tranportation behavior in liquid teel. (2) An optical fiber enor meaurement ytem i developed to meaure the concentration of the Methylene blue olution ith good accuracy, fat repone and neglectable influence on the flo. (3) The multi-concentration-pouring proce of a 438 t ingot i invetigated ith the developed ytem. The concentration of the ladle decreae ith the pouring conequence. The tundih outlet concentration change continuouly and gradually during pouring proce, and almot no fluctuation occur during change of ladle. A the mixing caued by convection and diffuion in tundih and mold happen, the effective concentration difference beteen the firt and lat ladle ill be narroed. The olute ditribution in the mold ho a negative concentration gradient in the ingot from bottom to up, hich can be helpful for controlling the macroegregation in the ingot. Acknoledgement The project i funded by National Science and Technology Major Project of the Minitry of Science and Technology of China under Project No. 2012ZX and National Baic Reearch Program of China (No. 2011CB012900). REFERENCES 1) K. Sakamoto, T. Kuamichi, S. Nanba, T. Nakagaa, K. Nakayama and T. Takebayahi: Kobe Re. Dev. (Japan), 47 (1997), 62. 2) D. R. Liu: Int. J. Cat Met. Re., 26 (2013), ) D. R. Liu, X. H. Kang, P. X. Fu and D. Z. Li: Kovove Mater., 49 (2011), 1. 4) J. P. Gu and C. Beckermann: Metall. Mater. Tran. A, 30 (1999), ) W. S. Li and H. F. Shen: IOP Conf. Serie: Mater. Sci. Eng., 33 (2012), ) L. Natac: ISIJ Int., 50 (2010), ) H. Combeau, M. Zaloznik, S. Han and P. E. Richy: Metall. Mater. Tran. B, 40 (2009), ) J. Li, D. R. Liu, X. H. Kang and D. Z. Li: IOP Conf. Serie: Mater. Sci. Eng., 33 (2012), ) A. J. Davi and S. J. Aquith: 13th SDCE International Die Cating Expoition & Congre, Society of Die Cating Engineer, Illinoi, (1985). 10) X. Xue and Y. B. Zhang: Mater. Sci. Technol., 10 (2002), ) S. H. Zhang: Studie on Multi-Phae Flo Tranport Phenomena in Several Chemical and Metallurgical Reactor, Central South Univerity, Changha, (2004). 12) K. Michalek, K. Gryc, M. Tkadleckova and D. K. Bocek: Arch. Metall. Mater., 57 (2012), ) C. H. Chen, G. G. Cheng, H. B. Sun, Z. B. Hou, X. CH. Wang and J. Q. Zhang: Steel Re. Int., 83 (2012), ) J. Li: Study on the Fluid Flo in a Multi-heat Teeming Tundih for Heavy Steel Ingot, Chongqing Univerity, Chongqing, (2011). 15) B. Liu: Heavy Cating Forging, 2 (2006), ) B. J. Wang, Y. B. Zhong and Y. Wang: J. Univ. Sci. Technol. Beijing, 31 (2009), ) S. Bhattacharya and S. T. Hang: J. Membrane Sci., 132 (1997), ) F. Larachi, C. Alix, B. P. A. Grandjean and A. Berni: Tran. Icheme, 81 (2003), ) D. Goldberg and G. R. Belton: Metall. Tran., 5 (1974), ) S. Mochzuki: Proc. PSFVIP-4, Chamonix, (2003), ISIJ 280