Article pubs.acs.org/IECR
Experimental Investigation on Transition Characteristics of Different Rotary Disk Configurations Hao Peng,*,† Xiang Ling,*,† Dongxiang Wang,†,‡ and Na Wang† †
Jiangsu Key Laboratory of Process Enhancement and New Energy Equipment Technology, School of Mechanical and Power Engineering, Nanjing Tech University, No. 30 Pu Zhu South Road, Nanjing 211816, P. R. China ‡ School of Mechanical Engineering, Jiangnan University, No. 1800 Li Hu Road, Wuxi 214122, China S Supporting Information *
ABSTRACT: An experimental study was performed to investigate the liquid granulation process on the rotary disks. Four groups of rotary disks were specially designed, and rosin/ paraffin mixture was used as the working fluid. At first, the nondimensional transition equations between different breakup modes were obtained. Then, comparative analyses were performed to characterize the critical transition characteristics. Higher Q+ values for bulged-block disk from direct drop to ligament and ligament to fully ligament were observed, while the first appearance of the sheet mode nearly coincided for all types of disks. Finally the transition maps were proposed, and the effects of operational conditions and liquid properties on transition characteristics were analyzed. The transition maps showed that the broadest transition area from ligament to sheet mode was indentified in arc-edge disk, while the narrowest area appeared in bulged-block disk. Moreover, the transition between different modes was promoted by decreasing Q and ω or increasing μ.
1. INTRODUCTION
As reported, the transition characteristics for rotary disk atomizer depend on the operational parameters (flow rate, rotational speed), liquid properties (density, viscosity, and surface tension), and geometrical configurations (surface morphology, diameter). Kamiya and Kayano20 developed a transition correlation from ligament to sheet mode. Matsumoto et al.21,22 analyzed the effect of fluid properties and disk diameter on the transition characteristics and proposed the relevant correlations from direct drop to ligament mode and ligament to sheet mode. Frost23 reported the criteria which can predict whether the disk operates in direct drop, ligament, or sheet mode. These transition modes appeared as similar to the regimes obtained by Kamiya and Kayano20 and Matsumoto et al.21,22 Glahn et al.24 established a transition map on rotary disks by using oil as the working fluids and modified the correlations for critical flow rates. Recently, a complementary work to extend the range of the above operational conditions was performed by our team.25 The nondimensional critical transition correlations between different breakup modes and the corresponding transition map were proposed through the visualized experiments. These correlations for rotary disks are listed in Table.1. All the expressions show that the flow rate and rotary speed are
Rotary disk, as a liquid atomizer, is widely used to produce droplets, granules, sprays, and powders, and it has found successful applications in chemical,1−3 pyrometallurgical,4−6 and food7 industries recently, especially in various chemical engineering processes, including syntheses, catalyzed reactions, and many other gas-contact fields.8−11 The most attractive merit of rotary disk atomizer is the ability to disintegrate high viscous liquid, emulsions, and slurries.12,13 In addition, it can produce metal powders with a narrow range of droplet sizes.14 In the rotary disk granulation, liquid is directly poured into the center of a rotating disk, and then centrifugal force causes the liquid to spread outward and subsequently be broken into small droplets. These droplets are generated around or beyond the disk rim in light of different breakup modes (direct drop, ligament, and sheet modes). Admittedly, ligament breakup mode, especially fully ligament mode, is chosen as the most reasonable granulation process because it can achieve a quasi-steady state and produce droplets within a narrower size range. Most of the research focuses on the ligaments or droplets characteristics in the ligament breakup regime, including ligament number, tail end diameter of ligament, and mean diameter of droplets, etc.15−19 In addition, from our point of view, it is also important to identify the critical transition regimes for different breakup modes in rotary disk at a given set of operational conditions, since it is an essential prerequisite for further investigating granulation. However, the relative works and literature are still limited. © 2017 American Chemical Society
Received: Revised: Accepted: Published: 11281
June 30, 2017 September 11, 2017 September 12, 2017 September 12, 2017 DOI: 10.1021/acs.iecr.7b02675 Ind. Eng. Chem. Res. 2017, 56, 11281−11291
Article
Industrial & Engineering Chemistry Research Table 1. Critical Transition Correlations for Rotary Disk Atomization authors
correlations −0.5⎡
Kamiya and Kayano20
⎡ ρ ⎤ Q > 24.16⎢ 3 ⎥ ⎣ σD ⎦
Matsumoto et al.21
Q + = 0.096We ‐1.15Re 0.95
nondimensional variables 2
3 ⎤−0.403
ρω D ⎢ ⎥ ⎣ 8σ ⎦
−
breakup mode ligament−sheet
Q + = 2Q /(πD2 μω/ρ ) 2
ligament−sheet
3
We = ρω D /8σ
Re = ωρD2 /4μ Matsumoto et al.22
Q + = 0.0333On−0.9We−0.85
Q + = ρ Q 2 / σD 3 2
direct drop−ligament
3
We = ρω D /8σ
On = μ/ ρσD 2 ⎤0.95
⎛ ρσD ⎞⎛ μD ⎞ ⎛ ωρD Q < 1.52⎜ 2 ⎟⎜ ⎥ ⎟/⎜ ⎝ μ ⎠⎝ ρ ⎠ ⎝ μ ⎦
Frost23
−
⎛ ρσD ⎞0.9⎛ μD ⎞ ⎛ ωρD2 ⎤0.63 Q > 0.46⎜ 2 ⎟ ⎜ ⎥ ⎟/⎜ ⎝ μ ⎠ ⎝ ρ ⎠ ⎝ μ ⎦
ligament−fully ligament
⎛ ρσD ⎞0.9⎛ μD ⎞ ⎛ ωρD2 ⎤0.84 Q < 19.8⎜ 2 ⎟ ⎜ ⎥ ⎟/⎜ ⎝ μ ⎠ ⎝ ρ ⎠ ⎝ μ ⎦
ligament−sheet
Q + = 0.0854On−0.9We−0.85
Glahn24
direct drop−ligament
Q + = ρ Q 2 / σD 3 2
direct drop−ligament
3
We = ρω D /8σ +
Q = 0.1378On Peng et al.
25
Q* = 0.308We
−0.33
We
−0.994
Re
−0.435
On = μ/ ρσD
0.201
Q* = Q /ωD
3
ligament−sheet direct drop−ligament
Q * = 0.126We
‐0.779
0.118
We = ρω D /8σ
ligament−fully ligament
Q * = 0.257We
−0.75
0.133
Re = ρQ /μD
fully ligament−sheet
Re
Re
2
3
Since the Q term was on both sides of our transition equations, to avoid this confusion, in the present work, a modified equation by considering the physical properties of working fluids and disk surface configurations was derived according to Kamiya’s work,26 which is shown below
important in causing a transition, and the liquid properties density is less influential than the viscosity and surface tension. By calculating these correlations, it is also found that there are some discrepancies among them, and this is possibly attributed to the various operational variables and measurement methodologies which have been emphasized by Peng et al.25 and Ahmed and Youssef.16 In addition, most of the correlations are nondimensional which makes it convenient to utilize these correlations for atomization system design. Obviously, the above highlighted efforts are significant and original. Nevertheless, the effect of disk configurations on transition process is either not available or not yet fully understood, especially for the molten slag rotary disk granulation in pyrometallurgical industries. Since the molten slag flow pattern on the surface changes with different disk configurations, it may significantly affect the transition characteristics and accordingly the final conclusions. Therefore, the objective of the present work is to investigate the effect of disk configurations on molten slag granulation process with rosin/paraffin mixture (RP mixture) as working fluid according to the granulation mechanism of Newtonian liquid and similarity principle.17 The evolution of breakup modes, critical transition correlations, and maps are analyzed. This study is performed at the same operational variables by means of high-speed camera visualization. Moreover, the transition areas for different disk configurations in terms of liquid flow rates are specified.
Q+ = CWe aSt b
(1)
where
Q+ =
Q R3ω
(2)
We =
ρω 2R3 σ
(3)
St =
μ2 ρRσ
(4)
As shown in eq 1, the nondimensional critical volume flow rate Q+ is determined by We and St. It indicates that the critical Q+ can be obtained by adjusting the working fluid properties (ρ, μ, σ) and angular speeds (ω) for a given disk structure, thus proving a basis for design of the experimental system. 2.2. Experimental Devices. Figure 1 shows the flow chart of the experimental system. Major parts include a working fluid supply system, a granulation system, and a visualization system. The working fluid supply system has a fusion pot, an electric heater, a control valve, and an ultrasonic flowmeter. The rosin/P \paraffin mixture (RP mixture) is utilized as the working fluid, which is melted by an electric heater in the fusion pot. The mass ratio between rosin and paraffin is 4:1. The volume flow rates of working fluid are measured by an ultrasonic flowmeter (FLEXIM
2. EXPERIMENTAL SETUP 2.1. Critical Transition Equations. The critical transition equations from direct drop to ligament mode and ligament to fully ligament mode were presented in our previous work.25 11282
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Table 3. Geometric Parameters of Different Disks (Unit: mm) no.
disk type
D
R1
R2
R3
R4
L1
L2
W2
1 2 3 4 5 6 7 8
flat disk (a)
50 100 50 100 50 100 50 100
25 50 25 50 25 50 25 50
−
−
−
−
−
−
10 15 −
−
−
−
−
16.5 16.5 −
65 130 −
6 6 −
−
−
3 3
1.5 1.5
slotted disk (b) arc-edge disk (c) bulged-block disk (d)
−
−
During the experiments, the RP mixture is heated to the operational temperatures in the fusion pot and then poured into the rotating disk. Different breakup modes will be observed by high-speed camera at various volume flow rates and rotating angular speeds. The corresponding operational conditions of the experiments are shown in Table 4. Figure 1. Schematic of the experimental system process.
Table 4. Operational Conditions G601) and can be controlled by the valve. As mentioned in section 2.1, the experiments with two different temperatures are conducted to investigate the influence of properties on the critical transition characteristics, and the corresponding physical properties are listed in Table 2.
density (kg/m3)
viscosity (Pa·s)
surface tension (N/m)
110 130
961.1 927.8
0.119 0.050
0.0424 0.0397
volume flow rate (mL/s)
rotating angular speed (rad/s)
0−20
62.8−188.5
2.3. Experimental Uncertainty. The volume flow rates of RP mixture are measured by an ultrasonic flowmeter, which has the uncertainty of ±1%. The disk rotating angular speed is obtained by a frequency transducer, and the uncertainty is ±1%. The ambient and mixture temperatures are measured by two PT100 platinum thermistors with the uncertainty of ±0.2K. By using the standard single-sample uncertainty analysis, the calculated experimental uncertainty of Q+ is estimated to be 4.38%. Accordingly, the normalized mean squared error (MSR) and correlation coefficient (R2) are defined for the statistical analyses of eq 1.
Table 2. Physical Properties of the Working Fluid at Different Temperatures (110 and 130 °C) temp of mixture (°C)
temp (°C) 110 and 130
The granulation system is comprised of a rotary disk and an acpowered motor (450W380 V-2P). Eight rotary disks with different surface configurations are investigated. The configurations and the main geometric parameters of these rotary disks are shown in Figure 2 and Table 3. The thicknesses of all disks are 3 mm. The motor is driven by a frequency converter. The visualization system is employed to capture the phenomena of the granulation, which has a high-speed camera (Phantom Miro R320S) and a high-brightness cold light source (1 kW). In the present work, the acquisition rate is 1700 FPS and the pixel size is 1024 × 1024, respectively.
N
MSE =
∑i = 1 (Q i+e − Q i+p)2 N
(5)
R2 = N
N
N
(N ∑i = 1 (Q i+eQ i+p) − ∑i = 1 Q i+e ∑i = 1 Q i+p)2 N
N
N
N
(N ∑i = 1 (Q i+e)2 − (∑i = 1 Q i+e)2 )(N ∑i = 1 (Q i+p)2 − (∑i = 1 Q i+p)2 )
(6)
Figure 2. Photograph of the experimental setup: (a) flat disk; (b) slotted disk; (c) arc-edge disk; (d) bulged-block disk. 11283
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Figure 3. Breakup mode of liquid film with different volume flow rates (ω = 62.83 rad/s): (a) Q = 1.32 mL/s; (b) Q = 4.37 mL/s; (c) Q = 8.85 mL/s; (d) Q = 14.98 mL/s; (e) Q = 19.65 mL/s; (f) Q = 23.92 mL/s.
Figure 4. CVFR for transition from direct drop to ligament mode: (a) flat disks 1 and 2; (b) slotted disks 3and 4; (c) arc-edge disks 5 and 6; (d) bulgedblock disks 7 and 8.
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Figure 5. CVFR of different disk configurations (direct drop to ligament).
Table 5. Transition Correlations from Direct Drop−Ligament Mode operation variables disk type flat slotted arc-edge bulged-block
correlations
Q + = 1.049We−0.953St −0.188 +
−0.989
−0.179
+
−0.960
−0.202
+
−0.943
−0.130
Q = 1.567We Q = 1.219We Q = 1.842We
St
St
St
e
(7)
R2
We
St
MSE
1.40 × 103−1.04 × 105
1.38 × 10−3−1.39 × 10−2
9.01 × 10−5
(8) (9) (10)
1.17 × 10
−4
1.22 × 10
−4
7.03 × 10
−5
0.9876 0.9872 0.9885 0.9965
of sheeted film. It moves along the disk perimeter with a wide torus around the disk rim (Figure 3f). As the Q further increased, fully sheet mode appeared and the thickness of liquid film on the disk increased accordingly, thus giving rise to the extension of liquid film with a larger out diameter (Figure 3e). It should be pointed out that the flying trajectories of this breakup mode became fluctuating and unstable, leading to the various droplet shapes and a wider range of droplet diameters. Admittedly, ligament breakup mode can produce droplets with a narrower range of size than those produced by sheet mode and can provide higher liquid flow rates than those obtained via direct drop mode, which is chosen as the most reasonable process of granulation. Accordingly, for the bulged-block disk, the ligament mode is available when the corresponding RP mixture volume flow rate is from 8.85 to 14.98 mL/s in the present operational conditions. 3.2. Transition from Direct Drop to Ligament. Figure 4 shows the relationships between critical volume flow rate (CVFR) and angular speed of four types of disks. The RP mixture temperatures are 110 and 130 °C, and the disk diameters are 0.05 and 0.10 m, respectively. Obviously, in Figure 4, the CVFR of four types of disks decreases fast at the initial stage and then represents a reduced slope when the angular speed exceeds 100 rad/s. With the increase of disk diameter, the CVFR is increasing accordingly because more working fluid is required to make the disk surface fully immersed. It is also clear that the RP mixture temperature has significant influence on the CVFR, especially in lower angular speed, which is mainly attributed to the influence of viscosity. Take the flat disk for example (Figure 4a); when the angular speed is below 100 rad/s, the CVFR increases dramatically with the increase in fluid temperature, as the viscosity of RP mixture decreases over 50% from 0.119 to 0.05 Pa·s (Table 2).
3. RESULTS AND DISCUSSIONS 3.1. Evolution of Different Breakup Modes. Taking disk sample 7 (bulged-block disk, Figure 2d) for instance, the temperature of the working fluid is 130 °C and the rotary disk diameter D is 0.05 m. Figure 3 clearly demonstrates the transition process of three different breakup modes (direct drop, ligament, and sheet) when the RP mixture flow rate increases from 1.32 to 23.92 mL/s in a given angular speed of 62.83 rad/s. Direct drop mode was formed first at the rim of the disk when the mixture flow rate was relatively low (Q = 1.32 mL/s), as shown in Figure 3a. The portion of RP mixture was observed to stick on the disk surface due to fast cooling, resulting in randomly distributed droplet sizes and irregular droplet shapes (threadlikeshaped, ellipsoidal-shaped, spherical-shaped, etc.). The transition from direct drop to ligament occurs when the RP mixture flow rate increased to 4.37 mL/s, as shown in Figure 3b. In this stage, ligaments were observed, but the distributions were chaotic and unordered. Most of the droplets were tearing away from the lip of ligaments, and a few were broken from the liquid film around the disk rim directly. When the Q increased to 8.85 mL/s, clearly patterned ligaments were established with stable and orderly flying trajectories (Figure 3c). Each ligament was stretched outward by a head droplet, which has a larger diameter than the ligament. This mode appears with thinner liquid columns, and the number of liquid columns will remain a maximum value within a certain range of volume flow rate. Simultaneously, ligament mode was chosen as a stable and appropriate process of the granulation because it can offer smaller and more uniform droplets than those produced by direct drop mode, as well as sheet mode. At approximately Q = 14.98 mL/s, the centrifugal force was dominated, hence destabilizing the movement of ligaments. Some adjacent ligaments begin to merge, resulting in the transition from ligament to sheet mode (Figure 3d). When Q approaches 19.65 mL/s, a whole liquid film was formed instead 11285
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Figure 6. Number of ligament at different volume flow rate for D = 0.05 m and ω = 94.25 rad/s: (a) Q = 5.78 mL; (b) Q = 6.72 mL/s; (c) Q = 7.57 mL/s.
Figure 7. CVFR for transition from ligament to fully ligament: (a) flat disks 1 and 2; (b) slotted disks 3 and 4; (c) arc-edge disks 5 and 6; (d) bulgedblock disks 7 and 8.
The aforementioned eq 1 presented the transition criteria from one mode to another. Based on the experimental data, the transition correlations (eqs 7 −10) from direct drop to ligament for four types of disk are developed by least-squares fitting. The ranges of operational variables, the mean-squared errors (MSE), and the correlation coefficients (R2) are also determined, as listed in Table 5. 3.3. Characteristics of Fully Ligament Mode. Figure 6 shows the number of ligaments with the increase of volume flow rate in the fully developed ligament mode for bulged-block disk, while the disk diameter is 0.05 m and the RP mixture temperature is 130 °C. It can be seen that the ligament number remains constant (KL = 56) with the Q increasing from 5.78 to 7.57 mL/s,
Meanwhile, the effect of disk configuration on the CVFR from direct drop to ligament is shown in Figure 5. It is indicated that the CVFRs for the transition from direct drop to ligament for flat/slotted/arc-edge disks are almost identical. This leads to the conclusion that these three disk configurations have almost no effect on the breakup regime. However, the CVFR for bulgedblock disk is obviously higher than that of the other three types of disks, which means the first appearance of ligament disk occurs later in a bulged-block disk. This is due to the fact that the formed around-flow behind the bulged blocks will cause a higher flow resistance, resulting in a thinner film thickness near the disk rim; therefore, a higher volume flow rate is required to form a ligament breakup mode. 11286
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Industrial & Engineering Chemistry Research which indicated that the KL is irrelevant to the Q at fully development ligament stage. In this stage, clearly ligaments with stable flying trajectories are formed at the lip of the disk, and these trajectories are demonstrated as an involute profile due to the fact that the tangential velocity of liquid film at disk rim is much higher than the radial velocity. It must be pointed out that the constant ligament number is not observed for the first time; it has also been reported in the literature of Kamiya and Kayano20 and Frost,23 as well as our own works (Peng et al.;25 Wang et al.18). This is because the breakup of the liquid film results from the wave with the fastest growth rate, while the liquid film thickness at the disk rim is much smaller than the disk diameter. Therefore, if the surface of rotary disk is fully wetted, the growth rate of waves and the corresponding wavenumber will not affected by the volume flow rate. In this situation, the wavenumber that determines the ligament number is now totally controlled by the disk diameter, angular speed, and liquid physical properties (σ and μ). In other words, the working fluid volume flow rate has no impact on the ligaments number for a given angular speed at fully developed ligament stage; instead, a longer length and a wider diameter of ligaments are observed by increasing the volume flow rate. Figure 7 shows the CVFR against the angular speed for four types of disks. Comparison shows that the transition curves have very similar tendency compared with the previous curves from direct drop to ligament mode. It is observed that, with the decrease of RP mixture viscosity or increase of the disk diameter, the CVFR decreases accordingly. Compared with the effect of the fluid viscosity, the disk diameter has a stronger impact on the CVFR in a certain angular speed. Take flat disk for instance (Figure 7a), when the ω = 125.7 rad/s, the CVFR increases 43.7% from 3.57 to 5.13 mL/s with the increase of disk diameter from 0.05 to 0.1 m, but increases 30.2% from 3.57 to 4.65 mL/s with the increase of temperature from 110 to 130 °C. Similar to the characteristics for the transition from direct drop to ligament, the transition from ligament to fully ligament occurs earlier in flat/slotted/arc-edge disks before that in bulged-block disk; thus, a higher CVFR is needed to form a fully ligament mode for the bulged-block disk, as shown in Figure 8.
ligament to sheet mode are depicted in Figure 9, with the angular speed of 157.1 rad/s and the disk diameter of 0.05 m, respectively. It has been observed in our experiments that the ligament number remains constant with the increase of liquid volume flow rate in fully ligament stage. When the flow rate is ontinuously increased, the stable flying of the ligaments becomes fluctuate, especially at the root portion of the ligament, resulting in the first mergence of two adjacent ligaments at the disk rim (Figure 9a). When the liquid flow rate increases from 13.25 to 14.35 mL/s, a small liquid torus with enlarged outer diameter is formed at some part of disk rim (Figure 9b and 9c). Finally, the further increased flow rate accelerates the movement of the liquid medium and provides the chance for the gathering of small liquid torus (Figure 9d). As a consequence, a thin and whole liquid film, instead of partial torus, appeared at the lip of the rotary disk. Moreover, it also can be seen in Figure 9d that the droplets produced by sheet mode are in quite irregular shapes (spherical, threadlike, rod, etc.) compared with the granulation process in direct drop and ligament mode. The relationship between CVFR and angular speed, at which transition from fully ligament to sheet mode occurs, is shown in Figure 10. The influence of ω, μ, and D on the CVFR is almost identical to the above phenomena (in sections 3.2 and 3.3), and the relevant explanations will not repeat here. Figure 11 shows the CVFR of four different types of disk for the transition from fully ligament to sheet mode. Unlike the above two transition processes, the CVFR for bulged-block disk is close to the arc-edge disk and slightly higher than that in flat/ slotted disks, which indicated that the disk configurations have almost no effect on this breakup regime. The reason for this tendency will be discussed later. Equations 15 −18 are formulated separately for describing the transition from fully ligament to sheet breakup mode of four types of disks, shown in Table 7. 3.5. Comparison Analysis of Correlations and Critical Transition Characteristics for Different Disk Types. To sum up, Table S1 lists the correlations for the transition criteria from one mode to another, which are applicable in a wide range of operational variables. Figure 12, Figure 13, and Figure 14 are drawn in order to compare and in-depth analyze the critical transition characteristics between different types of disk. Figures 12−14 show the logarithmic plots of Q+Stn against the We, including the experimental data and the fitting transition curves according to eqs 7−18. These curves show that eqs 7−18 fit well with the present experimental data. The regions below and above the curves show the areas where the direct drop/ligament, ligament/ fully ligament, and fully ligament/sheet modes are formed for the four types of disk. These transition processes have a lot in common. Taking Figure 12 for example, as mentioned before, the Q+ is controlled by the Weber number (We) and Stanton number (St), and increasing the We or decreasing the St can contribute to a reduction of the Q+. In addition, We is predominantly affected by ω as the σ and ρ are nearly the same for the RP mixture at different temperatures (eq 3). Therefore, the direct drop may exist at a high flow rate if the ω is low, and the transition from direct drop to ligament will appear as the ω is further increased. As shown in the direct drop/ligament and ligament/fully ligament transition curves (Figures 12−13), the transition areas of bulged-block disk are moving up to a certain distance other than that of the other three types of disk, representing a higher CVFR under the same operational conditions. This is due to the
Figure 8. CVFR of different disk configurations (ligament to fully ligament).
According to the experimental data, the transition correlations (eq 11 −14) from ligament to fully ligament, the ranges of operational variables, the MSE, and R2 values are listed in Table 6. 3.4. Transition from Fully Ligament to Sheet. Also taking bulged-block disk as an example, the transition images from fully 11287
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Industrial & Engineering Chemistry Research Table 6. Transition Correlations from Ligament−Fully Ligament Mode operation variables disk type flat slotted arc-edge bulged-block
Q + = 2.477We−0.907St −0.115 +
−0.846
−0.138
+
−0.791
−0.143
+
−0.860
−0.091
Q = 1.331We
Q = 1.009We Q = 2.863We
St
St St
(11)
R2
We
St
MSE
1.40 × 103−1.04 × 105
1.38 × 10−3−.39 × 10−2
1.13 × 10−4
correlations
−4
1.03 × 10
(12)
−4
1.73 × 10
(13)
−4
2.64 × 10
(14)
0.9972 0.9981 0.9955 0.9919
Figure 9. Transition images from fully ligament to sheet for D = 0.05 m and ω = 125.70 rad/s: (a) Q = 13.25 mL; (b) Q = 13.88 mL/s; (c) Q = 14.35 mL/ s; (d) Q = 16.53 mL/s.
Figure 10. CVFR for the transition from ligament to sheet breakup mode: (a) flat disks 1 and 2; (b) slotted disks 3 and 4; (c) arc-edge disks 5 and 6; (d) bulged-block disks 7 and 8.
disturbed flow pattern occurring behind the bulged blocks, thus making the liquid film thinner near the disk rim. Therefore, a
larger CVFR is needed to form the ligament or fully ligament breakup mode. However, the first appearance of the sheet mode 11288
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Figure 12. Transition curves from direct drop to ligament mode.
Figure 11. CVFR of different disk configurations (fully ligament to sheet).
for bulged-block disk nearly coincides with the other disks (Figure 14). This may also be attributed to the change in liquid film thickness. In the state of sheet formation, the liquid film at the disk surface maybe thicker because the liquid volume flow rate and the RP mixture properties (σ and μ) are relatively high. This trend is observed in Figure 3f and Figure 9d. Obviously, a portion of bulged blocks is immerged in the thicker liquid film that acts to reduce the flow instability. As a consequence, the transition curves of four types of disk from fully ligament to sheet mode are almost identical. 3.6. Effect of Operational Conditions and Fluid Properties on Transition Characteristics. The segments of transition curves for all types of disk have been illustrated in section 3.5. Therefore, a whole transition map (includes direct drop to ligament, fully ligament, and ligament to sheet) can be obtained by integrating these segments, as shown in Figure 15, Figure 16, Figure 17, and Figure 18. It is well-known that the ligament formation or fully ligament formation is chosen as the most appropriate process because it represents a stable process and can produce the uniform size of droplets in molten slag rotary disk granulation, while fully ligament formation can provide higher liquid flow rate. Therefore, in general, a broader transition area from ligament to sheet (Area 1 + Area 2 in Figures 15−18) can contribute to a more flexible operational condition in the real application. Accordingly, it can be seen from Figures 15−18 that the broadest transition area from ligament mode to sheet mode is identified in arc-edge disk configuration (Figure 16), while the narrowest area appears in bulged-block disk (Figure 18). The relative narrow areas from ligament to fully ligament (Area 1) and from fully ligament to sheet (Area 2) are identified in slotted disk and bulged-blocked disk, respectively. This ostensible information can provide a framework for selecting the disk configurations for a given range of volume flow rates.
Figure 13. Transition curves from ligament to fully ligament mode.
Figure 14. Transition curves from fully ligament to sheet mode.
Next to that, the transition map of bulged-block disk (Figure 18) is chosen for analyzing the effect of operational conditions (liquid flow rate Q, angular speed ω, and disk diameter D) and fluid properties (fluid viscosity μ, surface tension σ) on transition characteristics. First of all, it was found that the transitions from direct drop to ligament and ligament to sheet take place by
Table 7. Transition Correlations from Fully Ligament-Sheet Mode operation variables disk type
correlations
flat
Q + = 1.374We−0.763St −0.136
slotted
Q + = 1.862We−0.799St −0.128
arc-edge
Q + = 2.474We−0.796St −0.119
bulged-block
+
Q = 1.601We
−0.766
St
−0.153
(15)
R2
We
St
MSE
1.40 × 103−1.04 × 105
1.38 × 10−3−1.39 × 10−2
3.01 × 10−4 −4
0.9942
(16)
1.83 × 10
0.9981
(17)
1.73 × 10−4
0.9867
(18)
2.64 × 10−4
0.9967
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Industrial & Engineering Chemistry Research
increasing the Q and ω. However, the influence of D is more complicated. The increase in D can contribute to a higher We number and a lower Q+, but the breakup mode may not change accordingly. This appearance has been captured in our visible experiments. For example, the breakup mode in the ligament stage is observed for the case of ω = 125.7 rad/s, Q = 2.65 mL/s, T = 110 °C, and D = 0.05 m (point 1 in Figure 18). As the D increases from 0.05 to 0.1 m, there is no change in the breakup mode (shown in the point moving trajectory from point P1 to P2 in Figure 18). The reason for this appearance is due to the fact that the increased D enhances the effect of centrifugal force, thus destabilizing the movement of ligament. On the other hand, the increased D also results in a thinner liquid film near the disk rim, while the surface tension force at the film edge is also reinforced. Both two aspects counteract each other, and the resultant force may be well balanced, leading to a stable and unchanged breakup mode. Second, the effect of μ on transition processes is opposite to the effect of Q. The transition from direct drop−ligament and ligament−sheet appears earlier by decreasing the μ, which corresponds to the transition correlations. In addition, the increased surface tension σ acts to increase the contraction velocity at the liquid film free edge. This leads to the contraction and convergence of the film free edge at the disk rim, so that the breakup mode of liquid film is probably maintained in direct drop or ligament mode even if the Q and ω are relatively high.
Figure 15. Transition map of flat disk.
4. CONCLUSIONS This work experimentally investigated the influence of disk configurations on molten slag granulation process by using the high-speed camera visualized system. Rosin/paraffin mixture (RP mixture) is adopted as the working fluid according to the similarity theory, and the critical transition characteristics of four groups of rotary disks are studied. Key findings are shown below: (1) The nondimensional transition correlations (eqs 7−18) and the transition maps for four types of disks are proposed from the experimental data, which show high precision for predicting the transition criteria (Q+) from one mode to another in wide ranges of operational variables (We and St). (2) Compared with the four types of disk, the transition areas of bulged-block disk from direct drop to ligament and ligament to fully ligament represent a higher CVFR under the same operational conditions due to the disturbed flow pattern behind the bulged blocks, while the first appearance of the sheet mode for bulged-block disk nearly coincides with the other types of disks. (3) The integrated transition maps indicate that the narrowest transition area from ligament mode to sheet mode is identified in bulged-block disk. In contrast, the broadest area appears in arcedge disk, which contributes to a wider range of liquid volume flow rates in the real molten slag granulation application. (4) Generally, the transitions from sheet to ligament, and ligament to direct drop, are promoted by decreasing Q and ω or increasing μ. However, the effects of D and σ on transition characteristics are more complicated, which are closely related to the interaction between centrifugal force and surface tension force and need comprehensive estimate according to the actual working conditions.
Figure 16. Transition map of slotted disk.
Figure 17. Transition map of arc-edge disk.
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ASSOCIATED CONTENT
S Supporting Information *
Figure 18. Transition map of bulged-block disk.
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.7b02675. 11290
DOI: 10.1021/acs.iecr.7b02675 Ind. Eng. Chem. Res. 2017, 56, 11281−11291
Article
Industrial & Engineering Chemistry Research
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Correlations for the transition criteria from one mode to another of four different types of disks (Table S1); correlation of the critical transition condition for all types of rotary disks (Table S2) (PDF)
AUTHOR INFORMATION
Corresponding Authors
*Tel.: 86-25-83243112 E-mail address:
[email protected] (H.P.). *Tel.: 86-25-83587321 E-mail address:
[email protected] (X.L.). ORCID
Hao Peng: 0000-0002-6645-4852 Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors acknowledge the financial support provided by National Natural Science Foundation of China (Grant No. 51406078, No. 51606086), Major Collegiate Project of Natural Science Foundation of Jiangsu Province (Grant No. 15KJA480001), and Natural Science Foundation of Jiangsu Province (Grant No. BK20151539).
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NOMENCLATURE a constant value b constant value C constant value D disk diameter [m] MSE mean squared error On Ohnesorge number Q volume flow rate [mL/s] Q+ dimensionless critical volume flow rate R disk radius [m] Re Reynolds number R2 correlation coefficient St Stanton number We Weber number Greek Symbols
ω ρ σ μ ν
angular speed [rad/s] density [kg/m3] surface tension [N/m] dynamic viscosity [Pa·s] kinematic viscosity [m2/s]
Upper Scripts
e experimental p predicted
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DOI: 10.1021/acs.iecr.7b02675 Ind. Eng. Chem. Res. 2017, 56, 11281−11291
