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Centrifugal granulation performance of liquid with various viscosities for heat recovery of blast furnace slag
Applied Thermal Engineering 89 (2015) 494e504
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Research paper
Centrifugal granulation performance of liquid with various viscosities for heat recovery of blast furnace slag Jun-Jun Wu b, Hong Wang a, b, *, Xun Zhu a, b, Qiang Liao a, b, Bin Ding a a b
Key Laboratory of Low-grade Energy Utilization Technologies and Systems, Chongqing University, Chongqing 400030, China Institute of Engineering Thermophysics, Chongqing University, Chongqing 400030, China
h i g h l i g h t s Centrifugal granulation is crucial for heat recovery of blast furnace slag. The disintegration mode transition was experimentally investigated. The mechanism of disintegration mode transition was analyzed. The variation ligaments and droplets with viscosities were discussed. The analogy analysis was applied to the molten blast furnace slag.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 18 March 2015 Accepted 13 June 2015 Available online 25 June 2015
Centrifugal granulation is a crucial step in the most promising heat recovery technique for molten blast furnace slag. Facing the fact that slag viscosity changes during the granulation process, in the present work, visualization experiments were conducted for centrifugal granulation of mixture liquids by a spinning disc. Then, the effect of liquid viscosity on granulation performance was discussed. It was found that the increase in liquid viscosity resulted in granulation mode translation under the same disc rotating speed and liquid flow rate, that is, from direct droplet formation mode to ligament formation mode. The Sauter Mean Diameter of the granulated droplets was increased and the droplets size distribution was narrowed with increasing liquid viscosity. Meanwhile, the ligament number increased in direct drop formation mode while decreased in ligament formation mode as the liquid viscosity was increased. Furthermore, for a specific mixture liquid, the increase in flow rate also resulted in the translation from direct droplet formation mode to the ligament formation mode and from ligament formation mode to the film formation mode in the end. The critical flow rate for this translation was found for various liquid mixtures. Finally, dimensionless correlations were developed to predict the average diameter and critical flow rate, and the analogy analysis was applied to the molten blast furnace slag. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Centrifugal granulation Viscosity Ligament Droplet Critical flow rate Blast furnace slag
1. Introduction Blast furnace slag (BF slag) is one of the main solid by-products in steel making with the yield of 300 kg per ton of crude steel. Moreover, the slag is exhausted in high temperature of about 1500 C with huge heat content amounting to 1770 MJ per ton BF slag [1]. In 2013, China's crude steel production reached up to about 822 million tons [2], namely, the total waste heat contained in hot slag was almost equivalent to 14.8 million tons standard coal.
* Corresponding author. Institute of Engineering Thermophysics, Chongqing University, Chongqing 400030, China. Tel.: þ86 023 65102474. E-mail address: [email protected] (H. Wang). http://dx.doi.org/10.1016/j.applthermaleng.2015.06.031 1359-4311/© 2015 Elsevier Ltd. All rights reserved.
Currently, water quench technique has been widely adopted to directly cool the molten slag in most of the steel plants, giving rise to huge loss in both the water and heat. Therefore, great efforts have been made by researchers to explore an effective heat recovery technique. A heat recovery technology coupling dry granulation of the molten slag with air cooling has aroused general concern since 1984 [3]. During the following development process of this technology, several granulation techniques have been proposed and investigated by various researchers including rotary drum [3], air blast [4], centrifugal granulation [5e7]and so on. Among all the techniques, the centrifugal granulation coupling with heat recovery by air is considered as one of the most promising techniques for BF
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slag due to its simple construction, easy operation, sufficient capacity, less energy consumption and suitable granule size distribution. Therefore, intensive studies have been performed since Pickering et al. [5] firstly designed a centrifugal granulation system. During the centrifugal granulating process of molten BF slag, liquid slag firstly flows from the top injection port onto the center of a rotating atomizer and spreads radially along the atomizer surface to form a thin liquid film. The liquid film is then broken into droplets at the rim of or out of the atomizer, and these droplets are finally solidified by air cooling. The centrifugal granulation, in deed, is a complex and comprehensive process affected by multifarious parameters. These influential parameters can be sorted to three aspects: (1) Atomizer material and structure [8,9]; (2) Physical properties of liquid slag such as density, viscosity and surface tension; (3) Operational conditions including atomizer rotary speed [10e14] and liquid slag feeding rate [15e17]. However, superhigh temperature as well as blinding light of the released molten BF slag brings grave difficulties in experimental study (especially the visualization experiments) on the mechanism of BF slag granulation. Consequently, most of the researches, up to now, adopted low-temperature working media to investigate the granulation phenomena under various conditions. Mizuochi and Akiyama [18] experimentally investigated water granulation by vaned-disc and vaned-wheels, and found that vaned-atomizers were helpful to decrease the large-size droplets. Ahmed and Youssef [9] also employed water as the working medium to investigate the droplets size and velocity characteristics produced by various cup atomizers. They found that, compared with the droplets generated by flat disc, the Sauter Mean Diameter of droplets produced by atomizer with different configurations varied between 8% and 12%. Frost [19] studied the granulation using water and glycerol mixture and tackled the mechanism of ligament formation in detail. A criteria for ligament disintegration occurrence and the expression to predict the resultant droplets size were developed. Recently, Liu et al. [20,21] also carried out cold experiments using water and glycerol mixture with three kinds of cups to investigate the transition of different disintegration modes. Yi et al. [22] compounded rosin and wax with a mass ratio of 4:1 to simulate the liquid molten slag and then investigated the influence of operational conditions on granulation process of this mixture liquid. Zhu et al. [23] proposed a granulation system combining a rotating cup with air blast and investigated the granulation performance by adopting a mixture of rosin and paraffin wax. The effects of rotating speed, liquid flow rate and blast air flow rate were discussed, and the results indicated that higher rotating speed and lower liquid feeding rate gave rise to smaller particle as well as higher fibers fraction. In addition to the low-temperature working media, very few experimental works and numerical simulations were conducted for the real BF slag. Mizuochi et al. [6] investigated the feasibility of the rotary cup atomizer for slag granulation, and found that the BF slag droplets were strongly dependent on the rotating speed of atomizer. Higher rotating speed resulted in more uniform and spherical particles. Liu et al. [24] experimentally investigated the ligament formation in BF slag granulation, and found the slag wools took place inevitably during the granulation. Qin et al. [25] adopted a rotating multi-nozzle cup atomizer to granulate the molten slag and discussed the characterization of slag particles. Moreover, some numerical simulations were carried out on the centrifugal granulation. Pan et al. [26,27] adopted a CFD model to simulate free surface flow of liquid slag on a spinning disc and discussed the effects of operating parameters on the liquid spreading. Wang et al. [28] developed a theoretical analysis for free-surface flow on the disc, and it was found that the film thickness distribution of molten slag was mainly determined by liquid volume flow rate, rotary
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speed of atomizer and viscosity. Only two documents [29,30] reported the simulation on slag droplets or ligaments formation by the spinning disc. The previous works mainly focused on the effects of atomizer structure and operating conditions (rotating speed and liquid feeding rate) on the granulation performance for a certain working medium with constant physical properties. It was noticed that diverse outcomes even contradictory statements were exhibited among the references for different working media. However, a systematic study on the granulation of liquid with different physical properties has not been reported, and the centrifugal granulation mechanism also has not been well understood. Moreover, almost all of the references ignore a reality that is unavoidable in practical dry heat recovery system of BF slag, that is, the physical properties of slag, especially the viscosity, change during the granulation process due to air cooling. This requires a well understanding of the effect of liquid viscosity on granulation performance. For this purpose, in the present study, the effect of liquid physical properties on the disintegration mode translation and granulation performance was investigated by visualization experiments using various glycerol/water mixtures. The mechanism of granulation under different disintegration modes were analyzed in detail and the experimental results were compared to the granulation of blast furnace slag. 2. Experimental system and method 2.1. Experimental setup The visualization experimental setup for centrifugal granulation, as shown in Fig. 1, consisted of a granulation system, a liquid supply system and a data acquisition system. In the granulation system, a disc atomizer with 55 mm in radius was connected to a motor by a live shaft. A frequency converter was utilized to control the rotary speed of disc atomizer in a range of 0e3000 rpm. According to Qin [25], the aforementioned attempts for slag granulation revealed that the rotary speed in a range of 600e1800 rpm is suitable for particle production. Thus in this study, the rotary speed of disc was fixed at 1200 rpm for all cases. The liquid supply system consisted of a pump, a stabilivolt tank, a valve, a flowmeter, a nozzle and a collecting tray. The nozzle of 8 mm in inner diameter located centrically above the disc with a distance 20 mm from the disc surface. The size ratio of the nozzle to the disc was 15%. The working medium from the tank flowed through the nozzle to hit the disc surface and then, it was collected in the collecting tray and was pumped into the tank. The liquid volume flow rate was adjusted by the valve. The data acquisition system consisted of a high speed camera (i-Speed TR, Olympus), a light source and a computer. The high speed camera was set at the rim of the disc and the plane LED light was installed underneath the disc rim, as shown in Fig. 1b. The dynamic behavior of the granulation process was then recorded by the high speed camera with a shooting speed of 2000 fps. All the experiments were carried out under the room temperature. 2.2. Data processing For numerous gray-scale images obtained during the granulation process, a self-compiled MATLAB program was utilized to extract the diameter of produced droplets. The extraction process is shown in Fig. 2. Firstly, choose an image which was shot during the stable granulation stage, cf. Fig. 2a. Secondly, set a processing area on the image that contains droplets or ligaments, cf. Fig. 2b. Thirdly, convert the chosen area into binary images according to a threshold value, that is,
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Fig. 1. Schematic of centrifugal atomization apparatus.
k¼
1; Ia < Ig 0; Ia > Ig
(1)
where Ig is the threshold value, Ia is the gray scale of the chosen area. Finally, extract the droplets edge using Candy operator, cf.
Fig. 2c, and then calculate the diameter of droplets with reference to standard length scale. In the present study, to ensure the data reliability, over 2000 samples in statistics were chosen under each operational condition. Furthermore, by compared with the data obtained in i-Speed Suite (Olympus software), the relative measurement error was within
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Fig. 2. Droplets diameter extraction process.
3. Results and discussion 3.1. Granulating evolution and analysis
Fig. 3. Physical properties of the mixture at different glycerol volume ratios.
2.0%. Besides, the relative uncertainty in Sauter Mean Diameter is with 4.0% by calculation. 2.3. Working media In order to investigate the effect of liquid physical properties on granulation process, the mixtures of glycerol and water with various volume ratios were used as the working media. The variation of physical properties of the mixtures with the glycerol volume ratio is shown in Fig. 3. One can see that the density of the mixture increased slightly while the surface tension decreased slightly with increasing glycerol volume ratio. The viscosity of the mixture slightly increased when the glycerol volume ratio was increased from 0 to 80%. However, it dramatically increased when the glycerol volume ratio was over 80% and reached 1.2 Pa s at the glycerol volume ratio of 100%. The detailed information about the physical properties of the mixtures used in the present study is listed in Table 1. Compared with the density and surface tension of the liquid mixture, the changes in viscosity were remarkable.
The representative granulating evolutions of water and glycerol/ water mixture (Samples 1, 3 and 5) were recorded and displayed in Fig. 4, where the liquid flow rate was set at 20 L h1. For the granulation of water (Sample 1), as shown in Fig. 4a, water departed from the disc rim in form of discrete droplets after a thin film spreading on the disc surface driven by the centrifugal force. It was also observed that some droplets even formed on the disc surface. A few ligaments transitorily and randomly presented at somewhere around the disc circumference and then quickly disintegrated into droplets due to their instability. Furthermore, the morphology of the formed droplets were in short rod, cf. Fig. 4d. For the granulation of liquid mixture with viscosity of 0.085 Pa s (Sample 3), as seen in Fig. 4b, thin and dense ligaments were drawn from the disc rim instead of the appearance of discrete droplets. Meanwhile, these ligaments presented an arc-shaped around the disc due to the effect of centrifugal force. The disintegration was observed to occur at the frontend of ligaments far from the disc, where part of the ligaments broke up into a row of droplets almost simultaneously. The produced droplets were small and of good sphericity, cf. Fig. 4e. When the mixture viscosity was further increased to 0.465 Pa s (Sample 5), similar phenomena, including ligaments formation and breakup at the frontend, were found in Fig. 4c. However, compared with the former case, the ligaments became thicker, longer and more curved accompanying with increased spacing. The breakup of the ligament frontend gave rise to a mass of droplets in a shape of tadpole or dragging long liquid trails (see Fig. 4f). Based on different phenomena above, one can conclude that two kinds of granulation modes happened to the liquid mixtures under the present experimental condition: the direct droplet formation mode and the ligament formation mode. In fact, the centrifugal granulation of liquid on a disc is an exceedingly complex process, in which the liquid dynamic behavior is determined by the synthetical effects of inertial force from liquid jet to the disc, centrifugal force offered by the rotating disc, shear
Table 1 Physical properties of mixture solutions. Sample Sample Sample Sample Sample Sample Sample
1 2 3 4 5 6
Glycerol ratio (%)
Viscosity (Pa s)
Density (kg m3)
Surface tension (N m1)
Oh number (102)
0 20 80 90 95 100
0.001 0.043 0.085 0.250 0.456 1.200
998 1047 1209 1235 1248 1261
0.073 0.071 0.065 0.064 0.0635 0.063
0.05 2.12 4.09 12.04 21.85 57.43
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Fig. 4. Granulation phenomena for different working media.
stress due to liquid viscous flow on the disc surface, friction force resulted from liquid flying in the air and liquid surface tension as well as the Rayleigh-Plateau instability. The destruction of the counter-balance of these forces is responsible for the differences in the granulation mode and performance. In the present experiments, the incentive to the destruction can be attributed to the change in the physical properties of the liquid, especially the viscosity. For liquid which has smaller viscosity and higher surface tension, the inertial force and centrifugal force outperform the shear stress and surface tension to spread liquid over the disc surface, as seen in Fig. 5-1a. Along with the film moving forward to
the disc edge, perturbations from the surface instability at both the circumferential direction and radial direction give rise to the digitate bulge surface of the thin film, cf. Fig. 5-1b. Some thin fingers are then prematurely smashed on the disc owing to the instability and others are pinched at the rim of the disc due to the disturbance from the abrupt absence of the solid surface, as shown in Fig. 5-1c. Thereafter, the shattered liquid contracts to small droplets under the action of surface tension, and this is the so-called typical direct droplet formation mode. When the liquid mixture is used, the significant increase in the viscosity results in enhanced shear stress. This slows down the
Fig. 5. Schematic of disintegration modes during centrifugal granulation: (1) direct droplet formation, (2) ligament formation.
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spreading of liquid film considering the given jet velocity and rotary speed of the disc, hence resulting in thick liquid film on the disc (cf. Fig. 5-2a). Therefore, stumpy fingers are formed at the bulge surface of the film due to the increased anti-disturbance capability of the thick liquid film and lower surface tension, as shown in Fig. 5-2b. Instead of the premature pinch-off, these fingers are then drawn out from the disc rim to form ligaments with an arc-shaped due to the centrifugal effect. The flying ligaments gradually attenuate under the action of drag force and surface tension, and finally breakup at frontend owing to the Rayleigh-Plateau instability, as shown in Fig. 5-2c. The produced droplets are small and of good sphericity due to the smaller surface tension. This results in the socalled ligament formation mode. When the viscosity of mixture liquid is further increased, as a result of higher shear stress, the liquid spreading on the disc is further decelerated with thicker liquid film. Meanwhile, the bulge surface of the film exhibits corrugated with long-wavelength instead of fingerlike due to the enhanced stability. Therefore, ligaments with larger diameter and spacing are drawn out from the disc rim, and the distance required for the pinch-off as well as droplets formation is longer due to the larger initial diameter and lower surface tension. The experimental results and analysis suggest that, for a working medium whose viscosity changes with temperature or components, such as BF slag, appropriate operational conditions should be set to ensure good granulation performance.
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3.2. Effect of liquid viscosity on droplet size distribution Droplets are the major products in the centrifugal granulation process. For the purpose of efficient heat recovery of the molten BF slag by air flow, tiny droplets with a narrow diameter distribution are expected due to larger specific surface area for heat transfer. Therefore, the droplets size and their diameter distribution is one of the main concerns in the experiments. Fig. 6 shows the effect of liquid viscosity on the droplets diameter distribution during the granulation process where the liquid flow rate was 20 L h1. In the experiments, as discussed above, the translation of granulation mode happened when the liquid viscosity was increased from 0.001 Pa s to 1.2 Pa s. Working media with viscosity of 0.001 Pa s and 0.043 Pa s were centrifuged to droplets in direct droplet formation mode and the diameter of produced droplets covered a range of 0e1.0 mm, as shown in Fig. 6a. For the liquid with viscosity of 0.001 Pa s, 72% of the droplets possessed the diameter range of 0e0.2 mm. However, the maximum probability of diameter decreased to 51% and moved to the range of 0.2e0.4 mm for the liquid with viscosity of 0.043 Pa s. Meanwhile, the droplets with probability of diameter in the range of 0.8e1.0 mm increased from 1.2% for liquid with 0.001 Pa s to 8.7% for liquid with 0.043 Pa s. This is resulted from the increasing liquid film and thus the incrassate bulge which is pinched off right at the disc rim. The granulation mode is transformed from direct droplet formation mode to ligament formation mode when the liquid viscosity was increased from 0.043 Pa s to 0.085 Pa s. It was found that the maximum probability of diameter still remained in the range of
Fig. 6. Effect of liquid viscosity on droplet size: (a) diameter distribution in direct droplet formation mode, (b) diameter distribution in ligament formation mode, (c) SMD during granulation.
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Table 2 Standard deviation of droplets diameter for different liquid viscosities. Viscosity (Pa s) Standard deviation
0.001 0.381
0.043 0.311
0.085 0.122
0.251 0.113
0.456 0.233
1.2 0.173
0.2e0.4 mm, however, its value significantly increased to 67%, cf. Fig. 6b. Meanwhile, the probability of diameter in the range of 0.6e1.0 mm decreased to zero. As thus, the droplets size range was narrowed to 0e0.6 mm. This can be attributed to the ligaments formation and the disintegration of the frontend of ligaments. Although the increase in viscosity results in thicker liquid film, the fingerlike film experiences a stretching of ligament instead of break-up right at the disc rim, and then the pinch-off of the thin frontend of the ligaments gives rise to the large amount of small droplets. However, the probability variation showed a different trend when the granulation was in the ligament formation mode, as shown in Fig. 6b. The probability of diameter in the range of 0.2e0.4 mm gradually decreased to about 25% when the liquid viscosity was increased from 0.085 Pa s to 1.2 Pa s. For the highest liquid viscosity, the maximum probability of diameter shifted to fall in the range of 0.4e0.6 mm and reached 46%. The enlarged initial ligament diameter at higher liquid viscosity is responsible to the increment in droplets size. Moreover, it was noted that the droplets larger than 0.8 mm were not produced for all cases in the ligament formation mode, and thus the droplets diameter distribution was in a narrow range. Besides the droplets size distribution, the average diameter of the droplets is another key parameter to assess the granulation performance. Fig. 6c shows the variation of Sauter Mean Diameter (SMD) of the granulated droplets with liquid viscosity. It is shown that a sharp increase in the droplets SMD presented when the liquid viscosity was increased from 0.001 Pa s to 0.043 Pa s, and the increase rate reached to 3.6 mm Pa1 s1. However, the SMD plummeted from 0.565 mm to 0.34 mm when the liquid viscosity was further increased to 0.085 Pa s, which is resulted from the transformation in granulation mode. For the granulation in the ligament formation mode, the SMD almost linearly increased with a rate of 0.30 mm Pa1 s1 when the viscosity was increased to 0.456 Pa s, while the growth rate reduced to 0.18 mm Pa1 s1 for the further increment in the liquid viscosity. Furthermore, standard deviation was calculated to evaluate the concentration of various droplet diameter distributions,
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u n u 1 X S¼t ðd d32 Þ2 n 1 i¼1 i
mode. During the centrifugal granulation process, ligament plays a role as bridge between liquid film and droplets. The number and the length of ligaments directly affect the number and size of the droplets. For this reason, the ligament number and length were measured and the effect of liquid viscosity on the ligaments was investigated. Here, the ligament length was defined as the radical distance between droplet pinch-off point and the edge of disc, cf. Fig. 1b. Fig. 7a shows the effect of liquid viscosity on the average ligament number. It can be seen that, with increasing liquid viscosity, the average ligament number rapidly rose to reach a peak value and then turned to drop gradually. It is also noted that for the liquids with viscosity of 0.001 Pa s and 0.043 Pa s the ligaments were approximate in the average number. Besides, the ligament number covered a wide range of 70e100 with regard to all the calculated samples. This is because of the transitory and random presence of ligaments in the two cases in which the liquids were granulated in the direct droplet formation mode. These ligaments had a little contribution to the droplets formation. When the granulation was transformed from the direct droplet formation to the ligament formation mode, that is, the case with liquid viscosity of 0.086 Pa s, the ligament number jumped to 152 with somewhat variance. This
(2)
where di represents diameter of each droplet, d32 is the SMD for each test and n is the total number of droplets. The results are listed in Table 2. It indicated that the standard deviation was more than 0.3 in the direct droplet formation mode, while it was less than 0.24 in the ligament formation mode. This suggests that the droplets produced in the ligament formation mode were more concentrated than that in the direct droplet formation mode. Moreover, the above results imply that the operational condition which leads to centrifugal granulation in the early stage of the ligament formation mode is preferred to achieve small droplets. 3.3. Effect of liquid viscosity on ligaments formation As analyzed above, one can benefit from granulation in the ligament formation mode to obtain small and concentrated droplets, as thus, special attention should be paid to this granulation
Fig. 7. Effect of liquid viscosity on ligament formation: (a) ligament number, (b) ligament length.
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can be understood that the granulation of liquid with higher viscosity gives rise to the stably thin and dense ligaments. Thereafter, the average ligament number significantly decreased to 62 when the viscosity was increased to 0.456 Pa s. This is resulted from thickening liquid film and ligament diameter as well as enlarged wavelength of the disturbance. However, the downtrend was flatten out when the viscosity was further increased to 1.2 Pa s. This suggests that the ligament granulation is trending towards stability until the granulation mode is changed again. Fig. 7b shows the effect of liquid viscosity on the ligament length. The average break-up length of ligaments dramatically increased from 3.9 mm to 49.1 mm when the liquid viscosity was increased from 0.001 Pa s to 0.456 Pa s. This can be attributed to the increased ligament diameter at the disc rim. It should be noted that the ligament length for the case with the viscosity of 1.2 Pa s was absent since the ligaments were much longer than the high-speed camera's field of view. The above experimental results imply that, besides the expected small droplets ruptured from the frontier of ligament, a set number of ligaments will be remained during the granulation process. It should be pointed out that the remaining ligaments are unfavorable in their sequential utilization for most of the practical applications. As thus, indeed, the multiple and long ligaments are undesirable. The experimental results imply that for the BF slag the molten slag should not be cooled too fast before it reaches the atomizer, otherwise, the significant increase in its viscosity due to drop in temperature will result in a large amount of ligaments. This not only goes against efficient heat recovery but it also impedes the release of slag particles from the equipment. Therefore, auxiliary equipments that can smash the remained ligaments are expected to the existing atomizer to achieve better granulation performance. 3.4. Critical liquid flow rate for granulation mode translation of various liquids It is clear that the granulation mode will be translated from the direct droplet formation mode to the ligament formation mode with increasing liquid viscosity. Not only that, for the same liquid at the same rotating speed of disc, the granulation mode translation will also happen due to variation on liquid flow rate. Fig. 8 displays different granulation modes for the mixing liquid with the viscosity of 0.251 Pa s under liquid flow rates of 5 L h1, 20 L h1 and 60 L h1. One can see that a typical direct droplet formation mode presented at lower liquid flow rate, cf. Fig. 8a, where a fewer discrete droplets departed from the disc surface. When the liquid flow rate was increased to 20 L h1, the granulation process was translated to a typical ligament formation mode, as shown in Fig. 8b, where the dense ligaments were drew from the liquid film on the disc and then the frontier of the ligaments was disrupted into smaller droplets. However, another granulation mode is presented when
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Fig. 9. Morphology of products in film formation mode (0.251 Pa s, 1200 rpm, 60 L h1).
the liquid flow rate was further increased to 60 L h1. For this case, it was observed that a stably thicker film formed and spread on the disc without the appearance of digitate bulge surface due to over high flow rate. The film was then integrally pushed out of the disc by the centrifugal force and inertial force since the flow disturbance was not in sufficient strength to dilacerate the thicker film. As a result, an integral liquid film was kept out of the disc and then it was disintegrated at the front edge, as seen in Fig. 8c. This granulation mode can be called film (or sheet) formation mode. Moreover, compared with the granulation in direct droplet formation and ligament formation, it was found that the produced droplets in the film formation mode appeared in quite irregular shape, including spherical, short rod and silk-like, as shown in Fig. 9. Considering the purpose of granulation, one can conclude that the film formation mode must be avoided. This encouraged us to find out the critical flow rate at which the granulation process translated from the ligament formation mode to the film formation mode. The result will definitely give a guide to determine the operational conditions in the practical applications. It should be pointed out that the critical flow rate for the granulation mode translation is related to the rotary speed of atomizer and the physical properties of liquid. In the present study, the effect of liquid viscosity on the critical flow rate was focused under a fixed rotary speed of 1200 rpm, and the results are shown in Fig. 10. The critical flow rate decreased sharply with slight increase in the liquid viscosity. For example, the critical flow rate was up to 160.1 L h1 when the liquid viscosity was 0.001 Pa s, but it dropped down to 43.7 L h1 for liquid of 0.251 Pa s. However, the
Fig. 8. Granulation modes at different liquid flow rates (0.251 Pa s, 1200 rpm): (a) 5 L h1; (b) 20 L h1; (c) 60 L h1.
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3.5. Correlation and analogous analysis for melt blast furnace slag For the centrifugal granulation process, three kinds of parameters will influence the performance. One is the physical properties of working medium including density, viscosity and surface tension. The second one is the structural parameters including the atomizer size, injector size and injection height. The third one is operational conditions including rotary speed of the atomizer and flow rate of working medium. Based on this understanding, three dimensionless parameters including Reynold's number Re, Ohnesorge number Oh and Weber number We, are introduced as following,
Re ¼
Fig. 10. Critical flow rate under different liquid viscosities.
rRu m
m Oh ¼ pffiffiffiffiffiffiffiffi rsR We ¼
sharp reduction in the critical flow rate was stopped and turned to quite gentle declination once the liquid viscosity was further increased to 1.2 Pa s (33.6 L h1). Moreover, the corresponding transition phenomena for various liquids are shown in Fig. 11. It can been seen that, at the critical state from the ligament formation mode to the film formation mode, disordered and instable ligaments formed along the film frontier. Thereafter, the resulted ligaments crushed into droplets at random. It was also found that the disorder around the liquid film frontier gradually faded with increasing liquid viscosity. For the mixing liquid with viscosity of 1.2 Pa s, the film appeared much more stable and only one ligament was observed in the field of view to be drawn out from the film. This can be understood that high-viscosity liquid inherently results in stable film due to higher shear stress. Therefore, lower flow rate is required for a thin film on the disc which is prone to form linear protrusion and then ligaments. The results suggest that the design flow rate of the specific working medium for a centrifugal granulation equipment must be lower than the corresponding critical flow rate.
ru2 R3 : s
(3)
(4)
(5)
where r, m and s are the density, viscosity and surface tension of liquid medium, respectively; R is the radius of the atomizer; u is the rotary speed of the atomizer; u is the injection velocity, u ¼ Q =pr 2 , and r is the radius of injector, Q is the liquid flow rate, d32 is the SMD of granulated droplets. Considering the introduced dimensionless parameters, the dimensionless correlation of SMD of granulated droplets was obtained by fitting the experimental data:
d32 ¼ 9:9ðReÞ0:42 ðOhÞ0:61 ðWeÞ0:68 : R
(6)
The correlation is available for 300 < Re < 5000, 0.0005 < Oh < 0.57, 45,000 < We < 55,000. The divergence between the fitting results and the experimental data is exhibited in Fig. 12, where the prediction results derived from the correlation promoted by Kitamura [31] were shown as a comparison. It can be seen that the prediction results by Kitamura underestimated the SMD of granulated droplets, however, the prediction by the promoted
Fig. 11. Transition phenomenon at critical flow rate for different working media.
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available range of the promoted correlation. That is, the analysis above and the promoted correlation can be used to predict the granulation performance of BF slag. Consequently, for the BF slag the SMD of produced slag droplets is 0.75 mm at 1380 C (1200 rpm, 20 L h1) and 0.62 mm at 1500 C. In the same way, the critical flow rate is calculated as 570.8 L h1 at 1380 C and 601.7 L h1 at 1500 C when the rotary speed keeps at 1200 rpm. 4. Conclusions In the present study, the effect of liquid viscosity on centrifugal granulation was experimentally investigated using various water/ glycerol mixtures as working media. The granulation evolution was discussed and analyzed in detail. The variation of key parameters such as droplets size and distribution, ligaments number and length as well as critical flow rate of granulation mode translation with the liquid viscosity were discussed. Dimensionless correlations to predict SMD of the produced droplets and the critical flow rate for BF slag were developed. The main results were obtained as following:
Fig. 12. Divergence in experiment data and correlations.
correlation shows good agreement with the experimental data with an error of ±4%. Moreover, in order to predict the critical liquid flow rate at which the granulation translated from the ligament formation mode to the film formation mode, the dimensionless flow rate was introduced as
Qþ ¼
Qc ; uR3
(7)
where Qc is the critical liquid flow rate, R is the disc radius, u is the rotary speed of disc. Then, the correlation was also obtained by fitting the experimental data.
Q þ ¼ 2:36 105 ðWeÞ0:12 ðOhÞ1:86 :
(8)
It shows good agreement between the prediction and the experimental data with the error of ±3%. Although water and mixed liquids were adopted as working media in the present study, it is expected that the experimental results can be used for reference of the molten BF slag granulation. It is known that the blinding light of slag due to superhigh temperature brings great difficulties in conducting visualization experiments. As a consequence, the inherent law of molten BF slag centrifugal granulation has not been well understood, resulting in the lack of guidance on equipment design and operation. An alternative way to approximate the molten BF slag granulation is to utilize the results of cold-state experiments based on the similarity principles, that is, two physical processes can be treated as similar once the necessary dimensionless numbers of the processes are equal to each other, respectively. Supposing that the same atomizer is used for the molten BF slag with the same rotary speed, meanwhile, considering the viscosity variation due to air cooling, the relevant parameters of mixtures and BF slag are listed in Table 3. It is clear that the dimensionless parameters of the BF slag fall into the
Table 3 The physical property parameters of mixture and the BF slag. Parameter
Mixtures (at 20 C)
BF slag (at 1380e1500 C) [22]
r/kg m3 m/Pa s s/N m1
998e1260 0.001e1.2 0.063e0.073 0.0005e0.5743
2606e2622 0.4e1.0 0.530e0.549 0.0459e0.1124
Oh
(1) Under the given disc rotary speed and liquid flow rate, variation on the liquid viscosity resulted in the change of disintegration mode. High-viscosity gave rise to the granulation in ligament formation mode rather than in direct droplet formation mode. (2) With increasing liquid viscosity, the SMD of the granulated droplets was increased and the droplets size distribution was narrowed. Besides, droplets produced in the ligament formation mode presented more uniform compared with that in the direct droplets formation mode. (3) For the granulation in the ligament formation mode, the ligament number rose rapidly at first and then turned to decrease gradually with increasing liquid viscosity. The ligament length kept increasing with the increase in viscosity. (4) For a certain mixture liquid, high flow rate induced the film formation out of the disc, which was not expected for good granulation performance. The transition flow rate from ligament formation to film formation decreased as the liquid viscosity was increased. (5) Dimensionless correlations based on the experimental data were developed to predict the SMD and critical flow rate in the range of Oh number from 0.0005 to 0.5743, respectively. Acknowledgements The author would like to thank National Basic Research Program of China (973 program) (No. 2012CB720403), Fundamental Research Funds for the State Key Laboratory Of Mechanical Transmission, Chongqing University (No. SKLMT-ZZKT-2012 MS 17) and Chongqing Graduate Student Research Innovation Project (No. CYS14016). Nomenclature di d32 I k L n N Oh Q Qc
droplet diameter, mm Sauter Mean Diameter, mm threshold value binary value of image ligament length, mm droplets number ligament number Ohnesorge number liquid flow rate, L h1 critical flow rate, L h1
504
Qþ r R Re S We
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dimensionless liquid flow rate radium of nozzle, mm radium of rotary disc, m Reynolds number standard deviation Weber number
Greek
m r s u
dynamic viscosity, Pa s density, kg m3 surface tension, N m1 rotary speed, rad s1
Subscript a area g gray i random liquid droplet 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] Worldsteel Committee on Economic Studies, World Steel Association, Brussels, 2014. [3] Y. Nara, H. Yoshida, G. Nakatani, T. Anazi, H. Sato, in: The Technology of Slag Heat Recovery at NKK SEAISI Conference of Energy Utilization in the Iron and Steel Industry, 1984. [4] T. Koehler, L. Rodd, C. Walker, N. Voermann, Economics of slag heat recovery from ferronickel slags, in: Sustainability for Profit, Conference of Metallurgists (COM2010), 2010, pp. 3e17. [5] S. Pickering, N. Hay, T. Roylance, G. Thomas, New process for dry granulation and heat recovery from molten blast-furnace slag, Ironmak. Steelmak. 12 (1985) 14e20. [6] Toshio Mizuochi, Tomohiro Akiyama, Taihei Shimada, Eiki Kasai, JunIchiro Yagi, Feasibility of Rotary Cup Atomizer for Slag Granulation, Iron and Steel Institute of Japan, Tokyo, JAPAN, 2001. [7] B. Washington, D. Xie, T. Norgate, S. Jahanshahi, Dry Granulation of SlagseTurning Waste into Valuable Cement Binder, 1088e1091. [8] J. Xie, Y. Zhao, J. Dunkley, Effects of processing conditions on powder particle size and morphology in centrifugal atomisation of tin, Powder Metall. 47 (2004) 168e172. [9] M. Ahmed, M.S. Youssef, Influence of spinning cup and disk atomizer configurations on droplet size and velocity characteristics, Chem. Eng. Sci. 107 (2014) 149e157. [10] J. Liu, Q. Yu, X. Hu, Experimental Study on Granulation Process of Blast Furnace Slag, National Conference of Energy and Thermal Engineering, 2008.
[11] J. Liu, Q. Yu, C. Dou, X. Hu, Experimental Study on RCA of Blast Furnace Slag, National Conference of Energy and Thermal Engineering, 2008. [12] Q. Yu, J. Liu, C. Dou, X. Hu, Dry granulation experiment of blast furnace slag by RCA, J. Northeast. Univ. (Nat. Sci.) 30 (8) (2009) 1163e1165+1173. [13] Z.-Y. Yang, Y.-M. Zhou, Z.-M. Yan, C.-X. Dou, Experimental study of dry centrifugal granulation of molten furnace slag, Sci. Technol. Eng. (2009) 7257e7260. [14] Z. Yang, Y. Zhou, Z.-m. Yan, Experimental study of dry centrifugal granulation for molten blast slag, Sci. Technol. Eng. 9 (2009). [15] L.J. Qingbo Yu, Xianzhong Hu, Simulation experimental research of granulation process for iron slag, Iron Steel 44 (4) (2009) 82e85. [16] H. Zhang, H.-W. Ni, X.-W. Li, W.-Y. Zhu, J.-C. Xiong, R.-J. Cheng, et al., Experimental study on dry centrifugal granulation for blast furnace slag, Energy Metall. Indus. 31 (5) (2012) 15e19. [17] B. Du, Y.-G. Zhang, Centrifugal granulation exoerimental study of molten blast furnace slag by rotary disc, Energy Metall. Indus. 32 (4) (2013) 29e32. [18] T. Mizuochi, T. Akiyama, Cold experiments of rotary vaned-disks and wheels for slag atomization, ISIJ Int. 43 (2003) 1469e1471. [19] A. Frost, Rotary atomization in the ligament formation mode, J. Agric. Eng. Res. 26 (1981) 63e78. [20] J. Liu, Q. Yu, Q. Guo, Experimental investigation of liquid disintegration by rotary cups, Chem. Eng. Sci. 73 (2012) 44e50. [21] J. Liu, Q. Yu, P. Li, W. Du, Cold experiments on ligament formation for blast furnace slag granulation, Appl. Therm. Eng. 40 (2012) 351e357. [22] Y. Min, J. Huang, C.-j. Liu, M.-f. Jiang, X.-q. Yu, Physical simulation of molten slag granulation by rotary disk, J. Iron Steel Res. Int. 20 (2013) 26e32. [23] X. Zhu, H. Zhang, Y. Tan, H. Wang, Q. Liao, Analogue experimental study on centrifugal-air blast granulation for molten slag, Appl. Therm. Eng. (2014), http://dx.doi.org/10.1016/j.applthermaleng.2014.11.077. [24] J. Liu, Q. Yu, W. Duan, Q. Qin, Experimental investigation on ligament formation for molten slag granulation, Appl. Therm. Eng. 73 (2014) 886e891. [25] Y. Qin, X. Lv, C. Bai, P. Chen, G. Qiu, Dry granulation of molten slag using a rotating multi-nozzle cup atomizer and characterization of slag particles, Steel Res. Int. 84 (2013) 852e862. [26] Y. Pan, P. Witt, B. Kuan, D. Xie, CFD modelling of the effects of operating parameters on the spreading of liquids on a spinning disc, J. Comput. Multiph. Flows 6 (2014) 49e64. [27] Y. Pan, P.J. Witt, D. Xie, CFD simulation of free surface flow and heat transfer of liquid slag on a spinning disc for a novel dry slag granulation process, Prog. Comput. Fluid Dyn. Int. J. 10 (2010) 292e299. [28] D. Wang, X. Ling, H. Peng, Theoretical analysis of free-surface film flow on the rotary granulating disk in waste heat recovery process of molten slag, Appl. Therm. Eng. 63 (2014) 387e395. [29] Y. Pan, P. Witt, B. Kuan, D. Xie, CFD simulation of slag droplet formation by a spinning disc in dry slag granulation processes, in: 8th Int. Conference on Computational Fluid Dynamics in the Oil & Gas, Metallurgical and Process Industries, Trondheim, 2011. [30] D. Wang, H. Peng, X. Ling, Ligament mode disintegration of liquid film at the rotary disk rim in waste heat recovery process of molten slag, Energy Procedia 61 (2014) 1824e1829. [31] Y. Kitamura, T. Takahashi, Atomization of highly viscous liquids by a spinning disk, Atomization Sprays 2 (1992).
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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Research paper
Centrifugal granulation performance of liquid with various viscosities for heat recovery of blast furnace slag Jun-Jun Wu b, Hong Wang a, b, *, Xun Zhu a, b, Qiang Liao a, b, Bin Ding a a b
Key Laboratory of Low-grade Energy Utilization Technologies and Systems, Chongqing University, Chongqing 400030, China Institute of Engineering Thermophysics, Chongqing University, Chongqing 400030, China
h i g h l i g h t s Centrifugal granulation is crucial for heat recovery of blast furnace slag. The disintegration mode transition was experimentally investigated. The mechanism of disintegration mode transition was analyzed. The variation ligaments and droplets with viscosities were discussed. The analogy analysis was applied to the molten blast furnace slag.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 18 March 2015 Accepted 13 June 2015 Available online 25 June 2015
Centrifugal granulation is a crucial step in the most promising heat recovery technique for molten blast furnace slag. Facing the fact that slag viscosity changes during the granulation process, in the present work, visualization experiments were conducted for centrifugal granulation of mixture liquids by a spinning disc. Then, the effect of liquid viscosity on granulation performance was discussed. It was found that the increase in liquid viscosity resulted in granulation mode translation under the same disc rotating speed and liquid flow rate, that is, from direct droplet formation mode to ligament formation mode. The Sauter Mean Diameter of the granulated droplets was increased and the droplets size distribution was narrowed with increasing liquid viscosity. Meanwhile, the ligament number increased in direct drop formation mode while decreased in ligament formation mode as the liquid viscosity was increased. Furthermore, for a specific mixture liquid, the increase in flow rate also resulted in the translation from direct droplet formation mode to the ligament formation mode and from ligament formation mode to the film formation mode in the end. The critical flow rate for this translation was found for various liquid mixtures. Finally, dimensionless correlations were developed to predict the average diameter and critical flow rate, and the analogy analysis was applied to the molten blast furnace slag. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Centrifugal granulation Viscosity Ligament Droplet Critical flow rate Blast furnace slag
1. Introduction Blast furnace slag (BF slag) is one of the main solid by-products in steel making with the yield of 300 kg per ton of crude steel. Moreover, the slag is exhausted in high temperature of about 1500 C with huge heat content amounting to 1770 MJ per ton BF slag [1]. In 2013, China's crude steel production reached up to about 822 million tons [2], namely, the total waste heat contained in hot slag was almost equivalent to 14.8 million tons standard coal.
* Corresponding author. Institute of Engineering Thermophysics, Chongqing University, Chongqing 400030, China. Tel.: þ86 023 65102474. E-mail address: [email protected] (H. Wang). http://dx.doi.org/10.1016/j.applthermaleng.2015.06.031 1359-4311/© 2015 Elsevier Ltd. All rights reserved.
Currently, water quench technique has been widely adopted to directly cool the molten slag in most of the steel plants, giving rise to huge loss in both the water and heat. Therefore, great efforts have been made by researchers to explore an effective heat recovery technique. A heat recovery technology coupling dry granulation of the molten slag with air cooling has aroused general concern since 1984 [3]. During the following development process of this technology, several granulation techniques have been proposed and investigated by various researchers including rotary drum [3], air blast [4], centrifugal granulation [5e7]and so on. Among all the techniques, the centrifugal granulation coupling with heat recovery by air is considered as one of the most promising techniques for BF
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slag due to its simple construction, easy operation, sufficient capacity, less energy consumption and suitable granule size distribution. Therefore, intensive studies have been performed since Pickering et al. [5] firstly designed a centrifugal granulation system. During the centrifugal granulating process of molten BF slag, liquid slag firstly flows from the top injection port onto the center of a rotating atomizer and spreads radially along the atomizer surface to form a thin liquid film. The liquid film is then broken into droplets at the rim of or out of the atomizer, and these droplets are finally solidified by air cooling. The centrifugal granulation, in deed, is a complex and comprehensive process affected by multifarious parameters. These influential parameters can be sorted to three aspects: (1) Atomizer material and structure [8,9]; (2) Physical properties of liquid slag such as density, viscosity and surface tension; (3) Operational conditions including atomizer rotary speed [10e14] and liquid slag feeding rate [15e17]. However, superhigh temperature as well as blinding light of the released molten BF slag brings grave difficulties in experimental study (especially the visualization experiments) on the mechanism of BF slag granulation. Consequently, most of the researches, up to now, adopted low-temperature working media to investigate the granulation phenomena under various conditions. Mizuochi and Akiyama [18] experimentally investigated water granulation by vaned-disc and vaned-wheels, and found that vaned-atomizers were helpful to decrease the large-size droplets. Ahmed and Youssef [9] also employed water as the working medium to investigate the droplets size and velocity characteristics produced by various cup atomizers. They found that, compared with the droplets generated by flat disc, the Sauter Mean Diameter of droplets produced by atomizer with different configurations varied between 8% and 12%. Frost [19] studied the granulation using water and glycerol mixture and tackled the mechanism of ligament formation in detail. A criteria for ligament disintegration occurrence and the expression to predict the resultant droplets size were developed. Recently, Liu et al. [20,21] also carried out cold experiments using water and glycerol mixture with three kinds of cups to investigate the transition of different disintegration modes. Yi et al. [22] compounded rosin and wax with a mass ratio of 4:1 to simulate the liquid molten slag and then investigated the influence of operational conditions on granulation process of this mixture liquid. Zhu et al. [23] proposed a granulation system combining a rotating cup with air blast and investigated the granulation performance by adopting a mixture of rosin and paraffin wax. The effects of rotating speed, liquid flow rate and blast air flow rate were discussed, and the results indicated that higher rotating speed and lower liquid feeding rate gave rise to smaller particle as well as higher fibers fraction. In addition to the low-temperature working media, very few experimental works and numerical simulations were conducted for the real BF slag. Mizuochi et al. [6] investigated the feasibility of the rotary cup atomizer for slag granulation, and found that the BF slag droplets were strongly dependent on the rotating speed of atomizer. Higher rotating speed resulted in more uniform and spherical particles. Liu et al. [24] experimentally investigated the ligament formation in BF slag granulation, and found the slag wools took place inevitably during the granulation. Qin et al. [25] adopted a rotating multi-nozzle cup atomizer to granulate the molten slag and discussed the characterization of slag particles. Moreover, some numerical simulations were carried out on the centrifugal granulation. Pan et al. [26,27] adopted a CFD model to simulate free surface flow of liquid slag on a spinning disc and discussed the effects of operating parameters on the liquid spreading. Wang et al. [28] developed a theoretical analysis for free-surface flow on the disc, and it was found that the film thickness distribution of molten slag was mainly determined by liquid volume flow rate, rotary
495
speed of atomizer and viscosity. Only two documents [29,30] reported the simulation on slag droplets or ligaments formation by the spinning disc. The previous works mainly focused on the effects of atomizer structure and operating conditions (rotating speed and liquid feeding rate) on the granulation performance for a certain working medium with constant physical properties. It was noticed that diverse outcomes even contradictory statements were exhibited among the references for different working media. However, a systematic study on the granulation of liquid with different physical properties has not been reported, and the centrifugal granulation mechanism also has not been well understood. Moreover, almost all of the references ignore a reality that is unavoidable in practical dry heat recovery system of BF slag, that is, the physical properties of slag, especially the viscosity, change during the granulation process due to air cooling. This requires a well understanding of the effect of liquid viscosity on granulation performance. For this purpose, in the present study, the effect of liquid physical properties on the disintegration mode translation and granulation performance was investigated by visualization experiments using various glycerol/water mixtures. The mechanism of granulation under different disintegration modes were analyzed in detail and the experimental results were compared to the granulation of blast furnace slag. 2. Experimental system and method 2.1. Experimental setup The visualization experimental setup for centrifugal granulation, as shown in Fig. 1, consisted of a granulation system, a liquid supply system and a data acquisition system. In the granulation system, a disc atomizer with 55 mm in radius was connected to a motor by a live shaft. A frequency converter was utilized to control the rotary speed of disc atomizer in a range of 0e3000 rpm. According to Qin [25], the aforementioned attempts for slag granulation revealed that the rotary speed in a range of 600e1800 rpm is suitable for particle production. Thus in this study, the rotary speed of disc was fixed at 1200 rpm for all cases. The liquid supply system consisted of a pump, a stabilivolt tank, a valve, a flowmeter, a nozzle and a collecting tray. The nozzle of 8 mm in inner diameter located centrically above the disc with a distance 20 mm from the disc surface. The size ratio of the nozzle to the disc was 15%. The working medium from the tank flowed through the nozzle to hit the disc surface and then, it was collected in the collecting tray and was pumped into the tank. The liquid volume flow rate was adjusted by the valve. The data acquisition system consisted of a high speed camera (i-Speed TR, Olympus), a light source and a computer. The high speed camera was set at the rim of the disc and the plane LED light was installed underneath the disc rim, as shown in Fig. 1b. The dynamic behavior of the granulation process was then recorded by the high speed camera with a shooting speed of 2000 fps. All the experiments were carried out under the room temperature. 2.2. Data processing For numerous gray-scale images obtained during the granulation process, a self-compiled MATLAB program was utilized to extract the diameter of produced droplets. The extraction process is shown in Fig. 2. Firstly, choose an image which was shot during the stable granulation stage, cf. Fig. 2a. Secondly, set a processing area on the image that contains droplets or ligaments, cf. Fig. 2b. Thirdly, convert the chosen area into binary images according to a threshold value, that is,
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Fig. 1. Schematic of centrifugal atomization apparatus.
k¼
1; Ia < Ig 0; Ia > Ig
(1)
where Ig is the threshold value, Ia is the gray scale of the chosen area. Finally, extract the droplets edge using Candy operator, cf.
Fig. 2c, and then calculate the diameter of droplets with reference to standard length scale. In the present study, to ensure the data reliability, over 2000 samples in statistics were chosen under each operational condition. Furthermore, by compared with the data obtained in i-Speed Suite (Olympus software), the relative measurement error was within
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497
Fig. 2. Droplets diameter extraction process.
3. Results and discussion 3.1. Granulating evolution and analysis
Fig. 3. Physical properties of the mixture at different glycerol volume ratios.
2.0%. Besides, the relative uncertainty in Sauter Mean Diameter is with 4.0% by calculation. 2.3. Working media In order to investigate the effect of liquid physical properties on granulation process, the mixtures of glycerol and water with various volume ratios were used as the working media. The variation of physical properties of the mixtures with the glycerol volume ratio is shown in Fig. 3. One can see that the density of the mixture increased slightly while the surface tension decreased slightly with increasing glycerol volume ratio. The viscosity of the mixture slightly increased when the glycerol volume ratio was increased from 0 to 80%. However, it dramatically increased when the glycerol volume ratio was over 80% and reached 1.2 Pa s at the glycerol volume ratio of 100%. The detailed information about the physical properties of the mixtures used in the present study is listed in Table 1. Compared with the density and surface tension of the liquid mixture, the changes in viscosity were remarkable.
The representative granulating evolutions of water and glycerol/ water mixture (Samples 1, 3 and 5) were recorded and displayed in Fig. 4, where the liquid flow rate was set at 20 L h1. For the granulation of water (Sample 1), as shown in Fig. 4a, water departed from the disc rim in form of discrete droplets after a thin film spreading on the disc surface driven by the centrifugal force. It was also observed that some droplets even formed on the disc surface. A few ligaments transitorily and randomly presented at somewhere around the disc circumference and then quickly disintegrated into droplets due to their instability. Furthermore, the morphology of the formed droplets were in short rod, cf. Fig. 4d. For the granulation of liquid mixture with viscosity of 0.085 Pa s (Sample 3), as seen in Fig. 4b, thin and dense ligaments were drawn from the disc rim instead of the appearance of discrete droplets. Meanwhile, these ligaments presented an arc-shaped around the disc due to the effect of centrifugal force. The disintegration was observed to occur at the frontend of ligaments far from the disc, where part of the ligaments broke up into a row of droplets almost simultaneously. The produced droplets were small and of good sphericity, cf. Fig. 4e. When the mixture viscosity was further increased to 0.465 Pa s (Sample 5), similar phenomena, including ligaments formation and breakup at the frontend, were found in Fig. 4c. However, compared with the former case, the ligaments became thicker, longer and more curved accompanying with increased spacing. The breakup of the ligament frontend gave rise to a mass of droplets in a shape of tadpole or dragging long liquid trails (see Fig. 4f). Based on different phenomena above, one can conclude that two kinds of granulation modes happened to the liquid mixtures under the present experimental condition: the direct droplet formation mode and the ligament formation mode. In fact, the centrifugal granulation of liquid on a disc is an exceedingly complex process, in which the liquid dynamic behavior is determined by the synthetical effects of inertial force from liquid jet to the disc, centrifugal force offered by the rotating disc, shear
Table 1 Physical properties of mixture solutions. Sample Sample Sample Sample Sample Sample Sample
1 2 3 4 5 6
Glycerol ratio (%)
Viscosity (Pa s)
Density (kg m3)
Surface tension (N m1)
Oh number (102)
0 20 80 90 95 100
0.001 0.043 0.085 0.250 0.456 1.200
998 1047 1209 1235 1248 1261
0.073 0.071 0.065 0.064 0.0635 0.063
0.05 2.12 4.09 12.04 21.85 57.43
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Fig. 4. Granulation phenomena for different working media.
stress due to liquid viscous flow on the disc surface, friction force resulted from liquid flying in the air and liquid surface tension as well as the Rayleigh-Plateau instability. The destruction of the counter-balance of these forces is responsible for the differences in the granulation mode and performance. In the present experiments, the incentive to the destruction can be attributed to the change in the physical properties of the liquid, especially the viscosity. For liquid which has smaller viscosity and higher surface tension, the inertial force and centrifugal force outperform the shear stress and surface tension to spread liquid over the disc surface, as seen in Fig. 5-1a. Along with the film moving forward to
the disc edge, perturbations from the surface instability at both the circumferential direction and radial direction give rise to the digitate bulge surface of the thin film, cf. Fig. 5-1b. Some thin fingers are then prematurely smashed on the disc owing to the instability and others are pinched at the rim of the disc due to the disturbance from the abrupt absence of the solid surface, as shown in Fig. 5-1c. Thereafter, the shattered liquid contracts to small droplets under the action of surface tension, and this is the so-called typical direct droplet formation mode. When the liquid mixture is used, the significant increase in the viscosity results in enhanced shear stress. This slows down the
Fig. 5. Schematic of disintegration modes during centrifugal granulation: (1) direct droplet formation, (2) ligament formation.
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spreading of liquid film considering the given jet velocity and rotary speed of the disc, hence resulting in thick liquid film on the disc (cf. Fig. 5-2a). Therefore, stumpy fingers are formed at the bulge surface of the film due to the increased anti-disturbance capability of the thick liquid film and lower surface tension, as shown in Fig. 5-2b. Instead of the premature pinch-off, these fingers are then drawn out from the disc rim to form ligaments with an arc-shaped due to the centrifugal effect. The flying ligaments gradually attenuate under the action of drag force and surface tension, and finally breakup at frontend owing to the Rayleigh-Plateau instability, as shown in Fig. 5-2c. The produced droplets are small and of good sphericity due to the smaller surface tension. This results in the socalled ligament formation mode. When the viscosity of mixture liquid is further increased, as a result of higher shear stress, the liquid spreading on the disc is further decelerated with thicker liquid film. Meanwhile, the bulge surface of the film exhibits corrugated with long-wavelength instead of fingerlike due to the enhanced stability. Therefore, ligaments with larger diameter and spacing are drawn out from the disc rim, and the distance required for the pinch-off as well as droplets formation is longer due to the larger initial diameter and lower surface tension. The experimental results and analysis suggest that, for a working medium whose viscosity changes with temperature or components, such as BF slag, appropriate operational conditions should be set to ensure good granulation performance.
499
3.2. Effect of liquid viscosity on droplet size distribution Droplets are the major products in the centrifugal granulation process. For the purpose of efficient heat recovery of the molten BF slag by air flow, tiny droplets with a narrow diameter distribution are expected due to larger specific surface area for heat transfer. Therefore, the droplets size and their diameter distribution is one of the main concerns in the experiments. Fig. 6 shows the effect of liquid viscosity on the droplets diameter distribution during the granulation process where the liquid flow rate was 20 L h1. In the experiments, as discussed above, the translation of granulation mode happened when the liquid viscosity was increased from 0.001 Pa s to 1.2 Pa s. Working media with viscosity of 0.001 Pa s and 0.043 Pa s were centrifuged to droplets in direct droplet formation mode and the diameter of produced droplets covered a range of 0e1.0 mm, as shown in Fig. 6a. For the liquid with viscosity of 0.001 Pa s, 72% of the droplets possessed the diameter range of 0e0.2 mm. However, the maximum probability of diameter decreased to 51% and moved to the range of 0.2e0.4 mm for the liquid with viscosity of 0.043 Pa s. Meanwhile, the droplets with probability of diameter in the range of 0.8e1.0 mm increased from 1.2% for liquid with 0.001 Pa s to 8.7% for liquid with 0.043 Pa s. This is resulted from the increasing liquid film and thus the incrassate bulge which is pinched off right at the disc rim. The granulation mode is transformed from direct droplet formation mode to ligament formation mode when the liquid viscosity was increased from 0.043 Pa s to 0.085 Pa s. It was found that the maximum probability of diameter still remained in the range of
Fig. 6. Effect of liquid viscosity on droplet size: (a) diameter distribution in direct droplet formation mode, (b) diameter distribution in ligament formation mode, (c) SMD during granulation.
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Table 2 Standard deviation of droplets diameter for different liquid viscosities. Viscosity (Pa s) Standard deviation
0.001 0.381
0.043 0.311
0.085 0.122
0.251 0.113
0.456 0.233
1.2 0.173
0.2e0.4 mm, however, its value significantly increased to 67%, cf. Fig. 6b. Meanwhile, the probability of diameter in the range of 0.6e1.0 mm decreased to zero. As thus, the droplets size range was narrowed to 0e0.6 mm. This can be attributed to the ligaments formation and the disintegration of the frontend of ligaments. Although the increase in viscosity results in thicker liquid film, the fingerlike film experiences a stretching of ligament instead of break-up right at the disc rim, and then the pinch-off of the thin frontend of the ligaments gives rise to the large amount of small droplets. However, the probability variation showed a different trend when the granulation was in the ligament formation mode, as shown in Fig. 6b. The probability of diameter in the range of 0.2e0.4 mm gradually decreased to about 25% when the liquid viscosity was increased from 0.085 Pa s to 1.2 Pa s. For the highest liquid viscosity, the maximum probability of diameter shifted to fall in the range of 0.4e0.6 mm and reached 46%. The enlarged initial ligament diameter at higher liquid viscosity is responsible to the increment in droplets size. Moreover, it was noted that the droplets larger than 0.8 mm were not produced for all cases in the ligament formation mode, and thus the droplets diameter distribution was in a narrow range. Besides the droplets size distribution, the average diameter of the droplets is another key parameter to assess the granulation performance. Fig. 6c shows the variation of Sauter Mean Diameter (SMD) of the granulated droplets with liquid viscosity. It is shown that a sharp increase in the droplets SMD presented when the liquid viscosity was increased from 0.001 Pa s to 0.043 Pa s, and the increase rate reached to 3.6 mm Pa1 s1. However, the SMD plummeted from 0.565 mm to 0.34 mm when the liquid viscosity was further increased to 0.085 Pa s, which is resulted from the transformation in granulation mode. For the granulation in the ligament formation mode, the SMD almost linearly increased with a rate of 0.30 mm Pa1 s1 when the viscosity was increased to 0.456 Pa s, while the growth rate reduced to 0.18 mm Pa1 s1 for the further increment in the liquid viscosity. Furthermore, standard deviation was calculated to evaluate the concentration of various droplet diameter distributions,
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u n u 1 X S¼t ðd d32 Þ2 n 1 i¼1 i
mode. During the centrifugal granulation process, ligament plays a role as bridge between liquid film and droplets. The number and the length of ligaments directly affect the number and size of the droplets. For this reason, the ligament number and length were measured and the effect of liquid viscosity on the ligaments was investigated. Here, the ligament length was defined as the radical distance between droplet pinch-off point and the edge of disc, cf. Fig. 1b. Fig. 7a shows the effect of liquid viscosity on the average ligament number. It can be seen that, with increasing liquid viscosity, the average ligament number rapidly rose to reach a peak value and then turned to drop gradually. It is also noted that for the liquids with viscosity of 0.001 Pa s and 0.043 Pa s the ligaments were approximate in the average number. Besides, the ligament number covered a wide range of 70e100 with regard to all the calculated samples. This is because of the transitory and random presence of ligaments in the two cases in which the liquids were granulated in the direct droplet formation mode. These ligaments had a little contribution to the droplets formation. When the granulation was transformed from the direct droplet formation to the ligament formation mode, that is, the case with liquid viscosity of 0.086 Pa s, the ligament number jumped to 152 with somewhat variance. This
(2)
where di represents diameter of each droplet, d32 is the SMD for each test and n is the total number of droplets. The results are listed in Table 2. It indicated that the standard deviation was more than 0.3 in the direct droplet formation mode, while it was less than 0.24 in the ligament formation mode. This suggests that the droplets produced in the ligament formation mode were more concentrated than that in the direct droplet formation mode. Moreover, the above results imply that the operational condition which leads to centrifugal granulation in the early stage of the ligament formation mode is preferred to achieve small droplets. 3.3. Effect of liquid viscosity on ligaments formation As analyzed above, one can benefit from granulation in the ligament formation mode to obtain small and concentrated droplets, as thus, special attention should be paid to this granulation
Fig. 7. Effect of liquid viscosity on ligament formation: (a) ligament number, (b) ligament length.
J.-J. Wu et al. / Applied Thermal Engineering 89 (2015) 494e504
can be understood that the granulation of liquid with higher viscosity gives rise to the stably thin and dense ligaments. Thereafter, the average ligament number significantly decreased to 62 when the viscosity was increased to 0.456 Pa s. This is resulted from thickening liquid film and ligament diameter as well as enlarged wavelength of the disturbance. However, the downtrend was flatten out when the viscosity was further increased to 1.2 Pa s. This suggests that the ligament granulation is trending towards stability until the granulation mode is changed again. Fig. 7b shows the effect of liquid viscosity on the ligament length. The average break-up length of ligaments dramatically increased from 3.9 mm to 49.1 mm when the liquid viscosity was increased from 0.001 Pa s to 0.456 Pa s. This can be attributed to the increased ligament diameter at the disc rim. It should be noted that the ligament length for the case with the viscosity of 1.2 Pa s was absent since the ligaments were much longer than the high-speed camera's field of view. The above experimental results imply that, besides the expected small droplets ruptured from the frontier of ligament, a set number of ligaments will be remained during the granulation process. It should be pointed out that the remaining ligaments are unfavorable in their sequential utilization for most of the practical applications. As thus, indeed, the multiple and long ligaments are undesirable. The experimental results imply that for the BF slag the molten slag should not be cooled too fast before it reaches the atomizer, otherwise, the significant increase in its viscosity due to drop in temperature will result in a large amount of ligaments. This not only goes against efficient heat recovery but it also impedes the release of slag particles from the equipment. Therefore, auxiliary equipments that can smash the remained ligaments are expected to the existing atomizer to achieve better granulation performance. 3.4. Critical liquid flow rate for granulation mode translation of various liquids It is clear that the granulation mode will be translated from the direct droplet formation mode to the ligament formation mode with increasing liquid viscosity. Not only that, for the same liquid at the same rotating speed of disc, the granulation mode translation will also happen due to variation on liquid flow rate. Fig. 8 displays different granulation modes for the mixing liquid with the viscosity of 0.251 Pa s under liquid flow rates of 5 L h1, 20 L h1 and 60 L h1. One can see that a typical direct droplet formation mode presented at lower liquid flow rate, cf. Fig. 8a, where a fewer discrete droplets departed from the disc surface. When the liquid flow rate was increased to 20 L h1, the granulation process was translated to a typical ligament formation mode, as shown in Fig. 8b, where the dense ligaments were drew from the liquid film on the disc and then the frontier of the ligaments was disrupted into smaller droplets. However, another granulation mode is presented when
501
Fig. 9. Morphology of products in film formation mode (0.251 Pa s, 1200 rpm, 60 L h1).
the liquid flow rate was further increased to 60 L h1. For this case, it was observed that a stably thicker film formed and spread on the disc without the appearance of digitate bulge surface due to over high flow rate. The film was then integrally pushed out of the disc by the centrifugal force and inertial force since the flow disturbance was not in sufficient strength to dilacerate the thicker film. As a result, an integral liquid film was kept out of the disc and then it was disintegrated at the front edge, as seen in Fig. 8c. This granulation mode can be called film (or sheet) formation mode. Moreover, compared with the granulation in direct droplet formation and ligament formation, it was found that the produced droplets in the film formation mode appeared in quite irregular shape, including spherical, short rod and silk-like, as shown in Fig. 9. Considering the purpose of granulation, one can conclude that the film formation mode must be avoided. This encouraged us to find out the critical flow rate at which the granulation process translated from the ligament formation mode to the film formation mode. The result will definitely give a guide to determine the operational conditions in the practical applications. It should be pointed out that the critical flow rate for the granulation mode translation is related to the rotary speed of atomizer and the physical properties of liquid. In the present study, the effect of liquid viscosity on the critical flow rate was focused under a fixed rotary speed of 1200 rpm, and the results are shown in Fig. 10. The critical flow rate decreased sharply with slight increase in the liquid viscosity. For example, the critical flow rate was up to 160.1 L h1 when the liquid viscosity was 0.001 Pa s, but it dropped down to 43.7 L h1 for liquid of 0.251 Pa s. However, the
Fig. 8. Granulation modes at different liquid flow rates (0.251 Pa s, 1200 rpm): (a) 5 L h1; (b) 20 L h1; (c) 60 L h1.
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3.5. Correlation and analogous analysis for melt blast furnace slag For the centrifugal granulation process, three kinds of parameters will influence the performance. One is the physical properties of working medium including density, viscosity and surface tension. The second one is the structural parameters including the atomizer size, injector size and injection height. The third one is operational conditions including rotary speed of the atomizer and flow rate of working medium. Based on this understanding, three dimensionless parameters including Reynold's number Re, Ohnesorge number Oh and Weber number We, are introduced as following,
Re ¼
Fig. 10. Critical flow rate under different liquid viscosities.
rRu m
m Oh ¼ pffiffiffiffiffiffiffiffi rsR We ¼
sharp reduction in the critical flow rate was stopped and turned to quite gentle declination once the liquid viscosity was further increased to 1.2 Pa s (33.6 L h1). Moreover, the corresponding transition phenomena for various liquids are shown in Fig. 11. It can been seen that, at the critical state from the ligament formation mode to the film formation mode, disordered and instable ligaments formed along the film frontier. Thereafter, the resulted ligaments crushed into droplets at random. It was also found that the disorder around the liquid film frontier gradually faded with increasing liquid viscosity. For the mixing liquid with viscosity of 1.2 Pa s, the film appeared much more stable and only one ligament was observed in the field of view to be drawn out from the film. This can be understood that high-viscosity liquid inherently results in stable film due to higher shear stress. Therefore, lower flow rate is required for a thin film on the disc which is prone to form linear protrusion and then ligaments. The results suggest that the design flow rate of the specific working medium for a centrifugal granulation equipment must be lower than the corresponding critical flow rate.
ru2 R3 : s
(3)
(4)
(5)
where r, m and s are the density, viscosity and surface tension of liquid medium, respectively; R is the radius of the atomizer; u is the rotary speed of the atomizer; u is the injection velocity, u ¼ Q =pr 2 , and r is the radius of injector, Q is the liquid flow rate, d32 is the SMD of granulated droplets. Considering the introduced dimensionless parameters, the dimensionless correlation of SMD of granulated droplets was obtained by fitting the experimental data:
d32 ¼ 9:9ðReÞ0:42 ðOhÞ0:61 ðWeÞ0:68 : R
(6)
The correlation is available for 300 < Re < 5000, 0.0005 < Oh < 0.57, 45,000 < We < 55,000. The divergence between the fitting results and the experimental data is exhibited in Fig. 12, where the prediction results derived from the correlation promoted by Kitamura [31] were shown as a comparison. It can be seen that the prediction results by Kitamura underestimated the SMD of granulated droplets, however, the prediction by the promoted
Fig. 11. Transition phenomenon at critical flow rate for different working media.
J.-J. Wu et al. / Applied Thermal Engineering 89 (2015) 494e504
503
available range of the promoted correlation. That is, the analysis above and the promoted correlation can be used to predict the granulation performance of BF slag. Consequently, for the BF slag the SMD of produced slag droplets is 0.75 mm at 1380 C (1200 rpm, 20 L h1) and 0.62 mm at 1500 C. In the same way, the critical flow rate is calculated as 570.8 L h1 at 1380 C and 601.7 L h1 at 1500 C when the rotary speed keeps at 1200 rpm. 4. Conclusions In the present study, the effect of liquid viscosity on centrifugal granulation was experimentally investigated using various water/ glycerol mixtures as working media. The granulation evolution was discussed and analyzed in detail. The variation of key parameters such as droplets size and distribution, ligaments number and length as well as critical flow rate of granulation mode translation with the liquid viscosity were discussed. Dimensionless correlations to predict SMD of the produced droplets and the critical flow rate for BF slag were developed. The main results were obtained as following:
Fig. 12. Divergence in experiment data and correlations.
correlation shows good agreement with the experimental data with an error of ±4%. Moreover, in order to predict the critical liquid flow rate at which the granulation translated from the ligament formation mode to the film formation mode, the dimensionless flow rate was introduced as
Qþ ¼
Qc ; uR3
(7)
where Qc is the critical liquid flow rate, R is the disc radius, u is the rotary speed of disc. Then, the correlation was also obtained by fitting the experimental data.
Q þ ¼ 2:36 105 ðWeÞ0:12 ðOhÞ1:86 :
(8)
It shows good agreement between the prediction and the experimental data with the error of ±3%. Although water and mixed liquids were adopted as working media in the present study, it is expected that the experimental results can be used for reference of the molten BF slag granulation. It is known that the blinding light of slag due to superhigh temperature brings great difficulties in conducting visualization experiments. As a consequence, the inherent law of molten BF slag centrifugal granulation has not been well understood, resulting in the lack of guidance on equipment design and operation. An alternative way to approximate the molten BF slag granulation is to utilize the results of cold-state experiments based on the similarity principles, that is, two physical processes can be treated as similar once the necessary dimensionless numbers of the processes are equal to each other, respectively. Supposing that the same atomizer is used for the molten BF slag with the same rotary speed, meanwhile, considering the viscosity variation due to air cooling, the relevant parameters of mixtures and BF slag are listed in Table 3. It is clear that the dimensionless parameters of the BF slag fall into the
Table 3 The physical property parameters of mixture and the BF slag. Parameter
Mixtures (at 20 C)
BF slag (at 1380e1500 C) [22]
r/kg m3 m/Pa s s/N m1
998e1260 0.001e1.2 0.063e0.073 0.0005e0.5743
2606e2622 0.4e1.0 0.530e0.549 0.0459e0.1124
Oh
(1) Under the given disc rotary speed and liquid flow rate, variation on the liquid viscosity resulted in the change of disintegration mode. High-viscosity gave rise to the granulation in ligament formation mode rather than in direct droplet formation mode. (2) With increasing liquid viscosity, the SMD of the granulated droplets was increased and the droplets size distribution was narrowed. Besides, droplets produced in the ligament formation mode presented more uniform compared with that in the direct droplets formation mode. (3) For the granulation in the ligament formation mode, the ligament number rose rapidly at first and then turned to decrease gradually with increasing liquid viscosity. The ligament length kept increasing with the increase in viscosity. (4) For a certain mixture liquid, high flow rate induced the film formation out of the disc, which was not expected for good granulation performance. The transition flow rate from ligament formation to film formation decreased as the liquid viscosity was increased. (5) Dimensionless correlations based on the experimental data were developed to predict the SMD and critical flow rate in the range of Oh number from 0.0005 to 0.5743, respectively. Acknowledgements The author would like to thank National Basic Research Program of China (973 program) (No. 2012CB720403), Fundamental Research Funds for the State Key Laboratory Of Mechanical Transmission, Chongqing University (No. SKLMT-ZZKT-2012 MS 17) and Chongqing Graduate Student Research Innovation Project (No. CYS14016). Nomenclature di d32 I k L n N Oh Q Qc
droplet diameter, mm Sauter Mean Diameter, mm threshold value binary value of image ligament length, mm droplets number ligament number Ohnesorge number liquid flow rate, L h1 critical flow rate, L h1
504
Qþ r R Re S We
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dimensionless liquid flow rate radium of nozzle, mm radium of rotary disc, m Reynolds number standard deviation Weber number
Greek
m r s u
dynamic viscosity, Pa s density, kg m3 surface tension, N m1 rotary speed, rad s1
Subscript a area g gray i random liquid droplet 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] Worldsteel Committee on Economic Studies, World Steel Association, Brussels, 2014. [3] Y. Nara, H. Yoshida, G. Nakatani, T. Anazi, H. Sato, in: The Technology of Slag Heat Recovery at NKK SEAISI Conference of Energy Utilization in the Iron and Steel Industry, 1984. [4] T. Koehler, L. Rodd, C. Walker, N. Voermann, Economics of slag heat recovery from ferronickel slags, in: Sustainability for Profit, Conference of Metallurgists (COM2010), 2010, pp. 3e17. [5] S. Pickering, N. Hay, T. Roylance, G. Thomas, New process for dry granulation and heat recovery from molten blast-furnace slag, Ironmak. Steelmak. 12 (1985) 14e20. [6] Toshio Mizuochi, Tomohiro Akiyama, Taihei Shimada, Eiki Kasai, JunIchiro Yagi, Feasibility of Rotary Cup Atomizer for Slag Granulation, Iron and Steel Institute of Japan, Tokyo, JAPAN, 2001. [7] B. Washington, D. Xie, T. Norgate, S. Jahanshahi, Dry Granulation of SlagseTurning Waste into Valuable Cement Binder, 1088e1091. [8] J. Xie, Y. Zhao, J. Dunkley, Effects of processing conditions on powder particle size and morphology in centrifugal atomisation of tin, Powder Metall. 47 (2004) 168e172. [9] M. Ahmed, M.S. Youssef, Influence of spinning cup and disk atomizer configurations on droplet size and velocity characteristics, Chem. Eng. Sci. 107 (2014) 149e157. [10] J. Liu, Q. Yu, X. Hu, Experimental Study on Granulation Process of Blast Furnace Slag, National Conference of Energy and Thermal Engineering, 2008.
[11] J. Liu, Q. Yu, C. Dou, X. Hu, Experimental Study on RCA of Blast Furnace Slag, National Conference of Energy and Thermal Engineering, 2008. [12] Q. Yu, J. Liu, C. Dou, X. Hu, Dry granulation experiment of blast furnace slag by RCA, J. Northeast. Univ. (Nat. Sci.) 30 (8) (2009) 1163e1165+1173. [13] Z.-Y. Yang, Y.-M. Zhou, Z.-M. Yan, C.-X. Dou, Experimental study of dry centrifugal granulation of molten furnace slag, Sci. Technol. Eng. (2009) 7257e7260. [14] Z. Yang, Y. Zhou, Z.-m. Yan, Experimental study of dry centrifugal granulation for molten blast slag, Sci. Technol. Eng. 9 (2009). [15] L.J. Qingbo Yu, Xianzhong Hu, Simulation experimental research of granulation process for iron slag, Iron Steel 44 (4) (2009) 82e85. [16] H. Zhang, H.-W. Ni, X.-W. Li, W.-Y. Zhu, J.-C. Xiong, R.-J. Cheng, et al., Experimental study on dry centrifugal granulation for blast furnace slag, Energy Metall. Indus. 31 (5) (2012) 15e19. [17] B. Du, Y.-G. Zhang, Centrifugal granulation exoerimental study of molten blast furnace slag by rotary disc, Energy Metall. Indus. 32 (4) (2013) 29e32. [18] T. Mizuochi, T. Akiyama, Cold experiments of rotary vaned-disks and wheels for slag atomization, ISIJ Int. 43 (2003) 1469e1471. [19] A. Frost, Rotary atomization in the ligament formation mode, J. Agric. Eng. Res. 26 (1981) 63e78. [20] J. Liu, Q. Yu, Q. Guo, Experimental investigation of liquid disintegration by rotary cups, Chem. Eng. Sci. 73 (2012) 44e50. [21] J. Liu, Q. Yu, P. Li, W. Du, Cold experiments on ligament formation for blast furnace slag granulation, Appl. Therm. Eng. 40 (2012) 351e357. [22] Y. Min, J. Huang, C.-j. Liu, M.-f. Jiang, X.-q. Yu, Physical simulation of molten slag granulation by rotary disk, J. Iron Steel Res. Int. 20 (2013) 26e32. [23] X. Zhu, H. Zhang, Y. Tan, H. Wang, Q. Liao, Analogue experimental study on centrifugal-air blast granulation for molten slag, Appl. Therm. Eng. (2014), http://dx.doi.org/10.1016/j.applthermaleng.2014.11.077. [24] J. Liu, Q. Yu, W. Duan, Q. Qin, Experimental investigation on ligament formation for molten slag granulation, Appl. Therm. Eng. 73 (2014) 886e891. [25] Y. Qin, X. Lv, C. Bai, P. Chen, G. Qiu, Dry granulation of molten slag using a rotating multi-nozzle cup atomizer and characterization of slag particles, Steel Res. Int. 84 (2013) 852e862. [26] Y. Pan, P. Witt, B. Kuan, D. Xie, CFD modelling of the effects of operating parameters on the spreading of liquids on a spinning disc, J. Comput. Multiph. Flows 6 (2014) 49e64. [27] Y. Pan, P.J. Witt, D. Xie, CFD simulation of free surface flow and heat transfer of liquid slag on a spinning disc for a novel dry slag granulation process, Prog. Comput. Fluid Dyn. Int. J. 10 (2010) 292e299. [28] D. Wang, X. Ling, H. Peng, Theoretical analysis of free-surface film flow on the rotary granulating disk in waste heat recovery process of molten slag, Appl. Therm. Eng. 63 (2014) 387e395. [29] Y. Pan, P. Witt, B. Kuan, D. Xie, CFD simulation of slag droplet formation by a spinning disc in dry slag granulation processes, in: 8th Int. Conference on Computational Fluid Dynamics in the Oil & Gas, Metallurgical and Process Industries, Trondheim, 2011. [30] D. Wang, H. Peng, X. Ling, Ligament mode disintegration of liquid film at the rotary disk rim in waste heat recovery process of molten slag, Energy Procedia 61 (2014) 1824e1829. [31] Y. Kitamura, T. Takahashi, Atomization of highly viscous liquids by a spinning disk, Atomization Sprays 2 (1992).