The article presents results of physical modelling of phenomena occurring during the process of blowing steel by inert gases. The aim of the research was to determine the optimal ceramic material for the porous plugs. Three different materials varying in porosity were tested. Water model of industrial tundish with nominal capacity 320 Mg was used in research. This model was made at 1:10 geometrical scale. Results of the research were presented graphically in the form of Resistance Time Distribution (RTD) curves and graphs of mixing efficiency for particular ceramic materials

J. Pieprzyca

M. Saternus

T. Merder

English

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327METALURGIJA 53 (2014) 3, 327-330J. PIEPRZYCA, T. MERDER, M. SATERNUSPHYSICAL MODELLING OF THE PROCESS OF MIXING LIQUID METAL IN A TUNDISH BLOWN BY GASReceived – Prispjelo: 2013-08-26Accepted – Prihvaćeno: 2014-01-10Original scientifi c paper – Izvorni znanstveni radISSN 0543-5846METABK 53(3) 327-330 (2014)UDC – UDK 669.186:518.1:531.3=111J. Pieprzyca, T. Merder, M. Saternus: Silesian University of Technol-ogy, Department of Metallurgy, Katowice, Poland The article presents results of physical modelling of phenomena occurring during the process of blowing steel by inert gases. The aim of the research was to determine the optimal ceramic material for the porous plugs. Three dif-ferent materials varying in porosity were tested. Water model of industrial tundish with nominal capacity 320 Mg was used in research. This model was made at 1:10 geometrical scale. Results of the research were presented graphi-cally in the form of Resistance Time Distribution (RTD) curves and graphs of mixing effi  ciency for particular ceramic materials. Key words: steel, physical modelling, ladle metallurgy, blowing by argonINTRODUCTIONModern metallurgy applies mixing of melt almost in all stages of liquid steel production. For this purpose different metallurgical apparatus are used. The process of steel mixing by oxygen introduced by the lance takes place during steel melting in oxygen converter. The movement of metal is often supported by inert gas, blown by nozzles or plugs placed in the bottom of the converter. Electric furnaces are equipped with argon plugs and oxygen lances. However, the most frequently the melt mixing is done in a ladle metallurgy. Blowing argon into the melt is commonly used in secondary metallurgy. The important, simplest and most economical technique of ladle metallurgy is a process conducted in a steel ladle. The process of melt mixing in a ladle in order to achieve chemical and thermal homogeneity is a complex phenomenon. There are attempts to describe it by means of characteristic sequence of physical partial processes with the simultaneous help of data coming from model-ling research. Despite of the diversity of such trials the description of mixing is always made by means of char-acteristic behaviour and features such elements of the system as gas bubble, its movement and the structure and properties of gas-liquid column. These elements are pos-sible to be identifi ed using physical modelling. Physical modelling depends on carrying out the measurements of a chosen quantity on the built model of a real object. Model should map the phenomena oc-curring in a real industrial process – this is realized by keeping to the rules of similarity. Such similarity is de-termined basing on rules contained in the fi eld of ap-plied mathematics called theory of similarity. It says that the geometric similarity is the basic requirement taking into account the modelling of a full size object. It means that similar ratio and characteristic linear dimen-sions in the model and a real object are kept. This condi-tion is relatively easy to fulfi ll and consists of geometri-cal scale of the model. However, it does not ensure the similarity of fl uid fl ow applied in the model to the fl uid fl ow in a real apparatus. Hydrodynamic similarity is ob-tained by fulfi lling the condition of equality of the di-mensionless criterial numbers determined for the stud-ied phenomena. These numbers can be determined ac-cording to the laws of dimensional analysis and they are the ratio of physical dimensions essential for the exam-ined process. The total similarity of fl ows is extraordi-narily hard to reach, therefore the partial similarity is often considered as suffi cient. In practice the conver-gence of one or two most important criterial numbers for the examined case is checked.The majority of physical models of metallurgical re-actors are scaled-down models. They are built from transparent materials which enable to observe occurring phenomena. Liquid steel is then replaced by water at ambient temperature [1-4], that is why the kinematic viscosity of water is almost equal to the viscosity of liq-uid steel at casting temperature. The blown gas is usu-ally air [5, 6] and sporadically nitrogen or helium [7].EXAMINED OBJECT AND RESEARCH PROCEDURE Research was carried out using water model built to simulate condition of the apparatus used for steel refi ning by argon blowing. This apparatus should cooperate with steel ladles with nominal capacity of 350 Mg. The indus-trial stand for steel blown by argon consists of [5]:328  METALURGIJA 53 (2014) 3, 327-330J. PIEPRZYCA et al.: PHYSICAL MODELLING OF THE PROCESS OF MIXING LIQUID METAL IN A TUNDISH BLOWN...was 2GB. The registered data were transmitted to the computer; where they were treated and visualized in a real time by means of dedicate software MPICRAP-ORT. Figure 2 shows the scheme of the test stand.The aim of modelling research was to determine the working effi ciency of three plugs of different porosity in the process of argon blowing through steel. The porous plugs were made from granular refractory materials due to applying modern technologies. The basic raw materi-als used to their production were corundum characterized by fi re resistance under load in the range of 1860÷1900 oC or corundum mullite (MgO · Al2O3) by fi re resistance under load in the range of 1900÷1920 oC. Porosity of ma-terials for porous plugs also called open porosity should stay in the range of 25 to 40 %. Radius of the capillary (wormholes) in such materials depends on the granular fraction of refractory material applied for production and can be expressed in the following form: r = 0,22 · R (2)where: R – average dimension of loose fraction of material used for plug production. Table 1 shows model values of material parameters that can be used for porous plugs.To identify the plugs they were marked as: A – plug with the smallest radius of wormholes, B – intermediate plug, C – plug with the highest radius of wormholes. For all those plugs the series of tests were conducted in dif-ferent fl ow rate of inert gas. The jet of gas fl ow was deter-mined basing on the real parameters of argon blow. Ad-ditionally the fl ow rate of gas bigger than the one applied in industry was calculated and then applied. It was done in order to know better the working effi ciency of differ-ent plugs and to determine precisely their characteristics. Therefore, for every plug four different variants of test were carried out (they varied in the jet of gas fl ow). Table 2 presents parameters assumed in the model-ling.First the ladle model was fi lled with water. Air with the determined values of jet fl ow was introduced into − lance to introduce argon,−  installation for blowing argon from the bottom through plugs,− two-strands apparatus to feed wire,−  apparatus to measure temperature and activity of oxygen in metal,−  apparatus to measure FeO and MnO content in slag.Such model was made at geometrical scale SL = 1 : 10. As a dominant criterion of hydrodynamic similarity the modifi ed Froude`s criterion was determined [8]:  LgvFrl2gM ⋅⋅ρ⋅ ρ=  (1)where:  ρg- density of gas / g · cm-3, ρl - density of liquid / g · cm-3, v- velocity of gas / cm · s-1, g - gravita-tional acceleration / cm · s-2, L - characteristic dimension / cm.The modifi cation of such criterion enabled to obtain the required similarity in case of diphase fl ows (liquid-gas). Kinetic similarity concerning the jet of gas fl ow in the model of steel ladle was determined using the scale method. Water was used as a modelling agent and NaCl solution as a tracer. Figure 1 presents the scheme and main dimensions of a ladle model.The model was equipped with specialist control and measuring apparatus. It included the microprocessor controller to steer the gas fl ow provided with LED dis-play for the measured and set values. To measure the changes of modelling liquid conduc-tivity the conductometer with the range of 0 ÷ 20 mS/cm with submersed sensors was used. All signals were directed to the multi-channel electronic register which was equipped with: 16 universal inputs (RTD, TC, mA, V), 4 two-state inputs, 16 mathematical functions, 8 outputs and colourful LCD display. The operating store Figure 1 Scheme of the ladle model /mmFigure 2 Scheme the test stand329METALURGIJA 53 (2014) 3, 327-330J. PIEPRZYCA et al.: PHYSICAL MODELLING OF THE PROCESS OF MIXING LIQUID METAL IN A TUNDISH BLOWN...the model through the microprocessor fl ow controller. Tracer (water solution of NaCl) was given on the water surface. The change of electric conductivity of water was registered by means of conductometers installed in the ladle model. Water conductivity was treated as an analogy to the tracer concentration. Data obtained in such a way was stored in computer memory and then treated appropriately to obtain retention curves RTD, they characterize the hydrodynamic conditions occur-ring in the ladle model.EKSPERIMENTAL RESULTSFigure 3 shows model results of the change of water electric conductivity registered in monitoring points. The presented results of water conductivity change in the function of time depend on the concentration of NaCl water solution introduced as a tracer. Such con-centration can be different in particular experiments. To compare objectively the results of experiments the measured values were transformed into dimensionless form. The following relationship was used [9,10]: 00tb CCCCC−−=∞ (3)where: Ct, C0, C∞ – tracer concentration respectively in t time, at the beginning of the process and at the end of the process. In this way RTD curves of resident time [11,12] for all variants of experiments were determined. Figures 4 to 6 present model results of working effi ciency for par-ticular ceramic porous plugs A, B and C respectively in the form of RTD curves for the fl ow rate of gas equal 2,7 dm3/min.Basing on the presented graphs the minimal times of total mixing of the modelling liquid in the volume of Table 1  Parameters of the material used for ceramic porous plugsDimension of material fraction / mm Open porosity / %0,0 ÷ 0,5 28,20,5 ÷ 1,0 27,61,0 ÷ 3,0 25,0Table 2 Values of parameters used in modelling Variant of test Jet of gas fl ow / dm3∙min-1argon air1 170 1,22 383 2,73 737 5,24 1 006 7,1Figure 3 Example results of researchFigure 4 RTD curve for ceramic porous plug AFigure 5 RTD curve for ceramic porous plug BFigure 6 RTD curve for ceramic porous plug C 330  METALURGIJA 53 (2014) 3, 327-330J. PIEPRZYCA et al.: PHYSICAL MODELLING OF THE PROCESS OF MIXING LIQUID METAL IN A TUNDISH BLOWN...ladle model were determined. The point of total mixing was defi ned in the moment of reaching value 1 in all curves of the dimensionless tracer concentration. Hav-ing such data the characteristic of working effi ciency of studied ceramic porous plugs were determined graphi-cally. Figure 7 presents the obtained results.The equations of the function of total mixing and coeffi cient R2 were determined for particular curves characterizing the working effi ciency of ceramic porous plugs. Table 3 presents such equations.Table 3 Equation of mixing function and values of R2Plugs Equation of function R2A y = 65,223x-0,3116 R2 = 0,9412B y = 59,071x-0,3436 R2 = 0,9378C y = 49,829x-0,3685 R2 = 0,9025CONCLUSIONConducted research shows that it is essential to change the conditions of argon blowing through steel if applying different ceramic porous plugs – these condi-tions depend on the plugs porosity. To conduct research in industrial conditions it is really diffi cult and expen-sive, at the same time the obtained results could not be satisfactory. Physical modelling enables to get informa-tion that could be applied in real apparatus with rela-tively lower cost. Research conducted by this method showed that the ceramic porous plug A has the best properties because the steel mixing time is shorter com-paring with time of applying plugs B and C. In steel-making practice it can be stated that the consumption of gas and energy will decrease, so it will bring economic benefi ts. REFERENCES[1] P. E. Anagbo, J.˝K. Brimacombe: Metal. and Mater. Trans. B, 21B (1990), 637-648.[2] M. C. Diaz, S. V. Komarov, M. Sano: ISIJ International, 37 (1997) 1, 1-8.[3] J. Mietz, S. Schneider, F. Oeters: Steel Research, 62 (1991) 1, 1-9.[4] C. Kamata, K. Ito: ISIJ International, 35 (1995) 7, 859-865.[5] M. Iguchi, Y. Terauchi, S. I. Yokoya: Metal. and Mater. Trans. B, 29B (1998), 1219-1225.[6] M. Iguchi, H. Kawabata, Y. Ito, K. Nakajima, Z. Morita: ISIJ International, 34 (1994) 12, 980-985.[7] M. Iguchi, T. Nakatani, H. Tokunaga: Metal. Trans. B, 28B (1997), 417-423.[8] C.-J. Su; J.-M. Chou; S.-H. Liu: Materials Transactions, 50 (2009) 6, 1502-1509.[9] T. Merder, J. Pieprzyca: Metalurgija, 50 (2011) 4, 223–226.[10] J. Pieprzyca: Metalurgija, 52 (2013) 2, 157-160. [11] M. Warzecha, T. Merder: Metalurgija, 52 (2013) 2, 153–156.[12] K. Michalek, J. Morávka, K. Gryc: Metalurgija, 48 (2009) 4, 219–222.Note:  The responsible translator for English language is M. Kingsford, Katowice, PolandFigure 7  Working characteristics of studied ceramic porous plus

Physical modelling of the process of mixing liquid metal in a tundish blown by gas

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327 METALURGIJA 53 (2014) 3, 327-330J. PIEPRZYCA, T. MERDER, M. SATERNUSPHYSICAL MODELLING OF THE PROCESS OF MIXING LIQUID METAL IN A TUNDISH BLOWN BY GASReceived – Prispjelo: 2013-08-26Accepted – Prihvaćeno: 2014-01-10Original scientifi  c paper – Izvorni znanstveni radISSN 0543-5846METABK 53(3) 327-330 (2014)UDC – UDK 669.186:518.1:531.3=111J. Pieprzyca, T. Merder, M. Saternus: Silesian University of Technol-ogy, Department of Metallurgy, Katowice, Poland The article presents results of physical modelling of phenomena occurring during the process of blowing steel by inert gases. The aim of the research was to determine the optimal ceramic material for the porous plugs. Three dif-ferent materials varying in porosity were tested. Water model of industrial tundish with nominal capacity 320 Mg was used in research. This model was made at 1:10 geometrical scale. Results of the research were presented graphi-cally in the form of Resistance Time Distribution (RTD) curves and graphs of mixing effi   ciency for particular ceramic materials. Key words: steel, physical modelling, ladle metallurgy, blowing by argonINTRODUCTIONModern metallurgy applies mixing of melt almost in all stages of liquid steel production. For this purpose different metallurgical apparatus are used. The process of steel mixing by oxygen introduced by the lance takes place during steel melting in oxygen converter. The movement of metal is often supported by inert gas, blown by nozzles or plugs placed in the bottom of the converter. Electric furnaces are equipped with argon plugs and oxygen lances. However, the most frequently the melt mixing is done in a ladle metallurgy. Blowing argon into the melt is commonly used in secondary metallurgy. The important, simplest and most economical technique of ladle metallurgy is a process conducted in a steel ladle. The process of melt mixing in a ladle in order to achieve chemical and thermal homogeneity is a complex phenomenon. There are attempts to describe it by means of characteristic sequence of physical partial processes with the simultaneous help of data coming from model-ling research. Despite of the diversity of such trials the description of mixing is always made by means of char-acteristic behaviour and features such elements of the system as gas bubble, its movement and the structure and properties of gas-liquid column. These elements are pos-sible to be identiﬁ  ed using physical modelling. Physical modelling depends on carrying out the measurements of a chosen quantity on the built model of a real object. Model should map the phenomena oc-curring in a real industrial process – this is realized by keeping to the rules of similarity. Such similarity is de-termined basing on rules contained in the ﬁ  eld of ap-plied mathematics called theory of similarity. It says that the geometric similarity is the basic requirement taking into account the modelling of a full size object. It means that similar ratio and characteristic linear dimen-sions in the model and a real object are kept. This condi-tion is relatively easy to fulﬁ  ll and consists of geometri-cal scale of the model. However, it does not ensure the similarity of ﬂ  uid ﬂ  ow applied in the model to the ﬂ  uid ﬂ  ow in a real apparatus. Hydrodynamic similarity is ob-tained by fulﬁ  lling the condition of equality of the di-mensionless criterial numbers determined for the stud-ied phenomena. These numbers can be determined ac-cording to the laws of dimensional analysis and they are the ratio of physical dimensions essential for the exam-ined process. The total similarity of ﬂ  ows is extraordi-narily hard to reach, therefore the partial similarity is often considered as sufﬁ  cient. In practice the conver-gence of one or two most important criterial numbers for the examined case is checked.The majority of physical models of metallurgical re-actors are scaled-down models. They are built from transparent materials which enable to observe occurring phenomena. Liquid steel is then replaced by water at ambient temperature [1-4], that is why the kinematic viscosity of water is almost equal to the viscosity of liq-uid steel at casting temperature. The blown gas is usu-ally air [5, 6] and sporadically nitrogen or helium [7].EXAMINED OBJECT AND RESEARCH PROCEDURE Research was carried out using water model built to simulate condition of the apparatus used for steel reﬁ  ning by argon blowing. This apparatus should cooperate with steel ladles with nominal capacity of 350 Mg. The indus-trial stand for steel blown by argon consists of [5]:328   METALURGIJA 53 (2014) 3, 327-330J. PIEPRZYCA et al.: PHYSICAL MODELLING OF THE PROCESS OF MIXING LIQUID METAL IN A TUNDISH BLOWN...was 2GB. The registered data were transmitted to the computer; where they were treated and visualized in a real time by means of dedicate software MPICRAP-ORT. Figure 2 shows the scheme of the test stand.The aim of modelling research was to determine the working efﬁ  ciency of three plugs of different porosity in the process of argon blowing through steel. The porous plugs were made from granular refractory materials due to applying modern technologies. The basic raw materi-als used to their production were corundum characterized by ﬁ  re resistance under load in the range of 1860÷1900 oC or corundum mullite (MgO · Al2O3) by ﬁ  re resistance under load in the range of 1900÷1920 oC. Porosity of ma-terials for porous plugs also called open porosity should stay in the range of 25 to 40 %. Radius of the capillary (wormholes) in such materials depends on the granular fraction of refractory material applied for production and can be expressed in the following form:  r = 0,22 · R  (2)where: R – average dimension of loose fraction of material used for plug production. Table 1 shows model values of material parameters that can be used for porous plugs.To identify the plugs they were marked as: A – plug with the smallest radius of wormholes, B – intermediate plug, C – plug with the highest radius of wormholes. For all those plugs the series of tests were conducted in dif-ferent ﬂ  ow rate of inert gas. The jet of gas ﬂ  ow was deter-mined basing on the real parameters of argon blow. Ad-ditionally the ﬂ  ow rate of gas bigger than the one applied in industry was calculated and then applied. It was done in order to know better the working efﬁ  ciency of differ-ent plugs and to determine precisely their characteristics. Therefore, for every plug four different variants of test were carried out (they varied in the jet of gas ﬂ  ow). Table 2 presents parameters assumed in the model-ling.First the ladle model was ﬁ  lled with water. Air with the determined values of jet ﬂ  ow was introduced into − lance to introduce argon,−   installation for blowing argon from the bottom through plugs,− two-strands apparatus to feed wire,−   apparatus to measure temperature and activity of oxygen in metal,−   apparatus to measure FeO and MnO content in slag.Such model was made at geometrical scale SL = 1 : 10. As a dominant criterion of hydrodynamic similarity the modiﬁ  ed Froude`s criterion was determined [8]:  L gvFrl2gM ⋅ ⋅ ρ⋅  ρ=  (1)where:   ρg- density of gas / g · cm-3, ρl - density of liquid / g · cm-3, v- velocity of gas / cm · s-1, g - gravita-tional acceleration / cm · s-2, L - characteristic dimension / cm.The modiﬁ  cation of such criterion enabled to obtain the required similarity in case of diphase ﬂ  ows (liquid-gas). Kinetic similarity concerning the jet of gas ﬂ  ow in the model of steel ladle was determined using the scale method. Water was used as a modelling agent and NaCl solution as a tracer. Figure 1 presents the scheme and main dimensions of a ladle model.The model was equipped with specialist control and measuring apparatus. It included the microprocessor controller to steer the gas ﬂ  ow provided with LED dis-play for the measured and set values. To measure the changes of modelling liquid conduc-tivity the conductometer with the range of 0 ÷ 20 mS/cm with submersed sensors was used. All signals were directed to the multi-channel electronic register which was equipped with: 16 universal inputs (RTD, TC, mA, V), 4 two-state inputs, 16 mathematical functions, 8 outputs and colourful LCD display. The operating store Figure 1 Scheme of the ladle model /mmFigure 2 Scheme the test stand329 METALURGIJA 53 (2014) 3, 327-330J. PIEPRZYCA et al.: PHYSICAL MODELLING OF THE PROCESS OF MIXING LIQUID METAL IN A TUNDISH BLOWN...the model through the microprocessor ﬂ  ow controller. Tracer (water solution of NaCl) was given on the water surface. The change of electric conductivity of water was registered by means of conductometers installed in the ladle model. Water conductivity was treated as an analogy to the tracer concentration. Data obtained in such a way was stored in computer memory and then treated appropriately to obtain retention curves RTD, they characterize the hydrodynamic conditions occur-ring in the ladle model.EKSPERIMENTAL RESULTSFigure 3 shows model results of the change of water electric conductivity registered in monitoring points. The presented results of water conductivity change in the function of time depend on the concentration of NaCl water solution introduced as a tracer. Such con-centration can be different in particular experiments. To compare objectively the results of experiments the measured values were transformed into dimensionless form. The following relationship was used [9,10]: 00 tb C CC CC−−=∞ (3)where: Ct, C0, C∞ – tracer concentration respectively in t time, at the beginning of the process and at the end of the process. In this way RTD curves of resident time [11,12] for all variants of experiments were determined. Figures 4 to 6 present model results of working efﬁ  ciency for par-ticular ceramic porous plugs A, B and C respectively in the form of RTD curves for the ﬂ  ow rate of gas equal 2,7 dm3/min.Basing on the presented graphs the minimal times of total mixing of the modelling liquid in the volume of Table 1   Parameters of the material used for ceramic porous plugsDimension of material fraction / mm Open porosity / %0,0 ÷ 0,5 28,20,5 ÷ 1,0 27,61,0 ÷ 3,0 25,0Table 2 Values of parameters used in modelling Variant of test Jet of gas fl  ow / dm3∙min-1argon air11 7 0 1 , 223 8 3 2 , 737 3 7 5 , 241  0 0 6 7 , 1Figure 3 Example results of researchFigure 4 RTD curve for ceramic porous plug AFigure 5 RTD curve for ceramic porous plug BFigure 6 RTD curve for ceramic porous plug C 330   METALURGIJA 53 (2014) 3, 327-330J. PIEPRZYCA et al.: PHYSICAL MODELLING OF THE PROCESS OF MIXING LIQUID METAL IN A TUNDISH BLOWN...ladle model were determined. The point of total mixing was deﬁ  ned in the moment of reaching value 1 in all curves of the dimensionless tracer concentration. Hav-ing such data the characteristic of working efﬁ  ciency of studied ceramic porous plugs were determined graphi-cally. Figure 7 presents the obtained results.The equations of the function of total mixing and coefﬁ  cient  R2 were determined for particular curves characterizing the working efﬁ  ciency of ceramic porous plugs. Table 3 presents such equations.Table 3 Equation of mixing function and values of R2Plugs Equation of function R2A y = 65,223x-0,3116 R2 = 0,9412B y = 59,071x-0,3436 R2 = 0,9378C y = 49,829x-0,3685 R2 = 0,9025CONCLUSIONConducted research shows that it is essential to change the conditions of argon blowing through steel if applying different ceramic porous plugs – these condi-tions depend on the plugs porosity. To conduct research in industrial conditions it is really difﬁ  cult and expen-sive, at the same time the obtained results could not be satisfactory. Physical modelling enables to get informa-tion that could be applied in real apparatus with rela-tively lower cost. Research conducted by this method showed that the ceramic porous plug A has the best properties because the steel mixing time is shorter com-paring with time of applying plugs B and C. In steel-making practice it can be stated that the consumption of gas and energy will decrease, so it will bring economic beneﬁ  ts. REFERENCES[1]  P. E. Anagbo, J.˝K. Brimacombe: Metal. and Mater. Trans. B, 21B (1990), 637-648.[2]  M. C. Diaz, S. V. Komarov, M. Sano: ISIJ International, 37 (1997) 1, 1-8.[3]  J. Mietz, S. Schneider, F. Oeters: Steel Research, 62 (1991) 1, 1-9.[4]  C. Kamata, K. Ito: ISIJ International, 35 (1995) 7, 859-865.[5]  M. Iguchi, Y. Terauchi, S. I. Yokoya: Metal. and Mater. Trans. B, 29B (1998), 1219-1225.[6]  M. Iguchi, H. Kawabata, Y. Ito, K. Nakajima, Z. Morita: ISIJ International, 34 (1994) 12, 980-985.[7]  M. Iguchi, T. Nakatani, H. Tokunaga: Metal. Trans. B, 28B (1997), 417-423.[8]  C.-J. Su; J.-M. Chou; S.-H. Liu: Materials Transactions, 50 (2009) 6, 1502-1509.[9]  T. Merder, J. Pieprzyca: Metalurgija, 50 (2011) 4, 223–226.[10]  J. Pieprzyca: Metalurgija, 52 (2013) 2, 157-160. [11]  M. Warzecha, T. Merder: Metalurgija, 52 (2013) 2, 153–156.[12]  K. Michalek, J. Morávka, K. Gryc: Metalurgija, 48 (2009) 4, 219–222.Note:   The responsible translator for English language is M. Kingsford, Katowice, PolandFigure 7   Working characteristics of studied ceramic porous plus

Physical modelling of the process of mixing liquid metal in a tundish blown by gas

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