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Cold experiments on ligament formation for blast furnace slag granulation
Applied Thermal Engineering 40 (2012) 351e357
Contents lists available at SciVerse ScienceDirect
Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Cold experiments on ligament formation for blast furnace slag granulation Junxiang Liu, Qingbo Yu*, Peng Li, Wenya Du School of Materials and Metallurgy, Northeastern University, Shenyang, Liaoning, 110819, PR China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 26 September 2011 Accepted 30 January 2012 Available online 8 February 2012
Rotary cup atomization for molten slag granulation is an attractive alternative to water quenching. However, the mechanism of disintegration of molten slag must be assessed. In the present study, a glycerol/water mixture was substituted for molten slag, and the mechanism of ligament formation in a rotary cup was investigated using photos taken by a high-speed camera. The effects of the angular speed and inner depth of the rotary cup on ligament disintegration was investigated. The results showed that one state of disintegration may transform into another state as the angular speed of the rotary cup increases at a given liquid flow rate. During ligament formation, the number of ligaments increased with an increase in the angular speed of the rotary cup, and a decrease in the diameter of ligament and liquid drop was observed. Moreover, the initial point of disintegration of the ligament moved to the lip of the rotary cup as the angular speed increased. An equation describing the relationship between the diameter of the liquid drop and various factors was used to predict the diameter of the liquid drop. A rotary cup with an inner depth of 30 mm was the best choice for granulation. The results of the present study will be useful for designing devices used in molten slag granulation. Ó 2012 Elsevier Ltd. All rights reserved.
Keywords: Molten slag Waste heat recovery Granulation Rotary cup Ligament formation Angular speed
1. Introduction Currently, blast furnace slag, which is emitted at temperatures ranging from 1450 to 1650 C, is treated by water quenching, and the heat of the slag is not recovered, despite the large heat content of molten slag. Moreover, large amounts of energy are consumed during water quenching, and harmful waste is discharged into the environment. Dry granulation for molten slag has recently received a considerable amount of attention due to environmental and energy considerations. In dry granulation, molten slag granulates into particles, and the waste energy of slag can be recovered to produce steam or heated air in moving or fluidized beds. Thus, the waste heat recovery rate of the system is determined by the diameter of slag particles. Pickering et al. [1], Featherstone et al. [2], Purwanto et al. [3] and Mizuochi et al. [4] used a rotary cup as an atomizer for molten slag granulation, and Yoshinaga et al. [5], Xie et al. [6] and Purwanto et al. [7] used a rotary disk as an atomizer. Mizuochi et al. conducted cold experiments on rotary vaned-disks and wheels for slag granulation to determine the optimal atomizer
* Corresponding author. School of Materials and Metallurgy, PO Box 345, Northeastern University, No. 11, Lane 3, Wenhua Road, Heping District, Shenyang, Liaoning, PR China. Tel./fax: þ86 24 83672216. E-mail address: [email protected] (Q. Yu). 1359-4311/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2012.01.063
[8]. However, the mechanism of disintegration of molten slag must be further investigated. Rotary cups and disks have been widely used for gaseliquid contact processes in chemical, agricultural and food-related industries [9e11]. Hinze and Milborn identified three different types of disintegration, including direct drop formation, ligament formation and sheet formation, which may occur around and beyond the lip of the rotary cup, the central axis of which is horizontal [12]. For a given liquid, rotary cup and angular speed, the transition from one state to another likely occurs due to an increase in the liquid flow rate. Various factors affecting the dimensions of the liquid sheet from the rotary cup have been investigated, including the cup dimensions, speed, liquid flow rate and viscosity. However, ligament formation was chosen as the most appropriate process for the present study [13e15]. Ligament formation can offer sprays with narrower ranges of drop sizes than those produced by sheet formation and can provide higher liquid flow rates than those obtained via direct drop formation. In the present study, for a given liquid, liquid flow rate and rotary cup size, the transition from one state to another was assumed to occur due to an increase in the angular speed. The mechanism of disintegration of ligament formation was investigated by obtaining photos with a high-speed camera. The effects of the angular speed and inner depth of the rotary cup on the disintegration of ligaments were determined.
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Table 1 The chemical composition of blast furnace slag. Chemical composition
CaO
SiO2
Al2O3
MgO
Mass fraction (%)
30e56
28e38
8e24
1e18
2. Experimental methods Blast furnace slags are generally rich in silica (SiO2), alumina (Al2O3), lime (CaO) and magnesium (MgO). The typical chemical composition and generation rate of various slags for major metal manufacturing processes are provided in Table 1. As shown in Fig. 1, only minor changes in the viscosity of molten slag are observed at temperatures greater than 1420 C. The flow rate of high temperature molten slag is difficult to control, and granulation only occurs for a few minutes under experimental conditions. Molten blast furnace slag is a non-Newtonian fluid, and the rheological characteristics of glycerol/water mixture are comparable to those of molten blast furnace slag. In addition, the law of disintegration of glycerol/water mixture in a rotary cup is comparable to that of molten blast furnace slag. Thus, cold experiments on glycerol/water mixture are valuable, and the results can be used in the granulation of molten blast furnace slag. As shown in Fig. 2, the experimental apparatus consisted of four parts, including a liquid supplier, high-speed camera, rotary device and collector. Instead of molten slag, a glycerol/water mixture was supplied by the liquid supplier, and the flow rate of the glycerol/ water mixture was controlled by a valve installed on the tube. The height of liquid in supplier kept constant, 200 mm high. The collector, 1.5 m diameter, was made of stainless steel plates by welding. It was used to collect glycerol/water mixture and the mixture was recycled after filtration. The rotary cup was connected to an electric motor by flange, and the angular speed of the electric motor was controlled by a speed controller. The photographic study was performed using a high-speed camera (MotionPro Y3) connected to a computer. The acquisition rate of images is 1000 Hz. In the experimental procedure, a mixture of glycerol and water was poured into a rotary cup through a tube from the liquid supplier by an electric motor. Due to the action of centrifugal force, the glycerol/water mixture was granulated into drops. The procedure was captured in photos by a high-speed camera, and the images were stored on a computer.
Fig. 1. Viscosity of blast furnace slag at different temperatures.
Fig. 2. Schematic diagram of the experimental apparatus.
In the experiment, the flow rate of the glycerol/water mixture from the liquid supplier was maintained at 20.2 ml/s, and the mass fraction in glycerol/water mixtures is 10:1.2. The four types of rotary cups with the same diameter and angle and different inner depths (h) were used, as shown in Fig. 3. 3. Results and discussion 3.1. Three types of disintegration When the angular speed of the rotary cup is low, a liquid torus is formed around the lip of the cup and is deformed by disturbances. Under the action of centrifugal force, drops form at the bulges of the torus and are flung from the lip of the rotary cup, as shown in Fig. 4(a). As the angular speed increases, the bulges of the torus become thin, and a ligament forms. Thus, direct drop formation transforms into ligament formation, as shown in Fig. 4(b). The
Fig. 3. Schematic diagram of the rotary cups.
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number of ligaments increases with an increase in the angular speed of the cup until a maximum value is attained, after which bulges begin to merge, producing a thin and wide torus around the lip of the rotary cup. This phenomenon is called sheet formation, as shown in Fig. 4(c). 3.2. Disintegration by ligament formation The glycerol/water mixture, which was supplied to the center of the rotary cup, accumulated along the brim of the rotary cup as a thick liquid torus, as shown in Fig. 5, and disturbances were observed in the torus due to the formation of ligaments. As shown in Fig. 5(a), a bulge formed at the torus and grew into a ligament (Fig. 5(b)), and the shape of the ligament was an involute due to centrifugal force (Fig. 5(c)). As shown in Fig. 5(d), the long ligament became unstable and broke down into drops. Under the action of centrifugal force, the ligament may become very thin. Namely, the diameter of the ligament may become so small that interfacial stress (i.e., surface tension) becomes important. Due to the effect of surface tension, the ligaments tend to form spherical drops. As shown in Fig. 6(a,b), dilational waves may develop along the ligaments due to disturbances. Driven by surface tension, dilational waves may grow in amplitude or attenuate, depending on the stability of the system [16]. In an unstable state, waves grow in amplitude, and the wavelength becomes longer and longer, as shown in Fig. 6(cee). The ligaments are eventually granulated into an array of small spherical droplets, as shown in Fig. 6(f).
Fig. 5. Growth of the new ligament.
Fig. 4. (a) Direct drop formation from a cup with a diameter, depth and speed of 120 mm, 50 mm and 8 rad/s, respectively. (b) Ligament formation from a cup with a diameter, depth and speed of 120 mm, 50 mm and 30 rad/s, respectively. (c) Sheet formation from a cup with a diameter, depth and speed of 120 mm, 50 mm and 72 rad/s, respectively.
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In Fig. 8, suppose that liquid present at point A(a, b) at t ¼ 0 reaches point C(x, y) after t seconds. If the liquid moves from point A in the tangential direction of the cup at the same velocity as the tangential velocity, the distance (l) between point O and point C can be expressed by Eq. (1).
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi l ¼ r$ 1 þ u2 t 2
(1)
where r (m) is the radius of the rotary cup, and u (rad/s) is the angular velocity of the rotary cup. The u0 of liquid at point C can be given by Eq. (2).
. 1 þ u2 t 2
u0 ¼ u
(2)
The centrifugal force at point C can be expressed by Eq. (3).
i2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih . Fl ¼ mlu20 ¼ mr 1 þ u2 t 2 u 1 þ u2 t 2 . 3=2 1 þ u2 t 2 ¼ mr u2
(3)
According to the force balance, the surface tension (s, N/m) opposite to Fl can be expressed by Eq. (4).
Fd ¼ spD
(4)
where D (m) is the diameter of the end of the liquid string. The mass of the liquid drop (m) can be expressed by Eq. (5).
m ¼ 1=6rpd3
(5)
Combining Eqs. (3)e(5) yields
i1=3 1=2 h 1 þ u2 t *2 d ¼ 6sD=ðrr uÞ2
Fig. 6. Disintegration of the ligament.
Theoretically, due to friction between the liquid and the inner wall of the rotary cup, the drops obtain the same rotational speed as the rotary cup [4]. The liquid drops persist at their initial tangential velocity when they leave the brim of the rotary cup, and the shape of the ligament is exactly an involute. In fact, due to slippage between the liquid and inner wall, the rotational speed is lower than that of the rotary cup, and the trajectory of the liquid drop parallels the tangent line of the rotary cup, as shown in Fig. 7.
(6)
where d (m) is the diameter of the liquid drop, and r is the density of the liquid, which was assumed to be 1170 kg/m3. The surface tension (s) was assumed to be 48.75 103 N/m. The break up time (t*, s), which is related to the length of the ligaments (l*, m), can be calculated by Eq. (7) [17].
t * ¼ 1=u
qffiffiffiffiffiffiffiffiffiffiffi 2l* =r
(7)
In the present experiment, the diameter (D) of the end of the ligament was held constant at 0.69 mm. Thus, the diameter of the liquid drop can be expressed by Eq. (8).
Fig. 7. Trajectory of liquid drops.
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Fig. 10. The relationship between the diameter of the head of the ligament and the rotational speed of the rotary cup. Fig. 8. Schematic diagram of the disintegration of ligaments.
. i1=3 . 1=2 h 1 þ 2l* r d ¼ 4:14s rr u2
(8)
3.3. Effects of the angular speed of the rotary cup Fig. 9 shows the relationship between the number of ligaments and the angular speed of the rotary cup. The number of ligaments was proportional to the angular speed, especially when the angular speed was greater than 40 rad/s. The liquid torus became unstable releasing from the edge of rotary cup, and changed into several bulges due to the growth of disturbance. The number of ligaments was equal to that of bulges which were the origin of ligaments. Thus the number of ligaments was decided by the growth of disturbance. When the angular speed was high, stronger disturbances in the torus were observed, which resulted in a greater amount of bulges. Hence the number of ligaments increased with an increase in the angular speed of the rotary cup. Moreover, the diameter of the head of the ligament became small as the angular speed increased at a given flow rate of the glycerol/water mixture, as shown in Fig. 10.
Fig. 9. The relationship between the number of ligaments and the rotational speed of the rotary cup.
When the angular speed of the rotary cup was greater than 60 rad/ s, the diameter of the head of the ligament had little change. As mentioned above, the number of ligaments was over 80 when the angular speed was greater than 60 rad/s. For a given flow rate and a 120 mm diameter cup, there was about 80 ligaments around the edge of rotary cup and the diameter of the head of the ligament was very small, which was approximately equal to 0.833 mm. There was little change in diameter of the head of the ligament as the angular speed of the rotary cup was further increased. When the number of ligaments increased until a maximum value is attained, ligament formation transformed into sheet formation. In the process of disintegration by ligament formation, the distance between the initial point of ligament disintegration and the lip of the rotary cup is constant at a given angular speed. The initial points of disintegration can form a concentric circle in the rotary cup. The distance between the initial point of disintegration and the lip of the rotary cup was measured using photos taken with a high-speed camera. As shown in Fig. 11, the distance decreased with an increase in the angular speed of the rotary cup. In the experiment, the tail end of the ligament was 0.69 mm in diameter, and the diameter of the ligament head became smaller as the angular speed of the rotary cup increased. As a result, the ligament
Fig. 11. The relationship between the point of disintegration and the rotational speed of the rotary cup.
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Fig. 12. The relationship between the diameter of the liquid drop and the rotational speed of the rotary cup.
became so thin that disturbances occurred along the ligament at a short distance from the lip of the rotary cup. Fig. 12 shows the relationship between the diameter of the liquid drop and the angular speed of the rotary cup. The diameter of the liquid drop was smaller when the angular speed of the rotary cup was high. At a high angular speed, the wavelength became short, and the segment of ligament corresponding to the origin of the liquid drops became small. Eq. (8) fits quite well the trend shown by the experimental results and it can be used to predict the diameter of the liquid drop. At a given angular speed, a significant amount of liquid drops with uniform diameters were obtained by ligament formation, which is beneficial to the recovery of heat from high temperature slag particles. Fig. 13 shows the relationship between the velocity of liquid drops and the rotational speed of the rotary cup. The velocity of the liquid increased linearly with an increase in the rotational speed of the rotary cup and the slope of the fitted curve was less than 1.0. After releasing from the edge of rotating cup, the ligament persisted at their initial tangential velocity and the shape of the ligament is exactly an involute. The long ligament broke down into uniform
Fig. 14. The rotational speed of the rotary cup during ligament to sheet transition as a function of the depth of the rotary cup.
drops after t* seconds. At the point of disintegration, the angular velocity u0 is smaller than that of the rotary cup and it can be calculated by Eq. (2). The velocity of liquid drop at the point of disintegration can be expressed by Eq. (9).
vdrop ¼ ur=
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ u2 t *2
(9)
Hence, the velocity of the liquid drop was less than the rotational speed of the rotary cup. The relationship between the velocity of liquid drops vdrop and the rotational speed of the rotary cup vcup can be described as follows:
ndrop ¼ 0:29164 þ 0:72779 ncup
(10)
Eq. (10) can be used to predict the velocity of liquid drops flung from the rotary cup during ligament formation. 3.4. Effects of the inner depth of the rotary cup Figs. 9e12 show the effects of the angular speed of the rotary cup on the disintegration of ligaments in the four different types of rotary cups. The results indicated that the depth of the rotary cup did not affect the disintegration of ligaments. However, when the inner depth of the rotary cup was equal to 90 mm, a vestigial glycerol/water mixture was observed in the rotating cup. The space within the rotary cup was not fully utilized; thus, the optimal rotary cup is relatively shallow. During the transition from ligament formation to sheet formation, the rotary cup with an inner depth of 30 mm presented the highest angular speed, as shown in Fig. 14. Using a rotary cup with an inner depth of 30 mm, relatively high liquid drop velocities can be obtained, which is beneficial to the cooling of liquid drops. 4. Conclusions The results of the present study can be used to guide the granulation of high temperature blast furnace slag.
Fig. 13. The relationship between the velocity of the liquid drop and the rotational speed of the rotary cup.
(1) For a given liquid flow rate and rotary cup, direct drop formation may transform into ligament formation as the angular speed of the rotary cup increases. At a high angular speed, ligaments merge, and drops are produced by sheet formation.
J. Liu et al. / Applied Thermal Engineering 40 (2012) 351e357
(2) Ligament formation, which is the most appropriate state of disintegration for molten slag granulation, can produce more uniform drops than the other two processes, which is beneficial to the heat recovery of high temperature slag drop (Eq. (8));
h . i1=3 . 1=2 d ¼ 4:14s rr u2 1 þ 2l* r can be used to predict the diameter of the liquid drop, which was used to calculate the cooling time and to identify the optimal dimensions of the granulation device. (3) A rotary cup with an inner depth of 30 mm is optimal for granulation. The space of this rotary cup can be fully utilized, and liquid drops with a high velocity can be produced, which is beneficial to the cooling of liquid drops. Acknowledgements This research was supported by Fundamental Research Funds from the Central Universities (N100602013), National High-tech R&D Program (2006AA05Z209), National Natural Science FundJoint Fund of Iron and Steel Research (50574021), and Key Technologies R&D program (2006BAE03A11). Nomenclature d diameter of liquid drop D diameter of the end of the liquid string surface tension force Fd centrifugal force Fl l the distance between point O and point C the length of ligament l* m weight of liquid drop r radius of rotary cup t time breakup time t* velocity of liquid drops vdrop rotational speed of the rotary cup vcup
r s u u0
357
density of liquid surface tension of liquid angular speed of rotary cup angular speed of liquid at point C
References [1] 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. [2] W.B. Featherstone, K.A. Holliday, Slag treatment improvement by dry granulation, Iron Steel Eng. 75 (1998) 42e46. [3] H. Purwanto, T. Mizuochi, H. Tobo, M. Takagi, T. Akiyama, Characteristics of glass beads from molten slag produced by rotary cup atomizer, Mater. Trans. 45 (2004) 3286e3290. [4] T. Mizuochi, T. Akiyama, T. Shimada, E. Kasai, J. Yagi, Feasibility of rotary cup atomizer for slag granulation, ISIJ Int. 41 (2001) 1423e1428. [5] M. Yoshinaga, K. Fujii, T. Shigematsu, T. Nakata, Dry granulation and solidification of molten blast furnace slag, Trans. ISIJ 22 (1982) 823e829. [6] D. Xie, B. Washingto, T. Norgate, S. Jahanshahi, Dry granulation of slags e turning waste into valuable products, CAMP-ISIJ 18 (2005) 1088e1091. [7] H. Purwanto, T. Mizuochi, T. .Akiyama, Prediction of granulated slag properties produced from spinning disk atomizer by mathematically model, Mater. Trans. 46 (2005) 1324e1330. [8] T. Mizuochi, T. Akiyama, Cold experiments of rotary vaned-disks and wheels for slag atomization, ISIJ Int. 43 (2003) 1469e1471. [9] C. Dogan, S. Saritas, Metal powder production by centrifugal atomization, Int. J. Powder Metal. 30 (1994) 419e427. [10] R. Angers, R. Tremblay, D. Dubé, Formation of irregular particles during centrifugal atomization of AZ91 alloy, Mater. Lett. 33 (1997) 13e18. [11] 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 Metal. 47 (2004) 168e172. [12] J.O. Hinze, H. Milborn, Atomization of liquids by means of a rotating cup, J. Appl. Mech. 17 (1950) 145e153. [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. Kawase, A. De, Ligament-type disintegration of non-Newtonian fluid in spinning disk atomization, J. Non-Newton Fluid 19 (1982) 367e371. [16] 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. [17] C. Weber, Disintegration of liquid jets, Angew. Math. Mech. 11 (1931) 136.
Contents lists available at SciVerse ScienceDirect
Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Cold experiments on ligament formation for blast furnace slag granulation Junxiang Liu, Qingbo Yu*, Peng Li, Wenya Du School of Materials and Metallurgy, Northeastern University, Shenyang, Liaoning, 110819, PR China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 26 September 2011 Accepted 30 January 2012 Available online 8 February 2012
Rotary cup atomization for molten slag granulation is an attractive alternative to water quenching. However, the mechanism of disintegration of molten slag must be assessed. In the present study, a glycerol/water mixture was substituted for molten slag, and the mechanism of ligament formation in a rotary cup was investigated using photos taken by a high-speed camera. The effects of the angular speed and inner depth of the rotary cup on ligament disintegration was investigated. The results showed that one state of disintegration may transform into another state as the angular speed of the rotary cup increases at a given liquid flow rate. During ligament formation, the number of ligaments increased with an increase in the angular speed of the rotary cup, and a decrease in the diameter of ligament and liquid drop was observed. Moreover, the initial point of disintegration of the ligament moved to the lip of the rotary cup as the angular speed increased. An equation describing the relationship between the diameter of the liquid drop and various factors was used to predict the diameter of the liquid drop. A rotary cup with an inner depth of 30 mm was the best choice for granulation. The results of the present study will be useful for designing devices used in molten slag granulation. Ó 2012 Elsevier Ltd. All rights reserved.
Keywords: Molten slag Waste heat recovery Granulation Rotary cup Ligament formation Angular speed
1. Introduction Currently, blast furnace slag, which is emitted at temperatures ranging from 1450 to 1650 C, is treated by water quenching, and the heat of the slag is not recovered, despite the large heat content of molten slag. Moreover, large amounts of energy are consumed during water quenching, and harmful waste is discharged into the environment. Dry granulation for molten slag has recently received a considerable amount of attention due to environmental and energy considerations. In dry granulation, molten slag granulates into particles, and the waste energy of slag can be recovered to produce steam or heated air in moving or fluidized beds. Thus, the waste heat recovery rate of the system is determined by the diameter of slag particles. Pickering et al. [1], Featherstone et al. [2], Purwanto et al. [3] and Mizuochi et al. [4] used a rotary cup as an atomizer for molten slag granulation, and Yoshinaga et al. [5], Xie et al. [6] and Purwanto et al. [7] used a rotary disk as an atomizer. Mizuochi et al. conducted cold experiments on rotary vaned-disks and wheels for slag granulation to determine the optimal atomizer
* Corresponding author. School of Materials and Metallurgy, PO Box 345, Northeastern University, No. 11, Lane 3, Wenhua Road, Heping District, Shenyang, Liaoning, PR China. Tel./fax: þ86 24 83672216. E-mail address: [email protected] (Q. Yu). 1359-4311/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2012.01.063
[8]. However, the mechanism of disintegration of molten slag must be further investigated. Rotary cups and disks have been widely used for gaseliquid contact processes in chemical, agricultural and food-related industries [9e11]. Hinze and Milborn identified three different types of disintegration, including direct drop formation, ligament formation and sheet formation, which may occur around and beyond the lip of the rotary cup, the central axis of which is horizontal [12]. For a given liquid, rotary cup and angular speed, the transition from one state to another likely occurs due to an increase in the liquid flow rate. Various factors affecting the dimensions of the liquid sheet from the rotary cup have been investigated, including the cup dimensions, speed, liquid flow rate and viscosity. However, ligament formation was chosen as the most appropriate process for the present study [13e15]. Ligament formation can offer sprays with narrower ranges of drop sizes than those produced by sheet formation and can provide higher liquid flow rates than those obtained via direct drop formation. In the present study, for a given liquid, liquid flow rate and rotary cup size, the transition from one state to another was assumed to occur due to an increase in the angular speed. The mechanism of disintegration of ligament formation was investigated by obtaining photos with a high-speed camera. The effects of the angular speed and inner depth of the rotary cup on the disintegration of ligaments were determined.
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Table 1 The chemical composition of blast furnace slag. Chemical composition
CaO
SiO2
Al2O3
MgO
Mass fraction (%)
30e56
28e38
8e24
1e18
2. Experimental methods Blast furnace slags are generally rich in silica (SiO2), alumina (Al2O3), lime (CaO) and magnesium (MgO). The typical chemical composition and generation rate of various slags for major metal manufacturing processes are provided in Table 1. As shown in Fig. 1, only minor changes in the viscosity of molten slag are observed at temperatures greater than 1420 C. The flow rate of high temperature molten slag is difficult to control, and granulation only occurs for a few minutes under experimental conditions. Molten blast furnace slag is a non-Newtonian fluid, and the rheological characteristics of glycerol/water mixture are comparable to those of molten blast furnace slag. In addition, the law of disintegration of glycerol/water mixture in a rotary cup is comparable to that of molten blast furnace slag. Thus, cold experiments on glycerol/water mixture are valuable, and the results can be used in the granulation of molten blast furnace slag. As shown in Fig. 2, the experimental apparatus consisted of four parts, including a liquid supplier, high-speed camera, rotary device and collector. Instead of molten slag, a glycerol/water mixture was supplied by the liquid supplier, and the flow rate of the glycerol/ water mixture was controlled by a valve installed on the tube. The height of liquid in supplier kept constant, 200 mm high. The collector, 1.5 m diameter, was made of stainless steel plates by welding. It was used to collect glycerol/water mixture and the mixture was recycled after filtration. The rotary cup was connected to an electric motor by flange, and the angular speed of the electric motor was controlled by a speed controller. The photographic study was performed using a high-speed camera (MotionPro Y3) connected to a computer. The acquisition rate of images is 1000 Hz. In the experimental procedure, a mixture of glycerol and water was poured into a rotary cup through a tube from the liquid supplier by an electric motor. Due to the action of centrifugal force, the glycerol/water mixture was granulated into drops. The procedure was captured in photos by a high-speed camera, and the images were stored on a computer.
Fig. 1. Viscosity of blast furnace slag at different temperatures.
Fig. 2. Schematic diagram of the experimental apparatus.
In the experiment, the flow rate of the glycerol/water mixture from the liquid supplier was maintained at 20.2 ml/s, and the mass fraction in glycerol/water mixtures is 10:1.2. The four types of rotary cups with the same diameter and angle and different inner depths (h) were used, as shown in Fig. 3. 3. Results and discussion 3.1. Three types of disintegration When the angular speed of the rotary cup is low, a liquid torus is formed around the lip of the cup and is deformed by disturbances. Under the action of centrifugal force, drops form at the bulges of the torus and are flung from the lip of the rotary cup, as shown in Fig. 4(a). As the angular speed increases, the bulges of the torus become thin, and a ligament forms. Thus, direct drop formation transforms into ligament formation, as shown in Fig. 4(b). The
Fig. 3. Schematic diagram of the rotary cups.
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number of ligaments increases with an increase in the angular speed of the cup until a maximum value is attained, after which bulges begin to merge, producing a thin and wide torus around the lip of the rotary cup. This phenomenon is called sheet formation, as shown in Fig. 4(c). 3.2. Disintegration by ligament formation The glycerol/water mixture, which was supplied to the center of the rotary cup, accumulated along the brim of the rotary cup as a thick liquid torus, as shown in Fig. 5, and disturbances were observed in the torus due to the formation of ligaments. As shown in Fig. 5(a), a bulge formed at the torus and grew into a ligament (Fig. 5(b)), and the shape of the ligament was an involute due to centrifugal force (Fig. 5(c)). As shown in Fig. 5(d), the long ligament became unstable and broke down into drops. Under the action of centrifugal force, the ligament may become very thin. Namely, the diameter of the ligament may become so small that interfacial stress (i.e., surface tension) becomes important. Due to the effect of surface tension, the ligaments tend to form spherical drops. As shown in Fig. 6(a,b), dilational waves may develop along the ligaments due to disturbances. Driven by surface tension, dilational waves may grow in amplitude or attenuate, depending on the stability of the system [16]. In an unstable state, waves grow in amplitude, and the wavelength becomes longer and longer, as shown in Fig. 6(cee). The ligaments are eventually granulated into an array of small spherical droplets, as shown in Fig. 6(f).
Fig. 5. Growth of the new ligament.
Fig. 4. (a) Direct drop formation from a cup with a diameter, depth and speed of 120 mm, 50 mm and 8 rad/s, respectively. (b) Ligament formation from a cup with a diameter, depth and speed of 120 mm, 50 mm and 30 rad/s, respectively. (c) Sheet formation from a cup with a diameter, depth and speed of 120 mm, 50 mm and 72 rad/s, respectively.
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In Fig. 8, suppose that liquid present at point A(a, b) at t ¼ 0 reaches point C(x, y) after t seconds. If the liquid moves from point A in the tangential direction of the cup at the same velocity as the tangential velocity, the distance (l) between point O and point C can be expressed by Eq. (1).
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi l ¼ r$ 1 þ u2 t 2
(1)
where r (m) is the radius of the rotary cup, and u (rad/s) is the angular velocity of the rotary cup. The u0 of liquid at point C can be given by Eq. (2).
. 1 þ u2 t 2
u0 ¼ u
(2)
The centrifugal force at point C can be expressed by Eq. (3).
i2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih . Fl ¼ mlu20 ¼ mr 1 þ u2 t 2 u 1 þ u2 t 2 . 3=2 1 þ u2 t 2 ¼ mr u2
(3)
According to the force balance, the surface tension (s, N/m) opposite to Fl can be expressed by Eq. (4).
Fd ¼ spD
(4)
where D (m) is the diameter of the end of the liquid string. The mass of the liquid drop (m) can be expressed by Eq. (5).
m ¼ 1=6rpd3
(5)
Combining Eqs. (3)e(5) yields
i1=3 1=2 h 1 þ u2 t *2 d ¼ 6sD=ðrr uÞ2
Fig. 6. Disintegration of the ligament.
Theoretically, due to friction between the liquid and the inner wall of the rotary cup, the drops obtain the same rotational speed as the rotary cup [4]. The liquid drops persist at their initial tangential velocity when they leave the brim of the rotary cup, and the shape of the ligament is exactly an involute. In fact, due to slippage between the liquid and inner wall, the rotational speed is lower than that of the rotary cup, and the trajectory of the liquid drop parallels the tangent line of the rotary cup, as shown in Fig. 7.
(6)
where d (m) is the diameter of the liquid drop, and r is the density of the liquid, which was assumed to be 1170 kg/m3. The surface tension (s) was assumed to be 48.75 103 N/m. The break up time (t*, s), which is related to the length of the ligaments (l*, m), can be calculated by Eq. (7) [17].
t * ¼ 1=u
qffiffiffiffiffiffiffiffiffiffiffi 2l* =r
(7)
In the present experiment, the diameter (D) of the end of the ligament was held constant at 0.69 mm. Thus, the diameter of the liquid drop can be expressed by Eq. (8).
Fig. 7. Trajectory of liquid drops.
J. Liu et al. / Applied Thermal Engineering 40 (2012) 351e357
355
Fig. 10. The relationship between the diameter of the head of the ligament and the rotational speed of the rotary cup. Fig. 8. Schematic diagram of the disintegration of ligaments.
. i1=3 . 1=2 h 1 þ 2l* r d ¼ 4:14s rr u2
(8)
3.3. Effects of the angular speed of the rotary cup Fig. 9 shows the relationship between the number of ligaments and the angular speed of the rotary cup. The number of ligaments was proportional to the angular speed, especially when the angular speed was greater than 40 rad/s. The liquid torus became unstable releasing from the edge of rotary cup, and changed into several bulges due to the growth of disturbance. The number of ligaments was equal to that of bulges which were the origin of ligaments. Thus the number of ligaments was decided by the growth of disturbance. When the angular speed was high, stronger disturbances in the torus were observed, which resulted in a greater amount of bulges. Hence the number of ligaments increased with an increase in the angular speed of the rotary cup. Moreover, the diameter of the head of the ligament became small as the angular speed increased at a given flow rate of the glycerol/water mixture, as shown in Fig. 10.
Fig. 9. The relationship between the number of ligaments and the rotational speed of the rotary cup.
When the angular speed of the rotary cup was greater than 60 rad/ s, the diameter of the head of the ligament had little change. As mentioned above, the number of ligaments was over 80 when the angular speed was greater than 60 rad/s. For a given flow rate and a 120 mm diameter cup, there was about 80 ligaments around the edge of rotary cup and the diameter of the head of the ligament was very small, which was approximately equal to 0.833 mm. There was little change in diameter of the head of the ligament as the angular speed of the rotary cup was further increased. When the number of ligaments increased until a maximum value is attained, ligament formation transformed into sheet formation. In the process of disintegration by ligament formation, the distance between the initial point of ligament disintegration and the lip of the rotary cup is constant at a given angular speed. The initial points of disintegration can form a concentric circle in the rotary cup. The distance between the initial point of disintegration and the lip of the rotary cup was measured using photos taken with a high-speed camera. As shown in Fig. 11, the distance decreased with an increase in the angular speed of the rotary cup. In the experiment, the tail end of the ligament was 0.69 mm in diameter, and the diameter of the ligament head became smaller as the angular speed of the rotary cup increased. As a result, the ligament
Fig. 11. The relationship between the point of disintegration and the rotational speed of the rotary cup.
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Fig. 12. The relationship between the diameter of the liquid drop and the rotational speed of the rotary cup.
became so thin that disturbances occurred along the ligament at a short distance from the lip of the rotary cup. Fig. 12 shows the relationship between the diameter of the liquid drop and the angular speed of the rotary cup. The diameter of the liquid drop was smaller when the angular speed of the rotary cup was high. At a high angular speed, the wavelength became short, and the segment of ligament corresponding to the origin of the liquid drops became small. Eq. (8) fits quite well the trend shown by the experimental results and it can be used to predict the diameter of the liquid drop. At a given angular speed, a significant amount of liquid drops with uniform diameters were obtained by ligament formation, which is beneficial to the recovery of heat from high temperature slag particles. Fig. 13 shows the relationship between the velocity of liquid drops and the rotational speed of the rotary cup. The velocity of the liquid increased linearly with an increase in the rotational speed of the rotary cup and the slope of the fitted curve was less than 1.0. After releasing from the edge of rotating cup, the ligament persisted at their initial tangential velocity and the shape of the ligament is exactly an involute. The long ligament broke down into uniform
Fig. 14. The rotational speed of the rotary cup during ligament to sheet transition as a function of the depth of the rotary cup.
drops after t* seconds. At the point of disintegration, the angular velocity u0 is smaller than that of the rotary cup and it can be calculated by Eq. (2). The velocity of liquid drop at the point of disintegration can be expressed by Eq. (9).
vdrop ¼ ur=
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ u2 t *2
(9)
Hence, the velocity of the liquid drop was less than the rotational speed of the rotary cup. The relationship between the velocity of liquid drops vdrop and the rotational speed of the rotary cup vcup can be described as follows:
ndrop ¼ 0:29164 þ 0:72779 ncup
(10)
Eq. (10) can be used to predict the velocity of liquid drops flung from the rotary cup during ligament formation. 3.4. Effects of the inner depth of the rotary cup Figs. 9e12 show the effects of the angular speed of the rotary cup on the disintegration of ligaments in the four different types of rotary cups. The results indicated that the depth of the rotary cup did not affect the disintegration of ligaments. However, when the inner depth of the rotary cup was equal to 90 mm, a vestigial glycerol/water mixture was observed in the rotating cup. The space within the rotary cup was not fully utilized; thus, the optimal rotary cup is relatively shallow. During the transition from ligament formation to sheet formation, the rotary cup with an inner depth of 30 mm presented the highest angular speed, as shown in Fig. 14. Using a rotary cup with an inner depth of 30 mm, relatively high liquid drop velocities can be obtained, which is beneficial to the cooling of liquid drops. 4. Conclusions The results of the present study can be used to guide the granulation of high temperature blast furnace slag.
Fig. 13. The relationship between the velocity of the liquid drop and the rotational speed of the rotary cup.
(1) For a given liquid flow rate and rotary cup, direct drop formation may transform into ligament formation as the angular speed of the rotary cup increases. At a high angular speed, ligaments merge, and drops are produced by sheet formation.
J. Liu et al. / Applied Thermal Engineering 40 (2012) 351e357
(2) Ligament formation, which is the most appropriate state of disintegration for molten slag granulation, can produce more uniform drops than the other two processes, which is beneficial to the heat recovery of high temperature slag drop (Eq. (8));
h . i1=3 . 1=2 d ¼ 4:14s rr u2 1 þ 2l* r can be used to predict the diameter of the liquid drop, which was used to calculate the cooling time and to identify the optimal dimensions of the granulation device. (3) A rotary cup with an inner depth of 30 mm is optimal for granulation. The space of this rotary cup can be fully utilized, and liquid drops with a high velocity can be produced, which is beneficial to the cooling of liquid drops. Acknowledgements This research was supported by Fundamental Research Funds from the Central Universities (N100602013), National High-tech R&D Program (2006AA05Z209), National Natural Science FundJoint Fund of Iron and Steel Research (50574021), and Key Technologies R&D program (2006BAE03A11). Nomenclature d diameter of liquid drop D diameter of the end of the liquid string surface tension force Fd centrifugal force Fl l the distance between point O and point C the length of ligament l* m weight of liquid drop r radius of rotary cup t time breakup time t* velocity of liquid drops vdrop rotational speed of the rotary cup vcup
r s u u0
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density of liquid surface tension of liquid angular speed of rotary cup angular speed of liquid at point C
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