The article presents results of physical modelling of the steel continuous casting process in the tundish. Technological parameters of casting and constructive parameters of tundish were under study. Three different kinds of flow control devices were considered as well as their influence on the kinetics of steel flow and mixing in tundish. Created physical model enabled to conduct simultaneously visualization research and determine the RTD curves. According to the theory of flow in reactors the proper characteristics for estimating the flow are RTD curves E- and F-type, and they were obtained and discussed

J. Pieprzyca

M. Saternus

T. Merder

English

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155 METALURGIJA 53 (2014) 2, 155-158T. MERDER, J. PIEPRZYCA, M. SATERNUSANALYSIS OF RESIDENCE TIME DISTRIBUTION (RTD) CURVES FOR T-TYPE TUNDISH EQUIPPED IN FLOW CONTROL DEVICES: PHYSICAL MODELLINGReceived – Prispjelo: 2013-07-26Accepted – Prihvaćeno: 2013-10-30Original ScientiĀ  c Paper – Izvorni znanstveni radISSN 0543-5846METABK 53(2) 155-158 (2014)UDC – UDK 669.186:518.1:531.39=111T. Merder, J. Pieprzyca, M. Saternus: Silesian University of Techno-logy, Department of Metallurgy, Katowice, Poland The article presents results of physical modelling of the st eel continuous casting process in the tundish.  Techno-logical parameters of casting and constructive parameters of tundish were under study. Three diff  erent kinds of fl  ow control devices were considered as well as their infl  uence on the kinetics of steel fl  ow and mixing in tundish. Cre-ated physical model enabled t o conduct simultaneously visualization r esearch and det ermine the R TD curves. According to the theory of fl  ow in reactors the proper characteristics for estimating the fl  ow are RTD curves E- and F-type, and they were obtained and discussed.Key words: steel fl  ow, tundish, physical modelling, RTD curveINTRODUCTIONTechnological parameters of casting and construc-tive parameters of tundish belong to basic properties that enforce the character of liquid steel ﬂ  ow through CC tundish [1-4]. Possibilities of forming the character of steel ﬂ  ow through tundish basing on technological parameters of casting, are rather limited. This is caused by the fact that these parameters are determined at the level of planning the casting technology of speciﬁ  c grades of steel, cross-sections of obtained cast strands, applied types of mould, parameters of secondary cooling etc. Thus, they consider mainly problems connected with solidiﬁ  cation rate of cast strand, and as a result the productivity of the process [5]. Problems concerning the character of steel mixing in the tundish are derivative of those factors and commonly require to undertake additional research con-nected with optimization of steel mixing in a tundish. Constructive parameters (geometry) of the tundish also do not give possibilities to inﬂ  uence the ﬂ  ow char-acter. This is why, all the changes in tundish shape are connected with the necessity to work out practically new casting technologies which, taking into considera-tion the economy of steel production, is unjustiﬁ  ed.Thus there is a necessity to regulate and/or form the character of steel ﬂ  ow in the tundish by other methods. The solution of such problem is applying additional equipment in the working zone of the tundish, which is commonly called ﬂ  ow control devices [6-1 1].  The choice of construction of ﬂ ow control devices is indi-vidual for a speciﬁ c tundish. Flow control devices can be divided (taking into account the construction, shape and the main aim) into: bafﬂ  es with notches, dams, weirs and turbulence inhibitors [6-1 1]. Such solutions are commonly used in industry and thanks to them good results of steel ﬂ  ow and mixing optimization in the tundish can be reached.To ensure the optimal working of control ﬂ  ow de-vices it is necessary to determine precisely their impact on hydrodynamic conditions of steel circulation in the tundish. That is why physical and mathematical model-ling is applied to determine constructive parameters of ﬂ  ow control devices [6-11]. Modelling research (physical and numerical) is com-monly used for analyzing (getting to know better) the phenomena occurring in reactors applied in metallur gy of steel and nonferrous metals [11-16].TESTING METHODOLOGYTwo-strand industrial  T-type tundish with capacity of 7,5 Mg was examined. Figure 1 presents the scheme of the tundish, whereas  Table 1 shows dimensions of the tundish model at 1:2 scale.Due to some problems occurring in a real tundish three variants of equipping its working zone were pro-posed. They do not exist; they are only the suggestion for the modiﬁ cation of the studied object interior . Fig-ure 2 presents the considered variants of tundish modi-ﬁ  cation. The research was carried out using physical model of continuous casting machine. It is a water segmental model built according to the theory of similarity. Figure 2 shows the test stand. Tundish model and elements of equipping were made from plexiglass. Presented model was described in details in work [12].156   METALURGIJA 53 (2014) 2, 155-158T. MERDER et al.: ANALYSIS OF RESIDENCE TIME DISTRIBUTION (RTD) CURVES FOR T-TYPE TUNDISH EQUIPPED...The construction of the model enables to conduct simultaneously visualization research and determine the RTD curves (Residence Time Distribution) describ-ing the way that liquid steel ﬂ  ows through the tundish.Every variant of experiment was carried out in the same working conditions of the tundish.  Water ﬂ  ow rate in a model was 24 dm3/min, which corresponds to cast-ing rate equal 1 m/min, for cast strand with φ 200.Modelling agent (water) was introduced to two tanks (Figure 3), which played the role of a ladle.  Then, through the reverse valve liquid is directed into tundish trough submerged pouring nozzle. Tundish model was ﬁ  lled to the required level of water . In the research it was 0,3 m. It corresponds to the level of steel in a real tundish after applying linear scale. During the research the constant level of water was kept in order to control the amount of water that was introduced to the model and drained from it.To determine RTD curve (F-type) in the moment of reaching the required level of water and stabilizing the ﬂ  ow, the tank with clear water was closed and then a tank with the tracer (water solution of KMnO 4 and NaCl) was opened. In the same time measuring series started. Tracer was introduced during the whole meas-uring time and registered by means of conductimeters continuously on the model tundish outlets. Simultane-ously the process was recorded by camera. To determine RTD curve (E-type) in the moment of reaching the required level of water and stabilizing the ﬂ  ow, small amount of 2 % NaCl was introduced to the tank.  The amount of tracer was 0,002 dm 3 and the change of its concentration was registered continuously on the model tundish outlets.RESULTS AND DISCUSSIONPresented results are part of the wide research pro-gram concerning the change of ﬂ ow control system in the examined tundish. Results were partly presented in works [12, 17]. Figure 1 Scheme of the studied tundish Figure 2   Geometric dimensions of proposed variants of tundish modiĀ  cation: a) case A, b) case B, c) case C, d) places of their installingTable 1 Dimensions of the tundish model at 1:2 scaleParameter Symbol ValueVolume of tundish at Ā  lling level H / m3 V0 , 1 2 5Tundish length / mL1 , 1 5 0L1 0,345Tundish width / mB0 , 5 7 0B1 0,300Filling level (steady-state casting) / mH0 , 3 0 0H1 0,220Inclination of the side walls / º α 8Shroud diameter /m dSH 0,025Shroud position / m LSH 0,466SEN diameter / m dSEN 0,01SEN position / m LSEN 0,350Figure 3 Scheme of test stand used in research 157 METALURGIJA 53 (2014) 2, 155-158T. MERDER et al.: ANALYSIS OF RESIDENCE TIME DISTRIBUTION (RTD) CURVES FOR T-TYPE TUNDISH EQUIPPED...a character that it spills over the upper edge of dam, whereas through the notch window, the ﬂ  ow practically does not exist. During dam construction it was assumed that this window would play the role of culvert increas-ing the kinetics of modelling agent ﬂ ow to the channel part of the tundish model. Results of visualization re-search were negative. For Cases C (Figure 7) beneﬁ cial character of mod-elling ﬂ  uid ﬂ  ow was observed in the area of well mixed ﬂ  ow. Mixing was sufﬁ cient and the strong mixing of ascending jet with surface layer of the bath was not ob-served. Turned up upper walls of turbulence infhibitors cause an additional rotational movement of a modelling agent in the area of well mixed ﬂ  ow. However, similarly to other cases, the kinetics of mixing in the area of back walls of the model is not sufﬁ  cient.RTD characteristcsRTD characteristics contain cumulated information about hydrodynamic conditions of steel ﬂ  ow through tundish and enable to estimate initially the quality of the object considering the steel mixing and possibilities of reﬁ  ning processes intensiﬁ  cation. According to the the-ory of ﬂ  ow in reactors [7-10], the proper characteristics for estimating the ﬂ  ow are RTD curve E- and F-type. Figure 8 presents the shape and course of the R TD curves (F-type) registered for analyzed conﬁ  gurations of tundish equipping. Presented curves show that the kinetics of steel mixing for all studied cases is much the same. To compare the results, the tracer concentration was transformed in dimensionless form in such a way that the minimal value was 0, whereas maximal was 1. Such operation was possible applying relationships de-scribed in works [2,12]. To make more detailed comparison time interval  ∆t was determined (range of mixing kinetics).The lower Flow of the fl  uidRegistered ﬁ lm enables to analyze the change of ﬂ  ow and mixing kinetics in studied cases. Figures 4 to 7 show the chosen results of tracer propagation during the experiment for examined cases.  Analysis of obtained results shows that the amount of well mixing area in bare tundish (Figure 34) is not sufﬁ cient. This area in-ﬂ  uences the quality of obtained cast strands; steel reﬁ  n-ing, by impurities ﬂ oating to slag, occurs.  The further ﬂ  ow has circulative character. Tracer propagated in the direction of water surface and on the head wall falls down creating right circulation (movement is in accord-ance with clockwise). Dangerously low kinetics of mix-ing is also seen in the area of back walls of the model. Such phenomenon can cause the creation of dead zones in this area of a real tundish. For cases A and B (Figures 5 and 6) in which dams were installed, kinetics of liquid ﬂ ow is more intensive than in a bare tundish.  The area of well mixing is also bigger. However kinetics of ascending the liquid to the surface is smaller. Such ﬂ ow does not threaten the co-herence of slag layer and in the same time makes non-metallic inclusions easily assimilated by this layer . Such equipping is the reason why tundish inlet area becomes integrated with its construction by high volume turbu-lence inhibitor. In case B (dam with notches) movement of model-ling liquid in an inlet part of the tundish model has such Figure 4   Tracer propagation in tundish model (bare tundish) after time: a) 30 s, b) 70 sFigure 5   Tracer propagation in tundish model (case A) after time: a) 30 s, b) 70 s Figure 6   Tracer propagation in tundish model (case B) after time: a) 30 s, b) 70 sFigure 7   Tracer propagation in tundish model (case C) after time: a) 30 s, b) 70 sFigure 8   The F-type characteristics obtained from water model: a) bare tundish [12], b) Case A, c) Case B, d) Case C158   METALURGIJA 53 (2014) 2, 155-158T. MERDER et al.: ANALYSIS OF RESIDENCE TIME DISTRIBUTION (RTD) CURVES FOR T-TYPE TUNDISH EQUIPPED...values of  ∆t, the better conditions of mixing.  Table 2 presents results characterizing the kinetics of mixing in examined cases. Table 2 Kinetics of steel mixing for studied cases Case∆t / sOutlet No 1 Outlet No 2Bare tundish  348,5 349,5Dam (Case A) 350 354Dam notched (Case B) 315,5 322Turbulence inhibitor (Case C) 292,5 290Additionally Table 2 shows the data for both outlets to check the symmetry condition. Values of ∆t on both outlets of the examined variants dif fer insigniﬁ cantly. These differences come from abnormal levelling of the tundish model. Basing on E-type curves, using relationships de-scribed in works [2, 12], particular volume fraction of ﬂ  ows for studied cases were calculated.  Table 3 presents these results. The increase of mixing kinetics was ob-served for cases B and C, which is a positive phenome-non. Bare tundish used nowadays and proposed variant of its equipping – Case  A (dam) have kinetics of steel mixing at the same level. It is not optimal equipment for casting process taking into account the transient zone during sequence casting of different grades of steel. Ta-ble 3 shows that there is an increase of well mixed ﬂ  ow contribution mainly at the expense of dead ﬂ  ow for cas-es A to C. Table 3 RTD parameters and volume fraction of fl  owCase Volume fraction / %Dispersed plug volume (Vdp)Well mixed volume(Vm)Deadvolume (Vd)Bare tundish  18,8 45,6 35,6A1 7 , 4 5 3 2 9 , 6B 15,2 52,1 32,7C1 7 , 9 5 2 , 4 2 9 , 7The next analysis was done taking into account the  dependence between ratio of well mixed ﬂ  ow to dead  volume Vm/Vd and ratio of dispersed plug ﬂ  ow to dead volume Vdp/Vd (Table 4). The last one (ratio Vdp/Vd) indi-cated the quiescent region of tundish which promotes the inclusion ﬂ  oatation behaviour inside the tundish, whereas  ratio (V m/Vd) indicats the well mixed region which in  turn is supposed to provide better homogeneity inside the  tundish [2]. The best results were obtained for case C. Table 4 Comparison of diff  erent tundish volumes ratio Case Overall(Vm/Vd)Overall(Vdp/Vd)Bare tundish  1,28 0,53A1 , 7 9 0 , 5 9B1 , 5 6 0 , 4 6C1 , 7 6 0 , 6 0CONCLUSIONBasing on the carried out experiments it was stated that applying ﬂ ow control devices in working area of the tundish causes:•   favourable change of ﬂ  ow kinetics,•   increasing the volume of dead areas, however they cannot be totally eliminated; places especially suscep-tible to this disturbance of ﬂ  ow are areaa near the back wall of the tundish model (close by liquid surface),•   lengthening the time which tracer spent in the tundish; this inﬂ  uences the process of transient zone, forming at the same time favourable conditions to sequence casting,•   the dead area is smaller, as a consequence the area with well mixed ﬂ  ow increases,•   improving mixed to dead volume of about 13,2 % and plug to dead volume of about 37,5 %. Modelling research negatively veriﬁ ed assumption for Case B (dam equipped with notch window which should play the role of culvert increasing the kinetics of liquid ﬂ  ow).REFERENCES[1]  S. Lopez – Ramirez, J. Barreto, R. D. Morales: Steel Rese-arch Int. 69 (1998), 423–428. [2]  R. D. Morales, J. J. Barreto, S. Lopez-Ramirez, J. Palafox-Ramos and D. Zacharias: Metall. Mater . Trans. B, 31B (2000), 1505–1515.[3]  S. Singh, K. M. Godiwalla, D. K. Shaw: Scan. Journal of Metall., 30 (2001), 103–107.[4]  T. Merder , J. Jowsa,  A. Bogusławski: Metalur gija, 46 (2007) 4, 245–249.[5]  J. Pieprzyca: Metalurgija, 52 (2013) 2, 157-160. [6]  K. Janiszewski, Z. Kudliński: Steel Research Int., 3 (2006), 169-176.[7]  R. Schwarze, F . Obermeier, J. Hantusch,  A. Franke, D. Janke: Steel Research Int., 72 (2001), 215–220. [8]  A. Cwudziński: Steel Research Int., 81 (2010), 123–131.[9]  A. Sengupta P. Mishra, V. Singh, S. Mishra, P. J. Jha, S.K. Ajmani, S. C. Sharma: Ironmaking and Steelmaking, 40 (2013) 3, 159–166.[10]  K. Gryc, K. Michalek, Z. Hudzieczek, M.  Tkadlečkova: Metal 2010, Conference proceedings. 2010, 42–46. [11]  M. Warzecha: Metalurgija, 50 (2011) 3, 147-150.[12]  T. Merder, J. Pieprzyca: Steel Research Int., 1 1 (2012), 1029–1037.[13]  T. Merder, J. Pieprzyca: Metalur gija, 50 (201 1) 4, 223–226.[14]  B. Panic: Metalurgija, 52 (2013) 2, 177–180.[15]  K. Michalek, J. Morávka, K. Gryc: Metalurgija, 48 (2009) 4, 219–222.[16]  R. Przylucki, S. Golak: Int. Journal of Thermophysics, 34 (2013) 4, 642–654.[17]  M. Warzecha, T. Merder: Metalurgija, 52 (2013) 2, 153–156.Note:   The responsible translator for English language is M. Kingsford, Katowice, Poland

Analysis of residence time distribution (RTD) curves for t-type tundish equipped in flow control devices: physical modelling

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155METALURGIJA 53 (2014) 2, 155-158T. MERDER, J. PIEPRZYCA, M. SATERNUSANALYSIS OF RESIDENCE TIME DISTRIBUTION (RTD) CURVES FOR T-TYPE TUNDISH EQUIPPED IN FLOW CONTROL DEVICES: PHYSICAL MODELLINGReceived – Prispjelo: 2013-07-26Accepted – Prihvaćeno: 2013-10-30Original ScientiĀ c Paper – Izvorni znanstveni radISSN 0543-5846METABK 53(2) 155-158 (2014)UDC – UDK 669.186:518.1:531.39=111T. Merder, J. Pieprzyca, M. Saternus: Silesian University of Techno-logy, Department of Metallurgy, Katowice, Poland The article presents results of ph ysical modelling of the st eel continuous casting pr ocess in the tundish. Techno-logical parameters of casting and constructive parameters of tundish were under study. Three diff erent kinds of fl ow control devices were considered as well as their infl uence on the k inetics of steel fl ow and mixing in tundish. Cr e-ated ph ysical model enabled t o c onduct simultaneously visualization r esearch and det ermine the R TD cur ves. According to the theory of fl ow in reactors the proper characteristics for estimating the fl ow are RTD curves E- and F-type, and they were obtained and discussed.Key words: steel fl ow, tundish, physical modelling, RTD curveINTRODUCTIONTechnological parameters of casting and construc-tive parameters of tundish belong to basic properties that enforce the character of liquid steel fl  ow through CC tundish [1-4]. Possibilities of forming the character of steel fl  ow through tundish basing on technological parameters of casting, are rather limited. This is caused by the fact that these parameters are determined at the level of planning the casting technology of specifi c grades of steel, cross-sections of obtained cast strands, applied types of mould, parameters of secondary cooling etc. Thus, they consider mainly problems connected with solidifi cation rate of cast strand, and as a result the productivity of the process [5]. Problems concerning the character of steel mixing in the tundish are derivative of those factors and commonly require to undertake additional research con-nected with optimization of steel mixing in a tundish. Constructive parameters (geometry) of the tundish also do not give possibilities to infl uence the fl ow char-acter. This is why, all the changes in tundish shape are connected with the necessity to work out practically new casting technologies which, taking into considera-tion the economy of steel production, is unjustifi ed.Thus there is a necessity to regulate and/or form the character of steel fl ow in the tundish by other methods. The solution of such problem is applying additional equipment in the working zone of the tundish, which is commonly called fl  ow control devices [6-1 1]. The choice of construction of fl ow control devices is indi-vidual for a specifi c tundish. Flow control devices can be divided (taking into account the construction, shape and the main aim) into: baffl  es with notches, dams, weirs and turbulence inhibitors [6-1 1]. Such solutions are commonly used in industry and thanks to them good results of steel fl  ow and mixing optimization in the tundish can be reached.To ensure the optimal working of control fl  ow de-vices it is necessary to determine precisely their impact on hydrodynamic conditions of steel circulation in the tundish. That is why physical and mathematical model-ling is applied to determine constructive parameters of fl ow control devices [6-11]. Modelling research (physical and numerical) is com-monly used for analyzing (getting to know better) the phenomena occurring in reactors applied in metallur gy of steel and nonferrous metals [11-16].TESTING METHODOLOGYTwo-strand industrial T-type tundish with capacity of 7,5 Mg was examined. Figure 1 presents the scheme of the tundish, whereas Table 1 shows dimensions of the tundish model at 1:2 scale.Due to some problems occurring in a real tundish three variants of equipping its working zone were pro-posed. They do not exist; they are only the suggestion for the modifi cation of the studied object interior . Fig-ure 2 presents the considered variants of tundish modi-fi cation. The research was carried out using physical model of continuous casting machine. It is a water segmental model built according to the theory of similarity. Figure 2 shows the test stand. Tundish model and elements of equipping were made from plexiglass. Presented model was described in details in work [12].156  METALURGIJA 53 (2014) 2, 155-158T. MERDER et al.: ANALYSIS OF RESIDENCE TIME DISTRIBUTION (RTD) CURVES FOR T-TYPE TUNDISH EQUIPPED...The construction of the model enables to conduct simultaneously visualization research and determine the RTD curves (Residence Time Distribution) describ-ing the way that liquid steel fl ows through the tundish.Every variant of experiment was carried out in the same working conditions of the tundish. Water fl ow rate in a model was 24 dm3/min, which corresponds to cast-ing rate equal 1 m/min, for cast strand with φ 200.Modelling agent (water) was introduced to two tanks (Figure 3), which played the role of a ladle. Then, through the reverse valve liquid is directed into tundish trough submerged pouring nozzle. Tundish model was fi lled to the required level of water . In the research it was 0,3 m. It corresponds to the level of steel in a real tundish after applying linear scale. During the research the constant level of water was kept in order to control the amount of water that was introduced to the model and drained from it.To determine RTD curve (F-type) in the moment of reaching the required level of water and stabilizing the fl ow, the tank with clear water was closed and then a tank with the tracer (water solution of KMnO 4 and NaCl) was opened. In the same time measuring series started. Tracer was introduced during the whole meas-uring time and registered by means of conductimeters continuously on the model tundish outlets. Simultane-ously the process was recorded by camera. To determine RTD curve (E-type) in the moment of reaching the required level of water and stabilizing the fl ow, small amount of 2 % NaCl was introduced to the tank. The amount of tracer was 0,002 dm 3 and the change of its concentration was registered continuously on the model tundish outlets.RESULTS AND DISCUSSIONPresented results are part of the wide research pro-gram concerning the change of fl ow control system in the examined tundish. Results were partly presented in works [12, 17]. Figure 1 Scheme of the studied tundish Figure 2  Geometric dimensions of proposed variants of tundish modiĀ cation: a) case A, b) case B, c) case C, d) places of their installingTable 1 Dimensions of the tundish model at 1:2 scaleParameter Symbol ValueVolume of tundish at Ā lling level H / m3 V 0,125Tundish length / mL 1,150L1 0,345Tundish width / mB 0,570B1 0,300Filling level (steady-state casting) / mH 0,300H1 0,220Inclination of the side walls / º α 8Shroud diameter /m dSH 0,025Shroud position / m LSH 0,466SEN diameter / m dSEN 0,01SEN position / m LSEN 0,350Figure 3 Scheme of test stand used in research 157METALURGIJA 53 (2014) 2, 155-158T. MERDER et al.: ANALYSIS OF RESIDENCE TIME DISTRIBUTION (RTD) CURVES FOR T-TYPE TUNDISH EQUIPPED...a character that it spills over the upper edge of dam, whereas through the notch window, the fl ow practically does not exist. During dam construction it was assumed that this window would play the role of culvert increas-ing the kinetics of modelling agent fl ow to the channel part of the tundish model. Results of visualization re-search were negative. For Cases C (Figure 7) benefi cial character of mod-elling fl uid fl ow was observed in the area of well mixed fl ow. Mixing was suffi  cient and the strong mixing of ascending jet with surface layer of the bath was not ob-served. Turned up upper walls of turbulence infhibitors cause an additional rotational movement of a modelling agent in the area of well mixed fl ow. However, similarly to other cases, the kinetics of mixing in the area of back walls of the model is not suffi cient.RTD characteristcsRTD characteristics contain cumulated information about hydrodynamic conditions of steel fl  ow through tundish and enable to estimate initially the quality of the object considering the steel mixing and possibilities of refi ning processes intensifi cation. According to the the-ory of fl ow in reactors [7-10], the proper characteristics for estimating the fl ow are RTD curve E- and F-type. Figure 8 presents the shape and course of the R TD curves (F-type) registered for analyzed confi  gurations of tundish equipping. Presented curves show that the kinetics of steel mixing for all studied cases is much the same. To compare the results, the tracer concentration was transformed in dimensionless form in such a way that the minimal value was 0, whereas maximal was 1. Such operation was possible applying relationships de-scribed in works [2,12]. To make more detailed comparison time interval ∆t was determined (range of mixing kinetics).The lower Flow of the fl uidRegistered fi lm enables to analyze the change of fl ow and mixing kinetics in studied cases. Figures 4 to 7 show the chosen results of tracer propagation during the experiment for examined cases. Analysis of obtained results shows that the amount of well mixing area in bare tundish (Figure 34) is not suffi cient. This area in-fl uences the quality of obtained cast strands; steel refi n-ing, by impurities fl oating to slag, occurs. The further fl ow has circulative character. Tracer propagated in the direction of water surface and on the head wall falls down creating right circulation (movement is in accord-ance with clockwise). Dangerously low kinetics of mix-ing is also seen in the area of back walls of the model. Such phenomenon can cause the creation of dead zones in this area of a real tundish. For cases A and B (Figures 5 and 6) in which dams were installed, kinetics of liquid fl ow is more intensive than in a bare tundish. The area of well mixing is also bigger. However kinetics of ascending the liquid to the surface is smaller. Such fl ow does not threaten the co-herence of slag layer and in the same time makes non-metallic inclusions easily assimilated by this layer. Such equipping is the reason why tundish inlet area becomes integrated with its construction by high volume turbu-lence inhibitor. In case B (dam with notches) movement of model-ling liquid in an inlet part of the tundish model has such Figure 4  Tracer propagation in tundish model (bare tundish) after time: a) 30 s, b) 70 sFigure 5  Tracer propagation in tundish model (case A) after time: a) 30 s, b) 70 s Figure 6  Tracer propagation in tundish model (case B) after time: a) 30 s, b) 70 sFigure 7  Tracer propagation in tundish model (case C) after time: a) 30 s, b) 70 sFigure 8  The F-type characteristics obtained from water model: a) bare tundish [12], b) Case A, c) Case B, d) Case C158  METALURGIJA 53 (2014) 2, 155-158T. MERDER et al.: ANALYSIS OF RESIDENCE TIME DISTRIBUTION (RTD) CURVES FOR T-TYPE TUNDISH EQUIPPED...values of ∆t, the better conditions of mixing. Table 2 presents results characterizing the kinetics of mixing in examined cases. Table 2 Kinetics of steel mixing for studied cases Case∆t / sOutlet No 1 Outlet No 2Bare tundish 348,5 349,5Dam (Case A) 350 354Dam notched (Case B) 315,5 322Turbulence inhibitor (Case C) 292,5 290Additionally Table 2 shows the data for both outlets to check the symmetry condition. Values of ∆t on both outlets of the examined variants dif fer insignifi cantly. These differences come from abnormal levelling of the tundish model. Basing on E-type curves, using relationships de-scribed in works [2, 12], particular volume fraction of fl ows for studied cases were calculated. Table 3 presents these results. The increase of mixing kinetics was ob-served for cases B and C, which is a positive phenome-non. Bare tundish used nowadays and proposed variant of its equipping – Case A (dam) have kinetics of steel mixing at the same level. It is not optimal equipment for casting process taking into account the transient zone during sequence casting of different grades of steel. Ta-ble 3 shows that there is an increase of well mixed fl ow contribution mainly at the expense of dead fl ow for cas-es A to C. Table 3 RTD parameters and volume fraction of fl owCase Volume fraction / %Dispersed plug volume (Vdp)Well mixed volume(Vm)Deadvolume (Vd)Bare tundish 18,8 45,6 35,6A 17,4 53 29,6B 15,2 52,1 32,7C 17,9 52,4 29,7The next analysis was done taking into account the  dependence between ratio of well mixed fl  ow to dead  volume Vm/Vd and ratio of dispersed plug fl  ow to dead  volume Vdp/Vd (Table 4). The last one (ratio Vdp/Vd) indi-cated the quiescent region of tundish which promotes the inclusion fl oatation behaviour inside the tundish, whereas ratio (V m/Vd) indicats the well mixed region which in  turn is supposed to provide better homogeneity inside the tundish [2]. The best results were obtained for case C. Table 4 Comparison of diff erent tundish volumes ratio Case Overall(Vm/Vd)Overall(Vdp/Vd)Bare tundish 1,28 0,53A 1,79 0,59B 1,56 0,46C 1,76 0,60CONCLUSIONBasing on the carried out experiments it was stated that applying fl ow control devices in working area of the tundish causes:•  favourable change of fl ow kinetics,•  increasing the volume of dead areas, however they cannot be totally eliminated; places especially suscep-tible to this disturbance of fl ow are areaa near the back wall of the tundish model (close by liquid surface),•  lengthening the time which tracer spent in the tundish; this infl uences the process of transient zone, forming at the same time favourable conditions to sequence casting,•  the dead area is smaller, as a consequence the area with well mixed fl ow increases,•  improving mixed to dead volume of about 13,2 % and  plug to dead volume of about 37,5 %. 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Sharma: Ironmaking and Steelmaking, 40 (2013) 3, 159–166.[10] K. Gryc, K. Michalek, Z. Hudzieczek, M. Tkadlečkova: Metal 2010, Conference proceedings. 2010, 42–46. [11] M. Warzecha: Metalurgija, 50 (2011) 3, 147-150.[12] T. Merder , J. Pieprzyca: Steel Research Int., 1 1 (2012), 1029–1037.[13] T. Merder , J. Pieprzyca: Metalur gija, 50 (201 1) 4, 223–226.[14] B. Panic: Metalurgija, 52 (2013) 2, 177–180.[15] K. Michalek, J. Morávka, K. Gryc: Metalurgija, 48 (2009) 4, 219–222.[16] R. Przylucki, S. Golak: Int. Journal of Thermophysics, 34 (2013) 4, 642–654.[17] M. Warzecha, T. Merder: Metalur gija, 52 (2013) 2, 153–156.Note:  The responsible translator for English language is M. Kingsford, Katowice, Poland

Analysis of residence time distribution (RTD) curves for t-type tundish equipped in flow control devices: physical modelling

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