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Experimental investigation on ligament formation for molten slag granulation
Applied Thermal Engineering 73 (2014) 886e891
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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Experimental investigation on ligament formation for molten slag granulation Junxiang Liu, Qingbo Yu*, Wenjun Duan, Qin Qin School of Materials and Metallurgy, Northeastern University, Shenyang, Liaoning 110819, PR China
h i g h l i g h t s Dry granulation for molten blast furnace slag is an attractive alternative to wet granulation. Transition equation can be used to identify state of disintegration for molten slag granulation. The diameter of slag particles decreased as an increase in angular speed and diameter of rotary cup. There was no change in diameter of slag particles with an increase in molten slag temperature.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 6 May 2014 Accepted 19 August 2014 Available online 27 August 2014
During the dry granulation for molten blast furnace slag, rotary cup is used to atomize the molten slag. In this study, the mechanism of ligament formation for molten slag granulation was investigated. The results indicated that the transition equations from direct drop formation to ligament formation and ligament formation to sheet formation, obtained from glycerol/water mixture, can identify the type of disintegration for molten blast furnace slag granulation. Due to short wavelength of dilational wave along molten slag ligaments, the diameter of slag particles decreased with an increase in angular speed, and more and more slag particles were far away from the center of rotary cup. The slag particles diameter decreased with an increase in rotary cup diameter. The empirical equation can be used to predict the diameter of slag particles obtained by ligament formation for molten slag granulation at high angular speed. Because of slight change in viscosity and surface tension when the temperature of molten slag was over than 1300 C, there was no change in diameter and mass fraction of slag particles with an increase in molten slag temperature. All the results could provide guidance for the design of industrial plant for molten blast furnace slag granulation. © 2014 Elsevier Ltd. All rights reserved.
Keywords: Molten blast furnace slag Waste heat recovery Granulation Rotary cup Ligament formation
1. Introduction Blast furnace slag, generated by the iron-making process, is quickly quenched by water to form glassy granules which can be used as replacing material for Portland cement. During wet granulation, the waste heat of molten slag discharged at high temperatures, from 1450 to 1650 C, is usually not recovered. Besides that, a large amount of water is consumed and the waste gas including sulfide is emitted into the around air. Due to considerations regarding energy conservation and environmental protection, dry
* Corresponding author. P.O. Box 345, Northeastern University, No. 11, Lane 3, Wenhua Road, Heping District, Shenyang, Liaoning, PR China. Tel./fax: þ86 24 83672216. E-mail addresses: [email protected], [email protected] (Q. Yu). http://dx.doi.org/10.1016/j.applthermaleng.2014.08.042 1359-4311/© 2014 Elsevier Ltd. All rights reserved.
granulation for blast furnace slag is an attractive alternative to wet granulation [1,2]. From the late 1970s, some techniques of dry granulation for blast furnace slag, rotary cup, rotary disk, rotary drum, air granulation, continuous casting and rolling included, were proposed [3e7]. And there were many laboratory and pilot scale testing of the above methods. However, none of them was used in the ironmaking process due to the low recovery efficiency and high cost of investment. As an increase in energy prices, more and more iron and steel enterprises have paid close attention to the technique of dry granulation and waste heat recovery in recent years. Because of high treatment capacity and continuous working, the rotary cup has been extensively studied. Rotary cups are widely used in metallurgical industry, fuel oil atomization, chemical engineering, food processing and agriculture [8e10]. Hinze and his cooperators found three different types of disintegration in rotary cup
J. Liu et al. / Applied Thermal Engineering 73 (2014) 886e891
atomization using alcohol/water mixture. During rotary cup atomization, direct drop formation, ligament formation and sheet formation may occur in different technical parameters [11]. Liu et al. found that drop formation may transform into ligament formation and ligament formation may transform into sheet formation with an increase in angular speed for a fixed liquid flow rate. Basing on the experimental data, the transition equations from direct drop formation to ligament formation and ligament formation to sheet formation are derived. And the ligament formation used as the type of disintegration by rotary cup was investigated widely in the present study [12e14]. Ligament formation can provide droplets or particles with uniform diameter compared to sheet formation. In the ligament formation, the liquid flow rate can reach a high value which is unable to reach in direct drop formation. However, the sheet formation for molten slag granulation had been investigated widely by many researchers. In the present study, the effects of angular speed, cup diameter and molten slag temperature on the disintegration of ligament formation for molten slag granulation were investigated. The dimensionless equation which is used for calculating diameter of slag particles obtained from ligament formation for molten slag granulation was determined. 2. Experimental methods As shown in Fig. 1, the test unit consists of three parts, including a tundish, rotary device and collectors. The molten blast furnace slag is injected into the rotary cup via tundish, and the flow rate of molten slag can be controlled by the diameter of hole in the center axis of tundish. The rotary cup is connected to an electric motor by flange. During the experiment, the process of granulation is captured by a camera (MotionPro Y3). For security reasons, the vast majority of high temperature slag particles are captured by big circular collector. And the eight 2 cm width rectangular collectors, collecting the slag particles, are used for calculating average diameter of slag particles and mass fraction of slag particles. In the experimental procedure, the molten slag which is heated by electric furnace is injected into the rotary cup. And the linear velocity of molten slag is the same as that of the rotary cup which is caused by the friction between molten slag and the inner side surface of the rotary cup. Because of centrifugal force, the molten slag reaches the lip of rotary cup, and a circinate molten slag film occurs around the cup. At the edge of the circinate molten slag film, the film is deformed because of disturbances along the circinate molten slag film. And then, the bulges are deformed at the edge of the circinate molten slag film. In the end, the bulges break away from the molten slag film, and the molten slag drops form. The type of disintegration is called direct drop formation. With an increase in angular speed, the bulges do not break away
887
Fig. 2. Viscosity of blast furnace slag at different temperatures.
from the molten slag film, and the ligaments occur between bulges and molten slag film. The ligament breaks up into several molten slag drops in the flight. This phenomenon is called ligament formation. With a further increase in angular speed, the bulges combine around the lip of cup when the number of ligaments reaches the maximum value. Then, the ligaments emerge and the thin and wide molten slag film occurs instead. Finally, the molten slag film disintegrates into droplets at the edge of the film. This phenomenon is called sheet formation. The slag droplets are cooled and freeze in the flight. The main components of blast furnace slags used in the experiment are silica, alumina, lime and magnesium. The viscosity of molten slag with different temperature is shown in Fig. 2. Kashiwaya and his cooperators found that the surface tension of molten slag had slight change with an increase in temperature when the temperature of molten slag was over than 1300 C. The empirical equation can be expressed as follows [15]:
s ¼ ð767:5 0:15809TÞ 103
(1)
Where, s is surface tension of molten slag, N/m, and T is temperature of molten slag, C.
3. Results and discussions 3.1. Ligament formation for molten slag In the work of Liu, the mechanism of ligament formation for glycerol/water mixture was investigated [16,17]. The transition
Fig. 1. Schematic diagram of experimental apparatus.
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equations from direct drop formation to ligament formation and ligament formation to sheet formation, which were arranged by three dimensionless parameters, were obtained. The dimensionless equation obtained from their theoretical analysis and experimental data can be used for calculating diameter of droplets. The equations for transition from direct drop formation to ligament formation were expressed as follows [17]:
Q1þ ¼ 6:5We1:161 St 0:0705 Q1þ ¼
Q1 r3 u
(2)
(3)
where, Q1þ is critical dimensionless flow rate for transition from direct drop formation to ligament formation, Q1 is critical transition flow rate, cm3 s1, r is radius of rotary cup, cm, and u is angular speed of rotary cup, rad s1. If the volume flow rate, Q, is less than Q1 for a given We and St, there will be direct drop formation occurred. On the contrast, Q > Q1, there will be ligament formation or sheet formation occurred. The equations for transition from ligament formation to sheet formation were expressed as follows [17]:
Q2þ ¼ 5:13We0:789 St 0:036 Q2þ ¼
Q2 r3 u
(4)
to ligament formation for molten slag granulation. In the experiment, the volume flow rates of molten blast furnace slag were 79.8 cm3 s1 and 33.4 cm3 s1 respectively. The angular speed of rotary cup were 62.8 rad s1, 83.7 rad s1, 104.7 rad s1, 125.6 rad s1 and 157 rad s1. It is clear that the type of disintegration for molten blast furnace slag was ligament formation or sheet formation. Fig. 4 shows transition from ligament formation to sheet formation for molten slag granulation. There was ligament formation occurred around the rotary cup when the volume flow rate was 33.4 cm3 s1. And the sheet formation occurred around the rotary cup when the volume flow rate was 79.8 cm3 s1. Hinze and Kamiya [19,20] indicated that the number of ligaments was determined by We and St. There was no changes in number of ligaments with an increase in volume flow rate for a given angular speed. Moreover, the head of ligament at the lip of rotary cup became thick. With an increase in volume flow rate, the head of each adjacent ligaments combined and the liquid film occurred around the lip of rotary cup. Fig. 5 shows pictures for molten blast furnace slag granulation with different volume flow rates. The results gave fairly agreement with that shown in Figs. 3 and 4. During ligament formation, diameter of molten slag droplets was controlled by diameter dL of molten slag ligament tip and wavelength of dilational wave. Based on principle of mass conservation and experimental results of Liu et al. [17], diameter d of molten slag droplets can be expressed by Eq. (6).
(5)
where, Q2þ is critical dimensionless flow rate for transition from ligament formation to sheet formation and Q2 is critical transition flow rate, cm3 s1, If the volume flow rate, Q, is less than Q2 for a given We and St, there will be ligament formation occurred. On the contrast, Q > Q2, there will be sheet formation occurred. The Eq. (2) and Eq. (4) can be used under the condition of 103 < We < 105. During the disintegration by ligament formation, the bulges grew into molten slag ligaments which seemed involutes. Because of centrifugal force, the molten slag ligaments became unstable and dilational waves occurred along them. Under the action of surface tension, the wave grew in amplitude, and the wavelength became long. And then, the molten slag ligament break up into several round molten slag droplets [18]. For a given volume flow rate of molten blast furnace slag, angular speed and diameter of cup, it is possible to confirm the type of disintegration. Fig. 3 shows transition from direct drop formation
Fig. 3. Transition from direct drop formation to ligament formation for molten slag granulation.
2=3 d d ¼ 1:617 L We1=6 r r
(6)
After detaching from ligament, the molten slag droplets will tend to solidify as the temperature of molten slag reaches the freezing point. After solidification, the diameter of slag particle ds is calculated by Eq. (7).
3=2 r ds ¼ d l rs
(7)
where, ds is diameter of slag particle, rl and rs are density of molten slag and slag particle respectively. So, combining Eq. (6) and Eq. (7), the diameter of slag particle produced by ligament formation can be expressed as follows:
Fig. 4. Transition from ligament formation to sheet formation for molten slag granulation.
J. Liu et al. / Applied Thermal Engineering 73 (2014) 886e891
889
Fig. 5. Pictures for molten slag granulation.
ds ¼ 1:617
dL r
2=3 3=2 rl rWe1=6 rs
(8)
3.2. Effects of rotary cup angular speed The relationship between diameter of slag particles and rotary cup angular speed is illustrated in Fig. 6. As an increase in angular speed, the diameter of slag particles decreased. During ligament formation, the high angular speed resulted in short wavelength of dilational wave, and the disconnected molten slag ligament which was the origin of slag particle became small. So, the diameter of slag particles at high angular speed was smaller than that at low angular speed. It is clear that the value of calculation from Eq. (8) was in accord with the experimental data. The relative error was 14% when the angular speed was 62.8 rad s1. In the experiment, the adjacent two dilational waves in ligament did not segregate when they reached the bottom of collector. Thus, the value of slag particle diameter is higher than the value of calculation. To enhance the heat transfer between slag particles and heattransfer medium, the diameter of slag particles should be small. However, the angular speed will be high and the operating cost of rotary cup system, for example, the power consumption, will be high accordingly. So, there is an optimal angular speed of rotary cup with high heat transfer efficiency in waste heat recovery system and low cost in rotary cup system. Fig. 7 shows relationship between mass fraction of slag particles and rotary cup angular speed. The high peak indicates that more slag particles fell into the range. In reverse, slag particles fell into several ranges when there is no high peak, but flat peak instead. It can be seen that more and more slag particles were far away from the center of rotary cup with an increase in angular speed. when the molten slag was poured into the rotating cup, friction between molten slag and inner side surface of cup enabled molten slag to reach quickly the alike angular speed as that of rotary cup, and the angular speed of molten slag ligament was high. Thus, the angular speed of molten slag droplets, releasing from ligament just, was nearly equal to that of ligament. Hence, the flying distance was long at high angular speed of rotary cup. Besides that, there were small and uniform slag particles at high angular speed, and the majority of slag particles fell into several adjacent distance ranges as shown in Fig. 7 at u ¼ 157.0 rad s1.
Fig. 6. Relationship between diameter and angular speed.
the experimental data when the angular speed of rotary cup was over than 104.5 rad s1. The maximum value of the relative error was 15%, and the minimum value of the relative error was 3.6%. Under the condition of that the angular speed was less than 104.5 rad s1, the values of diameter of slag particles obtained from
3.3. Effects of rotary cup diameter Fig. 8 shows relationship between slag particles diameter and angular speed with three different diameters of rotary cup. It is clear that the value of calculation from Eq. (8) was in accord with
Fig. 7. Relationship between mass fraction and angular speed.
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J. Liu et al. / Applied Thermal Engineering 73 (2014) 886e891
Fig. 8. Relationship between diameter and angular speed with different cup diameters.
experiments were higher than that of calculation, especially at 2r ¼ 95 mm. Theoretically, there were a small number of thick molten slag ligaments around the cup chip at low angular speed. For low angular speed, there were thicker molten slag ligaments around the lip of small diameter rotary cup. Some ligaments reached the bottom of slag particles collector, but not break up into spherical droplets. Hence, to obtain uniform spherical slag particles, the rotary cup angular speed should be increased for small diameter rotary cup. Fig. 9 shows relationship between mass fraction of slag particles and rotary cup diameter. It can be seen that more and more slag particles were far away from the center of rotary cup with an increase in rotary cup diameter. For a given angular speed, the velocity of molten slag droplets increased as an increase in rotary cup diameter. As a result, there were small diameter slag particles and the horizontal flying distance was long when they reached the bottom of slag particles collector. 3.4. Effects of temperature of molten slag poured into rotary cup The molten blast furnace slag is discharged at high temperature, from 1450 to 1650 C and there will be temperature drop when the
Fig. 9. Relationship between mass fraction and rotary cup diameters.
Fig. 10. Relationship between diameter and temperature.
molten slag reaches the inner side surface of rotary cup. The relationship between slag particles diameter and molten slag temperature with different angular speeds is illustrated in Fig. 10. As an increase in molten slag temperature, there was almost no change in slag particles diameter. As shown in Fig. 2, the viscosity of molten slag increased with decrease in molten slag temperature when the temperature was less than 1400 C. As a further increase in viscosity, it caused molten slag to reach a state of such high viscosity that it acted effectively like a solid. There was almost no change in viscosity and surface tension when the molten slag temperature exceeded 1400 C. Hence, the number of ligaments had no change with an increase in molten slag temperature. For a given angular speed and rotary cup diameter, the slag particles diameter almost kept constant. Fig. 11 shows relationship between mass fraction of slag particles and temperature of molten slag poured into rotary cup. It can be seen that the majority of slag particles fell into the same range, although the molten slag was different. As mentioned above, the flying distance was controlled by velocity of slag particles after releasing from ligaments. For a given angular speed and rotary cup diameter, the diameter of slag particles obtained at different temperatures of molten slag kept constant. So the trend for mass
Fig. 11. Relationship between mass fraction and temperature.
J. Liu et al. / Applied Thermal Engineering 73 (2014) 886e891
fraction of slag particles was consistent with the trend for slag particles diameter as an increase in temperature of molten slag. 4. Conclusions Ligament formation for molten blast furnace slag granulation can produce more uniform drops which can enhance the efficiency of waste heat recovery for high temperature slag particles. The transition equations from direct drop formation to ligament formation and ligament formation to sheet formation, obtained from glycerol/water mixture, could be used for identifying the type of disintegration for molten slag granulation. And the empirical equation obtained from glycerol/water mixture could be used to predict the diameter of slag particles obtained by ligament formation for molten slag granulation. The diameter of slag particles decreased when the angular speed and cup diameter increased. The majority of slag particles were far away from the center of rotary cup with an increase in velocity of slag particles after releasing from molten slag ligaments. The viscosity of molten slag has on change when the temperature of molten slag poured into rotary cup exceeds 1400 C. With an increase in molten slag temperature, there was no change in diameter and mass fraction of slag particles. All the conclusions could provide guidance for the design of commercial unit for molten blast furnace slag granulation. Acknowledgements This research was supposed by The National Natural Science Foundation of China (51274066, 51304048), China Postdoctoral Science Foundation Funded Project (2013M541240), The Fundamental Research Funds for the Central Universities (N130402019), The National Key Technologies R&D Program of China (2013BAA03B03). Nomenclature d dL Q Q1 Q1þ Q2 Q2þ
diameter of molten blast furnace slag droplets diameter of molten slag ligament tip volume flow rate of molten slag critical transition flow rate for transition from direct drop formation to ligament formation critical dimensionless flow rate for transition from direct drop formation to ligament formation critical transition flow rate for transition from ligament formation to sheet formation critical dimensionless flow rate for transition from ligament formation to sheet formation
r St T We
rl rs u s m
891
radius of rotary cup Stokes number, St ¼ m2/rlrs temperature of molten slag Weber number, We ¼ rlr2u3/s density of molten blast furnace slag at 1450 C density of molten blast furnace slag particles angular speed of rotary cup surface tension of molten slag dynamic viscosity of molten slag
References [1] H. Zhang, H. Wang, X. Zhu, Y.J. Qiu, K. Li, R. Chen, Q. Liao, A review of waste heat recovery technologies towards molten slag in steel industry, Appl. Energy 112 (2013) 956e966. [2] M. Barati, S. Esfahani, T.A. Utigard, Energy recovery from high temperature slags, Energy 36 (2011) 5440e5449. [3] G. Bisio, Energy recovery from molten slag and exploitation of the recovered energy, Energy 22 (5) (1996) 501e509. [4] S.J. Pickering, N. Hay, T.F. Roylance, G.H. Thomas, New process for dry granulation and heat recovery from molten blast-furnace slag, Ironmak Steelmak 12 (1985) 14e21. [5] H. Shen, E. Forssberg, An overview of recovery of metals from slags, Waste. Manage. 23 (2003) 933e949. [6] N. Maruoka, T. Mizuochi, H. Purwanto, T. Akiyama, Feasibility study for recovering waste heat in the steelmaking industry using a chemical recuperator, ISIJ Int. 44 (2004) 257e262. [7] X.S. Liu, Y.S. Zhou, Feasible analysis on sensible heat recovery of blast furnace slag, Iron Steel 30 (1995) 107e111. [8] J.W. Xie, Y.Y. Zhao, J.J. Dunkley, Effects of processing conditions on powder particle size and morphology in centrifugal atomisation of tin, Powder Metall. 47 (2004) 168e172. , Formation of irregular particles during cen[9] R. Angers, R. Tremblay, D. Dube trifugal atomization of AZ91 alloy, Mater. Lett. 33 (1997) 13e18. [10] C. Dogan, S. Saritas, Metal powder production by centrifugal atomization, Int. J. Powder Metall. 30 (1994) 419e427. [11] J.O. Hinze, H. Milborn, Atomization of liquids by means of a rotating cup, J. Appl. Mech. 17 (1950) 145e153. [12] Y. Kawase, A. De, Ligament-type disintegration of non-Newtonian fluid in spinning disk atomization, J. Newt. Fluid 19 (1982) 367e371. [13] P. Eisenklam, On ligament formation from spinning discs and cups, Chem. Eng. Sci. 19 (1964) 693e694. [14] A.R. Frost, Rotary atomisation in the ligament formation mode, J. Agric. Eng. Res. 26 (1981) 63e78. [15] Y. Kashiwaya, Y. In-Nami, T. Akiyama, Mechanism of the formation of slag particles by the rotary cylinder atomization, ISIJ Int. 50 (2010) 1252e1258. [16] J.X. Liu, Q.B. Yu, P. Li, W.Y. Du, Cold experiments on ligament formation for blast furnace slag granulation, Appl. Therm. Eng. 40 (2012) 351e357. [17] J.X. Liu, Q.B. Yu, Q. Guo, Experimental investigation of liquid disintegration by rotary cups, Chem. Eng. Sci. 73 (2012) 44e50. [18] A.Y. Gunawan, J. Molenaar, A.A.F. van de Ven, In-phase and out-of-phase break-up of two immersed liquid threads under influence of surface tension, Eur. J. Mech. B Fluid 21 (2002) 399e412. [19] T. Kamiya, A. Kayano, Film-type disintegration by rotating disk, J. Chem. Eng. Jpn. 5 (1972) 174e182. [20] T. Kamiya, An analysis of the ligament-type disintegration of thin liquid film at the edge of rotating disk, J. Chem. Eng. Jpn. 5 (1972) 391e396.
Contents lists available at ScienceDirect
Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Experimental investigation on ligament formation for molten slag granulation Junxiang Liu, Qingbo Yu*, Wenjun Duan, Qin Qin School of Materials and Metallurgy, Northeastern University, Shenyang, Liaoning 110819, PR China
h i g h l i g h t s Dry granulation for molten blast furnace slag is an attractive alternative to wet granulation. Transition equation can be used to identify state of disintegration for molten slag granulation. The diameter of slag particles decreased as an increase in angular speed and diameter of rotary cup. There was no change in diameter of slag particles with an increase in molten slag temperature.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 6 May 2014 Accepted 19 August 2014 Available online 27 August 2014
During the dry granulation for molten blast furnace slag, rotary cup is used to atomize the molten slag. In this study, the mechanism of ligament formation for molten slag granulation was investigated. The results indicated that the transition equations from direct drop formation to ligament formation and ligament formation to sheet formation, obtained from glycerol/water mixture, can identify the type of disintegration for molten blast furnace slag granulation. Due to short wavelength of dilational wave along molten slag ligaments, the diameter of slag particles decreased with an increase in angular speed, and more and more slag particles were far away from the center of rotary cup. The slag particles diameter decreased with an increase in rotary cup diameter. The empirical equation can be used to predict the diameter of slag particles obtained by ligament formation for molten slag granulation at high angular speed. Because of slight change in viscosity and surface tension when the temperature of molten slag was over than 1300 C, there was no change in diameter and mass fraction of slag particles with an increase in molten slag temperature. All the results could provide guidance for the design of industrial plant for molten blast furnace slag granulation. © 2014 Elsevier Ltd. All rights reserved.
Keywords: Molten blast furnace slag Waste heat recovery Granulation Rotary cup Ligament formation
1. Introduction Blast furnace slag, generated by the iron-making process, is quickly quenched by water to form glassy granules which can be used as replacing material for Portland cement. During wet granulation, the waste heat of molten slag discharged at high temperatures, from 1450 to 1650 C, is usually not recovered. Besides that, a large amount of water is consumed and the waste gas including sulfide is emitted into the around air. Due to considerations regarding energy conservation and environmental protection, dry
* Corresponding author. P.O. Box 345, Northeastern University, No. 11, Lane 3, Wenhua Road, Heping District, Shenyang, Liaoning, PR China. Tel./fax: þ86 24 83672216. E-mail addresses: [email protected], [email protected] (Q. Yu). http://dx.doi.org/10.1016/j.applthermaleng.2014.08.042 1359-4311/© 2014 Elsevier Ltd. All rights reserved.
granulation for blast furnace slag is an attractive alternative to wet granulation [1,2]. From the late 1970s, some techniques of dry granulation for blast furnace slag, rotary cup, rotary disk, rotary drum, air granulation, continuous casting and rolling included, were proposed [3e7]. And there were many laboratory and pilot scale testing of the above methods. However, none of them was used in the ironmaking process due to the low recovery efficiency and high cost of investment. As an increase in energy prices, more and more iron and steel enterprises have paid close attention to the technique of dry granulation and waste heat recovery in recent years. Because of high treatment capacity and continuous working, the rotary cup has been extensively studied. Rotary cups are widely used in metallurgical industry, fuel oil atomization, chemical engineering, food processing and agriculture [8e10]. Hinze and his cooperators found three different types of disintegration in rotary cup
J. Liu et al. / Applied Thermal Engineering 73 (2014) 886e891
atomization using alcohol/water mixture. During rotary cup atomization, direct drop formation, ligament formation and sheet formation may occur in different technical parameters [11]. Liu et al. found that drop formation may transform into ligament formation and ligament formation may transform into sheet formation with an increase in angular speed for a fixed liquid flow rate. Basing on the experimental data, the transition equations from direct drop formation to ligament formation and ligament formation to sheet formation are derived. And the ligament formation used as the type of disintegration by rotary cup was investigated widely in the present study [12e14]. Ligament formation can provide droplets or particles with uniform diameter compared to sheet formation. In the ligament formation, the liquid flow rate can reach a high value which is unable to reach in direct drop formation. However, the sheet formation for molten slag granulation had been investigated widely by many researchers. In the present study, the effects of angular speed, cup diameter and molten slag temperature on the disintegration of ligament formation for molten slag granulation were investigated. The dimensionless equation which is used for calculating diameter of slag particles obtained from ligament formation for molten slag granulation was determined. 2. Experimental methods As shown in Fig. 1, the test unit consists of three parts, including a tundish, rotary device and collectors. The molten blast furnace slag is injected into the rotary cup via tundish, and the flow rate of molten slag can be controlled by the diameter of hole in the center axis of tundish. The rotary cup is connected to an electric motor by flange. During the experiment, the process of granulation is captured by a camera (MotionPro Y3). For security reasons, the vast majority of high temperature slag particles are captured by big circular collector. And the eight 2 cm width rectangular collectors, collecting the slag particles, are used for calculating average diameter of slag particles and mass fraction of slag particles. In the experimental procedure, the molten slag which is heated by electric furnace is injected into the rotary cup. And the linear velocity of molten slag is the same as that of the rotary cup which is caused by the friction between molten slag and the inner side surface of the rotary cup. Because of centrifugal force, the molten slag reaches the lip of rotary cup, and a circinate molten slag film occurs around the cup. At the edge of the circinate molten slag film, the film is deformed because of disturbances along the circinate molten slag film. And then, the bulges are deformed at the edge of the circinate molten slag film. In the end, the bulges break away from the molten slag film, and the molten slag drops form. The type of disintegration is called direct drop formation. With an increase in angular speed, the bulges do not break away
887
Fig. 2. Viscosity of blast furnace slag at different temperatures.
from the molten slag film, and the ligaments occur between bulges and molten slag film. The ligament breaks up into several molten slag drops in the flight. This phenomenon is called ligament formation. With a further increase in angular speed, the bulges combine around the lip of cup when the number of ligaments reaches the maximum value. Then, the ligaments emerge and the thin and wide molten slag film occurs instead. Finally, the molten slag film disintegrates into droplets at the edge of the film. This phenomenon is called sheet formation. The slag droplets are cooled and freeze in the flight. The main components of blast furnace slags used in the experiment are silica, alumina, lime and magnesium. The viscosity of molten slag with different temperature is shown in Fig. 2. Kashiwaya and his cooperators found that the surface tension of molten slag had slight change with an increase in temperature when the temperature of molten slag was over than 1300 C. The empirical equation can be expressed as follows [15]:
s ¼ ð767:5 0:15809TÞ 103
(1)
Where, s is surface tension of molten slag, N/m, and T is temperature of molten slag, C.
3. Results and discussions 3.1. Ligament formation for molten slag In the work of Liu, the mechanism of ligament formation for glycerol/water mixture was investigated [16,17]. The transition
Fig. 1. Schematic diagram of experimental apparatus.
888
J. Liu et al. / Applied Thermal Engineering 73 (2014) 886e891
equations from direct drop formation to ligament formation and ligament formation to sheet formation, which were arranged by three dimensionless parameters, were obtained. The dimensionless equation obtained from their theoretical analysis and experimental data can be used for calculating diameter of droplets. The equations for transition from direct drop formation to ligament formation were expressed as follows [17]:
Q1þ ¼ 6:5We1:161 St 0:0705 Q1þ ¼
Q1 r3 u
(2)
(3)
where, Q1þ is critical dimensionless flow rate for transition from direct drop formation to ligament formation, Q1 is critical transition flow rate, cm3 s1, r is radius of rotary cup, cm, and u is angular speed of rotary cup, rad s1. If the volume flow rate, Q, is less than Q1 for a given We and St, there will be direct drop formation occurred. On the contrast, Q > Q1, there will be ligament formation or sheet formation occurred. The equations for transition from ligament formation to sheet formation were expressed as follows [17]:
Q2þ ¼ 5:13We0:789 St 0:036 Q2þ ¼
Q2 r3 u
(4)
to ligament formation for molten slag granulation. In the experiment, the volume flow rates of molten blast furnace slag were 79.8 cm3 s1 and 33.4 cm3 s1 respectively. The angular speed of rotary cup were 62.8 rad s1, 83.7 rad s1, 104.7 rad s1, 125.6 rad s1 and 157 rad s1. It is clear that the type of disintegration for molten blast furnace slag was ligament formation or sheet formation. Fig. 4 shows transition from ligament formation to sheet formation for molten slag granulation. There was ligament formation occurred around the rotary cup when the volume flow rate was 33.4 cm3 s1. And the sheet formation occurred around the rotary cup when the volume flow rate was 79.8 cm3 s1. Hinze and Kamiya [19,20] indicated that the number of ligaments was determined by We and St. There was no changes in number of ligaments with an increase in volume flow rate for a given angular speed. Moreover, the head of ligament at the lip of rotary cup became thick. With an increase in volume flow rate, the head of each adjacent ligaments combined and the liquid film occurred around the lip of rotary cup. Fig. 5 shows pictures for molten blast furnace slag granulation with different volume flow rates. The results gave fairly agreement with that shown in Figs. 3 and 4. During ligament formation, diameter of molten slag droplets was controlled by diameter dL of molten slag ligament tip and wavelength of dilational wave. Based on principle of mass conservation and experimental results of Liu et al. [17], diameter d of molten slag droplets can be expressed by Eq. (6).
(5)
where, Q2þ is critical dimensionless flow rate for transition from ligament formation to sheet formation and Q2 is critical transition flow rate, cm3 s1, If the volume flow rate, Q, is less than Q2 for a given We and St, there will be ligament formation occurred. On the contrast, Q > Q2, there will be sheet formation occurred. The Eq. (2) and Eq. (4) can be used under the condition of 103 < We < 105. During the disintegration by ligament formation, the bulges grew into molten slag ligaments which seemed involutes. Because of centrifugal force, the molten slag ligaments became unstable and dilational waves occurred along them. Under the action of surface tension, the wave grew in amplitude, and the wavelength became long. And then, the molten slag ligament break up into several round molten slag droplets [18]. For a given volume flow rate of molten blast furnace slag, angular speed and diameter of cup, it is possible to confirm the type of disintegration. Fig. 3 shows transition from direct drop formation
Fig. 3. Transition from direct drop formation to ligament formation for molten slag granulation.
2=3 d d ¼ 1:617 L We1=6 r r
(6)
After detaching from ligament, the molten slag droplets will tend to solidify as the temperature of molten slag reaches the freezing point. After solidification, the diameter of slag particle ds is calculated by Eq. (7).
3=2 r ds ¼ d l rs
(7)
where, ds is diameter of slag particle, rl and rs are density of molten slag and slag particle respectively. So, combining Eq. (6) and Eq. (7), the diameter of slag particle produced by ligament formation can be expressed as follows:
Fig. 4. Transition from ligament formation to sheet formation for molten slag granulation.
J. Liu et al. / Applied Thermal Engineering 73 (2014) 886e891
889
Fig. 5. Pictures for molten slag granulation.
ds ¼ 1:617
dL r
2=3 3=2 rl rWe1=6 rs
(8)
3.2. Effects of rotary cup angular speed The relationship between diameter of slag particles and rotary cup angular speed is illustrated in Fig. 6. As an increase in angular speed, the diameter of slag particles decreased. During ligament formation, the high angular speed resulted in short wavelength of dilational wave, and the disconnected molten slag ligament which was the origin of slag particle became small. So, the diameter of slag particles at high angular speed was smaller than that at low angular speed. It is clear that the value of calculation from Eq. (8) was in accord with the experimental data. The relative error was 14% when the angular speed was 62.8 rad s1. In the experiment, the adjacent two dilational waves in ligament did not segregate when they reached the bottom of collector. Thus, the value of slag particle diameter is higher than the value of calculation. To enhance the heat transfer between slag particles and heattransfer medium, the diameter of slag particles should be small. However, the angular speed will be high and the operating cost of rotary cup system, for example, the power consumption, will be high accordingly. So, there is an optimal angular speed of rotary cup with high heat transfer efficiency in waste heat recovery system and low cost in rotary cup system. Fig. 7 shows relationship between mass fraction of slag particles and rotary cup angular speed. The high peak indicates that more slag particles fell into the range. In reverse, slag particles fell into several ranges when there is no high peak, but flat peak instead. It can be seen that more and more slag particles were far away from the center of rotary cup with an increase in angular speed. when the molten slag was poured into the rotating cup, friction between molten slag and inner side surface of cup enabled molten slag to reach quickly the alike angular speed as that of rotary cup, and the angular speed of molten slag ligament was high. Thus, the angular speed of molten slag droplets, releasing from ligament just, was nearly equal to that of ligament. Hence, the flying distance was long at high angular speed of rotary cup. Besides that, there were small and uniform slag particles at high angular speed, and the majority of slag particles fell into several adjacent distance ranges as shown in Fig. 7 at u ¼ 157.0 rad s1.
Fig. 6. Relationship between diameter and angular speed.
the experimental data when the angular speed of rotary cup was over than 104.5 rad s1. The maximum value of the relative error was 15%, and the minimum value of the relative error was 3.6%. Under the condition of that the angular speed was less than 104.5 rad s1, the values of diameter of slag particles obtained from
3.3. Effects of rotary cup diameter Fig. 8 shows relationship between slag particles diameter and angular speed with three different diameters of rotary cup. It is clear that the value of calculation from Eq. (8) was in accord with
Fig. 7. Relationship between mass fraction and angular speed.
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J. Liu et al. / Applied Thermal Engineering 73 (2014) 886e891
Fig. 8. Relationship between diameter and angular speed with different cup diameters.
experiments were higher than that of calculation, especially at 2r ¼ 95 mm. Theoretically, there were a small number of thick molten slag ligaments around the cup chip at low angular speed. For low angular speed, there were thicker molten slag ligaments around the lip of small diameter rotary cup. Some ligaments reached the bottom of slag particles collector, but not break up into spherical droplets. Hence, to obtain uniform spherical slag particles, the rotary cup angular speed should be increased for small diameter rotary cup. Fig. 9 shows relationship between mass fraction of slag particles and rotary cup diameter. It can be seen that more and more slag particles were far away from the center of rotary cup with an increase in rotary cup diameter. For a given angular speed, the velocity of molten slag droplets increased as an increase in rotary cup diameter. As a result, there were small diameter slag particles and the horizontal flying distance was long when they reached the bottom of slag particles collector. 3.4. Effects of temperature of molten slag poured into rotary cup The molten blast furnace slag is discharged at high temperature, from 1450 to 1650 C and there will be temperature drop when the
Fig. 9. Relationship between mass fraction and rotary cup diameters.
Fig. 10. Relationship between diameter and temperature.
molten slag reaches the inner side surface of rotary cup. The relationship between slag particles diameter and molten slag temperature with different angular speeds is illustrated in Fig. 10. As an increase in molten slag temperature, there was almost no change in slag particles diameter. As shown in Fig. 2, the viscosity of molten slag increased with decrease in molten slag temperature when the temperature was less than 1400 C. As a further increase in viscosity, it caused molten slag to reach a state of such high viscosity that it acted effectively like a solid. There was almost no change in viscosity and surface tension when the molten slag temperature exceeded 1400 C. Hence, the number of ligaments had no change with an increase in molten slag temperature. For a given angular speed and rotary cup diameter, the slag particles diameter almost kept constant. Fig. 11 shows relationship between mass fraction of slag particles and temperature of molten slag poured into rotary cup. It can be seen that the majority of slag particles fell into the same range, although the molten slag was different. As mentioned above, the flying distance was controlled by velocity of slag particles after releasing from ligaments. For a given angular speed and rotary cup diameter, the diameter of slag particles obtained at different temperatures of molten slag kept constant. So the trend for mass
Fig. 11. Relationship between mass fraction and temperature.
J. Liu et al. / Applied Thermal Engineering 73 (2014) 886e891
fraction of slag particles was consistent with the trend for slag particles diameter as an increase in temperature of molten slag. 4. Conclusions Ligament formation for molten blast furnace slag granulation can produce more uniform drops which can enhance the efficiency of waste heat recovery for high temperature slag particles. The transition equations from direct drop formation to ligament formation and ligament formation to sheet formation, obtained from glycerol/water mixture, could be used for identifying the type of disintegration for molten slag granulation. And the empirical equation obtained from glycerol/water mixture could be used to predict the diameter of slag particles obtained by ligament formation for molten slag granulation. The diameter of slag particles decreased when the angular speed and cup diameter increased. The majority of slag particles were far away from the center of rotary cup with an increase in velocity of slag particles after releasing from molten slag ligaments. The viscosity of molten slag has on change when the temperature of molten slag poured into rotary cup exceeds 1400 C. With an increase in molten slag temperature, there was no change in diameter and mass fraction of slag particles. All the conclusions could provide guidance for the design of commercial unit for molten blast furnace slag granulation. Acknowledgements This research was supposed by The National Natural Science Foundation of China (51274066, 51304048), China Postdoctoral Science Foundation Funded Project (2013M541240), The Fundamental Research Funds for the Central Universities (N130402019), The National Key Technologies R&D Program of China (2013BAA03B03). Nomenclature d dL Q Q1 Q1þ Q2 Q2þ
diameter of molten blast furnace slag droplets diameter of molten slag ligament tip volume flow rate of molten slag critical transition flow rate for transition from direct drop formation to ligament formation critical dimensionless flow rate for transition from direct drop formation to ligament formation critical transition flow rate for transition from ligament formation to sheet formation critical dimensionless flow rate for transition from ligament formation to sheet formation
r St T We
rl rs u s m
891
radius of rotary cup Stokes number, St ¼ m2/rlrs temperature of molten slag Weber number, We ¼ rlr2u3/s density of molten blast furnace slag at 1450 C density of molten blast furnace slag particles angular speed of rotary cup surface tension of molten slag dynamic viscosity of molten slag
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